Optical design of a laboratory-scale compact free-electron laser based on inverse Compton scattering

Abstract

The light source includes a linear accelerator for accelerating electron bunches to relativistic energies. The light source further includes a first grating downstream of the linear accelerator, which is positioned so that electron bunches pass through it to produce a diffraction pattern. The light source further includes an emittance exchange device downstream of the first grating, which rotates the diffraction pattern in a direction substantially parallel to the propagation direction of the electron bunches. The light source further includes a laser that generates light pulses. The light source is configured such that the light pulses from the laser interact with the electron bunches in an overtaking geometry at an interaction point downstream of the emittance exchange device, while the diffraction pattern is substantially parallel to the propagation direction of the electron bunches to produce light via inverse Compton scattering.

Description

Technical Field

[0001] Government Support This invention was made with government support under Grant No. 1935994 awarded by the National Science Foundation. The government has certain rights in this invention.

[0002] This invention relates to free electron lasers (FELs), and more particularly, to x-ray free electron lasers (XFELs).

Background Art

[0003] X-ray free electron lasers (XFELs) generate x-ray pulses having a duration shorter than 100 femtoseconds (fs) that each contain sufficient photons to generate a diffraction pattern from a nanocrystal in a single shot while escaping most of the effects of radiation damage. XFELs have proven to be powerful tools for a wide range of applications, including the crystal structure and dynamics of biomolecules in their native environment, the underlying charge and energy dynamics in molecules, emergent phenomena in correlated electron systems, single particle structure and dynamics, and matter in extreme environments. The shortest XFEL pulses approach 1 fs, corresponding to the natural timescale of the fastest electron excitations, opening up a new era in the exploration of atomic scale dynamics.

Summary of the Invention

[0004] This paper discloses 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, perfect spatial coherence, and short pulse duration, enabling experiments to examine materials on time and length scales of electronic and structural motion. In some embodiments, CXFELs seed inverse Compton scattering (ICS)-based XFELs, employing emittance exchange of diffracted electron beams to produce perfectly coherent radiation over relatively short accelerator lengths (e.g., 10 meters). The use of an optical undulator (e.g., ICS) reduces electron beam energy requirements and significantly reduces the required facility size, along with its cost. Tuning the intersection angle between the electron beam and the ICS laser allows for higher electron beam energies while maintaining a soft X-ray regime, which is necessary to minimize the space charge effects present in low-energy accelerators. As an example, we present an optimized optical design using a 10TW peak power driven laser to generate 1nm (1.2keV) radiation with a 30-degree intersection angle at a 30MeV electron beam, which is within the range of high repetition rate commercial laser sources.

[0005] To this end, in some embodiments, a light source is provided. The 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, which is positioned so that the electron bunch passes through the grating to produce a diffraction pattern. The light source further includes an emittance exchange device (e.g., an electron optical system) downstream of the grating, which rotates the diffraction pattern in a direction substantially parallel to the propagation direction of the electron bunch. The light source further includes a laser that generates light pulses. The light source is configured such that the light pulses from the laser interact 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 propagation direction of the electron bunch to produce light via inverse Compton scattering.

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

[0007] The present invention will be better understood by referring to the following detailed description of specific embodiments in conjunction with drawings that are not to exact scale. [Brief explanation of the drawing]

[0008] [Figure 1A] This is a schematic diagram showing a light source (e.g., a free-electron laser) according to several embodiments. [Figure 1B] This is a schematic diagram showing a light source (e.g., a free-electron laser) according to several embodiments. [Figure 1C] This is a schematic diagram showing a light source (e.g., a free-electron laser) according to several embodiments. [Figure 2A] This is a schematic diagram showing how electron bunches are divided by electron diffraction according to several embodiments. [Figure 2B] This is a schematic diagram showing how electron bunches are divided by electron diffraction according to several embodiments. [Figure 3] Several embodiments of optical (e.g., laser) systems (e.g., optical undulators) for generating light via inverse Compton scattering are shown. [Figure 4] Several embodiments of microbunching schemes for free-electron laser (FEL) seeding are shown, along with exemplary parameters. [Figure 5] Several embodiments of optical (e.g., laser) systems (e.g., optical undulators) for generating light via inverse Compton scattering are shown. [Figure 6A] Various simulation results from several embodiments are shown. [Figure 6B] Various simulation results from several embodiments are shown. [Figure 7] This is a flowchart of a method for generating light via inverse Compton scattering, according to several embodiments.

[0009] In general, the size and relative dimensions of elements within a drawing may be set differently from reality to facilitate the conciseness, clarity, and understanding of the drawing as appropriate. For the same reason, not all elements present in one drawing may necessarily be shown in another. [Modes for carrying out the invention]

[0010] Embodiments of the present disclosure provide a method and assembly for generating time-coherent X-ray pulses. First-generation XFELs provide only partial time coherence. The lack of time coherence is due to both the random spacing of bunched electrons in the SASE process and the lack of a coherent X-ray seed pulse for amplification. The output emission of the resulting first-generation XFEL is characterized by shot noise, random phase jumps, and abrupt fluctuations in intensity within the pulse, a wavelength spectrum filled with many distinct lines, as well as large fluctuations in spectral characteristics and pulse energy between shots.

[0011] Instead of seeding with coherent radiation, the methods and assemblies of the present disclosure arrange electrons (e.g., in a laboratory frame) in separate bunches (e.g., nano / micro bunches) with a periodicity equal to the desired X-ray wavelength, so that the electrons (e.g., when passed through an undulator) emit coherently at that wavelength. The herent spontaneous emission is then emitted by phased nanobunches amplified by the FEL process due to relatively modest electron bunch parameters. Such FEL gains generate a single optical mode that occupies the output, resulting in time-coherent laser-like radiation. Thereafter, the present disclosure overcomes the random electron spacing inherent in SASE processes by patterning the electron bunches to create bunches with nanometer separation matching the desired X-ray wavelength.

[0012] The electron bunching pattern is deterministically repeatable and can be controlled to generate a wide variety of phase relationships to achieve different experimental properties, such as a stable, conversion-limited (or nearly conversion-limited) single-spike spectrum, frequency-chirp 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 levels. In short, this method enables a temporal structure for generating a fully coherent X-ray beam from a pattern drawn on a semiconductor wafer (e.g., a single-crystal silicon film) by lithography.

[0013] For the purposes of this disclosure and the attached claims, the use of “substantially,” “approximately,” “about,” and similar terms with respect to descriptors of values, elements, properties, or characteristics is intended to emphasize that the values, elements, properties, or characteristics referred to are not necessarily as stated, but would still be considered as stated by those skilled in the art for practical purposes. When applied to descriptors of particular characteristics or qualities, these terms reasonably indicate language of approximation and mean “almost,” “mainly,” “fairly,” “generally,” “basically,” “to a large or considerable extent,” and “roughly the same, but not necessarily exactly the same,” for example, to describe the specified characteristics or descriptors in such a way that their range is understood by those skilled in the art. In certain particular cases, when the terms “approximately,” “substantially,” and “about” are used with respect to numbers, they represent a range of plus or minus 20%, more preferably plus or minus 10%, even more preferably plus or minus 5%, and most preferably plus or minus 2% with respect to the specified value. As a non-restrictive example, two values ​​being "substantially equal" means that the difference between the two values ​​may be within + / - 20% of the value itself, preferably within + / - 10% of the value itself, more preferably within + / - 5% of the value itself, and even more preferably within + / - 2% or less of the value itself.

[0014] The use of these terms in describing selected properties or concepts does not imply or provide a basis for uncertainty, nor does it imply or provide a basis for adding numerical limitations to any particular property or descriptor. As will be understood by those skilled in the art, any actual deviation of the exact value or property of such a value, element, or characteristic from that described will fall within and may vary within a numerical range defined by the experimental measurement error that is typical when using measurement methods accepted in the art for such purposes.

[0015] For example, a reference to an identified direction or vector or line or plane being substantially parallel to a referenced line or plane should be construed as being the same as or very close to such a direction or vector or line or plane (e.g., having an angular deviation from the referenced line or plane that is substantially typical in the relevant art of 0 to 15 degrees, preferably 0 to 10 degrees, more preferably 0 to 5 degrees, even more preferably 0 to 2 degrees, and most preferably 0 to 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 should be construed as being such a direction or vector or line or plane whose normal to its surface lies in or very close to the referenced line or plane (e.g., having an angular deviation from the referenced line or plane that is substantially typical in the relevant art of 0 to 15 degrees, preferably 0 to 10 degrees, more preferably 0 to 5 degrees, even more preferably 0 to 2 degrees, and most preferably 0 to 1 degree).

[0016] Other specific examples of the meaning of the terms "substantially", "about", and / or "approximately" as applied to different actual situations may be provided elsewhere in the present disclosure.

[0017] Embodiments of the system may generally include an electronic circuit (e.g., a computer processor) that manages the operation of at least the embodiment and is controlled by instructions stored in memory in order to perform certain data acquisition / processing and computation steps as disclosed above. The memory may be random access memory (RAM), read-only memory (ROM), flash memory, or any other memory, or a combination thereof, suitable for storing control software or other instructions and data. Those skilled in the art will readily understand that instructions or programs defining the operation of this embodiment(s) may be delivered to the processor in many forms, including, but not limited to, information permanently stored in non-writable storage media (e.g., read-only memory devices in a computer such as ROM, or devices readable by computer I / O attachments such as CD-ROM or DVD discs), information modifiablely stored in writable storage media (e.g., floppy disks, removable flash memory, and hard drives), or information transmitted to a computer via a communication medium, including wired or wireless computer networks. Furthermore, while the present invention can be embodied in software, the functions necessary to implement the method of the present invention may be embodied in part or in whole, optionally or alternatively, using combinational logic, application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other hardware, or any combination of hardware, software, and / or firmware components, such as firmware and / or hardware components.

[0018] The inventions described in the claims attached to this disclosure are intended to be evaluated in light of this disclosure as a whole. Various modifications of the described details, steps, and components can be made by those skilled in the art within the principles and scope of the invention.

[0019] Although the present invention has been described through the above exemplary embodiments, those skilled in the art will understand that modifications and variations of the illustrated embodiments can be made without departing from the concept of the invention disclosed herein. Therefore, the present invention should not be considered limited to the disclosed embodiment(s).

[0020] FIGS. 1A - 1C are schematic diagrams showing a light source 100 (e.g., a free electron laser) according to some embodiments. Note that for the sake of brevity, only the most suitable aspects of the light source 100 will be considered in detail below.

[0021] In some embodiments, the light source 100 generates X - rays. In some embodiments, the light source 100 generates hard X - rays (e.g., X - rays having an energy above 1 keV). In some embodiments, the light source 100 generates soft X - rays or extreme ultraviolet rays. In some embodiments, as described below, the light (e.g., X - rays) generated by the light source 100 is completely spatially and temporally coherent (e.g., the light source 100 generates light having coherence properties similar to those of conventional lasers used to generate light of optical wavelengths, ultraviolet wavelengths, infrared wavelengths, and other wavelengths). In some embodiments, the 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). However, note that in embodiments where an undulator is used, coherent light can be generated from the light source 100 using an undulator much shorter than that of a conventional FEL (e.g., 10 meters instead of 100 meters). Therefore, the light source 100 may be referred to as a compact X - ray free electron laser (CXFEL).

[0022] Starting from Figure 1C, an electron bunch is generated and initially accelerated using an electron photoinjector 102. For example, in some embodiments, a 4 MeV beam (note that the terms electron bunch, beam, and bunch are used synonymously throughout this disclosure) is generated by a 4.5-cell x-band photoinjector equipped with a solenoid and an RF gun. Following the photoinjector (e.g., downstream), there are one or more linear accelerator (LINAC) sections (LINAC sections 104a-104c, respectively) fed 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.

[0023] It should be noted that, as shown, RF power from a single klystron 106 may be applied to several different components (for example, klystron 106b may supply both LINAC sections 104b and 104c, as well as the RF deflector cavity and accelerator cavity 124, while klystron 106a may supply both the initial acceleration of the electron bunch and LINAC 105c). Furthermore, phase shifts may be applied to the power supplied to various components by the various klystrons 106 by phase shifters 108 (e.g., phase shifters 108a-108d). RF loads 128 (e.g., RF loads 128a, 128b) are included and positioned where necessary for load balancing and control.

[0024] In some embodiments, the diffraction grating 110 (e.g., a diffraction crystal such as a silicon grating described below) is located between two of the LINAC sections (or at least after the 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 positioned within a transmission geometry with respect to the path of the electron bunch (e.g., the direction of electron bunch propagation). In some embodiments, the diffraction grating 110 diffracts the electron beam at a tunable energy up to 12 MeV.

[0025] Referring here to Figures 1A and 1B, the light source 100 includes various electron optics for patterning and shaping electron bunches downstream of the LINAC section 104. The electron optics of the light source 100 include three main sections: a nanopattern imaging section 112, an emittance exchange (EEX) section 114, and an inverse Compton scattering (ICS) interaction section 116. However, it should be noted that in some embodiments, the ICS interaction section 116 is replaced by an undulator (e.g., an undulator less than 20 m in length).

[0026] The nanopatterning imaging section 112 is located downstream of the LINAC section 104c and, in some embodiments, comprises two quadrupole triplets 118 (e.g., quadrupole triplet 118a and quadrupole triplet 118b) that form a telescope system.

[0027] In some embodiments, the diffraction grating 110 generates a diffraction pattern across the direction of electron bunch propagation, and the emittance exchange section 114 converts (e.g., exchanges) the diffraction pattern in a direction parallel to the direction of electron bunch propagation. To this end, the EEX section 114 includes four independently phase-tuned and powered bent magnets 120a-120d, an RF deflector cavity, and an accelerator cavity (collectively 124), along with hexapole magnets 122a-122c and an octapole magnet 126 for aberration correction.

[0028] Following the EEX section 114, the ICS interaction section 116 begins with a focusing triplet 130 that reduces the beam size at the ICS interaction point 132 (e.g., to approximately 1 micron) before the electron beam collides with the ICS laser field from the inverse Compton scattering laser 138 (e.g., light from the inverse Compton scattering laser 138 is piped in and redirected to be nearly parallel to 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 of the ICS interaction point 132, two dipoles 134a and 134b bend the beam into beam dumps, respectively (e.g., bend them horizontally by 30 and 90 degrees, respectively, into vertical beam dumps). In some embodiments, the collision of the electron beam with the ICS laser field occurs within the magnetic field of the dipole magnet 134a. The ICS interaction section 116 is an example of a photogenerator. An undulator (not shown) is another example of a photogenerator.

[0029] Figures 2A and 2B are schematic diagrams of electron bunch splitting by electron diffraction according to several embodiments. Figure 2A shows a cross-sectional view of assembly 200 including a lattice 202 and a focusing magnet 206. The lattice 202 is fabricated from a single-crystal silicon film (e.g., the “UberFlat” silicon film provided by Norcada). For example, the lattice 202 is fabricated from a silicon film having a

[0100] crystalline structure. As shown in the inset of Figure 2A, the lattice 202 includes a nanoscale pattern 204 defining alternating longitudinal narrow and wide portions (e.g., alternating narrow portion 204-A and wide portion 204-B). In some embodiments, the lattice 202 has a thickness T defined between the surface of the wide portion 204-B of the lattice 202 (e.g., surface 202-2) and the opposing surface 202-1. In some embodiments, the thickness T is in the range of 50 nm to 1000 nm, 50 nm to 500 nm, 50 nm to 400 nm, 50 nm to 300 nm, 50 nm to 200 nm, or 50 nm to 100 nm. In some embodiments, the grid 202 has a thickness T in the range of 100 nm to 300 nm. In some embodiments, the thickness T is 200 nm. The grid 202 has regions defined by edges in the range of 50 micrometers to 500 micrometers (for example, the grid 202 has a rectangular or square shape). In some embodiments, the grid 202 has regions corresponding to 50 micrometers × 50 micrometers, 100 micrometers × 100 micrometers, or 200 micrometers × 200 micrometers.

[0030] The nanoscale patterning 204 is located at the center of the silicon film of the lattice 202. The nanoscale patterning 204 includes a plurality of longitudinal grooves or valleys cut (e.g., etched) through a portion of the silicon film of the lattice 202 that defines alternating narrow portions 204-A and broad portions 204-B. The broad portions 204-B have a thickness T between surface 202-1 and surface 202-2, as described above. The thickness T is greater than the thickness of the narrow portion 204-A between surface 202-1 and surface 202-3. In some embodiments, the grooves are aligned with the edges of the silicon film forming the lattice 202, thereby aligning the grooves with the crystal planes of the silicon film. In some embodiments, the nanoscale patterning 204 has regions defined by edges ranging from 20 micrometers to 100 micrometers. In some embodiments, the nanoscale patterning 204 covers a region on the silicon film corresponding to 20 micrometers × 20 micrometers, 50 micrometers × 50 micrometers, or 100 micrometers × 100 micrometers. The nanoscale patterning 204 has a pitch P corresponding to the sum of the widths of the broad portion 204-B and the narrow portion 204-A, as shown in the inset of Figure 2A. In some embodiments, the pitch P is 600 nm or less, 500 nm or less, 200 nm or less, 300 nm or less, or 200 nm or less. In some embodiments, the pitch P is 400 nm, corresponding to the sum of the width of the broad portion 204-B (e.g., 200 nm) and the width of the narrow portion 204-A (e.g., 200 nm). The pitch of the grating 202 (i.e., the periodicity of the grating 202) defines the X-ray wavelength of the generated X-ray light pulse, resulting in the coherent emission of electrons at that wavelength.

[0031] In some embodiments, the grid 202 is supported by a support mesh (not shown) such that the grid 202 is positioned at the center of the support mesh. For example, the support mesh is a polygon chip having a diameter of 3 mm or less.

[0032] In Figure 2A, the lattice 202 is configured to receive electron bunches 212-1 accelerated to relativistic energies (e.g., at least a few MeV) propagating in a direction substantially perpendicular to a reference plane defined by the surface 202-1 of the lattice 202 and the surface 202-2 of a broad portion 204-2 of the nanoscale patterning 204. In some embodiments, the lattice 202 is tilted perpendicular and / or horizontal to the propagation direction (e.g., forming pitch and / or yaw angles). The electron bunches 212-1 contain a uniform distribution of relativistic (e.g., MeV) electrons. The lattice 202 transmits and diffracts the electron bunches 212-1 as patterned electron bunches 212-2. The patterned electron bunch 212-2 is redirected by the focusing magnet 206 so that the patterned electron bunch 212-2 is directed towards individual Bragg spots (e.g., Bragg spots 212-A, 212-B, and 212-C) on the focal plane 208. The Bragg spots on the focal plane 208 correspond to crystallographic peaks of specific Bragg diffractions. The desired splitting of electron bunch 212-1 into diffraction patterns (e.g., patterned electron bunch 212-2) is caused by the diffraction of relativistic electrons in the transmission geometry through the lattice 202. The diffraction pattern of electron bunch 212-2 is controlled by Bragg diffraction from the crystal planes of the silicon film (e.g., the

[0100] crystal plane of the silicon film). While the diffraction pattern is controlled by Bragg diffraction, the nanoscale pattern 204 spatially controls some of the electrons diffracted to specific Bragg spots (e.g., Bragg spots 212-A and 212-B on the focal plane 208). Therefore, the electron bunch directed to Bragg spot 212-A has one or more electronic properties that differ from those of the electron bunch directed to Bragg spot 212-B. In some embodiments, the electronic properties include the spot size. The electronic properties of the electron bunch correlate with the optical properties of the X-ray pulse generated from the electron bunch. In some embodiments, the optical properties include the bandwidth of the X-ray pulse.

[0033] For example, a first portion of electron bunch 212-1 is directed onto Bragg spot 212-A as it passes through the grating 202 and the focusing magnet 206. At Bragg spot 212-A, the first portion of electron bunch 212-1 has a first spot size, and the X-ray 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 onto Bragg spot 212-B as it passes through the grating 202 and the focusing magnet 206. At Bragg spot 212-B, the second portion of electron bunch 212-1 has a second spot size, and the X-ray pulse subsequently generated from the second portion of electron bunch 212-1 has a second bandwidth. In some embodiments, the second spot size is different from the first spot size, and the second bandwidth is different from the first bandwidth.

[0034] In Figure 2A, the patterned electron bunch 212-2 is received on the image plane 212 so that the patterned electron bunch 212-2 projects a bright-field image of the grating 202. The bright-field image reconstructs the input electron bunch 212-1 on the image plane 210 (for example, the bright-field image on the image plane 210 has a uniform distribution of MeV electrons similar to that of the electron bunch 212-1). In contrast to Figure 2A, Figure 2B shows a dark-field image containing alternating bright and dark regions 216-A and 216-B across the image plane 210. The dark-field image is created by selecting only a single Bragg spot of the patterned electron pattern 210-2 transmitted onto the image plane 210. This selection is achieved by positioning an aperture 214 on the focal plane 208. The aperture 214 is configured to block everything except a single Bragg diffraction peak. As shown in Figure 2B, aperture 214 allows the electron bunch of Bragg spot 212-A to propagate on the image plane 210 while other electron bunches (e.g., the electron bunch of Bragg spot 212-B) are blocked.

[0035] At 1x magnification, laterally patterned electron bunches exhibit the same spatial periodicity as silicon structures. However, this spatial periodicity can be continuously tuned over a wide range of periodicities by using magnetic lenses (e.g., focusing magnet 206) to reduce / magnify the pattern (e.g., up to 100x magnification) and scaling the pattern to the X-ray range.

[0036] The disclosed electron bunch splitting (e.g., patterning) method defines an X-ray phase plane that is deterministically controlled by nanoscale patterning 204 of the grating 202. The disclosed method is applicable to controlling and stabilizing the properties of the X-ray beam, ultimately resulting in complete phase control through different nanoscale patterns on the silicon film. In some embodiments, different numbers of grating periods are irradiated by changing the electron spot size on the grating 202, thereby generating different numbers of patterned electron bunches. This will control both the length and bandwidth of the X-ray pulse, which is given by the reciprocal of the number of irradiated grating periods. Due to the high contrast ratio of the electron patterns, the X-ray output pulse is expected to be almost conversion-limited.

[0037] To generate XFEL radiation, two further steps are required. First, electrons must be accelerated to their final energy, and their patterns must be swapped from lateral space to time space using a technique called emittance exchange (EEX). Second, the electrons must propagate through a short static magnetic field undulator or, equivalently, scatter infrared (IR) laser pulses to produce coherent X-rays. The main difference between using an undulator and using an IR laser for X-ray emission purposes is the period of oscillation. The short duration of the IR laser allows electrons at tens of MeV, rather than the GeV required for an undulator, to produce hard X-rays, dramatically reducing the size and cost of the accelerator compared to an undulator-based XFEL. The trade-off for using an IR laser is that lower energy electron beams produce fewer photons and have more stringent beam quality requirements.

[0038] Figure 3 shows various embodiments of optical (e.g., laser) systems (e.g., optical undulators) for generating light via inverse Compton scattering, according to several embodiments.

[0039] Panel 302 shows a pulsed laser beam 304 that generates 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 the 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, and the light from the laser beams is directed at a certain angle.

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[0040] Panel 314 is shown as a so-called 4F imaging system that generates the Fourier transform of the laser pulse 306. The 4F imaging system reduces the image of the grating on panel 314 onto the interaction point 306 to generate an interaction length between the laser beam and the electron beam sufficient to produce the desired amount of X-rays. At image position 306, the pulse front tilt generated 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 length of the imaging optical system of panel 314.

[0041] Panels 310 and 312 illustrate the effect of tilting the laser pulse 306 with respect to its propagation direction (e.g., the propagation direction of the laser beam). In panel 310, the laser pulse is not tilted with respect to the propagation direction of the laser beam. Assuming the propagation direction of the laser pulse is defined as the Z direction, in this geometry, the interaction length between the e-beam and the laser pulse is tied 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 its propagation direction (e.g., rotating the long axis of the laser pulse in the XZ plane, as shown in panel 312), a longer interaction length is achieved between the laser pulse 306 and the e-beam 308, resulting in more photons being generated through the ICS. In other words, by tilting the laser pulse 306, the interaction length is decoupled from the width of the laser 306 in the XY plane, and as a result, the interaction length is instead controlled by the temporal length of the laser pulse.

[0042] As additional context, it is important to note that reducing accelerator energy is a cost-effective way to fabricate XFELs, which is difficult to do on a sub-millimeter scale, and therefore also requires shortening the undulator period and making magnetic field undulators unsuitable for their design. By colliding electron beams with near-infrared ultrafast lasers (inverse Compton scattering, or traveling-wave Thomson scattering), an alternative source of alternating magnetic fields is provided, and the undulator period is proportional to the laser wavelength.

[0043] To increase the beam energy while keeping the X-ray wavelength constant (which is desirable), the undulator period needs to be made longer. However, lasers typically operate at a fixed wavelength, and wavelength conversion is very inefficient. Fortunately, changing the angle between the electron beam and the laser serves the same purpose.

[0044] For example, to generate a 230 MeV electron beam and 12 keV X-rays with a laser wavelength of 1 micron, an intersection angle of 12 degrees is required for an effective undulator period of 4 microns. The interaction length of a seeded FEL is several hundred undulator periods, or in this case, approximately 1 cm.

[0045] Furthermore, since free electrons do not interact with light in a linear fashion, the interaction between electrons and lasers is relativistic. Therefore, the normalized vector potential a0 must be linear in order to drive the relativistic motion of the electrons in the reference coordinate system (the normalized vector potential a0 is Lorentz invariant and independent of the beam energy).

[0046] For a 1 micron of light, a0=1 means I=1.37×10 18 W / cm 2 Corresponds to the intensity. Regarding the scale, the Schwinger limit (the point at which light can cause spontaneous pair formation) is 10 29 W / cm 2 The energy range of harmonic generation (HHG) is approximately 1015 W / cm 2 This is on the order of magnitude. However, both of the above phenomena can be observed when the laser is confined to a small area, reducing the required laser power. In this case, the laser light must be strong over a wider area.

[0047] Current techniques for laser focusing involve astigmatically focusing the beam, independently of the X and Y dimensions of the beam propagating along the Z axis at the focal point of the laboratory frame. In this case, they focus at the Z position at the interaction point with the electron beam, but differ in beam divergence and waist.

[0048] The desired interaction length for an optical XFEL is approximately 1 cm, and at an intersection angle of 12 degrees, a laser beam diameter of 2 mm (1 mm beam waist) is required at the intersection plane. Furthermore, an interaction length of 1 cm limits the focusing within the Rayleigh range to less than half of the desired interaction length.

[0049] This forces the y-beam waist to be 35 microns in this geometry. Therefore, the peak power required for peak a0 to reach 1 with an interaction length of 7 mm is 400 TW. For a laser operating at 1 kHz, this peak power is almost two orders of magnitude more powerful than those currently accessible with existing technology, which are around 10 TW. While such lasers exist, they typically operate at low repetition rates and require a wide range of amplifiers and a large amount of maintenance personnel for optimization.

[0050] Therefore, some embodiments of this disclosure provide an optical system that decouples the interaction length from the focusing constraint that the Rayleigh range must be longer than the interaction length, thereby solving the above problem. This maintains the long interaction length required for XFELs while focusing the beam to achieve high intensity over interaction lengths of several millimeters. This decoupling reduces the required peak laser power by more than two orders of magnitude to approximately 10 TW for similar intensity cross-sections. Such a reduction in desired power requirements makes it possible to bring the intensity and interaction length requirements to the level of relatively cost-effective commercially available laser technology. This description of the function of the focusing optical system requires several definitions. The laser propagates along the Z-axis of the laboratory frame, and the electron beam is at an angle in the XZ plane.

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[0051] The fundamental idea is that the Rayleigh range of the y-focus is limited only when the beam focuses at the same location for all X on the interaction surface. Having optical systems with different focal lengths in Y along the interaction surface significantly reduces the effective numerical aperture (NA) limit, aside from practical and technical considerations of beam damage, aberrations, and collisions with the electron beam. This allows for a reduction in the spot size in Y to tens of microns to a few microns.

[0052] In some embodiments, the optical system is a modified one-dimensional off-axis parabola with an off-axis angle of approximately 12 degrees. The focal point is tilted at an angle of 72 degrees, meaning that for every 1 mm the beam moves along the optical system in X, the focal point in Y moves 4 mm in Z. This makes the intensity in the XZ plane appear as a diagonal with an angle of 72 degrees to the Z axis. However, it should be noted that this is merely an example.

[0053] The peak intensity is slightly lower than what is achievable for the same focal length with a fixed NA, but it is still an order of magnitude more powerful than current technology with a fixed input peak power.

[0054] Figure 4 shows a microbunching scheme for free electron laser (FEL) seeding, along with exemplary parameters, according to several embodiments. A relativistic electron bunch 306 passes through a grating downstream of a linear accelerator, which accelerates the electron bunch to relativistic energies. The electron bunch passes through the grating 402, generating a diffraction pattern in a direction transverse to the propagation direction of the electron bunch 306. An emittance exchange optical system downstream of the grating 402 (e.g., in an emittance exchange section 114) rotates the diffraction pattern in a direction substantially parallel to the propagation direction of the electron bunch. The interaction point, described with reference to Figure 3, where the laser pulse 306 interacts with the e-beam in overtaking geometry, is downstream of the emittance exchange optical system. In particular, at the interaction point, the microbunching provided by the grating is parallel to the propagation direction of the e-beam.

[0055] Figure 5 shows various embodiments of an optical (e.g., laser) system (e.g., optical undulator) for generating light via inverse Compton scattering, according to several embodiments. A laser beam 304 is reflected from a grating 502 (different from grating 402 in Figure 4), which generates the gradient pulse front described with respect to Figure 4. The laser beam 306 is then reflected from 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 the squareness or rectangularness of the laser beam 306 at the interaction point and also provides a 30-degree overtake geometry.

[0056] Figures 6A and 6B show various simulation results of the simulated electric field of a 10 TW Gaussian laser beam propagating through the equipment described herein, according to several embodiments. In some embodiments, the compact XFEL undulator requires a0 > 0.3 over approximately 100 undulator periods. The simulations demonstrate that a 10 TW peak power laser, combined with the optical design described herein, satisfies these requirements. The simulations account for optical aberrations, diffraction effects from the finite Rayleigh range, and beam dispersion. In these simulations, the intensity profile of the laser beam at the interaction point is 13.2 W / mm². 2 The maximum normalized irradiance is (a0=0.55). Figure 6B shows the normalized vector potential a0 in the plane of the laser and electron beam propagation vectors. Figure 6B shows the normalized vector potential a0 along the electron beam path. For undulator periods greater than 100 of the 10TW laser, a0>0.3 is demonstrated. The dashed line is the undulator period of 100 at a0=0.3 to show that the laser design meets or exceeds these requirements.

[0057] Figure 7 is a flowchart of a method for generating light via inverse Compton scattering (ICS) according to several embodiments.

[0058] Method 700 includes accelerating an electron bunch to a relativistic energy (702) (for example, using LINAC104a in Figure 1C). In some embodiments, the electron bunch is accelerated using a linear accelerator. In some embodiments, the electron bunch is accelerated using a non-linear accelerator.

[0059] Method 700 includes generating a diffraction pattern in an electron bunch (704) (for example, using the grating 402 in Figure 4). In some embodiments, generating a diffraction pattern in an electron bunch includes microbunching the electron bunch. In some embodiments, microbunching is used to seed the light generated via the ICS.

[0060] Method 700 includes rotating the diffraction pattern in a direction substantially parallel to the direction of electron bunch propagation (706) using an emittance exchange optical system, for example, an emittance exchange section 114 in Figure 1B.

[0061] Method 700 includes generating light via inverse Compton scattering by having an electron bunch having a rotated diffraction pattern interact with a light pulse from a laser (708), the light pulse from the laser interacting with the electron bunch in an overtaking geometry at the interaction point.

[0062] In some embodiments, the optical pulse is tilted at the interaction point (for example, the contour of a certain arrival time is tilted with respect to the propagation direction of the optical pulse, as shown in Figure 3, for example). In some embodiments, the optical pulse is tilted using a second grating (for example, grating 502 in Figure 5).

[0063] In some embodiments, the angle between the propagation direction of the light pulse and the propagation direction of the electron bunch at the interaction point is 25 to 30 degrees. In some embodiments, this angle is adjusted to control the energy of the light produced by the ICS. In some embodiments, the light produced by the ICS has a wavelength in the ultraviolet or X-ray range (e.g., the soft X-ray range).

[0064] In some embodiments, the laser has a peak power of less than 100 terawatts (or less than 50 TW, less than 20 TW, or approximately 10 TW).

[0065] In some embodiments, method 700 includes shaping the electron bunch using a vertical focusing mirror located upstream of the interaction point to make the cross-sectional shape of the optical pulse more square or rectangular at the interaction point.

Claims

1. A light source, A linear accelerator for accelerating electron bunches to relativistic energies, A first grating located downstream of the linear accelerator, wherein the electron bunches are arranged to pass through the first grating and generate diffraction patterns, An emittance exchange device located downstream of the first lattice, wherein the emission exchange device rotates the diffraction pattern in a direction substantially parallel to the propagation direction of the electron bunch, A laser that generates light pulses, The light source is configured such that the light pulses from the laser interact with the electron bunch in an overtaking geometry at an interaction point downstream of the emittance exchange optical system, while the diffraction pattern is substantially parallel to the propagation direction of the electron bunch in order to generate light via inverse Compton scattering.

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

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

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

5. The light source according to claim 1, wherein the light generated by inverse Compton scattering is X-ray light or ultraviolet light.

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

7. The light source according to claim 1, further comprising a vertical focusing mirror located upstream of the interaction point and configured to strongly focus the transverse shape of the light pulse in the out-of-plane direction.

8. The light source according to claim 1, further comprising the beam shape irradiating the grid being a substantially square pattern.

9. It is a method, Accelerating electron bunches to relativistic energies, To generate a diffraction pattern in the aforementioned electron bunch, Rotating the diffraction pattern in a direction substantially parallel to the propagation direction of the electron bunch, A method comprising generating light via inverse Compton scattering by interacting the electron bunch having the rotated diffraction pattern with a light pulse from a laser, wherein the light pulse from the laser interacts with the electron bunch at the interaction point in an overtaking geometry.

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

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

12. The light source according to claim 1, wherein the light generated by inverse Compton scattering is X-ray light or ultraviolet light.

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

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

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