Undulator system and method of operation

Abstract

An undulator system, preferably including one or more undulators and one or more transverse quadrupole arrays, and optionally including one or more ancillary elements. The undulator system is preferably integrated into a radiator system and / or a light source system. The radiator system can include one or more undulator systems, beam separators, and / or optical elements. The light source system can include one or more accelerator modules and / or radiator systems.

Description

UNDULATOR SYSTEM AND METHOD OF OPERATIONCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application serial number 63 / 622,520, filed on 18-JAN-2024, and of U.S. Provisional Application serial number 63 / 645,569, filed on 10-MAY-2024, each of which is incorporated in its entirety by this reference.TECHNICAL FIELD

[0002] This invention relates generally to the light source field, and more specifically to a new and useful undulator system and method of operation.BRIEF DESCRIPTION OF THE FIGURES

[0003] FIGURE 1A is a schematic representation of an embodiment of an undulator system.

[0004] FIGURE 1B is a schematic representation of an example of the undulator system.

[0005] FIGURE 1C is a schematic representation of an example of electron beams propagating through the undulator system.

[0006] FIGURE 2A is a schematic representation of an embodiment of a light source system.

[0007] FIGURE 2B is a schematic representation of an example of the light source system.

[0008] FIGURES 3A-3B are schematic representations of a plan view and an elevation view, respectively, of electron beams propagating through an example of the undulator system.

[0009] FIGURES 4A-4C are schematic representations of various examples of a transverse quadrupole array of the undulator system.

[0010] FIGURES 5-6 are schematic representations of a first and second example, respectively, of a Halbach array-based transverse quadrupole array of the undulator system.

[0011] FIGURE 7A is a schematic representation of an example of a windings- based transverse quadrupole array of the undulator system.

[0012] FIGURE 7B is a schematic representation of an example of a portion of a windings-based undulator system.

[0013] FIGURES 8A-8H are schematic representations of a plan view of electron beams propagating through various examples of the undulator system.

[0014] FIGURE 9 is a schematic representation of an example of a portion of the undulator system.

[0015] FIGURE 10A is a schematic representation of an embodiment of a method of operation.

[0016] FIGURES 10B-10C are schematic representations of a first and second example, respectively, of the method of operation.DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] The following description of the preferred embodiments of the invention is not intended to limit the invention to these preferred embodiments, but rather to enable any person skilled in the art to make and use this invention.1. Overview.

[0018] An undulator system 120 preferably functions to provide a plurality of light outputs (e.g., via free-electron lasing), such as extreme UV (EUV) and / or X-ray outputs. The undulator system 120 preferably includes one or more undulators 121 and one or more transverse quadrupole arrays (TQAs) 125 (e.g., wherein the TQAs are arranged into one or more focusing units), and can optionally include one or more ancillary elements 129 (e.g., as shown in FIGURES 1A-1C). However, the undulator system can additionally or alternatively include any other suitable elements in any suitable arrangement.

[0019] The undulator system 120 is preferably integrated into a radiator system 102 and / or a light source system 100.

[0020] The radiator system 102 can include one or more undulator systems 120 (e.g., arranged in parallel, preferably such that each undulator system of the plurality is traversed by a different set of electron beams). The radiator system can optionallyinclude one or more beam separators, optical elements, and / or any other suitable elements (e.g., as shown in FIGURES 2A-2B). However, the radiator system can additionally or alternatively include any other suitable elements in any suitable arrangement. The radiator system preferably functions to receive an electron beam (e.g., from an accelerator module) and use it to generate one or more light outputs.

[0021] The light source system 100 can include an accelerator module 101 and / or a radiator system 102 (e.g., as shown in FIGURES 2A-2B), or alternatively can include multiple accelerator modules and / or radiator systems. In some embodiments, the light source system 100 can include one or more elements such as described in U.S. Patent Application 18 / 374,911, filed 29-SEP-2023 and titled “POLARIZATION- MULTIPLEXED RADIATOR SYSTEM, LIGHT SOURCE SYSTEM, AND METHOD OF OPERATION”, and / or in U.S. Patent Application 18 / 794,414, filed 05-AUG-2024 and titled “LIGHT SOURCE SYSTEM AND METHOD OF OPERATION”, each of which is herein incorporated in its entirety by this reference. For example, the light source system 100 can include an accelerator module 101 that functions to provide a plurality of beams 201 of high-energy (e.g., relativistic) electrons (e.g., to the radiator system 102), such as wherein the accelerator module includes one or more elements such as described in U.S. Patent Application 18 / 374,911 and / or in U.S. Patent Application 18 / 794,414 (e.g., wherein the accelerator module is identical to that described in U.S. Patent Application 18 / 374,911 and / or in U.S. Patent Application 18 / 794,414, wherein the accelerator module includes a combination of elements from both U.S. Patent Application 18 / 374,911 and in U.S. Patent Application 18 / 794,414, wherein the accelerator module includes one or more electron splitters such as described in U.S. Patent Application 18 / 374,911 and / or in U.S. Patent Application 18 / 794,414, etc.). However, the light source system 100 can additionally or alternatively include any other suitable elements in any suitable arrangement.

[0022] The light source system preferably defines a free-electron laser (FEL) that generates one or more optical outputs (e.g., EUV light output); however, the light source system can additionally or alternatively be configured in any other suitable manner. The light source system 100 and / or radiator system 102 is preferably configured to perform the method of operation described below; however, the lightsource system 100 and / or radiator system 102 can additionally or alternatively have any other suitable functionality and / or be configured in any other suitable manner.

[0023] A method of operation preferably includes operating a system to generate a light output (e.g., a plurality of output beams), such as shown in FIGURE 10A. For example (e.g., as shown in FIGURE 10B), the method can include receiving one or more high-energy electron beams (e.g., spatially-separated electron beams, such as electron beams directed substantially parallel and / or arranged substantially coplanar to each other) such that the electron beams propagate through the undulator system and, as the electron beams propagate through the undulator system, focusing the electron beams (or any suitable subset thereof) at the TQAs (and / or at any other suitable elements of the system, such as in cooperation with one or more ancillary elements). The method is preferably performed using the undulator system 120, radiator system 102, and / or light source system 100 described herein, but can additionally or alternatively be performed using any other suitable system(s).

[0024] The light source system, radiator system, undulator system, and / or method of operation preferably function to provide a plurality of light outputs (e.g., wherein a plurality of these light outputs have spatial and / or temporal characteristics suitable and / or desirable for lithography applications, such as EUV lithography applications), such as a plurality of beams of light. Each light output preferably has high photon energy, such as being EUV light (e.g., 13.5 nm, 6.7 nm, etc.), X-ray light, and / or any other suitable high-energy light, but can additionally or alternatively have any other suitable photon energy. In examples, the light output can be X-ray light (e.g., 5 nm, 1 nm, 0.1 nm, 0.01-0.1 nm, 0.1-0.2 nm, o.2-0.5 nm, 0.5-1 nm, 1-2 nm, 2-5 nm, etc.), UV light, preferably EUV light (e.g., 13.5 nm, 6.7 nm, 5-8 nm, 8-15 nm, 15- 30 nm, 30-121 nm, etc.) but additionally or alternatively any other suitable UV light (e.g., 100-280 nm, 280-315 nm, 315-400 nm, etc.), and / or any other suitable high- energy light, but can additionally or alternatively have any other suitable photon energy (e.g., visible light such as light having a wavelength in the 400-750 nm range, infrared light such as light having a wavelength in the 0.75-15 pm range and / or the 15-1000 pm range, millimeter-wave radiation such as light having a wavelength in the 1-10 mm range, etc.). The light output is preferably substantially monochromatic (e.g., having a bandwidth less than 1, 0.5, 0.3, 0.2, 0.1 nm, or less, less than 10%, 5%, 2%,1%, or less of the nominal or central wavelength, etc.), but can alternatively have any other suitable bandwidth. The light output is preferably polarized or substantially polarized (e.g., to facilitate use with semiconductor fabrication equipment, such as photolithography equipment which may include steppers, scanners, and / or any other suitable equipment), but can alternatively be unpolarized, partially polarized, or have any other suitable polarization; in some embodiments, some or all light beams can have different polarizations as compared with each other. The light output is preferably coherent or substantially coherent, but can alternatively be incoherent or have any other suitable coherency. However, the light output by the system 100 can additionally or alternatively have any other suitable characteristics. In some embodiments, the light source system can define a free-electron laser (FEL) or a plurality of FELs (e.g., wherein each FEL of the output is configured to output a separate beam of light). The light source system may additionally or alternatively produce incidental electromagnetic radiation (e.g., in the THz range), such as in the course of conditioning one or more electron beams to drive the FEL(s). As used herein, the use of the term “light output” is typically not intended to indicate such incidental radiation; however, this incidental radiation can additionally or alternatively be used in any suitable manner, and in some embodiments, the system and / or method can optionally be configured to promote, increase, tune, and / or otherwise control this incidental radiation.

[0025] In some embodiments, the light source system 100, accelerator module 101, radiator system 102, undulator system 120, and / or method of operation (and / or any suitable elements thereof) can include one or more elements (and / or any suitable aspects thereof) such as described in U.S. Patent Application 14 / 803,068, filed 18- JUL-2015 and titled “METHOD, APPARATUS AND SYSTEM FOR PROVIDING MULTIPLE EUV BEAMS FOR SEMICONDUCTOR PROCESSING”, U.S. Patent 9,541,839, granted 10-JAN-2017 and titled “METHOD AND DEVICE FOR SPLITTING A HIGH-POWER LIGHT BEAM TO PROVIDE SIMULTANEOUS SUBBEAMS TO PHOTOLITHOGRAPHY SCANNERS”, U.S. Patent 9,392,679, granted 12- JUL-2016 and titled “METHOD, APPARATUS AND SYSTEM FOR USING FREE- ELECTRON LASER COMPATIBLE EUV BEAM FOR SEMICONDUCTOR WAFER PROCESSING”, and / or U.S. Patent 9,844,124, granted 12-DEC-2017 and titled“METHOD, APPARATUS AND SYSTEM FOR USING FREE-ELECTRON LASER COMPATIBLE EUV BEAM FOR SEMICONDUCTOR WAFER METROLOGY”, each of which is herein incorporated in its entirety by this reference.

[0026] In some embodiments, the light source system 100, accelerator module 101, radiator system 102, undulator system 120, and / or method of operation (and / or any suitable elements thereof) can include one or more elements (and / or any suitable aspects thereof) such as described in U.S. Patent Application 18 / 374,911, filed 29-SEP- 2023 and titled “POLARIZATION-MULTIPLEXED RADIATOR SYSTEM, LIGHT SOURCE SYSTEM, AND METHOD OF OPERATION”, and / or in U.S. Patent Application 18 / 794414, filed 05-AUG-2024 and titled “LIGHT SOURCE SYSTEM AND METHOD OF OPERATION”, each of which is herein incorporated in its entirety by this reference. For example, the radiator system 102 can include one or more elements such as described in U.S. Patent Application 18 / 374,911 (e.g., can include the entire ‘radiator module 102’ described therein, can include any suitable elements of the ‘radiator module 102’ described therein, etc.) and / or in U.S. Patent Application 18 / 794,414 (e.g., can include the entire ‘radiator module 140’ described therein, can include any suitable elements of the ‘radiator module 140’ described therein, etc.), the accelerator module 101 can include one or more elements such as described in U.S. Patent Application 18 / 374,911 and / or in U.S. Patent Application 18 / 794,414 (e.g., can include the entire ‘accelerator module 101’ described therein, can include any suitable elements of the ‘accelerator module 101’ described therein, etc.), and / or the undulator system 120 can include one or more elements such as described in U.S. Patent Application 18 / 374,911 (e.g., can include the entire ‘undulator network 120’ described therein, can include any suitable elements of the ‘undulator network 120’ described therein, etc.) and / or in U.S. Patent Application 18 / 794,414 (e.g., can include the entire ‘undulator system 120’ described therein, can include any suitable elements of the ‘undulator system 120’ described therein, etc.). However, the redundant light source system 100 can additionally or alternatively include any other suitable elements in any suitable arrangement and / or having any other suitable functionality.

[0027] A person of skill in the art will recognize that, as used herein, the terms ‘radiator system’, ‘radiator module’, and the like can be interpreted to refer to items (e.g., systems, modules, etc.) including any suitable undulator(s) used for free-electronlasing (e.g., undulator configured to receive high-energy electrons, generate microbunching in the electrons, and generate coherent radiation via free-electron lasing from the micro-bunched electrons; undulator configured to receive microbunched electrons, such as from a buncher undulator and / or any other suitable element(s), and generate coherent radiation via free-electron lasing from the microbunched electrons; etc.) and / or any other suitable structure(s), and is not necessarily limited to any particular kind of undulator; although the term ‘radiator’ may be used in certain communities to refer specifically to an undulator configured to receive micro-bunched electrons and generate coherent radiation via free-electron lasing from the micro-bunched electrons, the terms ‘radiator’, ‘radiator undulator’, ‘radiator system’, ‘radiator module’, and the like, as used herein, should not be interpreted to carry any such specific limitation, but instead may refer to any of a broad variety of items including one or more undulators that emit (and / or are configured to emit) light (e.g., undulator configured to receive high-energy electrons, generate microbunching in the electrons, and generate coherent radiation via free-electron lasing from the micro-bunched electrons; undulator configured to receive micro-bunched electrons, such as from a buncher undulator and / or any other suitable element(s), and generate coherent radiation via free-electron lasing from the micro-bunched electrons; etc.).2. Undulator system.

[0028] The undulator system 120 preferably includes one or more undulators 121 through which a plurality of electron beams 201 pass (e.g., wherein the plurality of electron beams are generated such as described in U.S. Patent Application 18 / 794,414, filed 05-AUG-2024 and titled “LIGHT SOURCE SYSTEM AND METHOD OF OPERATION”, which is herein incorporated in its entirety by this reference). The electron beams 201 are preferably arranged substantially coplanar one another and are preferably arranged with substantially equal spacing, more preferably wherein the electron beams propagate along substantially parallel coplanar paths of substantially equal spacing (e.g., as shown in FIGURES 1C and / or 3A-3B). However, some or all of the electron beams can alternatively propagate along substantially parallel coplanar paths of non-equal spacing (e.g., wherein the spacing between adjacent paths may differ from beam to beam), along non-parallel coplanar paths (e.g., divergent paths;convergent paths; paths having any other suitable relationship to each other, such as a first set of paths that are divergent with respect to the other paths of the first set and a second set of paths that are convergent with respect to the other paths of the second set; etc.), along substantially parallel non-coplanar paths (e.g., wherein an intersection of the paths with a plane normal to the paths defines a two-dimensional array, preferably with substantially equal spacing between the paths but additionally or alternatively with irregular spacing, such as a square, rectangular, or hexagonal array; etc.), along non-parallel non-coplanar paths (e.g., divergent paths; convergent paths; paths having any other suitable relationship to each other, such as a first set of paths that are divergent with respect to the other paths of the first set and a second set of paths that are convergent with respect to the other paths of the second set; etc.), and / or along paths having any other suitable relationship to each other.

[0029] Preferably, each electron beam 201 passes through each undulator 121 of the system 120. Accordingly, the undulators 121 maybe wider (along an axis transverse to the beam propagation direction) than may be typical for a free-electron laser undulator. For example, one or more of the undulators 121 (e.g., each undulator of the set) can have an active field width greater than a centimeter, such as between 1-20 cm (e.g., 2, 4, 6, 8, 10, 12, 14, 16, 18, or 20 cm, within any suitable open or closed interval bounded by one or more of the aforementioned values, etc.) or greater than 20 cm, but can alternatively be less than 1 cm and / or have any other suitable width.

[0030] Each undulator preferably defines a respective long axis running from an input side of the undulator to an output side of the undulator, wherein the electron beams preferably traverse the undulator from the input side to the output side (e.g., wherein the long axis defines a nominal beam propagation direction). Within the undulator, the direction of the magnetic field imposed by the undulator preferably alternates along the beam propagation direction (more preferably alternating in a periodic or substantially periodic manner along the beam propagation direction, thereby defining an undulator wavelength Aw, but alternatively alternating in an aperiodic manner). The magnetic field imposed by the undulator preferably defines a periodic (or substantially periodic) variation along (or substantially along) the long axis; however, the undulator can alternatively impose any other suitable magnetic fields. In one example, the undulator includes an array (e.g., regular or substantiallyregular array) of dipole magnets of alternating orientations (e.g., and of equal or substantially equal strength). However, the undulators can additionally or alternatively include any other suitable elements in any suitable arrangement.

[0031] In embodiments including more than one undulator, the undulators can be arranged contiguously (or substantially contiguously) or separate from each other (e.g., with TQAs 125 and / or ancillary elements 129 arranged between some of the undulators, such as shown by way of examples in FIGURES 1A-1B).

[0032] However, the system can additionally or alternatively include any other suitable undulators in any suitable arrangement.

[0033] The transverse quadrupole arrays (TQAs) 125 preferably function to impose a separate quadrupole magnetic field for each electron beam 201 traversing the undulator system (e.g., wherein each such quadrupole field is centered or substantially centered on the corresponding electron beam).

[0034] In a first embodiment, a TQA imposes substantially the same quadrupole field pattern for each electron beam (e.g., wherein the TQA field is periodic or substantially periodic, with the full period of the field equal to the spacing between electron beams, such as shown by way of example in FIGURE 4B).

[0035] In a second embodiment, the TQA imposes different field patterns for different electron beams (e.g., which can function to enable and / or assist with dispersion suppression, enable use of a TQA with larger-sized features as compared with the first embodiment, enable use of a tighter spacing between electron beams as compared with the first embodiment, etc.). For example, the quadrupole field polarity can vary between different beams, such as alternating between neighboring beams (e.g., the TQA field is periodic or substantially periodic, with the half period of the field equal to the spacing between electron beams, such as shown by way of examples in FIGURES 4A, 4C, and / or 5).

[0036] In a first embodiment, the magnetic elements of a TQA are similar (or substantially identical) to those of an undulator, but are oriented transverse to (as opposed to along) the beam propagation direction. In one example, an undulator structure may include an array of magnetic dipole elements with alternating orientations (e.g., north pole oriented upward, followed by south pole oriented upward, followed by north pole oriented upward, and so on), such as shown by way ofexample in FIGURE 4A. In this example, the space between two such dipoles can define a quadrupole field (e.g., as shown in FIGURES 4B-4C, in which magnetic field lines are depicted by purple arrows). In a first such example, an electron beam can pass through each such quadrupole region (wherein the quadrupole regions the beams pass through will exhibit alternating polarities, such as shown by way of examples in FIGURES 4A, 4C, and / or 5). In a second such example, the electron beams can pass through only every other such quadrupole region (wherein the electron beams will experience substantially identical quadrupole fields to each other, such as shown by way of example in FIGURE 4B).

[0037] In one example of this embodiment, the TQA can include one or more magnetic arrays, such as Halbach arrays. For example, the TQA can include two parallel magnetic arrays (e.g., Halbach arrays), with a gap in between them in which the quadrupole regions exist (e.g., as shown in FIGURE 5, in which magnetic field vectors are depicted by colored arrows). However, the TQA can additionally or alternatively include any other suitable arrangement of magnetic elements, including permanent magnets and / or electromagnets. The magnetic elements of any suitable undulator structure can typically be arranged transverse to the beam propagation direction in an analogous manner to create a TQA.

[0038] In some examples of this embodiment, the TQA includes one or more elements operable to tune the magnetic field strength of the TQA (and / or of any suitable subset thereof), such as to tune overall field strength (e.g., quadrupole field strength), to add and / or tune non-quadrupole magnetic field terms (e.g., dipole field terms, sextupole field terms, octupole field terms, etc.), to enable beam-based alignment techniques, and / or for any other suitable function(s). For example, the TQA can include one or more shorting plates (e.g., ferromagnetic shorting plates, such as iron shorting plates), preferably wherein such shorting plates are arranged on the exterior of the TQA (e.g., adjacent the weak side of each Halbach array), such as shown by way of example in FIGURE 6 (in which magnetic field vectors are depicted by colored arrows).

[0039] In a first such example, magnetic field strength can be tuned by changing the distance between a shorting plate and the exterior of one or more magnetic arrays (e.g., wherein the TQA includes two parallel magnetic arrays, an interior of eachmagnetic array faces toward the other magnetic array, and an exterior of each magnetic array opposes the interior across the magnetic array), wherein moving the shorting plate closer to the magnetic array will typically reduce the magnetic field strength within the TQA region. In a first specific example, in which the TQA includes one or more Halbach arrays (e.g., two parallel Halbach arrays), magnetic field strength can be tuned by changing the distance between a shorting plate and the weak side of the Halbach array (e.g., wherein such shorting plates are arranged near the weak side of each Halbach array or near any suitable subset of the Halbach arrays of the TQA), wherein moving the shorting plate closer to the Halbach array will typically reduce the magnetic field strength within the TQA region. In a second specific example, the magnetic arrays are not Halbach arrays, but rather arrays that result in greater magnetic field leakage to the exterior side than a Halbach array would; this increased field leakage can enable a greater amount of tuning via movement of the shorting plate(s), as the shorting plates are able to interact with the magnetic field to a greater degree.

[0040] Additionally or alternatively, in a second example, the shorting plate (e.g., soft iron plate) can include one or more conductive windings operable to pole and / or depole the shorting plate (e.g., wherein poling the shorting plate can function to reduce the magnetic field strength within the TQA region, and depoling the shorting plate can function to increase the magnetic field strength within the TQA region).

[0041] Additionally or alternatively, in a third example, the shorting plate can be operable to be heated, such as heated to and / or just below the Curie point of the shorting plate material (e.g., wherein the heated shorting plate will lose or reduce its ferromagnetic properties, thereby reducing the effect it has on the TQA, resulting in an increased magnetic field strength within the TQA region).

[0042] However, the TQA can additionally or alternatively be operable to tune the magnetic field strength within the TQA region in any other suitable manner.

[0043] In a second embodiment, the TQA includes one or more electromagnetic structures. For example, a typical superconducting undulator will include a pair of superconducting (e.g., high-temperature superconducting, room-temperature superconducting, low-temperature superconducting, etc.) windings (e.g., around a vacuum vessel through which one or more electron beams propagate), preferablydefining a double winding, typically on a tight (but non-zero) pitch, wherein currents through the two windings are preferably equal (or substantially equal) and opposite each other (e.g., such that magnetic fields within the vacuum vessel alternate). In this embodiment, a TQA can be constructed by adding an overlapping pair of windings (e.g., defining a second double winding) pitched in the opposite direction to the first pitch (e.g., having an equal but opposite pitch to the first pair of windings, such as shown by way of example in FIGURE 7A, in which the arrows represent current flow through windings such as superconducting windings and the circles represent intersections between two such windings, wherein: winding intersections that result in substantially cancelling magnetic fields are depicted with an open circle, winding intersections that result in a quadrupole field of a first polarity are depicted with a dot within a circle, and winding intersections that result in a quadrupole field of a second polarity opposite the first polarity are depicted with a cross within a circle). For example, an undulator system can include an arrangement of one or more undulators and TQAs, preferably wherein TQA regions and undulator regions are defined by the presence or absence of this second pair of windings with opposing pitch (e.g., as shown in FIGURE 7B).

[0044] In some examples of this embodiment, magnetic field strengths can be adjusted (e.g., by adjusting the current flow within any or all windings), such as to tune overall field strength (e.g., quadrupole field strength, undulator field strength, etc.), to add and / or tune non-quadrupole magnetic field terms (e.g., dipole field terms, sextupole field terms, octupole field terms, etc.), to enable beam-based alignment techniques, and / or for any other suitable function(s).

[0045] Additionally or alternatively, in some examples of this embodiment, the system can include one or more undulators and / or TQAs (e.g., adjacent undulators and / or TQAs) defined by superconducting windings (e.g., wherein a single winding can be part of multiple undulators and / or TQAs, such as shown by way of example in FIGURE 7B; wherein the windings of each undulator and / or TQA are separate from those of all other undulators and / or TQAs; etc.). In some such examples, all such windings (or any suitable subset thereof) are arranged nearby and / or adjacent to one another (e.g., wherein all such undulators and / or TQAs, or any suitable subset thereof, may be cooled together, such as all being located within a shared cryogeniccontainment vessel, preferably cooled by one or more cryogenic fluids such as liquid nitrogen, but additionally or alternatively cooled by heat pump-based refrigeration, evaporative refrigeration, and / or by any other suitable cooling technologies). For example, some or all such windings (e.g., windings that generate magnetic fields used for one or more undulators and / or one or more TQAs) can be arranged within a shared cryogenic vessel. However, the undulators and / or TQAs can additionally or alternatively be arranged in any other suitable manner, cooled individually and / or in any other suitable groups, and / or be otherwise configured.

[0046] However, the TQAs can additionally or alternatively include any other suitable elements in any suitable arrangement.

[0047] In some embodiments, a set of one or more TQAs can be arranged together to define a focusing unit 126. The focusing unit preferably functions to focus the electron beams traversing the undulator system. Each focusing unit preferably includes a plurality of TQAs 125 (but can alternatively include only a single TQA), and can optionally include one or more other elements (e.g., magnetic elements of other orders, such as dipoles, sextupoles, octupoles, etc.; undulators; etc.).

[0048] In a first embodiment, each electron beam experiences substantially the same field passing through each TQA. In this embodiment, there is typically wide latitude in the design of a focusing unit. Focusing unit design can be analogous to the design of focusing magnets (e.g., sets of quadrupole magnets) configured for use in a system having only a single electron beam propagating through an undulator (or set of undulators arranged in series, such as with one or more focusing elements and / or other elements arranged in between some or all undulators of the set). In a first example, the focusing unit defines a quadrupole doublet (e.g., antisymmetric doublet), including a sequence of two TQAs having opposite polarity from each other (e.g., wherein any given electron beam traversing the doublet will experience first one quadrupole field, then a second quadrupole field of the opposite polarity). In a second embodiment, the focusing unit defines a quadrupole triplet (e.g., symmetric triplet). In a first specific example, the quadrupole triplet includes a sequence of three TQAs, wherein the middle TQA has the opposite polarity (e.g., and twice the depth) of the outer TQAs. In a second specific example (e.g., in which all TQAs of the focusing unit have substantially the same dimensions and field strengths), the quadrupole tripletcan include a sequence of four TQAs, wherein the middle two TQAs have opposing polarity to the outer TQAs. In a third example, the focusing unit includes a single TQA. In a first specific example, the focusing unit TQA can be configured to act in cooperation with the focusing effects of the undulators, such as wherein the undulators provide focusing along a first transverse axis (and defocusing along a second orthogonal transverse axis), and the TQA provides focusing along the second transverse axis (and defocusing along the first transverse axis). Additionally or alternatively, the system can include a plurality of focusing units each including only a single TQA, wherein the plurality of focusing units are configured to act cooperatively to achieve the desired beam focus (e.g., wherein each focusing unit is arranged between a different gap between two undulators of the system, and the polarities of these TQAs alternate from one undulator gap to the next). However, the focusing units of this embodiment can additionally or alternatively include any other suitable arrangement of TQAs (e.g., analogous to designing an arrangement of quadrupole elements for a single electron beam passing through the undulator system).

[0049] In a second embodiment, alternate electron beams experience opposite quadrupole field polarities as they pass through the TQA (e.g., wherein the beam spacing is equal to half the period of the TQA).

[0050] In a first variant of this embodiment, the upstream beam transport (e.g., of the undulator system, radiator system, and / or light source system) can ensure that the electron beams arrive at the focusing unit with alternate (or substantially alternate) focus (e.g., wherein a first subset of the electron beams are focused along a first transverse axis and defocused along a second orthogonal transverse axis, whereas the remaining electron beams are focused along the second transverse axis and defocused along the first transverse axis; more preferably wherein the beams of the first subset each define a first aspect ratio and the beams of the second subset define the inverse aspect ratio, such as wherein all such beams are substantially congruent). For example, the system can include additional magnetic elements (e.g., upstream of the undulator(s), upstream of the focusing unit, upstream of all focusing units of the system, upstream of all focusing units through which the split beams traverse, etc.) configured to compensate for these different polarities; these additional magnetic elements can define a matching unit.

[0051] In a first example of this first variant, the beams are received at the matching unit having substantially identical focus conditions, wherein each beam is typically elongated (e.g., defocused) along a first transverse axis and narrowed (e.g., focused) along a second transverse axis normal to the first transverse axis. In this example, the additional magnetic elements compensate for the different polarities by altering the beam state of alternate beams (e.g., for 5 beams that will traverse the TQA, either altering the first, third, and fifth beams, or altering the second and fourth beams; optionally also altering the remaining beams in a different manner, such as altering the first, third, and fifth beams in a first manner, and altering the second and fourth beams in a second manner different from the first, wherein the magnetic fields imposed to achieve the first manner typically differ in more than just polarity, such as differing in magnitude and / or orientation, from those imposed to achieve the second manner); in a specific example, the system can include an independent quadrupole telescope for each beam to be altered in such a manner (e.g., including one or more additional TQAs, wherein each aperture of these TQAs can be used as part or all of one such quadrupole telescope).

[0052] In a second example of this first variant, the beams are received at the matching unit having substantially identical, substantially round (e.g., substantially unity aspect ratio, substantially equal envelopes and divergences in all transverse planes, etc.) focus conditions. For example, the beams can be configured to reach these additional magnetic elements in this substantially round / identical condition using one or more matching telescopes (e.g., quadrupole telescope(s)). In a specific example, in which the plurality of electron beams originate from a single beam (e.g., wherein the single electron beam is divided into a plurality of beams at an electron splitter upstream of the undulator(s), such as described by way of example in U.S. Patent Application 18 / 794414, filed 05-AUG-2024 and titled “LIGHT SOURCE SYSTEM AND METHOD OF OPERATION”, which is herein incorporated in its entirety by this reference), a single matching telescope (e.g., quadrupole telescope), arranged upstream of the electron splitter, may be used to achieve the desired (substantially round / identical) focus condition at the matching unit. In this example, the matching unit preferably includes four (or more) TQAs (but can additionally or alternatively include other quadrupole elements and / or ancillary elements), and preferablyfunctions to refocus the electron beams from the substantially identical, substantially circular condition (in which they are received at the matching unit) to an alternating condition (in which they are provided by the matching unit, such as to a downstream arrangement of undulators and focusing units) in which the first subset of beams are elongated in a first transverse direction and the second subset of beams are elongated along a second transverse direction orthogonal to the first (e.g., as shown in FIGURE 9, which depicts the beta function, also known as the Twiss beta function or beam envelope function, along two orthogonal transverse directions as a function of the location along the nominal beam trajectory, with beta for beams traversing even apertures of the TQAs depicted above, and beta for beams traversing odd apertures of the TQAs depicted below). Note that, for identical circular input beams, the matching unit can be tuned with consideration for any one beam, and the resulting outputs will be correct for all beams traversing the matching unit (regardless of whether they traverse the even apertures or the odd apertures of the TQAs). In a first specific example, the field amplitude of each TQA of the matching unit can be adjusted independently; in this specific example, the TQA field amplitudes can be tuned to achieve the desired output condition for the matching unit. In a second specific example (e.g., in which the field amplitudes of the TQAs are fixed or substantially fixed), the positions of the TQAs of the matching unit (relative to each other) can be determined in order to achieve the desired output condition for the matching unit. However, the matching unit can alternatively be configured in any other suitable manner.

[0053] In this first variant, the focusing unit can typically have any suitable structure, such as described above regarding the first embodiment of the focusing unit (e.g., as opposing focusing effects will be appropriate for alternating electron beams due to their entry into the focusing unit having opposing focus conditions). For example, focusing units can each include a single TQA, wherein the system includes a series (e.g., alternating) of undulators and TQAs (e.g., arranged downstream of the matching unit, such as shown by way of example in FIGURE 9). In specific examples, this series can begin with an undulator or a TQA (e.g., as the farthest-upstream element of an alternating sequence of TQAs and undulators), and / or can end with an undulator or a TQA (e.g., as the farthest-downstream element of an alternatingsequence of TQAs and undulators); however, this series can optionally omit one or more such elements from the otherwise-alternating sequence (e.g., including two or more TQAs with no undulators in between them, including two or more undulators with no TQAs in between them, etc.), can additionally or alternatively include one or more ancillary elements, and / or can include any other suitable elements in any suitable arrangement.

[0054] In a second variant of this embodiment, the upstream beam transport (e.g., of the undulator system, radiator system, and / or light source system) preferably delivers all electron beams to the focusing unit with a substantially round profile (e.g., having equal or substantially equal focus along all transverse directions, such as having equal or substantially equal envelopes and divergences in both transverse planes). In this example, the focusing unit is preferably a symmetric focusing unit (e.g., a quadrupole triplet, such as described above regarding the second example of the first embodiment); however, the focusing unit can alternatively be an antisymmetric focusing unit (e.g., a quadrupole pair, such as defined by a sequence of two TQAs of opposite polarity; a sequence of four or more TQAs and / or other quadrupoles defining an antisymmetric arrangement of polarities; etc.), an asymmetric focusing unit, or any other suitable focusing unit. A person of skill in the art will note that this quadrupole triplet will typically require more space than the quadrupole singlets enabled by the first variant.

[0055] Further, in some embodiments, such as embodiments in which the plurality of electron beams, or any suitable subset thereof, are to be recombined (e.g., as described in U.S. Patent Application 18 / 794,414, filed 05-AUG-2024 and titled “LIGHT SOURCE SYSTEM AND METHOD OF OPERATION”, which is herein incorporated in its entirety by this reference, such as described therein with respect to the ‘recombiner 160’), the system can optionally include an analogous downstream matching unit downstream of the undulators (e.g., at or downstream of a bend that spatially separates the electron beams from the generated light beams). This downstream matching unit can function to refocus the electron beams from the condition in which they are output into a desired output condition (e.g., substantially identical to the focus condition in which they are received at the upstream matching unit). For example, the desired output condition can be substantially identical,substantially circular focus, can be alternating focus conditions with inverse aspect ratios, or can be any other suitable focus condition. The downstream matching unit preferably mirrors (or substantially mirrors) the upstream matching unit (e.g., having the same, or substantially the same, elements in substantially the reverse arrangement), but can alternatively have any other suitable elements in any suitable arrangement. However, the focusing unit 126 can additionally or alternatively include any other suitable elements in any suitable arrangement (e.g., including a plurality of TQAs and / or other elements configured to define a focusing / defocusing (FODO) array).

[0056] The undulator system preferably includes one or more focusing units 126 arranged between undulators of the system (e.g., as shown by way of examples in FIGURES 1A, 1B, and / or 3A); note that, to keep the optical fields of light generated in the undulators in phase with each other, the spacing between undulators is preferably equal (or substantially equal) to an integer multiple of Aw(l + k"2), where Awis the undulator wavelength and K is the undulator strength parameter. Additionally or alternatively, the undulator system can include one or more focusing units arranged before and / or after the undulators, and / or in any other suitable locations. The focusing units are preferably configured to provide appropriate focusing along the transverse axes of the electron beams, but can additionally or alternatively have any other suitable functionality.

[0057] In some embodiments, one or more TQAs and / or focusing units can include and / or impose non-quadrupole terms (e.g., dipole terms, sextupole terms, octupole terms, etc.). For example, such non-quadrupole terms can arise from unequal tuning of the strength of different magnetic elements of the TQA, and / or from directing electron beams through the TQA away from the center of the apertures (e.g., “misaligning” the electron beams). These terms can be substantially uniform between the different apertures of the TQA(s) and / or applied substantially uniformly to the different beams traversing the TQA(s), and / or can substantially differ between apertures and / or beams. A person of skill in the art will note that, in embodiments in which electron beams traverse adjacent TQA apertures (or any TQA apertures with opposite polarities), substantially uniform non-quadrupole terms (e.g., dipole terms) will typically not be achieved by a uniform non-central alignment of all electron beams;rather, to achieve substantially uniform dipole terms via non-central alignment of electron beams, the electron beams traversing TQA apertures of a first polarity should typically be aligned off-center along a first direction, and the electron beams traversing TQA apertures of a second polarity (opposite the first polarity) should typically be aligned off-center along a second direction (e.g., opposite the first direction), such as wherein all such alignments are a substantially equal distance from the center of their respective apertures. In contrast, in embodiments in which electron beams traverse only alternate TQA apertures (or traverse only TQA apertures with identical polarities), substantially uniform non-quadrupole terms (e.g., dipole terms) typically can be achieved by a uniform non-central alignment of all electron beams.

[0058] In one such embodiment, one or more TQAs and / or focusing units can include dipole terms configured to steer the electron beams, such as steering the electron beams into an undulator (e.g., as shown in FIGURES 8A-8C, 8E, and / or 8F) and / or steering the beams away from light beams at the exit of an undulator (e.g., as shown in FIGURES 8C-8G). In a first example of this embodiment, the dipole term is applied uniformly (or substantially uniformly) to all electron beams traversing the TQA and / or focusing unit (e.g., as shown in FIGURES 8A and / or 8E, wherein parallel beams are redirected onto new parallel trajectories). In a second example of this embodiment, the dipole term is applied substantially non-uniformly to the different electron beams traversing the TQA and / or focusing unit, such as wherein incoming beams are collimated, such as for incoming convergent beams (e.g., as shown in FIGURE 8B), divergent beams (e.g., as shown in FIGURE 8C), or beams having any other suitable relationships between their trajectories; exiting parallel beams are put onto divergent trajectories (e.g., as shown in FIGURE 8D), convergent trajectories (e.g., as shown in FIGURE 8F), and / or any other suitable trajectories; and / or wherein any other suitable change in trajectory is imposed on any or all of the beams.

[0059] The undulator system can optionally include one or more ancillary elements 129. The ancillary elements are preferably arranged along the beam path(s) (e.g., electron beam paths 201 and / or light beam paths 301). The ancillary elements can be arranged next to (e.g., between, upstream of, downstream of, etc.) the undulators 121 and / or can have any other suitable arrangement (e.g., within the undulator region 120). In some examples, the ancillary elements include one or moredipole magnets (and / or magnets including dipole terms). For example, the ancillary elements can include one or more dipole elements (e.g., dipole magnets, magnets including dipole terms, etc.) configured to direct incoming electron beams into (e.g., align the incoming beams with) one or more undulators, TQAs, and / or focusing units (e.g., as shown by way of examples in FIGURES 8A, 8B, 8C, 8G, and / or 8H), and / or can include one or more dipole elements configured to redirect electron beams (e.g., away from light beams, such as light beams generated by free-electron lasing using the electron beam(s)) exiting one or more undulators, TQAs, and / or focusing units (e.g., as shown by way of examples in FIGURES 8D, 8E, 8F, 8G, and / or 8H). Additionally or alternatively, the ancillary elements can include one or more higher-order magnets (and / or magnets, such as dipole magnets, that include higher-order terms), such as quadrupole magnets, sextupole magnets, and the like. The higher-order magnets can function to perform corrective focusing of the electron beams. In some examples, these magnets can be analogous to the higher-order magnets described in U.S. Patent Application 18 / 794414, filed 05-AUG-2024 and titled “LIGHT SOURCE SYSTEM AND METHOD OF OPERATION”, which is herein incorporated in its entirety by this reference (e.g., as described therein with respect to the ‘splitter 120’). Additionally or alternatively, the ancillary elements can include one or more diagnostics modules, which can function to characterize system operation (e.g., characterize the state of the electron beams and / or the light generated thereby).

[0060] However, the undulator system 120 can additionally or alternatively include any other suitable elements in any suitable arrangement.3. Method.

[0061] As described above, the method can include receiving one or more high- energy electron beams (e.g., spatially-separated electron beams, such as electron beams directed substantially parallel and / or arranged substantially coplanar to each other) such that the electron beams propagate through the undulator system and, as the electron beams propagate through the undulator system, focusing the electron beams (or any suitable subset thereof) at the TQAs (and / or at any other suitable elements of the system, such as in cooperation with one or more ancillary elements), such as shown by way of example in FIGURE 10B. In some examples, the method caninclude altering one or more magnetic fields, such as to ensure appropriate (e.g., well- aligned and / or focused) electron beam propagation through the undulator system. For example, the method can include adjusting the magnetic field strength (e.g., by adjusting the current flow through one or more coils such as superconducting coils, by adjusting the position and / or orientation of one or more magnetic elements, by adjusting the position and / or orientation of one or more magnetically-interacting elements such as one or more shorting plates, etc.) generated by one or more steering (e.g., dipole) magnets, focusing magnets (e.g., generating quadrupole and / or higher- order field terms), undulators (and / or elements thereof, such as one or more dipoles thereof), TQAs (and / or elements thereof, such as one or more dipoles thereof), and / or any other suitable magnetic elements. In one example (e.g., as shown in FIGURE 10C), the method includes: optionally determining appropriate magnetic field configurations for one or more elements of an undulator system; receiving a plurality of electron beams (e.g., substantially parallel, coplanar, and / or regularly-spaced electron beams; substantially coplanar, non-parallel and / or irregularly-spaced electron beams; etc.), such as at an input region of the undulator system; optionally (e.g., at one or more input dipoles, TQAs, and / or other magnetic element(s), such as ancillary elements, of the undulator system) redirecting the received electron beams into the undulator system (e.g., onto substantially coplanar, parallel, and / or regularly- spaced trajectories aligned with the undulator system), such as redirecting (e.g., at a dipole magnet or TQA including a dipole term) the electron beams onto trajectories substantially parallel with one or more undulators of the undulator system; traversing the undulator system; optionally (e.g., at one or more output dipoles, TQAs, and / or other magnetic element(s), such as ancillary elements, of the undulator system; after the electron beams traverse the undulators) redirecting the electron beams away from the generated light beams (e.g., so that the electron beams are not substantially collinear with the light beams); providing the generated light beams (e.g., to one or more downstream optical elements, such as to one or more photolithography scanners and / or other endpoints); and / or optionally (e.g., after the electron beams traverse the undulators, after the electron beams are redirected away from the generated light outputs, etc.) providing the electron beams (e.g., to one or more energy recovery loops). Traversing the undulator system can include: at one or more undulators of theundulator system, generating a light beam from each electron beam (e.g., as the electron beams traverse the undulator(s)) via free-electron lasing; at one or more TQAs and / or ancillary elements of the undulator system (e.g., arranged into one or more FODO cells, arranged upstream, between, and / or downstream of the undulators), conditioning the electron beams (e.g., maintaining and / or restoring appropriate focus and / or alignment of the electron beams for efficient free-electron lasing) as they traverse the undulator system; and / or any other suitable elements performed in any suitable manner.

[0062] Although omitted for conciseness, the preferred embodiments include every combination and permutation of the various system components and the various method processes. Furthermore, various processes of the preferred method can be embodied and / or implemented at least in part as a machine configured to receive a computer-readable medium storing computer-readable instructions. The instructions are preferably executed by computer-executable components preferably integrated with the system. The computer-readable medium can be stored on any suitable computer readable media such as RAMs, ROMs, flash memory, EEPROMs, optical devices (CD or DVD), hard drives, floppy drives, or any suitable device. The computerexecutable component is preferably a general or application specific processing subsystem, but any suitable dedicated hardware device or hard war e / firm ware combination device can additionally or alternatively execute the instructions.

[0063] The FIGURES illustrate the architecture, functionality and operation of possible implementations of systems, methods and computer program products according to preferred embodiments, example configurations, and variations thereof. In this regard, each block in the flowchart or block diagrams may represent a module, segment, step, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block can occur out of the order noted in the FIGURES. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and / or flowchart illustration, and combinations of blocks in the block diagrams and / or flowchart illustration, can beimplemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

[0064] As a person skilled in the art will recognize from the previous detailed description and from the figures and claims, modifications and changes can be made to the preferred embodiments of the invention without departing from the scope of this invention defined in the following claims.

Claims

CLAIMSWe claim:

1. An undulator system comprising:• a first undulator defining a long axis, the first undulator imposing a first alternating magnetic field along the long axis; and• a first transverse quadrupole array (TQA) defining a broad axis orthogonal to the long axis, the first TQA imposing a second alternating magnetic field along the broad axis and defining a plurality of apertures along the broad axis, wherein the first TQA imposes a respective quadrupole magnetic field within each aperture of the plurality, wherein the long axis intersects a first aperture of the plurality.

2. The system of Claim 1, wherein:• the first undulator comprises a first plurality of permanent dipole magnets defining a first linear array parallel the long axis; and• the first TQA comprises a second plurality of permanent dipole magnets defining a second linear array parallel the broad axis.

3. The system of Claim 1, wherein:• the first TQA comprises a first, second, third, and fourth conductive winding;• the first, second, third, and fourth conductive winding are each wound about the long axis;• the first and second conductive windings each define a first spiral handedness;• the third and fourth conductive windings each define a second spiral handedness opposite the first spiral handedness; and• current flow through the first, second, third, and fourth conductive windings cooperatively generates the second alternating magnetic field.

4. The system of Claim 3, wherein:• the first undulator comprises a fifth and sixth conductive winding;• the fifth and sixth conductive winding are each wound about the long axis; and• current flow through the fifth and sixth conductive windings cooperatively generates the first alternating magnetic field.

5. The system of Claim 4, further comprising:• a first conductor comprising the first conductive winding and the fifth conductive winding; and• a second conductor comprising the second conductive winding and the sixth conductive winding.

6. The system of Claim 4, wherein the first, second, third, fourth, fifth, and sixth conductive windings are superconducting, the system further comprising a cryogenic vessel that contains the first, second, third, fourth, fifth, and sixth conductive windings.

7. The system of Claim 1, further comprising a plurality of TQAs, the plurality of TQAs comprising the first TQA, wherein the system defines a beam propagation path, wherein, throughout the first undulator and the first TQA, the beam propagation path is collinear with the long axis; wherein, for each TQA of the plurality:• the TQA defines a respective broad axis orthogonal to the beam propagation path;• the TQA imposes a respective alternating magnetic field along the broad axis and defines a respective plurality of apertures along the broad axis;• for each aperture of the respective plurality, the TQA imposes a respective quadrupole magnetic field within the aperture; and• the beam propagation path intersects a first aperture of the respective plurality.

8. The system of Claim 7, wherein:• the plurality of TQAs define a focusing-defocusing (FODO) array; and• the system further comprises a plurality of undulators, each undulator of the plurality arranged along the beam propagation path between a respective pair of TQAs of the plurality.

9. The system of Claim 8, wherein, for each adjacent pair of undulators of the plurality, only one TQA is arranged along the beam propagation path between the pair of undulators.

10. The system of Claim 7, further comprising a matching unit arranged along the beam propagation path upstream of the plurality of TQAs and the first undulator, the matching unit comprising a second set of TQAs, wherein, for each TQA of the second set:• the TQA defines a respective broad axis orthogonal to the beam propagation path;• the TQA imposes a respective alternating magnetic field along the broad axis;• the TQA defines a respective plurality of apertures along the broad axis, wherein the beam propagation path intersects a respective first aperture of the respective plurality of apertures; and• for each aperture, the TQA imposes a respective quadrupole magnetic field within the aperture. n. The system of Claim 10, further comprising a quadrupole telescope arranged along the beam propagation path upstream of the matching unit, wherein:• the quadrupole telescope is configured to focus an electron beam to a circular focus condition at an input of the matching unit;• the matching unit comprises four TQAs; and• the matching unit is configured to focus a plurality of electron beams to congruent, non-circular focus conditions at an output of the matching unit.

12. The system of Claim 11, further comprising an electron beam splitter arranged along the beam propagation path between the quadrupole telescope and the matching unit, the electron beam splitter configured to spatially separate electron bunches of an electron beam onto a plurality of beam paths, wherein, for each TQA of the system, each beam path of the plurality is directed through a different aperture of the TQA.

13. The system of Claim 8, wherein, for each adjacent pair of undulators of the plurality: at least three TQAs are arranged along the beam propagation path between the pair of undulators, wherein the at least three TQAs define a quadrupole triplet.

14. The system of Claim 1, wherein the first TQA further imposes a dipole magnetic field within the first aperture.

15. The system of Claim 14, wherein:• the first TQA is arranged upstream of the first undulator along the long axis;• the system further comprises a second TQA arranged downstream of the first undulator along the long axis;• the second TQA defines a second broad axis orthogonal to the long axis, the second TQA imposing a third alternating magnetic field along the second broad axis and defining a second plurality of apertures along the second broad axis;• the second TQA imposes a respective quadrupole magnetic field within each aperture of the second plurality;• the second TQA further imposes a second dipole magnetic field within a second aperture of the second plurality; and• the long axis intersects the second aperture.

16. A method comprising:• at a first undulator defining a long axis from an undulator input to an undulator output:• imposing a first alternating magnetic field along the long axis;• receiving a plurality of electron beams that traverse the first undulator from the undulator input to the undulator output;• outputting the plurality of electron beams at the undulator output; and• for each electron beam of the plurality, generating a respective light output via free-electron lasing; and• at a first transverse quadrupole array (TQA) defining a broad axis:• imposing a second alternating magnetic field along the broad axis, the second alternating magnetic field defining a plurality of apertures along the broad axis, the second alternating magnetic field defining a respective quadrupole magnetic field within each aperture of the plurality, wherein the plurality of apertures comprises:• a first set of apertures, each aperture of the first set containing a respective quadrupole magnetic field of a first polarity; and• a second set of apertures, each aperture of the second set containing a respective quadrupole magnetic field of a second polarity opposite the first polarity, wherein the first and second sets of apertures are disjoint; and• for each electron beam of the plurality, receiving the electron beam at a different aperture of the plurality.

17. The method of Claim 16, wherein each electron beam of the plurality is received at a respective aperture of the first set.

18. The method of Claim 16, wherein:• the plurality of electron beams comprises a first set of electron beams and a second set of electron beams;• each electron beam of the first set is received at an aperture of the first set; and• each electron beam of the second set is received at an aperture of the second set.

19. The method of Claim 18, further comprising, before receiving the plurality of electron beams at the first undulator, at a matching unit comprising at least four TQAs:• receiving the plurality of electron beams, wherein each electron beam of the plurality is received having a substantially identical, substantially circular focus condition;• for each electron beam of the plurality, refocusing the electron beam as it traverses each TQA of the matching unit via a different aperture of each TQA, wherein each TQA of the matching unit defines a respective plurality of apertures; and• outputting the plurality of electron beams, wherein each electron beam of the plurality is output having a substantially congruent, substantially non-circular focus condition, wherein a first focus condition of a first electron beam of the plurality is substantially different from a second focus condition of a second electron beam of the plurality.

20. The method of Claim 19, further comprising, before receiving the plurality of electron beams at the matching unit:• at an electron beam splitter, spatially separating electron bunches of a first electron beam into the plurality of electron beams; and• before spatially separating the electron bunches: at a quadrupole telescope, focusing the first electron beam such that each electron beam of the plurality arrives at the matching unit having the substantially identical, substantially circular focus condition.

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