Asymmetric nozzles for laser wakefield electron accelerators and methods of use thereof

Abstract

Disclosed herein are asymmetric nozzles for a laser wakefield electron accelerators and methods of use thereof. During laser wakefield electron acceleration, a nozzle is used to release a gas with a gas density profile, where the gas density profile is substantially flat-topped or ramped for a distance of at least five millimeters.

Description

ASYMMETRIC NOZZLES FOR LASER WAKEFIELD ELECTRON ACCELERATORSAND METHODS OF USE THEREOFCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of priority to U.S. Provisional Application 63 / 558,785, filed February 28, 2024, and U.S. Provisional Application 63 / 710,779, filed October 23, 2024, each of which is hereby incorporated herein by reference in its entirety.BACKGROUND

[0002] Laser-wakefield acceleration has the potential of shrinking ~km scale facilities down to room size machines. Depending on the laser power and specific experimental requirements, various gas targets are employed to generate and control the gas density profiles used in laser wakefield electron accelerators.SUMMARY

[0003] Considering the overall enhancement of the parameters of the electron beam in an up- ramp plasma density, the development of gas targets that permit the control of the gas density profile may be beneficial. The devices, methods, and systems discussed herein address these and other benefits.

[0004] In accordance with the purposes of the disclosed devices, methods, and systems as embodied and broadly described herein, the disclosed subject matter relates to asymmetric nozzles for a laser wakefield electron accelerators and methods of use thereof. Applicant has recognized that there is an unmet need for new methods and uses of asymmetric nozzles in particle accelerators. Methods and uses of the present disclosure may be used to further particle acceleration technology by allowing for increased research opportunity in the field.

[0005] In an aspect, the present disclosure provides a nozzle for a laser wakefield accelerator. The nozzle may comprise an inlet, an outlet spaced apart from and in fluid communication with the inlet, and a chamber fluidly coupling the inlet to the outlet, wherein the inlet is configured to receive a gas at a pressure, and the outlet is configured to release the gas with a gas density profile, and wherein the density profile comprises a substantially flat-topped or ramped profile for a distance of at least 5 millimeters.

[0006] In some embodiments, the inlet and outlet comprise geometrically similar cross-sectional shapes. In some embodiments, the geometrically similar cross-sectional shapes comprise shapes which are obtained from one another by uniformly scaling. In some embodiments, the inlet and the outlet comprise a geometric center, wherein the geometric center of the inlet is translated relative to a geometric center of the outlet along an axis perpendicular to an axis of propagationof the gas. In some embodiments, the area defined by the inlet is smaller than the area defined the outlet. In some embodiments, the corresponding inlet is rectangular and outlet is rectangular.

[0007] In some embodiments, the outlet length is the largest straight line distance between two points in the outlet, and the outlet width is the largest straight line distance between two points along a line perpendicular to the outlet length in the outlet. In some embodiments, the outlet length is longer than the outlet width. In some embodiments, the outlet length is 5 centimeters and the outlet width is 2 millimeters. In some embodiments, the outlet width is 1 millimeter to 2 millimeters. In some embodiments, the longitudinal distance between the inlet and the outlet is 30 centimeters. In some embodiments, the width of the outlet to the longitudinal distance possesses a ratio of at least 1 :5. In some embodiments, the width of the outlet to the longitudinal distance possesses a ratio of 1 :6. In some embodiments, the internal width of the longitudinal space between the inlet and outlet is equal to or less than the width of the outlet. In some embodiments, the inlet, the outlet, the distance between the inlet and the outlet, and a gas density are collectively configured to form the substantially flat-top or ramped profile.

[0008] In some embodiments, the density profile is substantially flat-topped or ramped for a distance of at least 2 centimeters. In some embodiments, the gas is helium. In some embodiments, the gas has a pressure of 100 kilopascals. In some embodiments, the gas density is at most 1 x 1018atoms / cm3. In some embodiments, the device is further comprising a wire coupled to the outlet. In some embodiments, the wire diameter is 200 pm.

[0009] In one aspect, the present disclosure provides an asymmetric nozzle for a laser wakefield electron accelerator. The asymmetric nozzle may comprise an inlet defining an inlet profile; a throat extending from the inlet; an outlet spaced apart from and in fluid communication with the inlet, the outlet defining an outlet plane, an outlet profile in the outlet plane and corresponding to the inlet profile, an outlet length, and an outlet width that is 50% or less of the outlet length; and a chamber fluidly coupling the throat and the outlet and defining a chamber height.

[0010] In some embodiments, the inlet profile is rectangular and the outlet profile is rectangular. In some embodiments, the outlet length is the largest straight line distance between two points in the outlet plane, and the outlet width is the largest straight line distance between two points along a line perpendicular to the outlet length in the outlet plane. In some embodiments, the outlet width is from 0.1 to 5 millimeters (mm). In some embodiments, the outlet width is from 0.1 to 2 millimeters (mm). In some embodiments, the outlet width is from 1 to 2 millimeters (mm). In some embodiments, the outlet length is from 1 millimeter (mm) to 500 centimeters (cm). In some embodiments, the outlet length is from 1 millimeter (mm) to 10 centimeters (cm). In some embodiments, the outlet length is from 1 centimeter to 10 centimeters. In someembodiments, the outlet length is 5 centimeters. In some embodiments, the outlet length is from 1 millimeter (mm) to 1 centimeter (cm).

[0011] In some embodiments, the chamber defines a longitudinal axis, and wherein the inlet profile and the outlet profile are defined perpendicular to the longitudinal axis. In some embodiments, the chamber defines a linearly expanding volume. In some embodiments, the chamber defines a longitudinal axis centered in the inlet, and the chamber defines an expanding volume that expands in a single direction perpendicular to the longitudinal axis between the throat and the outlet. In some embodiments, the chamber includes a first wall coplanar with the throat and a second wall arranged obliquely to the throat. In some embodiments, the chamber height is measured for the divergent part of the nozzle. In some embodiments, the chamber height is from 1 millimeter (mm) to 100 centimeters (cm). In some embodiments, the chamber height is from 20 centimeters to 40 centimeters. In some embodiments, the chamber height is 30 centimeters (cm). In some embodiments, the chamber height is dependent upon the other nozzle dimensions, including outlet width and outlet length. In some embodiments, the asymmetric nozzle defines a volume of from 0.05 cm3to 500,00 cm3. In some embodiments, the volume is dependent upon the chamber height, outlet length, and outlet width.

[0012] In some embodiments, the nozzle is further comprising a wire coupled to the outlet. In some embodiments, the wire bisects the outlet. In some embodiments, the wire extends parallel to the outlet length. In some embodiments, the inlet is configured to receive a gas at a pressure, and the outlet is configured to release the gas with a gas density profile, such that the asymmetric nozzle provides a path for gas flow from the inlet to the outlet, wherein the gas density profile has a longitudinal profile along the outlet length and a transverse profile along the outlet width and wherein: the longitudinal profile is controlled by selecting the chamber height, the outlet length, or both, the transverse profile is controlled by the presence or absence of the wire, and, when the wire is present, the transverse profile is further controlled by a dimension of the wire along the direction of the outlet width; and the gas density profile is further controlled by the pressure of the gas at the inlet. In some embodiments, the longitudinal profile is flat-topped or density tapered. In some embodiments, the transverse profile is parabolic. In some embodiments, the wire is present and the dimension of the wire along the direction of the outlet width is from 10 to 1000 micrometers. In some embodiments, the wire is present and the dimension of the wire along the direction of the outlet width is 200 micrometers. In some embodiments, the gas has a pressure at the inlet of from 0.1 to 1000 kilopascals. In some embodiments, the gas has a pressure at the inlet of 10 to 1000 kilopascals. In some embodiments, the gas has a pressure at the inlet of 100 kilopascals. In some embodiments, the gas has a density of from 1 * 1012to 1 *1022atoms / cm3. In some embodiments, the gas has a density of from 1 x 1012to 1 x 1022atoms / cm3. In some embodiments, the gas has a density of less than around 1 x 1018atoms / cm3. In some embodiments, the gas has a density of 1 x 1018atoms / cm3or more.

[0013] In an aspect, the present disclosure provides a method of use of the asymmetric nozzle. The method may comprise using the asymmetric nozzle in a laser wakefield electron accelerator. The method may further comprise injecting a gas into the inlet at a pressure, flowing the gas through the asymmetric nozzle, such that the gas is released from the outlet with a gas density profile, wherein the gas density profile has a longitudinal profile along the outlet length and a transverse profile along the outlet width, and wherein: the longitudinal profile is controlled by selecting the chamber height, the outlet length, or both, the transverse profile is controlled by the presence or absence of the wire, and, when the wire is present, the transverse profile is further controlled by a dimension of the wire along the direction of the outlet width; and the gas density profile is further controlled by the pressure of the gas at the inlet.

[0014] In some embodiments, the longitudinal profile is flat-topped or density tapered. In some embodiments, the transverse profile is parabolic. In some embodiments, the gas has a pressure at the inlet of from 0.1 to 1000 kilopascals, In some embodiments, the gas has a pressure at the inlet of from 10 to 1000 kilopascals. In some embodiments, the gas has a pressure at the inlet of 100 kilopascals. In some embodiments, the gas has a density of from 1 x io12to 1 x io22atoms / cm3. In some embodiments, the gas has a density of less than 1 x 1018atoms / cm3. In some embodiments, the gas has a density of 1 x 1018atoms / cm3or more. In some embodiments, the laser wakefield accelerator comprises a particle-assisted laser wakefield electron accelerator. In some embodiments, laser wakefield electron accelerator comprises the asymmetric nozzle disclosed herein.

[0015] In an aspect, the present disclosure provides a laser wakefield electron accelerator. The laser wakefield electron accelerator device comprises the laser wakefield electron acceleration device comprises: an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle; wherein the accelerator chamber is configured to receive a pulse, the pulse being configured to: ionize at least a portion of the gas, thereby generating a plasma wave comprising electrons in the accelerator chamber; and wherein at least a portion of the electrons from the plasma are injected into the wakefield, the portion of the electrons from the plasma being the injected electrons; and wherein the injected electrons are accelerated by the wakefield.

[0016] In some embodiments, the laser wakefield electron accelerator comprises a particle- assisted laser wakefield electron accelerator. In some embodiments, the particle-assisted laserwakefield electron accelerator further comprises a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber, such that the accelerator chamber includes the gas and the particle therein, and wherein the pulse is further configured to: ionize at least a portion of the particle, thereby generating free electrons; wherein at least a portion of the electrons from the plasma and at least a portion of the free electrons are injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons. In some embodiments, the injected electrons are accelerated to an energy that is greater than the energy generated in the absence of the particle. In some embodiments, laser wakefield electron accelerator comprises the asymmetric nozzle, disclosed herein.

[0017] In some embodiments, the particle-assisted wakefield electron acceleration device comprises: an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle; a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber; such that the accelerator chamber includes the gas and the particle therein, wherein the accelerator chamber is configured to receive a pulse, the pulse being configured to: ionize at least a portion of the gas, thereby generating a plasma wave comprising electrons in the accelerator chamber; and ionize at least a portion of the particle, thereby generating free electrons; wherein at least a portion of the electrons from the plasma and at least a portion of the free electrons are injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons; and wherein the injected electrons are accelerated by the wakefield.

[0018] In some embodiments, the injected electrons are accelerated to an energy that is greater than the energy generated in the absence of the particle. In some embodiments, the particle comprises a metallic particle. In some embodiments, the metallic particle comprises a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

[0019] In some embodiments, the particle has an average particle size of from 1 nanometer (nm) to 100 micrometers (pm). In some embodiments, the particle has an average particle size of from 1 nm to 1000 nm. In some embodiments, the particle has an average particle size of from 10 nm to 100 nm. In some embodiments, the particle has a substantially spherical shape. In some embodiments, the particle is a single particle. In some embodiments, the particle is a plurality of particles. In some embodiments, the gas comprises helium. In some embodiments, the pulse comprises a laser pulse. In some embodiments, the laser wakefield electron accelerator furthercomprises a laser source configured to generate the laser pulse. In some embodiments, the laser source comprises a Petawatt laser source.

[0020] In some embodiments, a method of generating an electron beam using the laser wakefield electron accelerator is applied. In some embodiments, a method of using the electron beam generated is applied. In some embodiments, a method of accelerating an electron using the laser wakefield electron accelerator is applied. In some embodiments, a method of using the accelerated electron generated is applied.

[0021] Additional advantages of the disclosed devices, systems, and methods will be set forth in part in the description which follows, and in part will be obvious from the description. The advantages of the disclosed devices, systems, and methods will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed devices, systems, and methods, as claimed.INCORPORATION BY REFERENCE

[0022] All publications, patents, and patent applications mentioned in this specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. To the extent publications and patents or patent applications incorporated by reference contradict the disclosure contained in the specification, the specification is intended to supersede and / or take precedence over any such contradictory material.BRIEF DESCRIPTION OF THE DRAWINGS

[0023] The novel features of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present invention will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings (also “Figure” and “FIG.” herein), of which:

[0024] Figure l is a schematic diagram of symmetric slit nozzle.

[0025] Figure 2A is a side view drawing of the asymmetric slit nozzle.

[0026] Figure 2B is a three-dimensional view of the asymmetric slit nozzle from Figure 2A.

[0027] Figure 2C is an outlet view of the asymmetric slit nozzle with the inserted wire.

[0028] Figure 3 is a flat-top profiles obtained from an asymmetric slit nozzle with a height of 30 cm and an outlet length of 5 cm.

[0029] Figure 4A is a flat-top profile obtained from an asymmetric slit nozzle with a height of 50 mm and an outlet length of 5 cm.

[0030] Figure 4B is a flat-top profile obtained from an asymmetric slit nozzle with a height of 100 mm and an outlet length of 5 cm.

[0031] Figure 4C is a flat-top profile obtained from an asymmetric slit nozzle with a height of 200 mm and an outlet length of 5 cm.

[0032] Figure 4D is a flat-top profile obtained from an asymmetric slit nozzle with a height of 300 mm and an outlet length of 5 cm.

[0033] Figure 5 is a transversely modulated density profile.

[0034] Figure 6 is a schematic illustration of a side view an example asymmetric nozzle as disclosed herein according to one embodiment.

[0035] Figure 7 is a schematic illustration of another view of the example asymmetric nozzle of Figure 6.

[0036] Figure 8 is a schematic illustration of a plan view of the example asymmetric nozzle of Figure 6 and Figure 7.

[0037] Figure 9 is a schematic illustration of a plan view of the example asymmetric nozzle of Figure 6 and Figure 7.

[0038] Figure 10 is a schematic illustration of an example asymmetric nozzle as disclosed herein according to one embodiment with a wire coupled to the outlet.

[0039] Figure 11 is a schematic illustration of a plan view of the example asymmetric nozzle of Figure 10.

[0040] Figure 12 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0041] Figure 13 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0042] Figure 14 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0043] Figure 15 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0044] Figure 16 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0045] Figure 17 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0046] Figure 18 is a schematic illustration of an example particle injector as disclosed hereinaccording to one embodiment.

[0047] Figure 19 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0048] Figure 20 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0049] Figure 21 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0050] Figure 22 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0051] Figure 23 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.

[0052] Figure 24 is a schematic illustration of an example particle injector as disclosed herein according to one embodiment.DETAILED DESCRIPTION

[0053] The devices, methods, and systems described herein may be understood more readily by reference to the following detailed description of specific aspects of the disclosed subject matter and the Examples included therein. In this specification and in the claims that follow, reference will be made to a number of terms, which shall be defined to have the following meanings.

[0054] Whenever the term “at least,” “greater than,” or “greater than or equal to” precedes the first numerical value in a series of two or more numerical values, the term “at least,” “greater than” or “greater than or equal to” applies to each of the numerical values in that series of numerical values. For example, greater than or equal to 1, 2, or 3 is equivalent to greater than or equal to 1, greater than or equal to 2, or greater than or equal to 3.

[0055] Whenever the term “no more than,” “less than,” or “less than or equal to” precedes the first numerical value in a series of two or more numerical values, the term “no more than,” “less than,” or “less than or equal to” applies to each of the numerical values in that series of numerical values. For example, less than or equal to 3, 2, or 1 is equivalent to less than or equal to 3, less than or equal to 2, or less than or equal to 1.

[0056] Certain inventive embodiments herein contemplate numerical ranges. When ranges are present, the ranges include the range endpoints. Additionally, every sub range and value within the range is present as if explicitly written out.

[0057] The term “about” or “approximately” may mean within an acceptable error range for the particular value, which will depend in part on how the value is measured or determined, e.g., thelimitations of the measurement system. For example, “about” may mean within 1 or more than 1 standard deviation, per the practice in the art. Alternatively, “about” may mean a range of up to 20%, up to 10%, up to 5%, or up to 1% of a given value. Where particular values are described in the application and claims, unless otherwise stated the term “about” meaning within an acceptable error range for the particular value may be assumed.

[0058] It is understood that throughout this specification the identifiers “first” and “second” are used solely to aid in distinguishing the various components and steps of the disclosed subject matter. The identifiers “first” and “second” are not intended to imply any particular order, amount, preference, or importance to the components or steps modified by these terms.ASYMMETRIC NOZZLES FOR LASER WAKEFIELD ELECTRON ACCELERATORS

[0059] In some examples, referring now to Figure 6-Figure 11, disclosed herein is an asymmetric nozzle 100 for a laser wakefield electron accelerator, the asymmetric nozzle 100 comprising an inlet 110 defining an inlet profile 112. In some examples, the asymmetric nozzle 100 may further comprise a throat 120 extending from the inlet 110. In some examples, the asymmetric nozzle 100 may further comprise an outlet 140 spaced apart from and in fluid communication with the inlet 110, the outlet 140 defining an outlet plane 142, an outlet profile 144 in the outlet plane 142 and corresponding to the inlet profile 112, an outlet length L, and an outlet width W. In some examples, the asymmetric nozzle 100 may further comprise a chamber 130 fluidly coupling the throat 120 and the outlet 140 and defining a chamber height H, where the chamber height is the height of the divergent part of the nozzle.

[0060] In some examples, the throat and the chamber can independently be formed of any suitable material. In some examples, the throat and the chamber can independently comprise a polymer, a composite material, a metal, or a combination thereof. In some examples, the throat and the chamber can be integrally formed.

[0061] In some examples, the inlet profile 112 and the outlet profile 144 can comprise any suitable shape. In some examples, the shape may be circular, ovate, ovoid, elliptic, triangular, rectangular, polygonal, etc. In some examples, the inlet profile 112 and the outlet profile 144 may comprise a similar shape. In some examples, two shapes may be geometrically similar if they have the same shape, or if one has the same shape as the mirror image of the other. In some examples, one can be obtained from the other by uniformly scaling (enlarging or reducing), possibly with additional translation, rotation and reflection. In some examples, the inlet profile may be rectangular 112 and the outlet profile 144 may be rectangular. In some examples, the inlet profile 112 may be circular, ovate, ovoid, elliptic, triangular, polygonal, etc. In someexamples, the outlet profile 144 may be circular, ovate, ovoid, elliptic, triangular, polygonal, etc.

[0062] In some examples, the outlet length L may be the largest straight line distance between two points in the outlet plane 142, and the outlet width W may be the largest straight line distance between two points along a line perpendicular to the outlet length L in the outlet plane 142

[0063] In some examples, the outlet width W may be less than the outlet length L. In some examples, the outlet width may be about 40% or less of the outlet length. In some examples, the outlet width may be about 30% or less of the outlet length. In some examples, the outlet width may be about 20% or less of the outlet length. In some examples, the outlet width may be about 10% or less of the outlet length.

[0064] In some examples, the outlet width W may be from about 0.1 to about 5 millimeters (mm). In some examples, the outlet width may be from about 0.1 to 1 mm. In some examples, the outlet width may be from about 1 mm to about 2 mm. In some examples, the outlet width may be from about 2 mm to about 3 mm. In some examples, the outlet width may be from about 3 mm to about 4 mm. In some examples, the outlet width may be from about 4 mm to about 5 mm. In some examples, the outlet width may be about 1 mm. In some examples, the outlet width may be about 2 mm. In some examples, the outlet width may be about 3 mm. In some examples, the outlet width may be about 4 mm. In some examples, the outlet width may be about 5 mm.

[0065] In some examples, the outlet width W may be a maximum of about 2 mm. In some examples, the outlet width W may be a maximum of about 1.5 mm. In some examples, the outlet width W may be a maximum of about 1 mm. In some examples, the outlet width W may be a maximum of about 0.5 mm.

[0066] In some examples, the outlet length L may be from about 1 millimeter (mm) to about 500 centimeters (cm). In some examples, the outlet length may be from about 1 mm to about 1 cm. In some examples, the outlet length may be from about 1 cm to about 10 cm. In some examples, the outlet length may be from about 10 cm to about 20 cm. In some examples, the outlet length may be from about 20 cm to about 30 cm. In some examples, the outlet length may be from about 30 cm to about 40 cm. In some examples, the outlet length may be from about 40 cm to about 50 cm. In some examples, the outlet length may be from about 50 cm to about 60 cm. In some examples, the outlet length may be from about 60 cm to about 70 cm. In some examples, the outlet length may be from about 70 cm to about 80 cm. In some examples, the outlet length may be from about 80 cm to about 90 cm. In some examples, the outlet length may be from about 90 cm to about 100 cm. In some examples, the outlet length may be from about 100 cm to about 200 cm. In some examples, the outlet length may be from about 200 cm to about 300 cm. Insome examples, the outlet length may be from about 300 cm to about 400 cm. In some examples, the outlet length may be from about 400 cm to about 500 cm. In some examples, the outlet length L is from about 1 millimeter (mm) to about 1 centimeter (cm).

[0067] In some examples, the outlet length L may vary in relation to the chamber height H. In some examples, when the chamber height increases, the outlet length also increases. In some examples, when the chamber height decreases, the outlet length decreases. In some examples, when the chamber height increases, the outlet length decreases. In some examples, when the chamber height decreases, the outlet length increases.

[0068] In some examples, the chamber 130 may define a linearly expanding volume.

[0069] In some examples, the chamber can define a longitudinal axis 132. In some examples, the inlet profile 112 and the outlet profile 144 may be defined perpendicular to the longitudinal axis 132. In some examples, the chamber 130 may be defined as a longitudinal axis 132 centered in the inlet 110, and the chamber 130 may be defined as an expanding volume that expands in a single direction perpendicular to the longitudinal axis 132 between the throat 120 and the outlet 140

[0070] In some examples, the chamber 130 may include a first wall 134 coplanar with the throat 120 and a second wall 136 arranged obliquely to the throat 120. In some examples, the second wall 136 can be arranged at an angle, as shown as a in Figure 8. In some examples the angle of the second wall may be from about 0° to about 80°. In some examples the angle of the second wall may be about 0°. In some examples the angle of the second wall may be about 10°. In some examples the angle of the second wall may be about 20°. In some examples the angle of the second wall may be about 30°. In some examples the angle of the second wall may be about 40°. In some examples the angle of the second wall may be about 50°. In some examples the angle of the second wall may be about 60°. In some examples the angle of the second wall may be about 70°. In some examples the angle of the second wall may be about 80°. In some examples the angle of the second wall may be less than about 90°. In some examples, the angle may be acute. In some examples, the angle may be independent of the outlet length and chamber height. In some examples, the angle may depend on the outlet length and chamber height. In some examples, the ratio between the outlet length and chamber height may affect the angle.

[0071] In some examples, the chamber height H can, for example, be from about 1 millimeter (mm) to about 100 centimeters (cm). In some examples, the chamber height may be from about 1 mm to about 10 cm. In some examples, the chamber height may be from about 10 cm to about 20 cm. In some examples, the chamber height may be from about 20 cm to about 30 cm. In some examples, the chamber height may be from about 30 cm to about 40 cm. In some examples, thechamber height may be from about 40 cm to about 50 cm. In some examples, the chamber height may be from about 50 cm to about 60 cm. In some examples, the chamber height may be from about 60 cm to about 70 cm. In some examples, the chamber height may be from about 70 cm to about 80 cm. In some examples, the chamber height may be from about 80 cm to about 90 cm. In some examples, the chamber height may be from about 90 cm to about 100 cm. In some examples, the chamber height H can be from about 20 cm to about 40 cm. In some examples, the chamber height H can be about 30 centimeters (cm).

[0072] In some examples, a relationship between the chamber height H and the outlet width W may be present, so as to produce an intended gas density profile. In some examples, the ratio between the chamber height to the outlet width may be around 5:1. In some examples, the ratio between the chamber height to the outlet width may be around 5.5 : 1. In some examples, the ratio between the chamber height to the outlet width may be around 6:1. In some examples, the ratio between the chamber height to the outlet width may be around 6.5 : 1. In some examples, the ratio between the chamber height to the outlet width may be around 7:1. In some examples, the ratio between the chamber height to the outlet width may be around 7.5 : 1. In some examples, the ratio between the chamber height to the outlet width may be around 8:1. In some examples, the ratio between the chamber height to the outlet width may be around 8.5 : 1. In some examples, the ratio between the chamber height to the outlet width may be around 9:1. In some examples, the ratio between the chamber height to the outlet width may be around 9.5 : 1. In some examples, the ratio between the chamber height to the outlet width may be around 10: 1.

[0073] In some examples, the width of the chamber between the sides defined by the chamber height H may be equal to the width of the outlet. In some examples, the width of the chamber may be less than the width of the outlet. In some examples, the width of the chamber may be more than the width of the outlet.

[0074] In some examples, the asymmetric nozzle may be defined as a volume derived from the parameters of the nozzle, such as its longitudinal height, width, and the inlet and outlet width and length. In some examples, the nozzle volume may be from about 0.05 cm3to about 500,000 cm3. In some examples, the nozzle volume may be from about 0.05 cm3to about 0.5 cm3. In some examples, the nozzle volume may be from about 0.5 cm3to about 5 cm3. In some examples, the nozzle volume may be from about 5 cm3to about 50 cm3. In some examples, the nozzle volume may be from about 50 cm3to about 500 cm3. In some examples, the nozzle volume may be from about 500 cm3to about 5,000 cm3. In some examples, the nozzle volume may be from about 5,000 cm3to about 50,000 cm3. In some examples, the nozzle volume may be from about 50,000 cm3to about 500,000 cm3.

[0075] In some examples, the asymmetric nozzle 100 can further comprise a wire 150 coupled to the outlet 140, as shown in Figure 10 and Figure 11. In some examples, the wire 150 may bisect the outlet 140. In some examples, the wire 150 may extend parallel to the outlet length L.

[0076] In some examples, the wire 150 can be formed of any suitable material. In some examples, the wire 150 can comprise a polymer, a composite material, a metal, or a combination thereof.

[0077] In some examples, the wire 150 can have a dimension along the direction of the outlet width W. In some examples, the dimension of the wire 150 along the direction of the outlet width W may be from about 10 to about 1000 micrometers (mm). In some examples, the wire dimension may be from about 10 mm to about 100 mm. In some examples, the wire dimension may be from about 100 mm to about 200 mm. In some examples, the wire dimension may be from about 200 mm to about 300 mm. In some examples, the wire dimension may be from about 300 mm to about 400 mm. In some examples, the wire dimension may be from about 400 mm to about 500 mm. In some examples, the wire dimension may be from about 500 mm to about 600 mm. In some examples, the wire dimension may be from about 600 mm to about 700 mm. In some examples, the wire dimension may be from about 700 mm to about 800 mm. In some examples, the wire dimension may be from about 800 mm to about 900 mm. In some examples, the wire dimension may be from about 900 mm to about 1000 mm. In some examples, the wire 150 can have a diameter, selected depending on the intended shape of the density profile modulation. In some examples, the wire diameter may be from about 1 micrometer (pm) and about 1 mm. In some examples, the wire diameter may be less than about 1 micrometer (pm) and about 1 mm. In some examples, the wire diameter is about 100 pm. In some examples, the wire diameter is about 200 pm. In some examples, the wire diameter is about 300 pm. In some examples, the wire diameter is about 400 pm. In some examples, the wire diameter is about 500 pm. In some examples, the wire diameter is about 600 pm. In some examples, the wire diameter is about 700 pm. In some examples, the wire diameter is about 800 pm. In some examples, the wire diameter is about 900 pm. In some examples, the wire diameter is about 1 mm.

[0078] In some examples, the asymmetric nozzle 100 may provide a path for gas flow from the inlet 110 to the outlet 140. For example, the inlet 110 may be configured to receive a gas at a pressure, and the outlet 140 may be configured to release the gas with a gas density profile. The gas density profile may have a longitudinal profile along the outlet length L and a transverse profile along the outlet width W. The longitudinal profile may be controlled by selecting the chamber height H, the outlet length L, or both. The transverse profile may be controlled by the presence or absence of the wire 150, and, when the wire 150 is present, the transverse profilemay be further controlled by a dimension of the wire 150 along the direction of the outlet width W. The gas density profile may be further controlled by the pressure of the gas at the inlet.

[0079] In some examples, the longitudinal profile may be flat-topped or density tapered.

[0080] In some examples, the transverse profile may be parabolic.

[0081] The gas can comprise any suitable gas. In some examples, the gas comprises hydrogen, helium, nitrogen, and the like, or a combination thereof. In some examples, the gas can comprise helium.

[0082] In some examples, the gas may have a pressure at the inlet from about 0.1 to about 1000 kilopascals. In some examples, the gas pressure may be from about 0.1 to about 100 kilopascals. In some examples, the gas pressure may be from about 100 to about 200 kilopascals. In some examples, the gas pressure may be from about 200 to about 300 kilopascals. In some examples, the gas pressure may be from about 300 to about 400 kilopascals. In some examples, the gas pressure may be from about 400 to about 500 kilopascals. In some examples, the gas pressure may be from about 500 to about 600 kilopascals. In some examples, the gas pressure may be from about 600 to about 700 kilopascals. In some examples, the gas pressure may be from about 700 to about 800 kilopascals. In some examples, the gas pressure may be from about 800 to about 900 kilopascals. In some examples, the gas pressure may be from about 900 to about 1000 kilopascals.

[0083] In some examples, the gas may have a density above the outlet from about 1 * 1012to 5 * 1018atoms / cm3. In some examples, the gas density may be from about 1 x 1012atoms / cm3to about 1 x 1013atoms / cm3. In some examples, the gas density may be from about 1 x 1013atoms / cm3to about 1 x io14atoms / cm3. In some examples, the gas density may be from about 1 x 1014atoms / cm3to about 1 x io15atoms / cm3. In some examples, the gas density may be from about 1 x 1015atoms / cm3to about 1 x io16atoms / cm3. In some examples, the gas density may be from about 1 x io16atoms / cm3to about 1 x io17atoms / cm3. In some examples, the gas density may be from about 1 x io17atoms / cm3to about 1 x io18atoms / cm3. In some examples, the gas density may be from about 1 x io18atoms / cm3to about 5 x io18atoms / cm3. In some examples, the gas density may be about 1 x io18atoms / cm3.METHODS OF USE

[0084] Also disclosed herein are methods of use of any of the asymmetric nozzles disclosed herein. For example, the methods can comprise using the asymmetric nozzle in a laser wakefield electron accelerator. In some examples, the laser wakefield accelerator comprises a particle- assisted laser wakefield electron accelerator.

[0085] In some examples, the method may comprise injecting a gas into the inlet at a pressure,flowing the gas through the asymmetric nozzle, such that the gas may be released from the outlet with a gas density profile, wherein the gas density profile may have a longitudinal profile along the outlet length and a transverse profile along the outlet width, and wherein: the longitudinal profile may be controlled by selecting the chamber height, the outlet length, or both, the transverse profile may be controlled by the presence or absence of the wire, and, when the wire may be present, the transverse profile may be further controlled by a dimension of the wire along the direction of the outlet width; and the gas density profile may be further controlled by the pressure of the gas at the inlet. In some examples, the longitudinal profile may be flat-topped or density tapered. In some examples, the transverse profile may be parabolic.

[0086] In some examples, the gas may have a pressure at the inlet from about 0.1 to about 1000 kilopascals. In some examples, the gas pressure may be from about 0.1 to about 100 kilopascals. In some examples, the gas pressure may be from about 100 to about 200 kilopascals. In some examples, the gas pressure may be from about 200 to about 300 kilopascals. In some examples, the gas pressure may be from about 300 to about 400 kilopascals. In some examples, the gas pressure may be from about 400 to about 500 kilopascals. In some examples, the gas pressure may be from about 500 to about 600 kilopascals. In some examples, the gas pressure may be from about 600 to about 700 kilopascals. In some examples, the gas pressure may be from about 700 to about 800 kilopascals. In some examples, the gas pressure may be from about 800 to about 900 kilopascals. In some examples, the gas pressure may be from about 900 to about 1000 kilopascals.

[0087] In some examples, the gas may have a density above the outlet from about 1 * 1012to 5 * 1018atoms / cm3. In some examples, the gas density may be from about 1 x 1012atoms / cm3to about 1 x 1013atoms / cm3. In some examples, the gas density may be from about 1 x 1013atoms / cm3to about 1 x io14atoms / cm3. In some examples, the gas density may be from about 1 x 1014atoms / cm3to about 1 x io15atoms / cm3. In some examples, the gas density may be from about 1 x 1015atoms / cm3to about 1 x io16atoms / cm3. In some examples, the gas density may be from about 1 x io16atoms / cm3to about 1 x io17atoms / cm3. In some examples, the gas density may be from about 1 x io17atoms / cm3to about 1 x io18atoms / cm3. In some examples, the gas density may be from about 1 x io18atoms / cm3to about 5 x io18atoms / cm3. In some examples, the gas density may be about 1 x 1Q18atoms / cm3.LASER WAKEFIELD ELECTRON ACCELERATORS

[0088] Also disclosed herein are laser wakefield electron accelerators comprising any of the asymmetric nozzles disclosed herein.

[0089] In some examples, the laser wakefield electron acceleration device may comprise an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle. In some examples, a single accelerator chamber is utilized.

[0090] The accelerator chamber may include the gas therein. The gas can comprise any suitable gas. In some examples, the gas comprises hydrogen, helium, nitrogen, and the like, or a combination thereof. In some examples, the gas may comprise helium.

[0091] The accelerator chamber may be configured to receive a pulse, the pulse being configured to: ionize a portion of the gas, thereby generating a plasma wave comprising electrons in the accelerator chamber; wherein a portion of the electrons from the plasma may be injected into the wakefield, the portion of the electrons from the plasma being the injected electrons. The injected electrons may be accelerated by the wakefield, for example to thereby generate an electron beam. If the acceleration length is long enough, initial acceleration in the wakefield can be followed by further acceleration in a plasma wakefield (PWFA) driven by the initial wakefield accelerated electron bunch. Electrons accelerated in this second process can reach even higher energies.

[0092] In some examples, the laser wakefield electron accelerator may comprise a particle- assisted laser wakefield electron accelerator. In some examples, the particle-assisted laser wakefield electron accelerator may further comprise a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber, such that the accelerator chamber may include the gas and the particle therein. In some examples, the pulse may be further configured to: ionize a portion of the particle, thereby generating free electrons; wherein a portion of the electrons from the plasma and a portion of the free electrons may be injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons. The injected electrons may be accelerated by the wakefield, for example to thereby generate an electron beam. In some examples, the injected electrons may be accelerated to an energy that is greater than the energy generated in the absence of the particle. If the acceleration length is long enough, initial acceleration in the wakefield can be followed by further acceleration in a plasma wakefield (PWFA) driven by the initial wakefield accelerated electron bunch. Electrons accelerated in this second process can reach even higher energies.

[0093] Also disclosed herein are particle-assisted laser wakefield electron accelerators comprising any of the asymmetric nozzles disclosed herein.

[0094] In some examples, the particle-assisted wakefield electron acceleration device maycomprise: an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle; a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber; such that the accelerator chamber includes the gas and the particle therein. In some examples, the accelerator chamber may be a single accelerator chamber. In some examples, the accelerator chamber may be configured to receive a pulse, the pulse may be configured to: ionize a portion of the gas, thereby generating a plasma wave, or a wakefield, comprising electrons in the accelerator chamber; and ionize a portion of the particle, thereby generating free electrons; wherein a portion of the electrons from the plasma and a portion of the free electrons may be injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons. In some examples, the injected electrons may be accelerated by the wakefield, In some examples, the injected electrons and wakefield may come together to generate an electron beam. In some examples, the injected electrons are accelerated to an energy that may be greater than the energy generated in the absence of the particle. In some examples, if the acceleration length is long enough, initial acceleration in the wakefield can be followed by further acceleration in a plasma wakefield (PWFA) driven by the initial wakefield accelerated electron bunch. In some examples, the electrons accelerated in this second process can reach even higher energies.

[0095] In some examples, the accelerator chamber may have a proximal end and a distal end, the proximal end being the end configured to receive the pulse. In some examples, the particle may be located at or near the proximal end of the accelerator chamber. In some examples, the particle can be located at or near the distal end of the accelerator chamber. In some examples, the particle may comprise a plurality of particles distributed throughout the accelerator chamber. In some examples, the plurality of particles may have a distribution. In some examples, the particle distribution may be throughout the accelerator chamber homogeneously. In some examples, the particle distribution may be throughout the accelerator chamber inhomogeneously. In some examples, the particle distribution may be throughout the accelerator chamber in an order. In some examples, the particle distribution may be throughout the accelerator chamber randomly.

[0096] As used herein, “a particle” and “the particle” are meant to include any number of particles in any arrangement. In some examples, the particle may be a single particle. In some examples, the particle may be a plurality of particles. In some examples, the plurality of particles may be 2 or more; 3 or more; 4 or more; 5 or more; 10 or more; 15 or more; 20 or more; 25 or more; 30 or more; 40 or more; 50 or more; 75 or more; 100 or more; 150 or more; 200 or more; 250 or more; 300 or more; 400 or more; 500 or more; 750 or more; 1000 or more; 1500 or more;2000 or more; 2500 or more; 3000 or more; 4000 or more; 5000 or more; 7500 or more; 1 x 104or more; 2.5 x 104or more; 5 x 104or more; 7.5 x 104or more; 1x105or more; 2.5 x 105or more; 5x 105or more; 7.5 x 105or more; 1x106or more; 5 x 106or more; 1x107or more; 5 x 107or more; 1x108or more; 5 x 108or more; 1x109or more; 5 x 109or more; 1 x 1010or more; 1 x 1011or more; 1 x 1012or more; 1 x 1013or morel 1 x 1014or more; 1 x 1015or more; 1 x 1016or more; 1x1017or more; 1x1018or more; 1x1019or more; or 1 x 1O20or more.

[0097] The particle can comprise any suitable material. For example, the particle can comprise a metal, a metalloid, a nonmetal, derivatives thereof, or combinations thereof. The particle can, for example, comprise a semiconductor, a ceramic, a transparent conducing oxide, a polymer, a carbon material, a metal, an alloy, a nitride, an oxide, a silicide, a germanide, a carbide, a derivative thereof, or a combination thereof.

[0098] In some examples, the particle can comprise Be, B, C, Mg, Al, Si, P, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, or a combination thereof.

[0099] In some examples, the particle comprises a metallic particle. In some examples, the metallic particle can comprise a metal selected from the group consisting of Be, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and combinations thereof. In some examples, the metallic particle can comprise a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

[0100] In some examples, the particle 1018 can have an average particle size. “Average particle size” and “mean particle size” are used interchangeably herein, and generally refer to the statistical mean particle size of the particles in a population of particles. In some examples, the average particle size for a plurality of particles with a substantially spherical shape can comprise the average diameter of the plurality of particles. In some examples, the particle with a substantially spherical shape, the diameter of a particle can be a hydrodynamic diameter. In some examples, the hydrodynamic diameter of a particle can be the largest linear distance between two points on the surface of the particle. In some examples, the mean particle size may be measured by scanning electron microscopy. In some examples, the mean particle size may be measured by transmission electron microscopy. In some examples, the mean particle size may be measured by atomic force microscopy. In some examples, the mean particle size may be measured by x-ray microscopy. In some examples, the mean particle size may be measured bydynamic light scattering.

[0101] In some examples, the particle 1018 can have an average particle size of about 1 nanometer (nm) or more. In some examples, the particle can have an average particle size of about 2 nm or more, about 3 nm or more, about 4 nm or more, about 5 nm or more, about 6 nm or more, about 7 nm or more, about 8 nm or more, about 9 nm or more, about 10 nm or more, about 15 nm or more, about 20 nm or more, about 25 nm or more, about 30 nm or more, about 35 nm or more, about 40 nm or more, about 45 nm or more, about 50 nm or more, about 60 nm or more, about 70 nm or more, about 80 nm or more, about 90 nm or more, about 100 nm or more, about 125 nm or more, about 150 nm or more, about 175 nm or more, about 200 nm or more, about 225 nm or more, about 250 nm or more, about 300 nm or more, about 350 nm or more, about 400 nm or more, about 450 nm or more, about 500 nm or more, about 600 nm or more, about 700 nm or more, about 800 nm or more, about 900 nm or more, about 1 micrometers (microns, pm) or more, about 1.25 pm or more, about 1.5 pm or more, about 1.75 pm or more, about 2 pm or more, about 2.5 pm or more, about 3 pm or more, about 3.5 pm or more, about 4 pm or more, about 4.5 pm or more, about 5 pm or more, about 6 pm or more, about 7 pm or more, about 8 pm or more, about 9 pm or more, about 10 pm or more. In some examples, the particle 1018 can have an average particle size of about 10 micrometers (microns, pm) or less. In some examples, the particle can have an average particle size of about 9 pm or less, about 8 pm or less, about 7 pm or less, about 6 pm or less, about 5 pm or less, about 4.5 pm or less, about 4 pm or less, about 3.5 pm or less, about 3 pm or less, about 2.5 pm or less, about 2 pm or less, about 1.75 pm or less, about 1.5 pm or less, about 1.25 pm or less, about 1 pm or less, about 900 nm or less, about 800 nm or less, about 700 nm or less, about 600 nm or less, about 500 nm or less, about 450 nm or less, about 400 nm or less, about 350 nm or less, about 300 nm or less, about 250 nm or less, about 225 nm or less, about 200 nm or less, about 175 nm or less, about 150 nm or less, about 125 nm or less, about 100 nm or less, about 90 nm or less, about 80 nm or less, about 70 nm or less, about 60 nm or less, about 50 nm or less, about 45 nm or less, about 40 nm or less, about 35 nm or less, about 30 nm or less, about 25 nm or less, about 20 nm or less, about 15 nm or less, about 10 nm or less, about 9 nm or less, about 8 nm or less, about 7 nm or less, about 6 nm or less, about 5 nm or less, about 4 nm or less, about 3 nm or less, or about 2 nm or less. In some examples, the average particle size of the particle 1018 can range from any of the minimum values described above to any of the maximum values described above. In some examples, the particle 1018 can have an average particle size of from about 1 nanometer (nm) to about 10 micrometers (microns, pm). In some examples, the particle can have an average particle size of from about 1 nm to about 100 nm, from about 100 nm toabout 10 pm, from about 1 nm to about 10 nm, from about 10 nm to about 100 nm, from about 100 nm to about 1000 nm, from about 1000 nm to about 10 pm, from about 10 nm to about 10 pm, from about 1 nm to about 9 pm, from about 10 nm to about 9 pm, or from about 1 nm to about 1000 nm). In some examples, the particle 1018 can have an average particle size of from about 1 nm to about 1000 nm, or from about 10 nm to about 100 nm.

[0102] In some examples, the particle 1018 can be substantially monodisperse. “Monodisperse” and “homogeneous size distribution,” as used herein, and generally describe a population of particles where the particles are the same or nearly the same size. In some examples, the monodisperse distribution may refer to particle distributions in which 80% of the distribution,., 85% of the distribution, 90% of the distribution, or 95% of the distribution lie within 25% of the median particle size, within 20% of the median particle size, within 15% of the median particle size, within 10% of the median particle size, or within 5% of the median particle size.

[0103] In some examples, the particle can comprise a particle of any shape. In some examples, the particle may be a sphere. In some examples, the particle may be a rod. In some examples, the particle may be a quadrilateral. In some examples, the particle may be an ellipse. In some examples, the particle may be a triangle. In some examples, the particle may be a polygon. In some examples, the particle may be a regular shape. In some examples, the particle may be an irregular shape. In some examples, the particle may be an isotropic shape, In some examples, the particle may be or an anisotropic shape. In some examples, the particle may have a substantially spherical shape.

[0104] In some examples, a particle injector may be used. In some examples, the particle injector may be any suitable particle injector. In some examples, the particle injector may comprise a gas jet. In some examples, the particle injector may comprise an aerodynamic lens. In some examples, the aerodynamic lens may be configured to inject a stream of particles into the accelerator chamber.

[0105] In some examples, the pulse may comprise a laser pulse. In some examples, the device can further comprise a laser source. In some examples, the laser source may be configured to generate the laser pulse. In some examples, the laser source can comprise any suitable laser source. In some examples, the laser source may comprise a Petawatt laser source.

[0106] Also disclosed herein are methods of generating an electron beam using any of the laser wakefield electron accelerator disclosed herein. Also disclosed herein are methods of using the electron beam generated by any of the methods disclosed herein.

[0107] Also disclosed herein are methods of accelerating an electron using any of the laser wakefield electron accelerators disclosed herein. Also disclosed herein are methods of using anyof the accelerated electrons generated by any of the methods disclosed herein.Particle Injectors

[0108] In some examples, referring now to Figure 12 - Figure 15, the particle injector 1000 can comprise a chamber 1002 defined by a wall 1004. The wall 1004 may define an inlet 1006 and an outlet 1008. The chamber 1002 may fluidly connect the inlet 1006 to the outlet 1008. The wall 1004 may further defines a window 1010. The particle injector may further comprise a target 1012 disposed within the chamber 1002 opposite and spaced apart from the window 1010.

[0109] In some examples, when assembled together with an ablation laser 1014 disposed outside the chamber 1002 and configured to generate a laser beam 1016, then the laser beam 1016 may traverse the window 1010 to ablate the target 1012, thereby generating a particle 1018 within the chamber 1002 from the target 1012. In some examples, the window 1010 may comprise a material that can be substantially transparent to the laser beam 1016. In some examples, the chamber 1002 may provide a path for fluid flow from the inlet 1006 to the outlet 1008. For example, the path for fluid flow through the chamber 1002 can traverse the laser beam 1016.

[0110] In some examples, the chamber 1002 may comprise a top portion 1002a and a bottom portion 1002b, the top portion 1002a being separable from the bottom portion 1002b, for example to provide access for removing the target, replacing the target, or both 1012.

[0111] Referring now to Figure 14 and Figure 15, in some examples the particle injector 1000 may further comprise a focusing element 1020 configured to focus the laser beam 1016 onto the target 1012, for example before traversing the window, after traversing the window, or both 1010. In some examples, the focusing element 1020 may comprise a lens.

[0112] In some examples, the target 1012 can be removable, replaceable, or both.

[0113] The target 1012 can comprise any suitable material. For example, the target 1012 can comprise a metal, a metalloid, a nonmetal, derivatives thereof, or combinations thereof. The target 1012 can, for example, comprise a semiconductor, a ceramic, a transparent conducing oxide, a polymer, a carbon material, a metal, an alloy, a nitride, an oxide, a silicide, a germanide, a carbide, a derivative thereof, or a combination thereof.

[0114] In some examples, the target 1012 can comprise Be, B, C, Mg, Al, Si, P, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, or a combination thereof.

[0115] In some examples, the target 1012 may comprise a metal. In some examples, the target 1012 may comprise a metal selected from the group consisting of Be, Mg, Al, Ca, Sc, Ti, V, Cr,Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and combinations thereof. In some examples, the target 1012 may comprise a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

[0116] The particle 1018 can be made of the ablated target 1012.

[0117] As used herein, “a particle” and “the particle” are meant to include any number of particles in any arrangement. In some examples, the particle 1018 can be a single particle. In some examples, the particle 1018 can be a plurality of particles. In some examples, the plurality of particles can be 2 or more; 3 or more; 4 or more; 5 or more; 10 or more; 15 or more; 20 or more; 25 or more; 30 or more; 40 or more; 50 or more; 75 or more; 100 or more; 150 or more; 200 or more; 250 or more; 300 or more; 400 or more; 500 or more; 750 or more; 1000 or more; 1500 or more; 2000 or more; 2500 or more; 3000 or more; 4000 or more; 5000 or more; 7500 or more; 1 x 104or more; 2.5 x 104or more; 5 x 104or more; 7.5 x 104or more; 1x105or more;2.5 x 105or more; 5x 105or more; 7.5 x 105or more; 1 x 106or more; 5 x 106or more; 1 x 107or more; 5 x 107or more; 1 x 108or more; 5 x 108or more; 1 x 109or more; 5 x 109or more; 1 x 1010or more; 1x1011or more; 1x1012or more; 1x1013or morel 1x1014or more; 1x1015or more; 1x1016or more; 1x1017or more; 1x1018or more; 1 x 1019or more; or 1 x 1O20or more.

[0118] The particle 1018 can comprise any suitable material. For example, the particle 1018 can comprise a metal, a metalloid, a nonmetal, derivatives thereof, or combinations thereof. The particle 1018 can, for example, comprise a semiconductor, a ceramic, a transparent conducing oxide, a polymer, a carbon material, a metal, an alloy, a nitride, an oxide, a silicide, a germanide, a carbide, a derivative thereof, or a combination thereof.

[0119] In some examples, the particle 1018 can comprise Be, B, C, Mg, Al, Si, P, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, or a combination thereof.

[0120] In some examples, the particle 1018 may comprise a metal. In some examples, the particle 1018 may comprise a metal selected from the group consisting of Be, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and combinations thereof. In some examples, the particle 1018 may comprise a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

[0121] The particle 1018 can have an average particle size. “Average particle size” and “mean particle size” are used interchangeably herein, and generally refer to the statistical mean particle size of the particles in a population of particles. For example, the average particle size for a plurality of particles with a substantially spherical shape can comprise the average diameter of the plurality of particles. For a particle with a substantially spherical shape, the diameter of a particle can refer, for example, to the hydrodynamic diameter. As used herein, the hydrodynamic diameter of a particle can refer to the largest linear distance between two points on the surface of the particle. Mean particle size can be measured by scanning electron microscopy, transmission electron microscopy, atomic force microscopy, x-ray microscopy, dynamic light scattering, or a combination thereof.

[0122] In some examples, the particle 1018 can have an average particle size of 1 nanometer (nm) or more. In some examples, the particle can have an average particle size of 2 nm or more, 3 nm or more, 4 nm or more, 5 nm or more, 6 nm or more, 7 nm or more, 8 nm or more, 9 nm or more, 10 nm or more, 15 nm or more, 20 nm or more, 25 nm or more, 30 nm or more, 35 nm or more, 40 nm or more, 45 nm or more, 50 nm or more, 60 nm or more, 70 nm or more, 80 nm or more, 90 nm or more, 100 nm or more, 125 nm or more, 150 nm or more, 175 nm or more, 200 nm or more, 225 nm or more, 250 nm or more, 300 nm or more, 350 nm or more, 400 nm or more, 450 nm or more, 500 nm or more, 600 nm or more, 700 nm or more, 800 nm or more, 900 nm or more, 1 micrometers (microns, pm) or more, 1.25 pm or more, 1.5 pm or more, 1.75 pm or more, 2 pm or more, 2.5 pm or more, 3 pm or more, 3.5 pm or more, 4 pm or more, 4.5 pm or more, 5 pm or more, 6 pm or more, 7 pm or more, 8 pm or more, or 9 pm or more. In some examples, the particle 1018 can have an average particle size of 10 micrometers (microns, pm) or less. In some examples, the particle can have an average particle size of 9 pm or less, 8 pm or less, 7 pm or less, 6 pm or less, 5 pm or less, 4.5 pm or less, 4 pm or less, 3.5 pm or less, 3 pm or less, 2.5 pm or less, 2 pm or less, 1.75 pm or less, 1.5 pm or less, 1.25 pm or less, 1 pm or less, 900 nm or less, 800 nm or less, 700 nm or less, 600 nm or less, 500 nm or less, 450 nm or less, 400 nm or less, 350 nm or less, 300 nm or less, 250 nm or less, 225 nm or less, 200 nm or less, 175 nm or less, 150 nm or less, 125 nm or less, 100 nm or less, 90 nm or less, 80 nm or less,70 nm or less, 60 nm or less, 50 nm or less, 45 nm or less, 40 nm or less, 35 nm or less, 30 nm or less, 25 nm or less, 20 nm or less, 15 nm or less, 10 nm or less, 9 nm or less, 8 nm or less, 7 nm or less, 6 nm or less, 5 nm or less, 4 nm or less, 3 nm or less, or 2 nm or less. The average particle size of the particle 1018 can range from any of the minimum values described above to any of the maximum values described above. For example, the particle 1018 can have an average particle size of from 1 nanometer (nm) to 10 micrometers (microns, pm). In some examples, theparticle can have an average particle size of from 1 nm to 100 nm, from 100 nm to 10 pm, from 1 nm to 10 nm, from 10 nm to 100 nm, from 100 nm to 1000 nm, from 1000 nm to 10 pm, from 10 nm to 10 pm, from 25 nm to 10 pm, from 50 nm to 10 pm, from 100 nm to 10 pm, from 250 nm to 10 pm, from 500 nm to 10 pm, from 750 nm to 10 pm, from 1 pm to 10 pm, from 1 nm to 9 pm, from 1 nm to 5 pm, from 1 nm to 1 pm, from 1 nm to 750 nm, from 1 nm to 500 nm, from 1 nm to 250 nm, from 10 nm to 9 pm, from 25 nm to 5 pm, from 1 nm to 1000 nm, or from 10 nm to 100 nm). In some examples, the particle 1018 can have an average particle size of from 1 nm to 1000 nm, or from 10 nm to 100 nm. In some examples, the particle may be a nanoparticle.

[0123] In some examples, the particle 1018 can be substantially monodisperse. “Monodisperse” and “homogeneous size distribution,” as used herein, and generally describe a population of particles where the particles are the same or nearly the same size. As used herein, a monodisperse distribution refers to particle distributions in which 80% of the distribution, 85% of the distribution, 90% of the distribution, or 95% of the distribution lie within 25% of the median particle size, within 20% of the median particle size, within 15% of the median particle size, within 10% of the median particle size, or within 5% of the median particle size.

[0124] The particle 1018 can comprise a particle of any shape. In some examples, the shape may be a sphere, a rod, a quadrilateral, an ellipse, a triangle, a polygon, etc. In some examples, the particle 1018 can have a regular shape, an irregular shape, an isotropic shape, or an anisotropic shape. In some examples, the particle 1018 has a substantially spherical shape.

[0125] In some examples, the particle injector 1000 may further comprise the ablation laser 1014

[0126] The ablation laser 1014 can comprise any suitable laser. In some examples, the ablation laser 1014 can be a pulsed laser, such that the laser beam 1016 can be pulsed. In some examples, the pulse duration can be nanoseconds, picoseconds, or femtoseconds long.

[0127] In some examples, the inlet 1006 can be configured to receive a fluid, the chamber 1002 providing path for fluid flow from the inlet 1006 to the outlet 1008, such that the fluid flowing through the chamber 1002 carries the particle 1018 and fluid out of the chamber 1002 through the outlet 1008.

[0128] In some examples, the fluid may be a gas.

[0129] In some examples, the gas can be provided to the chamber 1002 at a pressure of 0.01 pounds per square inch (PSI) or more. In some examples, the gas can be provided to the chamber at a pressure of 0.025 PSI or more, 0.05 PSI or more, 0.075 PSI or more, 0.1 PSI or more, 0.25 PSI or more, 0.5 PSI or more, 0.75 PSI or more, 1 PSI or more, 1.5 PSI or more, 2 PSI or more, 2.5 PSI or more, 3 PSI or more, 3.5 PSI or more, 4 PSI or more, 4.5 PSI or more, 5 PSI or more,6 PSI or more, 7 PSI or more, 8 PSI or more, 9 PSI or more, 10 PSI or more, 15 PSI or more, 20 PSI or more, 25 PSI or more, 30 PSI or more, 35 PSI or more, 40 PSI or more, 45 PSI or more, 50 PSI or more, 60 PSI or more, 70 PSI or more, 80 PSI or more, 90 PSI or more, 100 PSI or more, 125 PSI or more, 150 PSI or more, 175 PSI or more, 200 PSI or more, 225 PSI or more, 250 PSI or more, 300 PSI or more, 350 PSI or more, 400 PSI or more, 450 PSI or more, 500 PSI or more, 550 PSI or more, 600 PSI or more, 650 PSI or more, 700 PSI or more, 750 PSI or more, 800 PSI or more, 850 PSI or more, or 900 PSI or more. In some examples, the gas can be provided to the chamber 1002 at a pressure of 1000 pounds per square inch (PSI) or less. In some examples, the gas can be provided to the chamber at a pressure of 950 PSI or less, 900 PSI or less, 850 PSI or less, 800 PSI or less, 750 PSI or less, 700 PSI or less, 650 PSI or less, 600 PSI or less, 550 PSI or less, 500 PSI or less, 450 PSI or less, 400 PSI or less, 350 PSI or less, 300 PSI or less, 250 PSI or less, 225 PSI or less, 200 PSI or less, 175 PSI or less, 150 PSI or less, 125 PSI or less, 100 PSI or less, 90 PSI or less, 80 PSI or less, 70 PSI or less, 60 PSI or less, 50 PSI or less, 45 PSI or less, 40 PSI or less, 35 PSI or less, 30 PSI or less, 25 PSI or less, 20 PSI or less, 15 PSI or less, 10 PSI or less, 9 PSI or less, 8 PSI or less, 7 PSI or less, 6 PSI or less, 5 PSI or less, 4.5 PSI or less, 4 PSI or less, 3.5 PSI or less, 3 PSI or less, 2.5 PSI or less, 2 PSI or less, 1.5 PSI or less, 1 PSI or less, 0.75 PSI or less, 0.5 PSI or less, 0.25 PSI or less, 0.1 PSI or less, 0.075 PSI or less, or 0.05 PSI or less. The pressure at which the gas is provided to the chamber 1002 can range from any of the minimum values described above to any of the maximum values described above. For example, the gas can be provided to the chamber 1002 at a pressure of from 0.01 to 1000 pounds per square inch (PSI). In some examples, the gas can be provided to the chamber at a pressure of from 0.01 to 500 PSI, from 500 to 1000 PSI, from 0.01 to 200 PSI, from 200 to 400 PSI, from 400 to 600 PSI, from 600 to 800 PSI, from 800 to 1000 PSI, from 0.01 to 100 PSI, from 100 to 200 PSI, from 200 to 300 PSI, from 300 to 400 PSI, from 400 to 500 PSI, from 500 to 600 PSI, from 600 to 700 PSI, from 700 to 800 PSI, from 800 to 900 PSI, from 900 to 1000 PSI, from 0.01 to 800 PSI, from 0.01 to 600 PSI, from 0.01 to 400 PSI, from 0.01 to 75 PSI, from 0.01 to 50 PSI, from 0.01 to 25 PSI, from 0.01 to 10 PSI, from 0.01 to 1 PSI, from 1 to 1000 PSI, from 10 to 1000 PSI, from 25 to 1000 PSI, from 50 to 1000 PSI, from 75 to 1000 PSI, from 100 to 1000 PSI, from 200 to 1000 PSI, from 400 to 1000 PSI, from 600 to 1000 PSI, from 1 to 900 PSI, from 5 to 800 PSI, from 10 to 700 PSI, from 25 to 600 PSI, or from 50 to 500 PSI).

[0130] The gas can comprise any suitable gas. In some examples, the gas may comprise hydrogen, helium, nitrogen, and the like, or a combination thereof. In some examples, the gas can comprise a low-density gas. In some examples, the gas can comprise helium.

[0131] Referring now to Figure 16 - Figure 24, in some examples the particle injector 2000 can comprise an ablation stage 2100 and an ionization stage 2200, the ablation stage 2100 being upstream from and fluidly connected to the ionization stage 2200.

[0132] In some examples, the ablation stage 2100 can comprise a solid target 2112 and an ablation laser 2114, wherein the ablation laser 2114 is configured to ablate the solid target 2112 to form a particle 2118. In some examples, the ablation stage 2100 can further comprise a path for fluid flow 2120, such that fluid flow through the ablation stage 2100 is configured to carry the particle 2118 away from the ablation stage 2100 to the ionization stage 2200.

[0133] In some examples, the ionization stage 2200 can comprise an ionization laser 2202 configured to ionize the particle 2118 and fluid received from the ablation stage 2100, thereby forming ionized particles and ionized fluid. In some examples, the ionization stage 2200 can further comprise a path for fluid flow 2220, such that fluid flow through the ionization stage 2200 is configured to carry the ionized particle and ionized fluid away from the ionization stage 2200 to an acceleration stage 2300, the acceleration stage 2300 being downstream from and fluidly connected to the ionization stage 2200.

[0134] In some examples, the ionization laser 2202 may be distinct from the ablation laser 2114.

[0135] In some examples, the ionization stage 2200 and the ablation stage 2100 may be located in spatially distinct physical locations.

[0136] In some examples, the ablation stage 2100 can comprise a chamber 2102 defined by a wall 2104. In some examples, the wall 2104 can define an inlet 2106 and an outlet 2108. In some examples, the chamber 2102 can fluidly connect the inlet 2106 to the outlet 2108. In some examples, the wall 2104 can further define a window 2110. In some examples, the solid target 2112 can be disposed within the chamber 2102, such as opposite and spaced apart from the window 2110.

[0137] In some examples, the ablation laser 2114 may be disposed outside the chamber 2102 and may be configured to generate a laser beam 2116, then the laser beam 2116 traverses the window 2110 to ablate the solid target 2112, thereby generating the particle 2118 within the chamber 2102 from the solid target 2112. In some examples, the window 2110 may comprise a material that is substantially transparent to the laser beam 2116.

[0138] In some examples, the chamber 2102 can comprise a top portion 2102a and a bottom portion 2102b, the top portion 2102a being separable from the bottom portion 2102b, for example to provide access for removing the solid target, replacing the solid target, or both 2112.

[0139] In some examples, the particle injector 2000 may further comprise a focusing element 2020 configured to focus the laser beam 2116 onto the solid target 2112, for example beforetraversing the window, after traversing the window, or both 2110. In some examples, the focusing element 2020 may comprise a lens.

[0140] In some examples, the solid target 2112 may be removable, replaceable, or both.

[0141] The solid target 2112 can comprise any suitable material. For example, the solid target 2112 can comprise a metal, a metalloid, a nonmetal, derivatives thereof, or combinations thereof. The solid target 2112 can, for example, comprise a semiconductor, a ceramic, a transparent conducing oxide, a polymer, a carbon material, a metal, an alloy, a nitride, an oxide, a silicide, a germanide, a carbide, a derivative thereof, or a combination thereof.

[0142] In some examples, the solid target 2112 can comprise Be, B, C, Mg, Al, Si, P, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, or a combination thereof.

[0143] In some examples, the solid target 2112 may comprise a metal. In some examples, the solid target 2112 may comprise a metal selected from the group consisting of Be, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and combinations thereof. In some examples, the solid target 2112 may comprise a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

[0144] The particle 2118 can be made of the ablated solid target 2112.

[0145] As used herein, “a particle” and “the particle” are meant to include any number of particles in any arrangement. In some examples, the particle 2118 can be a single particle. In some examples, the particle 2118 can be a plurality of particles. In some examples, the plurality of particles may be 2 or more; 3 or more; 4 or more; 5 or more; 10 or more; 15 or more; 20 or more; 25 or more; 30 or more; 40 or more; 50 or more; 75 or more; 100 or more; 150 or more; 200 or more; 250 or more; 300 or more; 400 or more; 500 or more; 750 or more; 1000 or more; 1500 or more; 2000 or more; 2500 or more; 3000 or more; 4000 or more; 5000 or more; 7500 or more; 1 x 104or more; 2.5 x 104or more; 5 x 104or more; 7.5 x 104or more; 1x105or more;2.5 x 105or more; 5x 105or more; 7.5 x 105or more; 1 x 106or more; 5 x 106or more; 1 x 107or more; 5 x 107or more; 1 x 108or more; 5 x 108or more; 1 x 109or more; 5 x 109or more; 1 x 1010or more; 1x1011or more; 1x1012or more; 1x1013or morel 1x1014or more; 1x1015or more; 1x1016or more; 1x1017or more; 1x1018or more; 1 x 1019or more; or 1 x 1O20or more.

[0146] The particle 2118 can comprise any suitable material. For example, the particle 2118 cancomprise a metal, a metalloid, a nonmetal, derivatives thereof, or combinations thereof. The particle 2118 can, for example, comprise a semiconductor, a ceramic, a transparent conducing oxide, a polymer, a carbon material, a metal, an alloy, a nitride, an oxide, a silicide, a germanide, a carbide, a derivative thereof, or a combination thereof.

[0147] In some examples, the particle 2118 can comprise Be, B, C, Mg, Al, Si, P, S, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge, As, Se, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Sb, Te, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, Po, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, or a combination thereof.

[0148] In some examples, the particle 2118 may comprise a metal. In some examples, the particle 2118 may comprise a metal selected from the group consisting of Be, Mg, Al, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Sr, Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In, Sn, Ba, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb, Bi, La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, and combinations thereof. In some examples, the particle 2118 may comprise a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

[0149] The particle 2118 can have an average particle size. “Average particle size” and “mean particle size” are used interchangeably herein, and generally refer to the statistical mean particle size of the particles in a population of particles. For example, the average particle size for a plurality of particles with a substantially spherical shape can comprise the average diameter of the plurality of particles. For a particle with a substantially spherical shape, the diameter of a particle can refer, for example, to the hydrodynamic diameter. As used herein, the hydrodynamic diameter of a particle can refer to the largest linear distance between two points on the surface of the particle. Mean particle size can be measured by scanning electron microscopy, transmission electron microscopy, atomic force microscopy, x-ray microscopy, dynamic light scattering, or a combination thereof.

[0150] In some examples, the particle 2118 can have an average particle size of 1 nanometer (nm) or more. In some examples, the particle can have an average particle size of 2 nm or more, 3 nm or more, 4 nm or more, 5 nm or more, 6 nm or more, 7 nm or more, 8 nm or more, 9 nm or more, 10 nm or more, 15 nm or more, 20 nm or more, 25 nm or more, 30 nm or more, 35 nm or more, 40 nm or more, 45 nm or more, 50 nm or more, 60 nm or more, 70 nm or more, 80 nm or more, 90 nm or more, 100 nm or more, 125 nm or more, 150 nm or more, 175 nm or more, 200 nm or more, 225 nm or more, 250 nm or more, 300 nm or more, 350 nm or more, 400 nm or more, 450 nm or more, 500 nm or more, 600 nm or more, 700 nm or more, 800 nm or more, 900 nm or more, 1 micrometers (microns, pm) or more, 1.25 pm or more, 1.5 pm or more, 1.75 pmor more, 2 pm or more, 2.5 pm or more, 3 pm or more, 3.5 pm or more, 4 pm or more, 4.5 pm or more, 5 pm or more, 6 pm or more, 7 pm or more, 8 pm or more, or 9 pm or more. In some examples, the particle 2118 can have an average particle size of 10 micrometers (microns, pm) or less. In some examples, the particle can have an average particle size of 9 pm or less, 8 pm or less, 7 pm or less, 6 pm or less, 5 pm or less, 4.5 pm or less, 4 pm or less, 3.5 pm or less, 3 pm or less, 2.5 pm or less, 2 pm or less, 1.75 pm or less, 1.5 pm or less, 1.25 pm or less, 1 pm or less, 900 nm or less, 800 nm or less, 700 nm or less, 600 nm or less, 500 nm or less, 450 nm or less, 400 nm or less, 350 nm or less, 300 nm or less, 250 nm or less, 225 nm or less, 200 nm or less, 175 nm or less, 150 nm or less, 125 nm or less, 100 nm or less, 90 nm or less, 80 nm or less,70 nm or less, 60 nm or less, 50 nm or less, 45 nm or less, 40 nm or less, 35 nm or less, 30 nm or less, 25 nm or less, 20 nm or less, 15 nm or less, 10 nm or less, 9 nm or less, 8 nm or less, 7 nm or less, 6 nm or less, 5 nm or less, 4 nm or less, 3 nm or less, or 2 nm or less. The average particle size of the particle 2118 can range from any of the minimum values described above to any of the maximum values described above. For example, the particle 2118 can have an average particle size of from 1 nanometer (nm) to 10 micrometers (microns, pm). In some examples, the particle can have an average particle size of from 1 nm to 100 nm, from 100 nm to 10 pm, from 1 nm to 10 nm, from 10 nm to 100 nm, from 100 nm to 1000 nm, from 1000 nm to 10 pm, from 10 nm to 10 pm, from 25 nm to 10 pm, from 50 nm to 10 pm, from 100 nm to 10 pm, from 250 nm to 10 pm, from 500 nm to 10 pm, from 750 nm to 10 pm, from 1 pm to 10 pm, from 1 nm to 9 pm, from 1 nm to 5 pm, from 1 nm to 1 pm, from 1 nm to 750 nm, from 1 nm to 500 nm, from 1 nm to 250 nm, from 10 nm to 9 pm, from 25 nm to 5 pm, from 1 nm to 1000 nm, or from 10 nm to 100 nm). In some examples, the particle 2118 can have an average particle size of from 1 nm to 1000 nm, or from 10 nm to 100 nm. In some examples, the particle may be a nanoparticle.

[0151] In some examples, the particle 2118 can be substantially monodisperse. “Monodisperse” and “homogeneous size distribution,” as used herein, and generally describe a population of particles where the particles are the same or nearly the same size. As used herein, a monodisperse distribution refers to particle distributions in which 80% of the distribution, 85% of the distribution, 90% of the distribution, or 95% of the distribution) lie within 25% of the median particle size, within 20% of the median particle size, within 15% of the median particle size, within 10% of the median particle size, or within 5% of the median particle size.

[0152] The particle 2118 can comprise a particle of any shape. In some examples, the particle shape may be a sphere, a rod, a quadrilateral, an ellipse, a triangle, a polygon, etc. In some examples, the particle 2118 can have a regular shape, an irregular shape, an isotropic shape, or an anisotropic shape. In some examples, the particle 2118 has a substantially spherical shape.

[0153] In some examples, the particle injector 2000 may further comprise the ablation laser 2114

[0154] The ablation laser 2114 can comprise any suitable laser. In some examples, the ablation laser 2114 may be a pulsed laser, such that the laser beam 2116 can be pulsed. In some examples, the pulse duration can be nanoseconds, picoseconds, or femtoseconds long.

[0155] In some examples, the inlet 2106 may be configured to receive a fluid and the chamber 2102 provides a path for fluid flow from the inlet 2106 to the outlet 2108 such that the fluid flowing through the chamber 2102 is configured to carry the particle 2118 and fluid out of the chamber 2102 through the outlet 2108 towards the ionization stage 2200.

[0156] In some examples, the fluid may comprise a gas.

[0157] In some examples, the gas can be provided to the chamber 2102 at a pressure of 0.01 pounds per square inch (PSI) or more. In some examples, the gas can be provided to the chamber at a pressure of 0.025 PSI or more, 0.05 PSI or more, 0.075 PSI or more, 0.1 PSI or more, 0.25 PSI or more, 0.5 PSI or more, 0.75 PSI or more, 1 PSI or more, 1.5 PSI or more, 2 PSI or more, 2.5 PSI or more, 3 PSI or more, 3.5 PSI or more, 4 PSI or more, 4.5 PSI or more, 5 PSI or more, 6 PSI or more, 7 PSI or more, 8 PSI or more, 9 PSI or more, 10 PSI or more, 15 PSI or more, 20 PSI or more, 25 PSI or more, 30 PSI or more, 35 PSI or more, 40 PSI or more, 45 PSI or more, 50 PSI or more, 60 PSI or more, 70 PSI or more, 80 PSI or more, 90 PSI or more, 100 PSI or more, 125 PSI or more, 150 PSI or more, 175 PSI or more, 200 PSI or more, 225 PSI or more, 250 PSI or more, 300 PSI or more, 350 PSI or more, 400 PSI or more, 450 PSI or more, 500 PSI or more, 550 PSI or more, 600 PSI or more, 650 PSI or more, 700 PSI or more, 750 PSI or more, 800 PSI or more, 850 PSI or more, or 900 PSI or more. In some examples, the gas can be provided to the chamber 2102 at a pressure of 1000 pounds per square inch (PSI) or less. In some examples, the gas can be provided to the chamber at a pressure of 950 PSI or less, 900 PSI or less, 850 PSI or less, 800 PSI or less, 750 PSI or less, 700 PSI or less, 650 PSI or less, 600 PSI or less, 550 PSI or less, 500 PSI or less, 450 PSI or less, 400 PSI or less, 350 PSI or less, 300 PSI or less, 250 PSI or less, 225 PSI or less, 200 PSI or less, 175 PSI or less, 150 PSI or less, 125 PSI or less, 100 PSI or less, 90 PSI or less, 80 PSI or less, 70 PSI or less, 60 PSI or less, 50 PSI or less, 45 PSI or less, 40 PSI or less, 35 PSI or less, 30 PSI or less, 25 PSI or less, 20 PSI or less, 15 PSI or less, 10 PSI or less, 9 PSI or less, 8 PSI or less, 7 PSI or less, 6 PSI or less, 5 PSI or less, 4.5 PSI or less, 4 PSI or less, 3.5 PSI or less, 3 PSI or less, 2.5 PSI or less, 2 PSI or less, 1.5 PSI or less, 1 PSI or less, 0.75 PSI or less, 0.5 PSI or less, 0.25 PSI or less, 0.1 PSI or less, 0.075 PSI or less, or 0.05 PSI or less. The pressure at which the gas is provided to the chamber 2102 can range from any of the minimum values described above to any of the maximum valuesdescribed above. For example, the gas can be provided to the chamber 2102 at a pressure of from 0.01 to 1000 pounds per square inch (PSI) . In some examples, the gas can be provided to the chamber at a pressure of from 0.01 to 500 PSI, from 500 to 1000 PSI, from 0.01 to 200 PSI, from 200 to 400 PSI, from 400 to 600 PSI, from 600 to 800 PSI, from 800 to 1000 PSI, from 0.01 to 100 PSI, from 100 to 200 PSI, from 200 to 300 PSI, from 300 to 400 PSI, from 400 to 500 PSI, from 500 to 600 PSI, from 600 to 700 PSI, from 700 to 800 PSI, from 800 to 900 PSI, from 900 to 1000 PSI, from 0.01 to 800 PSI, from 0.01 to 600 PSI, from 0.01 to 400 PSI, from 0.01 to 75 PSI, from 0.01 to 50 PSI, from 0.01 to 25 PSI, from 0.01 to 10 PSI, from 0.01 to 1 PSI, from 1 to 1000 PSI, from 10 to 1000 PSI, from 25 to 1000 PSI, from 50 to 1000 PSI, from 75 to 1000 PSI, from 100 to 1000 PSI, from 200 to 1000 PSI, from 400 to 1000 PSI, from 600 to 1000 PSI, from 1 to 900 PSI, from 5 to 800 PSI, from 10 to 700 PSI, from 25 to 600 PSI, or from 50 to 500 PSI).

[0158] The gas can comprise any suitable gas. In some examples, the gas comprises hydrogen, helium, nitrogen, and the like, or a combination thereof. In some examples, the gas can comprise a low-density gas. In some examples, the gas can comprise helium.

[0159] In some examples, the ionization laser 2202 may be configured to interact with the particle 2118 and the fluid after the particle 2118 and the fluid have exited the ablation stage 2100 by passing through the outlet 2108. In some examples, the ionized particle and ionized fluid may be configured to flow away from the ionization stage 2200 to an acceleration stage 2300, the acceleration stage 2300 being downstream from and fluidly connected to the ionization stage 2200.

[0160] In some examples, the particle injector 2000 may further comprise the ionization laser 2202.

[0161] The ionization laser 2202 can comprise any suitable laser. In some examples, the ionization laser 2202 is a pulsed laser. In some examples, the pulse duration can be nanoseconds, picoseconds, or femtoseconds long.EXAMPLES

[0162] The following examples are provided to further illustrate some embodiments or examples of the present disclosure, but are not intended to limit the scope of the disclosure; it will be understood by their exemplary nature that other procedures, methodologies, or techniques known to those skilled in the art may alternatively be used.Example 1: Method and apparatus for generation of long flat-top or tapered gas density profiles with parabolic transverse profiles

[0163] A method and apparatus may be applied to generate centimeters-long gas density profiles. In some examples, the profiles may be flat-top or density tapered in the longitudinal direction and parabolic in the transverse direction. In some examples, the longitudinal profile may be controlled by changing the height H or the outlet length L. In some examples, the transverse profile can be controlled by using wires with various thicknesses.

[0164] A laser wakefield electron accelerator [1] (LWFA) uses the interaction between a high- power laser and a gas to generate Langmuir plasma waves. In an extreme nonlinear example, called bubble [2] or blowout regime [3], the Langmuir plasma wave takes a quasi -spherical shape and can trap and accelerate some of the background plasma electrons that have proper position and momentum relative to the plasma wave. Due to the structure of the electric potential inside the plasma wave [4], which resembles the electric field found in linear accelerators, the injected electrons may experience acceleration in the first half of the bubble and may not experience acceleration in the second half of the bubble as the injected electrons may be decelerated in the other half of the bubble. The acceleration fields can be 100 GV / m. In some examples, the acceleration fields can be three orders of magnitude or greater than the fields found in state-of-the-art radio-frequency particle accelerators. The phase velocity of the front of the bubble may be determined by the laser pulse group velocity and may continuously decrease as the laser pulse transfers its energy to the plasma wave [4], The group velocity of the injected electrons may vary in comparison to the phase velocity of the bubble; therefore, the electron bunch advances toward the center of the bubble and experiences different values of the acceleration gradient that leads to a decrease in the maximum achievable energy and an increase in energy spread. In some examples, the electron bunch reaches the middle of the bubble and decelerates. The distance traveled, in this case, is called the dephasing length and may be a limitation in current laser wakefield electron accelerators. A solution for the electron-plasma wave dephasing issue has been proposed initially by Katsouleas et al. [5] and uses an upward density ramp to increase the phase velocity of the back of the bubble until it matches the velocity of the electron bunch. In this scenario, the phase-matched electron bunch experiences the maximum acceleration gradient; thus, the energy of the electron beam greatly increases for the same laser energy compared with the case when the electron bunch is not phase-locked. Theoretical studies [6, 7] and experiments [8-10] show that most of the parameters of the electron beam can be improved in an up-ramp plasma density and not just the energy. For example, in an upward plasma density, due to the increased phase velocity, selective electron injection into the bubble leads to a significant decrease in divergence / emittance, or the constant acceleration gradient preserves or decreases the energy spread.

[0165] Depending on the laser power and specific experimental goals, various gas targets may be employed to generate and control the gas density profiles used in laser wakefield electron accelerators. For instance, laser wakefield electron accelerators with 10’s of terawatts (TW) power lasers comprise millimeters long tilted [9, 10] or straight gas jets [11-14], while laser wakefield electron accelerators with 100’s of TW laser power can use centimeters long slit nozzles

[0015] or gas cells [16-19], Laser wakefield electron accelerators with petawatt (PW) class lasers can use gas cells designed to produce long uniform density profiles [20, 21] or capillaries [22-25] when laser guiding is applied. The drawbacks of using gas cells or capillaries become apparent when the interaction zone is optically probed or the plasma is spectrally observed. The material ablated by the laser from the pinholes, in the case of gas cells, or from the capillary walls creates an opaque zone that makes the use of probe beams or optical spectrometers impossible. More complications may appear in head-on electron-laser beam colliders [26, 27], where the presence of walls / windows may make the experimental setup difficult to use, especially in the case of PW-class lasers comprising long interaction lengths. Another limitation may appear when optical probing is replaced by deep-UV, X-ray, or electron beam

[0028] probing. In this case, the presence of any optically transparent material can hinder the use of these kinds of diagnostics.

[0166] Considering the overall enhancement of the parameters of the electron beam in an up- ramp plasma density, as explained above, the development of gas targets that permit the control of the gas density profile may be beneficial. In some examples, these targets can be particularly useful for laser wakefield electron accelerators with PW lasers where the acceleration length is multiple centimeters long, and the existing gas cells cannot be used to generate this kind of density profile.

[0167] In some examples, in light of the limitations of existing gas targets, the development of new types of gas targets may be beneficial for the further development of laser wakefield electron accelerators. Such a gas target is shown in Figure 2A-Figure 2C and comprises a halved slit nozzle. In some examples, for a symmetric nozzle (Figure 1), the gas flow inside the slit nozzle may be symmetric and uniform (flat-top shape) for a few mm long outlets, but as the length of the outlet increases, the gas density profile becomes gaussian in shape, becoming unsuitable for laser wakefield electron accelerators, especially with low gas densities. In some examples, by choosing just half of a full slit nozzle (Figure 2A-Figure 2C), the density profile can be shaped by choosing the height H and gas outlet length L. In some examples, the combination of H and L may enable the asymmetric slit nozzle to generate unique density profiles, which can be tapered or uniform. In some examples, placing a thin wire at the nozzleoutput along the longitudinal axis (Figure 2C) may permit the creation of a parabolic-type density profile.

[0168] In some examples, the asymmetric slit nozzles described herein are shown in Figure 2A- Figure 2C. In some examples, the asymmetric slit nozzles may comprise a rectangular inlet (1) followed by a throat (2) and a divergent section (3) with the height H. In some examples, the rectangular outlet (4) of the asymmetric slit nozzle may have various lengths, L, and widths W, depending on the density profile to be generated. In some examples, a wire with various diameters (5) can be inserted in the middle of the outlet (4) when the transverse density profile may be to be modulated.

[0169] Working Principle of the Apparatus

[0170] In some examples, various gasses may be fed at various pressures through the rectangular inlet (1) and travel through the throat (2) into the diverging section (3). In some examples, due to friction with the walls of the nozzle and collisions with other atoms or molecules, the velocity components along the axes of propagation may be randomized. In some examples, to make the friction with walls and collision between atoms as efficient as possible, the width W of the asymmetric slit nozzle may be as small as possible. In some examples, the width of the asymmetric nozzle may be 1 mm. In some examples, the width of the asymmetric nozzle may be less than 1 mm. In some examples, the width of the asymmetric nozzle may be greater than 1 mm. In some examples, as the gas atoms or molecules propagate toward the outlet (4) where there may be a low pressure (quasi-vacuum), they may uniformize, and the gas density profile at the outlet nozzle may depend on the gas pressure at the rectangular inlet (1), the height H of the divergent section (3) of the nozzle and the length L of the rectangular outlet (4). In some examples, keeping the length L of the rectangular outlet (4) constant, the gas density profile may be transformed from ramped-type to flat-top as the height H of the divergent section (3) increases. In some examples, flat-top profiles may be obtained from an asymmetric slit nozzle at varying nozzle heights. As shown in Figure 3, a flat-top profile may be obtained from an asymmetric nozzle with a height of 30 cm and an outlet length of 5 cm, with the flat-top profile propagating out to around 4 millimeters above the nozzle. Further, as shown in Figures 4A-D, a flat-top profile may be obtained with varying nozzle heights and a constant outlet length. Flat- top profiles may be propagated at distances of around 3 millimeters from the nozzle when the nozzle heights of 50 mm (Figure 4A), 100 mm (Figure 4B), 200 mm (Figure 4C), and 300 mm (Figure 4D), where a longer nozzle height yielded a stronger flat-top density profile. The density profiles are shown at different heights above the nozzle outlet (4) and are obtained from fluid dynamics simulations using helium at 100000 pascals inlet (1) pressure.

[0171] In some examples, inserting a wire (5) in the middle of the rectangular outlet and along the long outlet axis, the transverse density profile can be modulated, generating in this way a gas density depression which can act as a guiding structure. In some examples, a transversely modulated density profile may be obtained, as shown in Figure 5, where a wire with a diameter of 200 pm may be introduced along the middle of the long axis of the rectangular outlet. In some examples, the profile is obtained from fluid dynamic simulation in the same conditions described above.

[0172] In some examples, features of the apparatus that enable the generation of flat-top or ramped gas density profiles may include but are not limited to the following features described herein.

[0173] In some examples, one feature in enabling the generation of flat-top or ramped gas density profiles, the inlet (1) shape may match the shape of the outlet (4), wherein the inlet and outlet shape may have the same geometric cross section enlarged by a fraction. In some examples, the shape of the inlet and the shape of the outlet may match where the inlet shape may be a smaller circle and the outlet shape may be a larger circle. In one example, as shown in Figure 2A-Figure 2C, the shape is chosen as rectangular. In other examples, alternate shapes may be chosen while still allowing for the method to work.

[0174] In some examples, another feature in enabling the generation of flat-top or ramped gas density profiles, the distance H between the inlet (1) and outlet (4) and the length L of the outlet (4) may determine the shape of the gas density profile above the outlet (4). In some examples, as the distance between the inlet and outlet H may be increased, the length L of the outlet may increase. In some examples, the increase in inlet to outlet distance H may transform the gas density profile from ramped-type to flat-top.

[0175] In some examples, another feature in enabling the generation of flat-top or ramped gas density profiles, the width W size of the outlet profile may be smaller than the length L of the outlet profile. In some examples, the width can be limited to a few mm. In some examples, the outlet width may be about 1 mm. In some examples, the outlet width may be about 2 mm. In some examples, the outlet width may be about 3 mm. In some examples, the outlet width may be about 4 mm. In some examples, the outlet width may be about 5 mm.

[0176] In some examples, ramped or flat-top density profiles about 1 cm or longer may be propagated when the gas density is less than 1018atoms / cm3. In some examples, nozzle outlets can produce ramped or flat-top density profiles under about 1 cm with other gas densities.Example 2: Method and apparatus for generation of long flat-top or tapered gas density profiles with parabolic transverse profiles

[0177] Described herein are gas nozzles that are intentionally asymmetric in order to shape the gas density profile. In some examples, additional gas density shaping can be obtained by inserting a wire into the gas flow.

[0178] In some examples, the devices described herein can generate multi-centimeters long uniform gas density profiles that cannot be generated using de Laval nozzles. In some examples, such multi-centimeters long uniform gas density profiles can be used in plasma-based wakefield accelerators.

[0179] In some examples, the nozzles described herein can be used to generate relatively low gas densities. In some examples, the nozzles can be used to generate gas densities less than 1018atoms / cm3.References

[0180] The following references are referred to by number throughout the specification:[1] T. Tajima and J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett., vol. 43, no. 4, pp. 267-270, 1979, doi: 10.1103 / PhysRevLett.43.267;[2] A. Pukhov and J. Meyer-ter-Vehn, “Laser wake field acceleration: The highly nonlinear broken-wave regime,” Appl. Phys. B Lasers Opt., vol. 74, no. 4-5, pp. 355— 361, 2002, doi: 10.1007 / s003400200795;[3] T. Lu, W., Huang, C., Zhou, M., Mori, W. B., Katsouleas, “Nonlinear theory for relativistic plasma wakefields in the blowout regime,” Phys. Rev. Lett., vol. 10, no. 5, p. 165002, 2006, doi: 10.1088 / 0034-4885 / 67 / 8 / C01;[4] E. Esarey, C. B. Schroeder, and W. P. Leemans, “Physics of laser-driven plasmabased electron accelerators,” Rev. Mod. Phys., vol. 81, no. 3, pp. 1229-1285, Aug. 2009, doi: 10.1103 / RevModPhys.81.1229;[5] T. Katsouleas, “Physical mechanisms in the plasma wake-field accelerator,” Phys. Rev. A, vol. 33, no. 3, pp. 2056-2064, 1986, doi: 10.1103 / PhysRevA.33.2056;[6] W. Rittershofer, C. B. Schroeder, E. Esarey, F. J. Gruner, and W. P. Leemans, “Tapered plasma channels to phase-lock accelerating and focusing forces in laser-plasma accelerators,” Phys. Plasmas, vol. 17, no. 6, p. 063104, 2010, doi: 10.1063 / 1.3430638;[7] M. Wen et al., “Controlled electron acceleration in the bubble regime by optimizing plasma density,” New J. Phys., vol. 12, pp. 1-9, 2010, doi: 10.1088 / 1367- 2630 / 12 / 4 / 045010;[8] E. Guillaume et al., “Electron Rephasing in a Laser-Wakefield Accelerator,” Phys. Rev. Lett., vol. 115, no. 15, 2015, doi: 10.1103 / PhysRevLett. l l5.155002.[9] J. Kim, G. J. Kim, and S. H. Yoo, “Energy Enhancement Using an Upward Density Ramp in Laser Wakefield Acceleration,” J. Korean Phys. Soc., vol. 59, no. 5(1), pp. 3166-3170, 2011, doi: 10.3938 / jkps.59.3166;

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[0025] A. J. Gonsalves et al., “Petawatt Laser Guiding and Electron Beam Acceleration to 8 GeV in a Laser-Heated Capillary Discharge Waveguide,” Phys. Rev. Lett., vol. 122, no.8, 2019, doi: 10.1103 / PhysRevLett.122.084801;

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[0027] J. M. Cole et al., “Experimental Evidence of Radiation Reaction in the Collision of a High-Intensity Laser Pulse with a Laser-Wakefield Accelerated Electron Beam,” Phys. Rev. X, vol. 8, no. 1, 2018, doi: 10.1103 / PhysRevX.8.011020; and

[0028] C. J. Zhang et al., “Femtosecond Probing of Plasma Wakefields and Observation of the Plasma Wake Reversal Using a Relativistic Electron Bunch,” Phys. Rev. Lett., vol. 119, no. 6, 2017, doi: 10.1103 / PhysRevLett.119.064801; each of which is incorporated herein by reference for all purposes.EXEMPLARY ASPECTS

[0181] In view of the described compositions, devices, systems, and methods, herein below are described certain more particularly described aspects of the inventions. The particularly recitedaspects should not, however, be interpreted to have any limiting effect on any different claims containing different or more general teachings described herein or that the “particular” aspects are somehow limited in some way other than the inherent meanings of the language and formulas literally used therein.

[0182] Example 1 : A nozzle for a laser wakefield electron accelerator, the nozzle comprising: an inlet; an outlet spaced apart from and in fluid communication with the inlet; and a chamber fluidly coupling the inlet to the outlet, wherein the inlet is configured to receive a gas at a pressure, and the outlet is configured to release the gas with a gas density profile, and wherein the density profile comprises a substantially flat-topped or ramped profile for a distance of at least 5 millimeters.

[0183] Example 2: The nozzle of any examples herein, particularly example 1, wherein the inlet and outlet comprise geometrically similar cross-sectional shapes.

[0184] Example 3: The nozzle of any examples herein, particularly example 2, wherein the geometrically similar cross-sectional shapes comprise shapes which are obtained from one another by uniformly scaling.

[0185] Example 4: The nozzle of any examples herein, particularly example 3, wherein the inlet and the outlet comprise a geometric center and area, wherein the geometric center of the inlet is translated relative to a geometric center of the outlet along an axis perpendicular to an axis of propagation of the gas.

[0186] Example 5: The nozzle of any examples herein, particularly example 4, wherein the area defined by the inlet is smaller than the area defined the outlet.

[0187] Example 6: The nozzle of any examples herein, particularly example 5, wherein the corresponding inlet is rectangular and outlet is rectangular.

[0188] Example 7: The nozzle of any examples herein, particularly example 1, wherein the outlet has a length and width, and that length is the largest straight line distance between two points in the outlet, and the outlet width is the largest straight line distance between two points along a line perpendicular to the outlet length in the outlet.

[0189] Example 8: The nozzle of any examples herein, particularly example 7, wherein the outlet length is longer than the outlet width.

[0190] Example 9: The nozzle of any examples herein, particularly example 8, wherein the outlet length is 5 centimeters and the outlet width is 1 to 2 millimeters.

[0191] Example 10: The nozzle of any examples herein, particularly example 9, wherein the outlet width is 2 millimeters.

[0192] Example 11 : The nozzle of any examples herein, particularly example 1, wherein theinlet and the outlet have a longitudinal distance, and the distance is 30 centimeters.

[0193] Example 12: The nozzle of any examples herein, particularly example 11, wherein the width of the outlet to the longitudinal distance possesses a ratio of at least 1 :5.

[0194] Example 13: The nozzle of any examples herein, particularly example 12, wherein the width of the outlet to the longitudinal distance possesses a ratio of 1 :6.

[0195] Example 14: The nozzle of any examples herein, particularly example 1, wherein the internal width of the longitudinal space between the inlet and outlet is equal to or less than the width of the outlet.

[0196] Example 15: The nozzle of any examples herein, particularly example 1, wherein the inlet, the outlet, the distance between the inlet and the outlet, and a gas density are collectively configured to form the substantially flat-top or ramped profile.

[0197] Example 16: The nozzle of any examples herein, particularly example 15, wherein the density profile is substantially flat-topped or ramped for a distance of at least 2 centimeters.

[0198] Example 17: The nozzle of any examples herein, particularly example 1, wherein the gas is helium.

[0199] Example 18: The nozzle of any examples herein, particularly example 1, wherein the gas has a pressure of 100 kilopascals.

[0200] Example 19: The nozzle of any examples herein, particularly example 1, wherein the gas density is at most 1 x 1018atoms / cm3.

[0201] Example 20: The nozzle of any examples herein, particularly examples 1-19, further comprising a wire coupled to the outlet.

[0202] Example 21 : The nozzle of any examples herein, particularly example 20, wherein the wire diameter is 200 pm.

[0203] Example 22: An asymmetric nozzle for a laser wakefield electron accelerator, the asymmetric nozzle comprising: an inlet defining an inlet profile; a throat extending from the inlet; an outlet spaced apart from and in fluid communication with the inlet, the outlet defining an outlet plane, an outlet profile in the outlet plane and corresponding to the inlet profile, an outlet length, and an outlet width that is less than the outlet length; and a chamber fluidly coupling the throat and the outlet and defining a chamber height.

[0204] Example 23 : An asymmetric nozzle for a laser wakefield electron accelerator, the asymmetric nozzle comprising: an inlet defining an inlet profile; a throat extending from the inlet; an outlet spaced apart from and in fluid communication with the inlet, the outlet defining an outlet profile and corresponding to the inlet profile; and a chamber fluidly coupling the throat and the outlet, wherein the inlet is configured to receive a gas at a pressure, and the outlet isconfigured to release the gas with a gas density profile, and wherein the density profile comprises a substantially flat-topped or ramped profile.

[0205] Example 24: The asymmetric nozzle of any examples herein, particularly examples 22- 23, wherein the inlet is configured to receive a gas at a pressure, and the outlet is configured to release the gas with a gas density profile, such that the asymmetric nozzle provides a path for gas flow from the inlet to the outlet, wherein the gas density profile has a longitudinal profile along the outlet length and a transverse profile along the outlet width, and wherein: the longitudinal profile is controlled by selecting the chamber height, the outlet length, or both, the transverse profile is controlled by the presence or absence of a wire coupled to the outlet, and, when the wire is present, the transverse profile is further controlled by a dimension of the wire along the direction of the outlet width; and the gas density profile is further controlled by the pressure of the gas at the inlet.

[0206] Example 25: The asymmetric nozzle of any examples herein, particularly example 24, wherein the longitudinal profile is flat-topped or density tapered.

[0207] Example 26: The asymmetric nozzle of any examples herein, particularly example 24 or example 25, wherein the transverse profile is parabolic.

[0208] Example 27: The asymmetric nozzle of any examples herein, particularly examples 23-26, wherein the gas density profile is a substantially flat-topped or ramped profile.

[0209] Example 28: The asymmetric nozzle of any examples herein, particularly examples 23-27, wherein the gas density profile is substantially flat-topped or ramped for a distance of at least 2 centimeters.

[0210] Example 29: The asymmetric nozzle of any examples herein, particularly examples 23- 28 wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile.

[0211] Example 30: The asymmetric nozzle of any examples herein, particularly examples 23-29, wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile to be substantially flat-topped or ramped.

[0212] Example 31 : The asymmetric nozzle of any examples herein, particularly examples 24-30, wherein the wire is present and the dimension of the wire along the direction of the outlet width is from 10 to 1000 micrometers.

[0213] Example 32: The asymmetric nozzle of any examples herein, particularly examples 24-31, wherein the wire is present and the dimension of the wire along the direction of the outlet width is 200 micrometers.

[0214]

[0213] Example 33: The asymmetric nozzle of any examples herein, particularly examples 23- 32, wherein the gas has a pressure at the inlet of from 0.1 to 1000 kilopascals, such as from 10 to 1000 kilopascals.

[0215] Example 34: The asymmetric nozzle of any examples herein, particularly examples 23-33, wherein the gas has a pressure at the inlet of 100 kilopascals.

[0216] Example 35: The asymmetric nozzle of any examples herein, particularly examples 23-34, wherein the gas has a density of from 1 x 1012to 1x1022atoms / cm3.

[0217] Example 36: The asymmetric nozzle of any examples herein, particularly examples 23-35, wherein the gas has a density of less than 1 x 1018atoms / cm3.

[0218] Example 37: The asymmetric nozzle of any examples herein, particularly examples 23-36, wherein the gas has a density of 1 x 1018atoms / cm3or more.

[0219] Example 38: The asymmetric nozzle of any examples herein, particularly examples 23-37, wherein the gas has a density of 1 x io18atoms / cm3.

[0220] Example 39: The asymmetric nozzle of any examples herein, particularly examples 23-38, wherein the outlet length is longer than the outlet width.

[0221] Example 40: The asymmetric nozzle of any examples herein, particularly examples 22-39, wherein the inlet profile and the outlet profile comprise geometrically similar cross-sectional shapes.

[0222] Example 41 : The asymmetric nozzle of any examples herein, particularly examples 22-40, wherein the inlet profile and outlet profile comprise shapes which are obtained from one another by uniformly scaling.

[0223] Example 42: The asymmetric nozzle of any examples herein, particularly examples 22-41, wherein the inlet profile and outlet profile comprise a geometric center, wherein the geometric center of the inlet profile is translated relative to the geometric center of the outlet profile along an axis perpendicular to an axis of propagation of the gas.

[0224] Example 43 : The asymmetric nozzle of any examples herein, particularly examples 22-42, wherein an area defined by the inlet profile is smaller than an area defined by the outlet profile.

[0225] Example 44: The asymmetric nozzle of any examples herein, particularly examples 22-43, wherein the inlet profile is rectangular and the outlet profile is rectangular.

[0226] Example 45: The asymmetric nozzle of any examples herein, particularly examples 22-44, wherein the outlet length is the largest straight line distance between two points in the outlet plane, and the outlet width is the largest straight line distance between two points along a line perpendicular to the outlet length in the outlet plane.

[0227] Example 46: The asymmetric nozzle of any examples herein, particularly examples 22-45, wherein the outlet width is 50% or less of the outlet length, the outlet width is 40% or less of the outlet length, the outlet width is 30% or less of the outlet length, the outlet width is 20% or less of the outlet length, or the outlet width is 10% or less of the outlet length.

[0228] Example 47: The asymmetric nozzle of any examples herein, particularly examples 22-46, wherein the outlet width is from 0.1 to 5 millimeters (mm).

[0229] Example 48: The asymmetric nozzle of any examples herein, particularly examples 22-47, wherein the outlet width is from 1 to 3 mm, such as 2 mm.

[0230] Example 49: The asymmetric nozzle of any examples herein, particularly examples 22- 47, wherein the outlet width is from 0.1 to 1 mm.

[0231] Example 50: The asymmetric nozzle of any examples herein, particularly examples 22-49, wherein the outlet length is from 1 millimeter (mm) to 500 centimeters (cm), such as from 1 millimeter to 10 centimeters.

[0232] Example 51 : The asymmetric nozzle of any examples herein, particularly examples 22-50, wherein the outlet length is from 1 centimeter to 10 centimeters, such as 5 centimeters.

[0233] Example 52: The asymmetric nozzle of any examples herein, particularly examples 22-51, wherein the outlet length is from 1 millimeter (mm) to 1 centimeter (cm).

[0234] Example 53: The asymmetric nozzle of any examples herein, particularly examples 22-52, wherein the outlet length is 5 centimeters and the outlet width is 2 millimeters.

[0235] Example 54: The asymmetric nozzle of any examples herein, particularly examples 22-53, wherein the chamber defines a longitudinal axis, and wherein the inlet profile and the outlet profile are defined perpendicular to the longitudinal axis.

[0236] Example 55: The asymmetric nozzle of any examples herein, particularly examples 22-54, wherein the chamber defines a linearly expanding volume.

[0237] Example 56: The asymmetric nozzle of any examples herein, particularly examples 22-55, wherein the chamber defines a longitudinal axis centered in the inlet, and the chamber defines an expanding volume that expands in a single direction perpendicular to the longitudinal axis between the throat and the outlet.

[0238] Example 57: The asymmetric nozzle of any examples herein, particularly examples 22-56, wherein the chamber includes a first wall coplanar with the throat and a second wall arranged obliquely to the throat.

[0239] Example 58: The asymmetric nozzle of any examples herein, particularly examples 22-57, wherein the chamber height is from 1 millimeter (mm) to 100 centimeters (cm), such as from 20 centimeters to 40 centimeters.

[0240] Example 59: The asymmetric nozzle of any examples herein, particularly examples 22-58, wherein the chamber height is 30 centimeters (cm).

[0241] Example 60: The asymmetric nozzle of any examples herein, particularly examples 22-59, wherein the asymmetric nozzle defines a volume of from 0.05 cm3to 500,00 cm3.

[0242] Example 61 : The asymmetric nozzle of any examples herein, particularly examples 22-60, further comprising a wire coupled to the outlet.

[0243] Example 62: The asymmetric nozzle of any examples herein, particularly example 61, wherein the wire bisects the outlet.

[0244] Example 63: The asymmetric nozzle of any examples herein, particularly example 61 or example 62, wherein the wire extends parallel to the outlet length.

[0245] Example 64: A method of use of the asymmetric nozzle of any examples herein, particularly examples 22-63, wherein the method comprises using the asymmetric nozzle in a laser wakefield electron accelerator.

[0246] Example 65: The method of any examples herein, particularly example 64, wherein the method comprises injecting a gas into the inlet at a pressure, flowing the gas through the asymmetric nozzle, such that the gas is released from the outlet with a gas density profile, wherein the gas density profile has a longitudinal profile along the outlet length and a transverse profile along the outlet width, and wherein: the longitudinal profile is controlled by selecting the chamber height, the outlet length, or both, the transverse profile is controlled by the presence or absence of the wire, and, when the wire is present, the transverse profile is further controlled by a dimension of the wire along the direction of the outlet width; and the gas density profile is further controlled by the pressure of the gas at the inlet.

[0247] Example 66: The method of any examples herein, particularly example 65, wherein the longitudinal profile is flat-topped or density tapered.

[0248] Example 67: The method of any examples herein, particularly example 65 or example 66, wherein the transverse profile is parabolic.

[0249] Example 68: The method of any examples herein, particularly examples 65-67, wherein the gas density profile is a substantially flat-topped or ramped profile.

[0250] Example 69: The method of any examples herein, particularly examples 65-68, wherein the gas density profile is substantially flat-topped or ramped for a distance of at least 2 centimeters.

[0251] Example 70: The method of any examples herein, particularly examples 65-69, wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile.

[0252] Example 71: The method of any examples herein, particularly examples 65-70, wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile to be substantially flat-topped or ramped.

[0253] Example 72: The method of any examples herein, particularly examples 65-71, wherein the gas has a pressure at the inlet of from 0.1 to 1000 kilopascals, such as from 10 to 1000 kilopascals.

[0254] Example 73: The method of any examples herein, particularly examples 65-72, wherein the gas has a pressure at the inlet of 100 kilopascals.

[0255] Example 74: The method of any examples herein, particularly examples 65-73, wherein the gas has a density of from 1 x io12to 1 x io22atoms / cm3.

[0256] Example 75: The method of any examples herein, particularly examples 65-74, wherein the gas has a density of less than 1 x 1018atoms / cm3.

[0257] Example 76: The method of any examples herein, particularly examples 65-75, wherein the gas has a density of 1 x io18atoms / cm3or more.

[0258] Example 77: The method of any examples herein, particularly examples 65-76, wherein the gas has a density of 1 x io18atoms / cm3.

[0259] Example 78: The method of any examples herein, particularly examples 64-77, wherein the laser wakefield accelerator comprises a particle-assisted laser wakefield electron accelerator.

[0260] Example 79: A laser wakefield electron accelerator comprising the asymmetric nozzle of any examples herein, particularly examples 22-63.

[0261] Example 80: The laser wakefield electron accelerator of any examples herein, particularly example 79, wherein the laser wakefield electron acceleration device comprises: an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle; wherein the accelerator chamber is configured to receive a pulse, the pulse being configured to: ionize at least a portion of the gas, thereby generating a plasma wave comprising electrons in the accelerator chamber; and wherein at least a portion of the electrons from the plasma are injected into the wakefield, the portion of the electrons from the plasma being the injected electrons; and wherein the injected electrons are accelerated by the wakefield.

[0262] Example 81 : The laser wakefield electron accelerator of any examples herein, particularly example 79 or example 80, wherein the laser wakefield electron accelerator comprises a particle-assisted laser wakefield electron accelerator.

[0263] Example 82: The laser wakefield electron accelerator of any examples herein, particularly example 81, wherein the particle-assisted laser wakefield electron accelerator furthercomprises a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber, such that the accelerator chamber includes the gas and the particle therein, and wherein the pulse is further configured to: ionize at least a portion of the particle, thereby generating free electrons; wherein at least a portion of the electrons from the plasma and at least a portion of the free electrons are injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons.

[0264] Example 83 : The laser wakefield electron accelerator of any examples herein, particularly example 82, wherein the injected electrons are accelerated to an energy that is greater than the energy generated in the absence of the particle.

[0265] Example 84: A particle-assisted laser wakefield electron accelerator comprising the asymmetric nozzle of any examples herein, particularly examples 22-63.

[0266] Example 85: The particle-assisted laser wakefield electron accelerator of any examples herein, particularly example 84, wherein the particle-assisted wakefield electron acceleration device comprises: an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle; a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber; such that the accelerator chamber includes the gas and the particle therein, wherein the accelerator chamber is configured to receive a pulse, the pulse being configured to: ionize at least a portion of the gas, thereby generating a plasma wave comprising electrons in the accelerator chamber; and ionize at least a portion of the particle, thereby generating free electrons; wherein at least a portion of the electrons from the plasma and at least a portion of the free electrons are injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons; and wherein the injected electrons are accelerated by the wakefield.

[0267] Example 86: The particle-assisted laser wakefield electron accelerator of any examples herein, particularly examples 81-85, wherein the injected electrons are accelerated to an energy that is greater than the energy generated in the absence of the particle.

[0268] Example 87: The particle-assisted laser wakefield electron accelerator of any examples herein, particularly examples 81-86, wherein the particle comprises a metallic particle.

[0269] Example 88: The particle-assisted laser wakefield electron accelerator of any examples herein, particularly example 87, wherein the metallic particle comprises a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

[0270] Example 89: The particle-assisted laser wakefield electron accelerator of any examplesherein, particularly examples 81-88, wherein the particle has an average particle size of from 1 nanometer (nm) to 100 micrometers (pm), from 1 nm to 1000 nm, or from 10 nm to 100 nm.

[0271] Example 90: The particle-assisted laser wakefi eld electron accelerator of any examples herein, particularly examples 81-89, wherein the particle has a substantially spherical shape.

[0272] Example 91 : The particle-assisted laser wakefi eld electron accelerator of any examples herein, particularly examples 81-90, wherein the particle is a single particle.

[0273] Example 92: The particle-assisted laser wakefield electron accelerator of any examples herein, particularly examples 81-90, wherein the particle is a plurality of particles.

[0274] Example 93: The laser wakefield electron accelerator of any examples herein, particularly examples 79-92, wherein the gas comprises helium.

[0275] Example 94: The laser wakefield electron accelerator of any examples herein, particularly examples 79-93, wherein the pulse comprises a laser pulse.

[0276] Example 95: The laser wakefield electron accelerator of any examples herein, particularly example 94, further comprising a laser source configured to generate the laser pulse.

[0277] Example 96: The laser wakefield electron accelerator of any examples herein, particularly example 95, wherein the laser source comprises a Petawatt laser source.

[0278] Example 97: A method of generating an electron beam using the laser wakefield electron accelerator of any examples herein, particularly examples 79-96.

[0279] Example 98: A method of using the electron beam generated by the method of any examples herein, particularly example 97.

[0280] Example 99: A method of accelerating an electron using the laser wakefield electron accelerator of any examples herein, particularly examples 79-96.

[0281] Example 100: A method of using the accelerated electron generated by the method of any examples herein, particularly example 98.

[0282] While preferred embodiments of the present disclosure have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will now occur to those skilled in the art without departing from the disclosure. It should be understood that various alternatives to the embodiments of the present disclosure may be employed in practicing the present disclosure. It is intended that the following claims define the scope of the present disclosure and that methods and structures within the scope of these claims and their equivalents be covered thereby.

Claims

CLAIMSWhat is claimed is:

1. A nozzle for a laser wakefield electron accelerator, the nozzle comprising: an inlet; an outlet spaced apart from and in fluid communication with the inlet; and a chamber fluidly coupling the inlet to the outlet, wherein the inlet is configured to receive a gas at a pressure, and the outlet is configured to release the gas with a gas density profile, and wherein the density profile comprises a substantially flat-topped or ramped profile for a distance of at least 5 millimeters.

2. The nozzle of claim 1, wherein the inlet and outlet comprise geometrically similar cross- sectional shapes.

3. The nozzle of claim 2, wherein the geometrically similar cross-sectional shapes comprise shapes which are obtained from one another by uniformly scaling.

4. The nozzle of claim 3, wherein the inlet and the outlet comprise a geometric center and area, wherein the geometric center of the inlet is translated relative to a geometric center of the outlet along an axis perpendicular to an axis of propagation of the gas.

5. The nozzle of claim 4, wherein the area defined by the inlet is smaller than the area defined the outlet.

6. The nozzle of claim 5, wherein the corresponding inlet is rectangular and outlet is rectangular.

7. The nozzle of claim 1, wherein the outlet has a length and width, and that length is the largest straight line distance between two points in the outlet, and the outlet width is the largest straight line distance between two points along a line perpendicular to the outlet length in the outlet.

8. The nozzle of claim 7, wherein the outlet length is longer than the outlet width.

9. The nozzle of claim 8, wherein the outlet length is 5 centimeters and the outlet width is 1 to 2 millimeters.

10. The nozzle of claim 9, wherein the outlet width is 2 millimeters.

11. The nozzle of claim 1, wherein the inlet and the outlet have a longitudinal distance, and the distance is 30 centimeters.

12. The nozzle of claim 11, wherein the width of the outlet to the longitudinal distance possesses a ratio of at least 1 :5.

13. The nozzle of claim 12, wherein the width of the outlet to the longitudinal distance possesses a ratio of 1 :6.

14. The nozzle of claim 1, wherein the internal width of the longitudinal space between the inlet and outlet is equal to or less than the width of the outlet.

15. The nozzle of claim 1, wherein the inlet, the outlet, the distance between the inlet and the outlet, and a gas density are collectively configured to form the substantially flat-top or ramped profile.

16. The nozzle of claim 15, wherein the density profile is substantially flat-topped or ramped for a distance of at least 2 centimeters.

17. The nozzle of claim 1, wherein the gas is helium.

18. The nozzle of claim 1, wherein the gas has a pressure of 100 kilopascals.

19. The nozzle of claim 1, wherein the gas density is at most 1 x 1018atoms / cm3.

20. The nozzle of any one of claims 1-19, further comprising a wire coupled to the outlet.

21. The nozzle of claim 20, wherein the wire diameter is 200 pm.

22. An asymmetric nozzle for a laser wakefield electron accelerator, the asymmetric nozzle comprising: an inlet defining an inlet profile; a throat extending from the inlet; an outlet spaced apart from and in fluid communication with the inlet, the outlet defining an outlet plane, an outlet profile in the outlet plane and corresponding to the inlet profile, an outlet length, and an outlet width that is less than the outlet length; and a chamber fluidly coupling the throat and the outlet and defining a chamber height.

23. An asymmetric nozzle for a laser wakefield electron accelerator, the asymmetric nozzle comprising: an inlet defining an inlet profile; a throat extending from the inlet; an outlet spaced apart from and in fluid communication with the inlet, the outlet defining an outlet profile and corresponding to the inlet profile; and a chamber fluidly coupling the throat and the outlet, wherein the inlet is configured to receive a gas at a pressure, and the outlet is configured to release the gas with a gas density profile, and wherein the density profile comprises a substantially flat-topped or ramped profile.

24. The asymmetric nozzle of any one of claims 22-23, wherein the inlet is configured to receive a gas at a pressure, and the outlet is configured to release the gas with a gas density profile, such that the asymmetric nozzle provides a path for gas flow from the inlet to the outlet,wherein the gas density profile has a longitudinal profile along the outlet length and a transverse profile along the outlet width, and wherein: the longitudinal profile is controlled by selecting the chamber height, the outlet length, or both, the transverse profile is controlled by the presence or absence of a wire coupled to the outlet, and, when the wire is present, the transverse profile is further controlled by a dimension of the wire along the direction of the outlet width; and the gas density profile is further controlled by the pressure of the gas at the inlet.

25. The asymmetric nozzle of claim 24, wherein the longitudinal profile is flat-topped or density tapered.

26. The asymmetric nozzle of claim 24 or claim 25, wherein the transverse profile is parabolic.

27. The asymmetric nozzle of any one of claims 23-26, wherein the gas density profile is a substantially flat-topped or ramped profile.

28. The asymmetric nozzle of any one of claims 23-27, wherein the gas density profile is substantially flat-topped or ramped for a distance of at least 2 centimeters.

29. The asymmetric nozzle of any one of claims 23-28, wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile.

30. The asymmetric nozzle of any one of claims 23-29, wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile to be substantially flat-topped or ramped.

31. The asymmetric nozzle of any one of claims 24-30, wherein the wire is present and the dimension of the wire along the direction of the outlet width is from 10 to 1000 micrometers.

32. The asymmetric nozzle of any one of claims 24-31, wherein the wire is present and the dimension of the wire along the direction of the outlet width is 200 micrometers.

33. The asymmetric nozzle of any one of claims 23-32, wherein the gas has a pressure at the inlet of from 0.1 to 1000 kilopascals, such as from 10 to 1000 kilopascals.

34. The asymmetric nozzle of any one of claims 23-33, wherein the gas has a pressure at the inlet of 100 kilopascals.

35. The asymmetric nozzle of any one of claims 23-34, wherein the gas has a density of from 1 x 1012to 1x1022atoms / cm3.

36. The asymmetric nozzle of any one of claims 23-35, wherein the gas has a density of less than 1 x 1018atoms / cm3.

37. The asymmetric nozzle of any one of claims 23-36, wherein the gas has a density of 1 x1018atoms / cm3or more.

38. The asymmetric nozzle of any one of claims 23-37, wherein the gas has a density of 1 x 1018atoms / cm3.

39. The asymmetric nozzle of any one of claims 23-38, wherein the outlet length is longer than the outlet width.

40. The asymmetric nozzle of any one of claims 22-39, wherein the inlet profile and the outlet profile comprise geometrically similar cross-sectional shapes.

41. The asymmetric nozzle of any one of claims 22-40, wherein the inlet profile and outlet profile comprise shapes which are obtained from one another by uniformly scaling.

42. The asymmetric nozzle of any one of claims 22-41, wherein the inlet profile and outlet profile comprise a geometric center, wherein the geometric center of the inlet profile is translated relative to the geometric center of the outlet profile along an axis perpendicular to an axis of propagation of the gas.

43. The asymmetric nozzle of any one of claims 22-42, wherein an area defined by the inlet profile is smaller than an area defined by the outlet profile.

44. The asymmetric nozzle of any one of claims 22-43, wherein the inlet profile is rectangular and the outlet profile is rectangular.

45. The asymmetric nozzle of any one of claims 22-44, wherein the outlet length is the largest straight line distance between two points in the outlet plane, and the outlet width is the largest straight line distance between two points along a line perpendicular to the outlet length in the outlet plane.

46. The asymmetric nozzle of any one of claims 22-45, wherein the outlet width is 50% or less of the outlet length, the outlet width is 40% or less of the outlet length, the outlet width is 30% or less of the outlet length, the outlet width is 20% or less of the outlet length, or the outlet width is 10% or less of the outlet length.

47. The asymmetric nozzle of any one of claims 22-46, wherein the outlet width is from 0.1 to 5 millimeters (mm).

48. The asymmetric nozzle of any one of claims 22-47, wherein the outlet width is from 1 to 3 mm, such as 2 mm.

49. The asymmetric nozzle of any one of claims 22-47, wherein the outlet width is from 0.1 to 1 mm.

50. The asymmetric nozzle of any one of claims 22-49, wherein the outlet length is from 1 millimeter (mm) to 500 centimeters (cm), such as from 1 millimeter to 10 centimeters.

51. The asymmetric nozzle of any one of claims 22-50, wherein the outlet length is from 1 centimeter to 10 centimeters, such as 5 centimeters.

52. The asymmetric nozzle of any one of claims 22-51, wherein the outlet length is from 1 millimeter (mm) to 1 centimeter (cm).

53. The asymmetric nozzle of any one of claims 22-52, wherein the outlet length is 5 centimeters and the outlet width is 2 millimeters.

54. The asymmetric nozzle of any one of claims 22-53, wherein the chamber defines a longitudinal axis, and wherein the inlet profile and the outlet profile are defined perpendicular to the longitudinal axis.

55. The asymmetric nozzle of any one of claims 22-54, wherein the chamber defines a linearly expanding volume.

56. The asymmetric nozzle of any one of claims 22-55, wherein the chamber defines a longitudinal axis centered in the inlet, and the chamber defines an expanding volume that expands in a single direction perpendicular to the longitudinal axis between the throat and the outlet.

57. The asymmetric nozzle of any one of claims 22-56, wherein the chamber includes a first wall coplanar with the throat and a second wall arranged obliquely to the throat.

58. The asymmetric nozzle of any one of claims 22-57, wherein the chamber height is from 1 millimeter (mm) to 100 centimeters (cm), such as from 20 centimeters to 40 centimeters.

59. The asymmetric nozzle of any one of claims 22-58, wherein the chamber height is 30 centimeters (cm).

60. The asymmetric nozzle of any one of claims 22-59, wherein the asymmetric nozzle defines a volume of from 0.05 cm3to 500,00 cm3.

61. The asymmetric nozzle of any one of claims 22-60, further comprising a wire coupled to the outlet.

62. The asymmetric nozzle of claim 61, wherein the wire bisects the outlet.

63. The asymmetric nozzle of claim 61 or claim 62, wherein the wire extends parallel to the outlet length.

64. A method of use of the asymmetric nozzle of any one of claims 22-63, wherein the method comprises using the asymmetric nozzle in a laser wakefield electron accelerator.

65. The method of claim 64, wherein the method comprises injecting a gas into the inlet at a pressure, flowing the gas through the asymmetric nozzle, such that the gas is released from the outlet with a gas density profile, wherein the gas density profile has a longitudinal profile along the outlet length and a transverse profile along the outlet width, and wherein:the longitudinal profile is controlled by selecting the chamber height, the outlet length, or both, the transverse profile is controlled by the presence or absence of the wire, and, when the wire is present, the transverse profile is further controlled by a dimension of the wire along the direction of the outlet width; and the gas density profile is further controlled by the pressure of the gas at the inlet.

66. The method of claim 65, wherein the longitudinal profile is flat-topped or density tapered.

67. The method of claim 65 or claim 66, wherein the transverse profile is parabolic.

68. The method of any one of claims 65-67, wherein the gas density profile is a substantially flat-topped or ramped profile.

69. The method of any one of claims 65-68, wherein the gas density profile is substantially flat-topped or ramped for a distance of at least 2 centimeters.

70. The method of any one of claims 65-69, wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile.

71. The method of any one of claims 65-70, wherein the inlet profile, the outlet profile, the chamber height, and the gas density are collectively configured to control the gas density profile to be substantially flat-topped or ramped.

72. The method of any one of claims 65-71, wherein the gas has a pressure at the inlet of from 0.1 to 1000 kilopascals, such as from 10 to 1000 kilopascals.

73. The method of any one of claims 65-72, wherein the gas has a pressure at the inlet of 100 kilopascals.

74. The method of any one of claims 65-73, wherein the gas has a density of from 1 x 1012to 1 x io22atoms / cm3.

75. The method of any one of claims 65-74, wherein the gas has a density of less than 1 x 1018atoms / cm3.

76. The method of any one of claims 65-75, wherein the gas has a density of 1 x 1018atoms / cm3or more.

77. The method of any one of claims 65-76, wherein the gas has a density of 1 x 1018atoms / cm3.

78. The method of any one of claims 64-77, wherein the laser wakefield accelerator comprises a particle-assisted laser wakefield electron accelerator.

79. A laser wakefield electron accelerator comprising the asymmetric nozzle of any one of claims 22-63.

80. The laser wakefield electron accelerator of claim 79, wherein the laser wakefield electron acceleration device comprises: an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle; wherein the accelerator chamber is configured to receive a pulse, the pulse being configured to: ionize at least a portion of the gas, thereby generating a plasma wave comprising electrons in the accelerator chamber; and wherein at least a portion of the electrons from the plasma are injected into the wakefield, the portion of the electrons from the plasma being the injected electrons; and wherein the injected electrons are accelerated by the wakefield.

81. The laser wakefield electron accelerator of claim 79 or claim 80, wherein the laser wakefield electron accelerator comprises a particle-assisted laser wakefield electron accelerator.

82. The laser wakefield electron accelerator of claim 81, wherein the particle-assisted laser wakefield electron accelerator further comprises a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber, such that the accelerator chamber includes the gas and the particle therein, and wherein the pulse is further configured to: ionize at least a portion of the particle, thereby generating free electrons; wherein at least a portion of the electrons from the plasma and at least a portion of the free electrons are injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons.

83. The laser wakefield electron accelerator of claim 82, wherein the injected electrons are accelerated to an energy that is greater than the energy generated in the absence of the particle.

84. A particle-assisted laser wakefield electron accelerator comprising the asymmetric nozzle of any one of claims 22-63.

85. The particle-assisted laser wakefield electron accelerator of claim 84, wherein the particle-assisted wakefield electron acceleration device comprises: an accelerator chamber upstream from the asymmetric nozzle and configured to receive a gas having a gas density profile from the outlet of the asymmetric nozzle; a particle injector downstream from the accelerator chamber and configured to inject a particle into the accelerator chamber; such that the accelerator chamber includes the gas and the particle therein,wherein the accelerator chamber is configured to receive a pulse, the pulse being configured to: ionize at least a portion of the gas, thereby generating a plasma wave comprising electrons in the accelerator chamber; and ionize at least a portion of the particle, thereby generating free electrons; wherein at least a portion of the electrons from the plasma and at least a portion of the free electrons are injected into the wakefield, the portion of the electrons from the plasma and the portion of the free electrons being the injected electrons; and wherein the injected electrons are accelerated by the wakefield.

86. The particle-assisted laser wakefield electron accelerator of any one of claims 81-85, wherein the injected electrons are accelerated to an energy that is greater than the energy generated in the absence of the particle.

87. The particle-assisted laser wakefield electron accelerator of any one of claims 81-86, wherein the particle comprises a metallic particle.

88. The particle-assisted laser wakefield electron accelerator of claim 87, wherein the metallic particle comprises a metal selected from the group consisting of Al, Cr, Mn, Fe, Co, Ni, Cu, Mo, Pd, Ag, Pt, Au, and combinations thereof.

89. The particle-assisted laser wakefield electron accelerator of any one of claims 81-88, wherein the particle has an average particle size of from 1 nanometer (nm) to 100 micrometers (pm), from 1 nm to 1000 nm, or from 10 nm to 100 nm.

90. The particle-assisted laser wakefield electron accelerator of any one of claims 81-89, wherein the particle has a substantially spherical shape.

91. The particle-assisted laser wakefield electron accelerator of any one of claims 81-90, wherein the particle is a single particle.

92. The particle-assisted laser wakefield electron accelerator of any one of claims 81-90, wherein the particle is a plurality of particles.

93. The laser wakefield electron accelerator of any one of claims 79-92, wherein the gas comprises helium.

94. The laser wakefield electron accelerator of any one of claims 79-93, wherein the pulse comprises a laser pulse.

95. The laser wakefield electron accelerator of claim 94, further comprising a laser source configured to generate the laser pulse.

96. The laser wakefield electron accelerator of claim 95, wherein the laser source comprises a Petawatt laser source.

97. A method of generating an electron beam using the laser wakefield electron accelerator of any one of claims 79-96.

98. A method of using the electron beam generated by the method of claim 97.

99. A method of accelerating an electron using the laser wakefield electron accelerator of any one of claims 79-96.

100. A method of using the accelerated electron generated by the method of claim 98.

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