Optical design for a laboratory-scale compact free electron laser based on inverse compton scattering

Abstract

A light source includes a linear accelerator for accelerating an electron bunch to a relativistic energy. The light source further includes a first grating, downstream of the linear accelerator and arranged such that the electron bunch is transmitted through the grating to produce a diffraction pattern. The light source further includes an emittance exchange device, downstream of the first grating, that rotates the diffraction pattern to a direction substantially parallel to a direction of propagation of the electron bunch. The light source further includes a laser that produces a pulse of light. The light source is configured such that the pulse of light from the laser interacts with the electron bunch in an overtaking geometry at an interaction point, downstream of the emittance exchange device, while the diffraction pattern is substantially parallel to the direction of propagation of the electron bunch to produce light via inverse Compton scattering.

Description

OPTICAL DESIGN FOR A LABORATORY-SCALE COMPACT FREE ELECTRON LASER BASED ON INVERSE COMPTON SCATTERINGGOVERNMENT SUPPORT

[0001] This invention was made with government support under 1935994 awarded by the National Science Foundation. The government has certain rights in the invention.TECHNICAL FIELD

[0002] The present invention relates to free-electron lasers (FELs), and in particular to X-ray free-electron lasers (XFELs).BACKGROUND

[0003] An x-ray free-electron laser (XFEL) produces x-ray pulses with durations shorter than 100 femtoseconds (fs) each containing enough photons to produce a diffraction pattern from a nanocrystal in a single shot, while outrunning most effects of radiation damage. XFELs are proving to be powerful tools across a range of applications including crystal structure and dynamics of biological molecules in their native environment, fundamental charge and energy dynamics in molecules, emergent phenomena in correlated electron systems, single-particle structures and dynamics, and matter in extreme environments. The shortest XFEL pulses approach 1 fs corresponding to a natural time scale of the fastest electronic excitations and are opening a new era in exploration of dynamics at an atomic scale.SUMMARY

[0004] Here, we disclose the design of an optical undulator and its impact on the design of a compact x-ray free electron laser (CXFEL). X-ray Free Electron Lasers (XFELs) are light sources characterized by high brightness, full spatial coherence, and short pulse durations, which enable experiments that probe materials at the time and length scales of electronic and structural motion. In some embodiments, a CXFEL employs emittance exchange of a diffracted electron beam to seed an Inverse Compton Scattering (ICS)-based XFEL, which generates fully coherent radiation with a relatively short accelerator length (e.g., 10 meters). By using an optical undulator (e.g., ICS), the electron beam energy requirements are lowered, and the necessary facility size is greatly reduced along with its cost. Tuning the crossing angle between the electron beam and ICS laser enables a higher electron beam energy, while lasing in the soft x-ray regime, which is necessary for minimizing the space-charge effects present in low-energy accelerators. As an example, we present an optical design optimized for generating 1 nm (1.2 keV) radiation with a 30 MeV electron beam at a 30 degree crossing angle using a 10 TW peak power drive laser, which is within reach of high repetition rate commercial laser sources.

[0005] To that end, in some embodiments, a light source is provided. The light sources includes a linear accelerator for accelerating an electron bunch to a relativistic energy. The light source further includes a first grating, downstream of the linear accelerator and arranged such that the electron bunch is transmitted through the grating to produce a diffraction pattern. The light source further includes an emittance exchange device (e.g., an electron optic), downstream of the grating, that rotates the diffraction pattern to a direction substantially parallel to a direction of propagation of the electron bunch. The light source further includes a laser that produces a pulse of light. The light source is configured such that the pulse of light from the laser interacts with the electron bunch in an overtaking geometry at an interaction point, downstream of the emittance exchange device, while the diffraction pattern is substantially parallel to the direction of propagation of the electron bunch to produce light via inverse Compton scattering.

[0006] In some embodiments, a method is provided. The method includes accelerating an electron bunch to a relativistic energy. The method further includes producing produce a diffraction pattern in the electron bunch. The method further includes rotating the diffraction pattern to a direction substantially parallel to a direction of propagation of the electron bunch. The method further includes producing light via inverse Compton scattering by interacting the electron bunch, having the rotated diffraction pattern, with a pulse of light from a laser that produces. The pulse of light from the laser interacts with the electron bunch in an overtaking geometry at an interaction point.BRIEF DESCRIPTION OF THE DRAWINGS

[0007] The invention will be more fully understood by referring to the following Detailed Description of Specific Embodiments in conjunction with the not-to scale Drawings, of which:

[0008] FIGS. 1A-1C are schematic diagrams illustrating a light source (e.g., a free- electron laser) in accordance with some embodiments.

[0009] FIGS. 2A-2B are schematic illustrations of partitioning an electron bunch by electron diffraction in accordance with some embodiments.

[0010] FIG. 3 illustrates various aspects of an optical (e.g., laser) system (e.g., an optical undulator) for producing light via inverse Compton scattering, in accordance with some embodiments.

[0011] FIG. 4 illustrates a micro -bunching scheme for free-electron laser (FEL) seeding, along with exemplary parameters, in accordance with some embodiments.

[0012] FIG. 5 illustrates various aspects of an optical (e.g., laser) system (e.g., an optical undulator) for producing light via inverse Compton scattering, in accordance with some embodiments.

[0013] FIGS. 6A-6B illustrates various simulation results, in accordance with some embodiments.

[0014] FIG. 7 is a flow chart of a method for generating light via inverse Compton scattering, in accordance with some embodiments.

[0015] Generally, the sizes and relative scales of elements in Drawings may be set to be different from actual ones to appropriately facilitate simplicity, clarity, and understanding of the Drawings. For the same reason, not all elements present in one Drawing may necessarily be shown in another.DETAILED DESCRIPTION

[0016] Embodiments of the present disclosure provide methods and assemblies for generating temporally coherent x-ray pulses. First generation XFELs provide only partial temporal coherence. The lack of temporal coherence is due to both the random spacing of the bunched electrons in a S ASE process and to the lack of a coherent x-ray seed pulse for amplification. The resulting output radiation of first generation XFELs has the characteristics of shot noise, random phase jumps, and rapid fluctuations in intensity during the pulse, a wavelength spectrum filled with many distinct lines, and large fluctuations in the spectral characteristics and pulse energy from shot-to-shot.

[0017] Instead of seeding with coherent radiation, the methods and assemblies of the present disclosure arrange the electrons into discrete bunches (e.g., nano / micro-bunches) with periodicity equal to a desired x-ray wavelength (e.g., in the laboratory frame) so that theelectrons then emit coherently at that wavelength (e.g., when subjected to an undulator). Coherent spontaneous emission is then emitted by phased nanobunches amplified by the FEL process for relatively modest electron bunch parameters. Such FEL gain produces a single optical mode that dominates the output resulting in temporally coherent laser-like radiation. The present disclosure thereby overcomes the random electronic spacing inherent in the SASE process by patterning the electron bunch to create bunches with nanometer separation matching the desired x-ray wavelengths.

[0018] The electron bunching pattern is deterministically repeatable and may be controlled to produce a wide variety of phase relationships to achieve different experimental properties including a stable transform-limited (or nearly-transform limited) single spike spectrum, frequency chirped x-rays, multiple wavelengths with fixed phase relationships, and / or multiple ultrashort x-ray pulses with precise and tunable time delays ranging from attosecond to femtosecond level. In short, the present methods allow the time-structure for a fully coherent x- ray beam to be generated from a pattern written on a semiconductor wafer (e.g., a single crystal silicon membrane) by lithography.

[0019] For the purposes of this disclosure and the appended claims, the use of the terms "substantially", "approximately", "about" and similar terms in reference to a descriptor of a value, element, property or characteristic at hand is intended to emphasize that the value, element, property, or characteristic referred to, while not necessarily being exactly as stated, would nevertheless be considered, for practical purposes, as stated by a person of skill in the art. These terms, as applied to a specified characteristic or quality descriptor means "mostly", "mainly", "considerably", "by and large", "essentially", "to great or significant extent", "largely but not necessarily wholly the same" such as to reasonably denote language of approximation and describe the specified characteristic or descriptor so that its scope would be understood by a person of ordinary skill in the art. In one specific case, the terms "approximately", "substantially", and "about", when used in reference to a numerical value, represent a range of plus or minus 20% with respect to the specified value, more preferably plus or minus 10%, even more preferably plus or minus 5%, most preferably plus or minus 2% with respect to the specified value. As a non- limiting example, two values being "substantially equal" to one another implies that the difference between the two values may be within the range of + / - 20% of the value itself, preferably within the + / - 10% range of the value itself, more preferably within the range of + / - 5% of the value itself, and even more preferably within the range of + / - 2% or less of the value itself.

[0020] The use of these term in describing a chosen characteristic or concept neither implies nor provides any basis for indefmiteness and for adding a numerical limitation to the specified characteristic or descriptor. As understood by a skilled artisan, the practical deviation of the exact value or characteristic of such value, element, or property from that stated falls and may vary within a numerical range defined by an experimental measurement error that is typical when using a measurement method accepted in the art for such purposes.

[0021] For example, a reference to an identified direction or vector or line or plane being substantially parallel to a referenced line or plane is to be construed as such a direction or vector or line or plane that is the same as or very close to that of the referenced line or plane (with angular deviations from the referenced line or plane that are considered to be practically typical in related art, for example between zero and fifteen degrees, preferably between zero and ten degrees, more preferably between zero and 5 degrees, even more preferably between zero and 2 degrees, and most preferably between zero and 1 degree). For example, a reference to an identified direction or vector or line or plane being substantially perpendicular to a referenced line or plane is to be construed as such a direction or vector or line or plane the normal to the surface of which lies at or very close to the referenced line or plane (with angular deviations from the referenced line or plane that are considered to be practically typical in related art, for example between zero and fifteen degrees, preferably between zero and ten degrees, more preferably between zero and 5 degrees, even more preferably between zero and 2 degrees, and most preferably between zero and 1 degree).

[0022] Other specific examples of the meaning of the terms "substantially", "about", and / or "approximately" as applied to different practical situations may have been provided elsewhere in this disclosure.

[0023] An embodiment of a system generally may include electronic circuitry (for example, a computer processor) at least governing an operation of the embodiment and controlled by instructions stored in a memory, to perform specific data collection / processing and calculation steps as disclosed above. The memory may be random access memory (RAM), read-only memory (ROM), flash memory or any other memory, or combination thereof, suitable for storing control software or other instructions and data. Those skilled in the art should would readily appreciate that instructions or programs defining the operation of the present embodiment(s) may be delivered to a processor in many forms, including, but not limited to, information permanently stored on non-writable storage media (e.g. read-only memory deviceswithin a computer, such as ROM, or devices readable by a computer I / O attachment, such as CD-ROM or DVD disks), information alterably stored on writable storage media (e.g. floppy disks, removable flash memory and hard drives) or information conveyed to a computer through communication media, including wired or wireless computer networks. In addition, while the invention may be embodied in software, the functions necessary to implement a method of the invention may optionally or alternatively be embodied in part or in whole using firmware and / or hardware components, such as combinatorial logic, Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs) or other hardware or some combination of hardware, software and / or firmware components.

[0024] The invention as recited in claims appended to this disclosure is intended to be assessed in light of the disclosure as a whole. Various changes in the details, steps and components that have been described may be made by those skilled in the art within the principles and scope of the invention.

[0025] While the invention is described through the above-described exemplary embodiments, it will be understood by those of ordinary skill in the art that modifications to, and variations of, the illustrated embodiments may be made without departing from the inventive concepts disclosed herein. Accordingly, the invention should not be viewed as being limited to the disclosed embodiment(s).

[0026] FIGS. 1A-1C are schematic diagrams illustrating a light source 100 (e.g., a free- electron laser) in accordance with some embodiments. Note that, for brevity, only the most pertinent aspects of light source 100 are discussed in detail below.

[0027] In some embodiments, light source 100 produces x-rays. In some embodiments, light source 100 produces hard x-rays (e.g., x-rays having energies above 1 keV). In some embodiments, light source 100 produces soft x-rays or extreme ultraviolet light. In some embodiments, as described below, the light (e.g., x-rays) produced by light source 100 is fully spatially- and temporally-coherent (e.g. light source 100 produces light with coherence properties similar to those of conventional lasers used for generating light in optical, ultraviolet, infrared, and other wavelengths). In some embodiments, light source 100 generates light by interacting a relativistic electron beam with an electromagnetic field (e.g., either from a UV laser, in the case of inverse Compton scattering, as described below, or from an undulator). Note, however, that for embodiments in which an undulator is used, coherent light can be generated from light source 100 using a much shorter undulator than conventional FELs (e.g., 10meters as opposed to 100 meters). Thus, light source 100 is sometimes referred to as a compact x-ray free-electron laser (CXFEL).

[0028] Starting with FIG. 1C, an electron bunch is generated and initially accelerated using an electron photoinjector 102. For example, in some embodiments, a 4 MeV beam (e.g., electron bunch, note that the terms beam and bunch are used synonymously through the present disclosure) is generated by a 4.5 cell x-band pho to injector, which comprises a solenoid and an RF gun. The pho to injector is followed (e.g., downstream) by one or more linear accelerator (LINAC) sections (LINAC sections 104a- 104c, respectively), powered by one or more klystrons (klystrons 106a- 106b). For example, in some embodiments, three 35 cm long LINAC sections 104a- 106c accelerate the beam to 35 MeV.

[0029] Note that, as shown, RF power from a single klystron 106 may be applied to several different components (e.g., klystron 106b powers both LINAC section 104b and LINAC section 104c as well as RF deflector cavity and accelerator cavity 124, whereas klystron 106a powers both the initial acceleration of the electron bunch and LINAC 105c). Further, a phase shift may be applied by phase shifters 108 (e.g., phase shifters 108a-108d) to the power supplied by the various klystrons 106 to the various components. RF loads 128 (e.g., RF loads 128a- 128b) are included and positioned where necessary for load balancing and control.

[0030] In some embodiments, a diffraction grating 110 (e.g., diffraction crystal, such as the silicon gratings described below) is located between two of the LINAC sections (or, at least, after a first LINAC section). For example, in some embodiments, the diffraction grating 110 is located between LINAC section 104a and LINAC section 104b. The diffraction grating 110 is arranged in a transmission geometry with respect to the path of the electron bunch (e.g., the direction of propagation of the electron bunch). In some embodiments, the diffraction grating 110 diffracts the electron beam at a tunable energy with a maximum of 12 MeV.

[0031] Referring now to FIGS. 1A-1B, light source 100 includes a variety of electron optics for patterning and shaping the electron bunch downstream of the LINAC sections 104. The electron optics of light source 100 includes three main sections: a nano-pattern imaging section 112, an emittance exchange (EEX) section 114, and an inverse Compton scattering (ICS) interaction section 116. Note, however, that in some embodiments, the ICS interaction section 116 is replaced with an undulator (e.g., an undulator less than 20 m in length).

[0032] The nano-patterning imaging section 112 is downstream of LINAC section 104c and, in some embodiments, comprises two quadrupole triplets 118 (e.g., quadrupole triplet 118a and quadrupole triplet 118b) forming a telescope system.

[0033] In some embodiments, the diffraction grating 110 produces a diffraction pattern transverse to the direction of propagation of the electron bunch and the emittance exchange section 114 transforms (e.g., swaps) the diffraction pattern into a direction parallel to the direction of propagation of the electron bunch. To that end, the EEX section 114 comprises four bend magnets 120a-120d, an RF deflector cavity and accelerator cavity (collectively 124) that are independently phased and powered, along with sextupoles magnets 122a-122-c and octopole magnets 126 for aberration correction.

[0034] After EEX section 114, the ICS interaction section 116 starts with a focusing triplet 130 that reduces the beam size at the ICS interaction point 132 (e.g., to approximately a micron) before colliding the electron beam with ICS laser field from an inverse Compton scattering laser 138 (e.g., light from the inverse Compton scattering laser 138 is piped in and redirected to be nearly parallel with the electron beam at the ICS interaction point 132). The collision of the electron beam with the ICS laser field produces x-rays (or other light) 136. Downstream the ICS interaction point 132, two dipoles 134a-134b respectively bend the beam into a beam dump (e.g., by 30 degrees horizontally and 90 degrees, respectively, into a vertical beam dump). In some embodiments, the collision of the electron beam with the ICS laser field is within a magnet field of dipole magnet 134a. ICS interaction section 116 is an example of a light-generating apparatus. An undulator (not shown) is another example of a light-generating apparatus.

[0035] FIGS. 2A-2B are schematic illustrations of partitioning an electron bunch by electron diffraction in accordance with some embodiments. FIG. 2A illustrates a cross-sectional view of an assembly 200 including a grating 202 and a focusing magnet 206. Grating 202 is made of a single crystal silicon membrane (e.g., “UberFlat” silicon membrane provided by Norcada). For example, grating 202 is made of a silicon membrane having

[0100] crystal structure. As shown in the inset of FIG. 2A, grating 202 includes a nano-scaled pattern 204 that defines alternating longitudinal narrow and wide portions (e.g., alternating narrow portions 204- A and wide portions 204-B). In some embodiments, grating 202 has a thickness T defined between a surface of wide portion 204-B (e.g., surface 202-2) and an opposing surface 202-1 of grating 202. In some embodiments, thickness T is ranging from 50 nm to 1000 nm, from 50 nmto 500 nm, from 50 nm to 400 nm, from 50 nm to 300 nm, from 50 nm to 200 nm, or from 50 nm to 100 nm. In some embodiments, grating 202 has thickness T ranging from 100 nm to 300 nm. In some embodiments, thickness T is 200 nm. Grating 202 has an area defined by edges ranging from 50 micrometer to 500 micrometer (e.g., grating 202 has a rectangular or square shape). In some embodiments, grating 202 has an area corresponding to 50 micrometer x 50 micrometer, 100 micrometer x 100 micrometer, or 200 micrometer x 200 micrometer.

[0036] Nano-scaled patterning 204 is located at a center of silicon membrane of grating 202. Nano-scaled patterning 204 includes a plurality of longitudinal grooves or valleys cut (e.g., etched) through a portion of the silicon membrane of grating 202 defining alternating narrow portions 204-A and wide portions 204-B. Wide portions 204-B have thickness T, as described above, between surface 202-1 and surface 202-2. Thickness T is greater than a thickness of narrow portions 204-A between surface 202-1 and surface 202-3. In some embodiments, the grooves are aligned with an edge of silicon membrane forming grating 202 and thereby the grooves are aligned with a crystal plane of the silicon membrane. In some embodiments, nanoscale patterning 204 has an area defined by edges ranging from 20 micrometer to 100 micrometer. In some embodiments, nano-scaled patterning 204 covers an area on the silicon membrane corresponding to 20 micrometer x 20 micrometer, 50 micrometer x 50 micrometer, or 100 micrometer x 100 micrometer. Nanoscale patterning 204 has a pitch P corresponding to a sum of widths of wide portion 204-B and narrow portion 204-A, as shown in the inset of FIG. 2A. In some embodiments, pitch P is less than or equal to 600 nm, less than or equal to 500 nm, less than or equal to 200 nm, less than or equal to 300 nm, or less than or equal to 200 nm. In some embodiments, pitch P is 400 nm corresponding to a sum of a width of wide portion 204-B (e.g., 200 nm) and a width of narrow portion 204-A (e.g., 200 nm). The pitch (i.e., periodicity of grating 202) of grating 202 defines an x-ray wavelength of a generated x-ray light pulse so that the electrons then emit coherently at that wavelength.

[0037] In some embodiments, grating 202 is supported by a supporting mesh (not shown) such that grating 202 is positioned at a center of the supporting mesh. For example, the supporting mesh is polygon chip having a diameter less or equal to 3 mm.

[0038] In FIG. 2 A, grating 202 is configured to receive an electron bunch 212-1 accelerated to a relativistic energy (e.g., at least several MeV) propagating in a direction substantially perpendicular to a reference plane defined by surface 202-1 of grating 202 and surfaces 202-2 of wide portions 204-2 of nano-scaled patterning 204. In some embodiments,grating 202 is tilted with respect to the direction of propagation in a vertical and / or horizontal direction (e.g., forming a pitch and / or a yaw angle). Electron bunch 212-1 includes a uniform distribution of relativistic (e.g. MeV) electrons. Grating 202 transmits and diffracts electron bunch 212-1 as a patterned electron bunch 212-2. Patterned electron bunch 212-2 is redirected by focusing magnet 206 such that patterned electron bunch 212-2 is directed to distinct Bragg spots (e.g., Bragg spots 212-A, 212-B and 212-C) on a focal plane 208. A Bragg spot on focal plane 208 corresponds to crystallographic peak of a particular Bragg diffraction. A desired partitioning of electron bunch 212-1 to a diffraction pattern (e.g., patterned electron bunch 212- 2) is created by diffraction of the relativistic electrons in a transmission geometry through grating 202. The diffraction pattern of electron bunch 212-2 is controlled by Bragg diffraction from the crystal planes of the silicon membrane (e.g.,

[0100] crystal planes of the silicon membrane). While the diffraction pattern is controlled by the Bragg diffraction, nano-scaled pattern 204 spatially controls a fraction of the electrons diffracted into a particular Bragg spot (e.g., Bragg spots 212-A and 212-B on focal plane 208). Therefore, an electron bunch directed onto Bragg spot 212-A has one or more distinct electronic characteristics from electronic characteristics of an electron bunch directed to Bragg spot 212-B. In some embodiments, the electronic characteristics include a spot size. The electronic characteristics of the electron bunch correlate to optical characteristics of an x-ray light pulse generated from the electron bunch. In some embodiments, the optical characteristics includes a bandwidth of the x-ray light pulse.

[0039] For example, a first portion of electron bunch 212-1 is directed, while passing through grating 202 and focusing magnet 206, onto Bragg spot 212-A. At the Bragg spot 212-A, the first portion of electron bunch 212-1 has a first spot size and an x-ray light pulse subsequently generated from the first portion of electron bunch 212-1 has a first bandwidth. A second portion of electron bunch 212-1 is directed, while passing through grating 202 and focusing magnet 206, to Bragg spot 212-B. At the Bragg spot 212-B, the second portion of electron bunch 212-1 has a second spot size an x-ray light pulse subsequently generated from the second portion of electron bunch 212-1 has a second bandwidth. In some embodiments, the second spot size is distinct from the first spot size and the second bandwidth is distinct from the first bandwidth.

[0040] In FIG. 2 A, patterned electron bunch 212-2 is received on image plane 212 such that patterned electron bunch 212-2 projects a bright field image of grating 202. The bright field image reproduces input electron bunch 212-1 on image plane 210 (e.g., the bright field image on image plane 210 has a uniform distribution of the MeV electrons similar to that of electronbunch 212-1). In contrast to FIG. 2A, FIG. 2B illustrates a dark field image including alternating bright 216-A and dark areas 216-B across image plane 210. The dark field image is created by selecting only a single Bragg spot of patterned electron pattern 210-2 to be transmitted onto image plane 210. The selection is done by positioning an aperture 214 on focal plane 208. Aperture 214 is configured to block all but a single Bragg diffraction peak. As shown in FIG. 2B, aperture 214 allows the electron bunch at Bragg spot 212- A to propagate onto image plane 210 while other electron bunches (e.g., the electron bunch at Bragg spot 212-B) are blocked.

[0041] At a unity magnification, transversely patterned electron bunches have a same spatial periodicity as the silicon structure. The spatial periodicity may, however, be continuously adjusted over a wide range of periodicity by demagnifying / magnifying the pattern (e.g., by a factor of up to 100) using magnetic lenses (e.g., focusing magnet 206) to scale the pattern into an x-ray range.

[0042] The disclosed partitioning (e.g., patterning) method of an electron bunch determines the x-ray phase fronts, which are deterministically controlled by nano-scaled patterning 204 of grating 202. The disclosed method is applicable for controlling and stabilizing the x-ray beam properties, eventually yielding full control of the phase through different nanoscaled patterns on the silicon membrane. In some embodiments, by changing the electron spot size on grating 202, different numbers of grating periods are illuminated thus producing different numbers of patterned electron bunches. This will control both the x-ray pulse length and its bandwidth, given by the reciprocal of the number of grating periods illuminated. Because of a high contrast ratio in the electron pattern, the x-ray output pulse is expected to be nearly transform limited.

[0043] To produce XFEL radiation two further steps are required, first the electrons must be accelerated to their final energy and the pattern swapped from transverse space to temporal space using a technique called emittance exchange (EEX). Then the electrons must propagate through either a short static magnetic undulator or equivalently scatter an infrared (IR) laser pulse to produce coherent x-rays. For the purpose of x-ray emission, the primary difference between using an undulator and an IR laser is the period of the oscillation. The short period of the IR laser allows electrons of a few tens of MeV to produce hard x-rays, rather than the GeV required for an undulator, dramatically shrinking the size and cost of the accelerator compared to undulator-based XFELs. The tradeoff to using an IR laser is that the lower energy electron beam produces fewer photons and has tighter beam quality requirements.

[0044] FIG. 3 illustrates various aspects of an optical (e.g., laser) system (e.g., an optical undulator) for producing light via inverse Compton scattering, in accordance with some embodiments.

[0045] Panel 302 illustrates a pulsed laser beam 304, which produces pulse 306. The pulsed laser beam is an example of the ICS laser, discussed above. Thus, the pulsed laser beam 304 interacts with pulses from an electron beam (e-beam) 308 (panels 310, 312). Spatial overlap between the pulsed laser beam 304 and the electron beam 308 is achieved using an off-axis focus, in which light from the laser beam is shone at an angle (which is 30 degrees in this example) onto a focusing mirror. The pulsed laser beam 304 is incident upon the e-beam 308 with the same angle in an overtaking geometry, meaning that the direction of propagation of the pulsed laser beam 304 and the e-beam 308 are separated by less than 90 degrees (such that the pulsed laser beam 304 overtakes the e-beam 308). Tuning the angle changes the effective undulator length and thus tunes the wavelength of the light that is produced via ICS.

[0046] Panel 314 illustrates as so-called 4F imaging system that produces a Fourier transform of the laser pulse 306. The 4F imaging system demagnifies the image of the grating in Panel 314 onto the interaction point 306 to produce an interaction length between the laser and electron beam sufficient to produce the desired amount of x-rays. At the image position 306, the pulse front tilt produced by the grating is scaled by the magnification of the laser beam. Control of the magnification and pulse front tilt angle is achieved by changing the distance and focal lengths of the imaging optics in panel 314.

[0047] Panels 310 and 312 illustrate the effect of tilting the laser pulse 306 with respect to a direction of propagation of the laser pulse 306 (e.g., the direction of propagation of the laser beam). In panel 310, the laser pulses are not tilted with respect to the direction of propagation of the laser beam. Assuming that the direction of propagation of the laser pulses is defined as the Z-direction, in this geometry, the interaction length between the e-beam and the laser pulses is coupled to the spot size in the out-of-plane dimension (e.g., the XY-plane). By tilting the shape of the laser pulse 306 with respect to the direction of propagation of the laser pulse 306 (e.g., rotating a long axis of the laser pulse into the XZ-plane, as shown in panel 312), a longer interaction length between the laser pulse 306 and the e-beam 308 is achieved, which results in a greater number of photons produced through ICS. Stated another way, tilting the laser pulse 306 decouples the interaction length from the width of the laser 306 in the XY-plane, such that the interaction length is instead governed by the temporal length of the laser pulse.

[0048] As additional context, it is important to note that methods to make XFELs in a cost-effective way by reducing the accelerator energy require reducing the undulator period as well, making magnetic undulators unsuitable for their design, as these are challenging to manufacture below a millimeter scale. Colliding an electron beam with near-infrared ultrafast lasers (inverse Compton scattering, or travelling-wave Thomson scattering) provides an alternate source of alternating magnetic field, and the undulator period is proportional to the laser wavelength.

[0049] In order to keep the wavelength of the x-rays constant while raising the beam energy, which is desirable, the undulator period needs to be longer. However, lasers typically operate at fixed wavelengths, and converting between wavelengths is very inefficient. Fortunately, changing the angle between the electron beam and laser serves the same purpose.

[0050] For example, to produce 12 keV x-rays with a 230 MeV electron beam and a 1 micron laser wavelength requires a crossing angle of 12 degrees, for an effective undulator period of 4 microns. The interaction length for a seeded FEL is a few hundred undulator periods, or in this case, approximately 1 cm.

[0051] Moreover, the interaction between electrons and the laser is relativistic, as free electrons do not interact with light to first order. Therefore, the normalized vector potential aO must be of order 1 to drive relativistic motion in the electron’s reference frame (the normalized vector potential aO is Lorentz invariant and independent of the beam energy).

[0052] For 1 micron light, aO = 1 corresponds to an intensity of I = 1.37xl018W / cm2. For scale, the Schwinger limit (where light can cause spontaneous pair production) is on the order of 1029W / cm2, and the energy range for high harmonic generation (HHG) is on the order of 1015W / cm2. However, both aforementioned phenomena can be observed where the laser is confined to a small area, reducing the required laser power. Here, the laser light must be intense over a larger area.

[0053] The current state of the art for laser focusing is to focus the beam astigmatically, meaning the X and Y dimensions of a beam propagating along the Z-axis in the lab frame focus independently. In this case, they focus to the Z position at the interaction point with the electron beam, but have different beam divergences and waists.

[0054] The desired interaction length for an optical XFEL is approximately 1 cm, which at 12 degree crossing angle requires a laser beam diameter of 2 mm (1 mm beam waist) in thecrossing plane. Furthermore, a 1 cm interaction length limits the Rayleigh range focusing to be less than half the desired interaction length.

[0055] This forces the y beam waist in this geometry to be 35 microns. Thus, the required peak power is 400 TW to reach a peak aO of 1 with an interaction length of 7 mm. For a laser running at 1 kHz, this peak power is almost two orders of magnitude more powerful than what is accessible with current technology, which is on the order of 10 TW. While such lasers exist, they typically operate at low repetition rates, require large areas of amplifiers, and large maintenance staff for optimization.

[0056] Thus, some embodiments of the present disclosure provide an optic that decouples the interaction length from the focusing restriction that the Rayleigh range must be longer than the interaction length, solving the problems described above. This preserves the long interaction length required for the XFEL, while focusing the beam such that we achieve high intensities over many millimeters of interaction length. This decoupling reduces the required peak laser power by more than an order of magnitude, to approximately 10 TW for similar intensity cross-section. This reduction in the desired power requirement allows us to bring the intensity and interaction length requirements into line with commercially available, relatively cost-effective laser technology. This explanation of the function of the focusing optic requires some definitions. The laser propagates along the Z-axis in the lab frame, and the electron beam crosses the laser beam at an angle in the XZ plane. The XZ plane will be referred to as such or as the “interaction plane”.

[0057] The fundamental idea is that the Rayleigh range in the y focus is a limit only if the beam focuses in the same place for all X in the interaction plane. If we have an optic that has different focal lengths in Y along the interaction plane, this significantly reduces the limits on the effective numerical aperture (NA), other than practical and technical considerations of beam damage, aberrations, and collisions of the optic with the electron beam. This allows us to reduce the spot size in Y from tens of microns to a few microns.

[0058] In some embodiments, the optic is a modified one-dimensional off-axis parabola, with an off-axis angle of approximately 12 degrees. The focus tilts at an angle of 72 degrees- that is, for every 1 mm the beam moves along the optic in X, the focus in Y moves by 4 mm in Z. This causes the intensity in the XZ plane to look like a diagonal line with a 72 degree angle with respect to the Z axis. Note, however, that this is just an example.

[0059] The peak intensity is slightly lower than achievable for the same focal length at fixed NA, but still an order of magnitude more intense than the current state of the art at fixed incoming peak power.

[0060] FIG. 4 illustrates a micro -bunching scheme for free-electron laser (FEL) seeding, along with exemplary parameters, in accordance with some embodiments. A relativistic electron bunch 306 is transmitted through a grating, downstream of a linear accelerator, which accelerated the electron bunch to the relativistic energy. The electron bunch is transmitted through the grating 402 to produce a diffraction pattern in a direction transverse to the direction of propagation of the electron bunch 306. An emittance exchange optic (e.g., in emittance exchange section 114), downstream of the grating 402, rotates the diffraction pattern to a direction substantially parallel to a direction of propagation of the electron bunch. The interaction point described with reference to FIG. 3, in which the laser pulse 306 interacts with the e-beam in an overtaking geometry, is downstream of the emittance exchange optic. In particular, at the interaction point, the micro-bunching provided by the grating is parallel to the direction of propagation of the e-beam.

[0061] FIG. 5 illustrates various aspects of an optical (e.g., laser) system (e.g., an optical undulator) for producing light via inverse Compton scattering, in accordance with some embodiments. The laser beam 304 is reflected off a grating 502 (distinct from grating 402, FIG. 4), which produces the tilted pulse front described with respect to FIG. 4. The laser beam 306 is then reflected off of one or more mirrors (e.g., cylindrical mirror 1 and cylindrical mirror 2) before being reflected by a final vertical focusing mirror (M3). In some embodiments, the final vertical focusing mirror increases a squareness or rectangularness of the laser beam 306 at the interaction point, and also provides the 30 degree overtaking geometry.

[0062] FIGS. 6A-6B illustrates various simulation results, in accordance with some embodiments, for a simulated electric field of a 10 TW Gaussian laser beam propagating through the setup described in this disclosure. In some embodiments, a he compact XFEL undulator requires ao > 0.3 over approximately 100 undulator periods. The simulation demonstrates that a 10 TW peak power laser combined with the optical design described in this disclosure meets these requirements. This simulation accounts for aberrations in the optics, diffraction effects from finite Rayleigh range, and dispersion of the beam. In this simulation, the laser beam intensity profile at the interaction point has a maximum normalized irradiance of 13.2 W / mm2(aO = 0.55). FIG. 6B illustrates a normalized vector potential ao in the plane of thelaser and electron beam propagation vectors. FIG. 6B illustrates a normalized vector potential ao along the electron beam path. Demonstrating ao > 0.3 for more than 100 undulator periods for a 10 TW laser. The dashed line is 100 undulator periods long at ao = 0.3 to illustrate that the laser design meets or exceeds these requirements.

[0063] FIG. 7 is a flow chart of a method for generating light via inverse Compton scattering (ICS), in accordance with some embodiments.

[0064] Method 700 includes accelerating (702) an electron bunch to a relativistic energy (e.g., using LINAC 104a, FIG. 1C). In some embodiments, the electron bunch is accelerated using a linear accelerator. In some embodiments, the electron bunch is accelerated using an accelerator that is not linear.

[0065] Method 700 includes producing (704) a diffraction pattern in the electron bunch (e.g., using grating 402, FIG. 4). In some embodiments, producing the diffraction pattern in the electron bunch comprises micro-bunching the electron bunch. In some embodiments, the microbunching is used to seed the light produced via ICS.

[0066] Method 700 includes rotating (706) the diffraction pattern to a direction substantially parallel to a direction of propagation of the electron bunch (e.g., using an emittance exchange optic, such as emittance exchange section 114, FIG. IB).

[0067] Method 700 includes 708 producing light via inverse Compton scattering by interacting the electron bunch, having the rotated diffraction pattern, with a pulse of light from a laser, wherein the pulse of light from the laser interacts with the electron bunch in an overtaking geometry at an interaction point.

[0068] In some embodiments, at the interaction point, the pulse of light is tilted (e.g., a contour of constant arrival time is tilted with respect to a direction of propagation of the pulse of light (e.g., as described in FIG. 3)). In some embodiments, the pulse of the light is tilted using a second grating (e.g., grating 502, FIG. 5).

[0069] In some embodiments, at the interaction point, an angle between a direction of propagation of the pulse of light and the direction of propagation of the electron bunch is between 25 and 30 degrees. In some embodiments, the angle is tuned to tune an energy of the light produced by ICS. In some embodiments, the light produced by ICS has a wavelength in an ultraviolet or x-ray range (e.g., a soft x-ray range).

[0070] In some embodiments, the laser has a peak power less than 100 terawatts (or less than 50 TW, less than 20 TW, or approximately 10 TW).

[0071] In some embodiments, method 700 includes shaping the electron bunch using a vertical focusing mirror upstream of the interaction point to make a transverse shape of the pulse of light more square or rectangular at the interaction point.

Claims

CLAIMSWhat is claimed is:

1. A light source, comprising: a linear accelerator for accelerating an electron bunch to a relativistic energy; a first grating, downstream of the linear accelerator and arranged such that the electron bunch is transmitted through the first grating to produce a diffraction pattern; an emittance exchange device, downstream of the first grating, that rotates the diffraction pattern to a direction substantially parallel to a direction of propagation of the electron bunch; a laser that produces a pulse of light, wherein: the light source is configured such that the pulse of light from the laser interacts with the electron bunch in an overtaking geometry at an interaction point, downstream of the emittance exchange optic, while the diffraction pattern is substantially parallel to the direction of propagation of the electron bunch to produce light via inverse Compton scattering.

2. The light source of claim 1, wherein, at the interaction point, the pulse of light is tilted with respect to a direction of propagation of the pulse of light.

3. The light source of claim 2, further comprising an optical diffraction grating and an imaging system to tilt the shape of the pulse of light with respect to the direction of propagation of the pulse of light.

4. The light source of claim 1, wherein, at the interaction point, an angle between a direction of propagation of the pulse of light and the direction of propagation of the electron bunch is between 25 and 35 degrees, and the arrival time pulse tilt is half of this angle.

5. The light source of claim 1, wherein the light produced via inverse Compton scattering is x-ray light or ultraviolet light.

6. The light source of claim 1, wherein the laser has a peak power less than 100 terawatts.

7. The light source of claim 1, further comprising a vertical focusing mirror upstream of the interaction point configured to make a transverse shape of the pulse of light tightly focused in the out of plane direction.

8. The light source of claim 1, further comprising that the beam shape illuminating the grating is in approximately a square pattern.

9. A method, comprising: accelerating an electron bunch to a relativistic energy; producing produce a diffraction pattern in the electron bunch; rotating the diffraction pattern to a direction substantially parallel to a direction of propagation of the electron bunch; producing light via inverse Compton scattering by interacting the electron bunch, having the rotated diffraction pattern, with a pulse of light from a laser, wherein the pulse of light from the laser interacts with the electron bunch in an overtaking geometry at an interaction point.

10. The light source of claim 1, wherein, at the interaction point, the pulse of light is tilted with respect to a direction of propagation of the pulse of light.

11. The light source of claim 1 , wherein, at the interaction point, an angle between a direction of propagation of the pulse of light and the direction of propagation of the electron bunch is between 25 and 35 degrees.

12. The light source of claim 1, wherein the light produced via inverse Compton scattering is x-ray light or ultraviolet light.

13. The light source of claim 1, wherein the laser has a peak power less than 50 terawatts.

14. The light source of claim 1, further comprising shaping the electron bunch using a vertical focusing mirror upstream of the interaction point to make a transverse shape of the pulse of light more square or rectangular at the interaction point.

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