COLD ALKALI PLASMA CATHODE ELECTRON BEAM SOURCE

CLAIM OF PRIORITY

[0001] This application claims the benefit of priority to U.S. Provisional Appl. No. 63/269,146 filed on March 10, 2022 and incorporated in its entirety by reference herein.

BACKGROUND

Field

[0002] This application relates generally to photoionization-based electron beam sources.

Description of the Related Art

[0003] The near-threshold photoionization of alkali gas atoms in a uniform electric field is an excellent basis for a high quality electron source with low inherent energy spread and emittance. See, e.g., W.I. Engelen, et al., “Analytical model of an isolated single-atom electron source,” Ultramicr. 147:61-69 (2014); J.G.H. Franssen et al., “Compact ultracold electron source based on a grating magneto-optical trap,” Phys. Rev. Accel. Beams, 22: 023401 (2019); J. Bommels, “Energy broadening due to photoion space charge in a high resolution laser photoelectron source,” Rev. Sci. Instr. 72: 4098 (2001). However, previous work has done little to consider the effects of the geometry of the ionization region on beam production.

SUMMARY

[0004] In certain implementations, an apparatus for generating a beam of electrons is provided. The apparatus comprises a first surface of a first electrically conductive element and a second surface of a second electrically conductive element. The second surface is substantially parallel to the first surface, and the first and second elements are configured to apply an electric field in a region between the first and second surfaces. The apparatus further comprises an atomic gas source configured to direct an atomic gas beam into the region. The atomic gas beam propagates from the atomic gas source to the region through at least one orifice of the first surface and impinging the second surface. The apparatus further comprises a first laser source configured to direct a first laser beam into the region, the first laser beam having a first wavelength, and a second laser source configured to direct a second laser beam into the region, the second laser beam having a second wavelength different from the first wavelength. One of the first and second wavelengths is configured to excite atoms of the atomic gas beam from a ground state to an excited state and another of the first and second wavelengths configured to ionize atoms of the atomic gas beam that arc in the excited state. The first and second laser beams and at least a portion of the atomic gas beam overlap one another in an ionization volume within the region. The ionization volume has a substantially planar shape that is substantially parallel to the first and second surfaces.

[0005] In certain implementations, an apparatus for generating a beam of electrons is provided. The apparatus comprises an electrically conductive enclosure comprising a plurality of orifices and an inner surface. The enclosure substantially shields a region within the enclosure from electric fields external to the enclosure. The apparatus further comprises an atomic gas source configured to direct an atomic gas beam into the region through at least a first orifice of the plurality of orifices and configured to impinge the inner surface of the enclosure. The apparatus further comprises an ionization laser source configured to direct a substantially linearly polarized laser beam into the region through at least a second orifice of the plurality of orifices. The laser beam is configured to ionize atoms of the atomic gas beam within the region. The apparatus further comprises at least one electron optic element configured to accelerate and/or focus electrons emitted from the enclosure through at least a third orifice of the plurality of orifices.

BRIEF DESCRIPTION OF THE DRAWINGS

[0006] FIG. 1 schematically illustrates an example energy level diagram for potassium gas atoms in accordance with certain implementations described herein.

[0007] FIG. 2A schematically illustrates a cross-sectional view of an example apparatus for generating a beam of electrons in accordance with certain implementations described herein.

[0008] FIG. 2B schematically illustrates a perspective view of a portion of another example apparatus in accordance with certain implementations described herein.

[0009] FIG. 3A schematically illustrates an atomic gas source comprising an elongate collimator having inner surfaces and a getter source in accordance with certain implementations described herein.

[0010] FIG. 3B schematically illustrates an atomic gas source comprising an elongate collimator having a backing-gas injection aperture and a getter source within the collimator in accordance with certain implementations described herein. [0011] FTG. 4 schematically illustrate example first and second laser beams overlapping one another in accordance with certain implementations described herein.

[0012] FIG. 5 schematically illustrates an optical set-up compatible with certain implementations described herein.

[0013] FIG. 6 schematically illustrates a cross-sectional view of another example apparatus for generating a beam of electrons in accordance with certain implementations described herein.

DETAILED DESCRIPTION

[0014] Certain implementations described herein utilize an alkali cold plasma cathode (CPC) scheme in which an electron beam is generated using a continuous-wave laser and a jet of alkali gas configured such that the ionization region is quasi-two dimensional and space-charge effects on the electron energy distribution are reduced (e.g., minimized). Analytic estimates indicate that sufficient electrical current can be drawn from certain implementations described herein to be useful as an electron source for electron energy loss spectroscopy (EELS), a technique with broad commercial and scientific appeal (see, e.g., Anshul Kogar, “Collective excitations in layered materials with momentum-resolved electron energy loss spectroscopy,” Ph.D. thesis, University of Illinois at Urbana-Champaign 2015). EELS finds applications in fields ranging from condensed matter physics to structural biology. In certain implementations, the electron beam can be used to provide a high impact nanometrology instrument for scientific research.

[0015] A key figure of merit characterizing electron sources for EELS is energy spread (see, e.g., R.F. Egerton, “Electron energy-loss spectroscopy in the TEM,” Rep. Prog. Phys. 72: 016502 (2008)), and simulations indicate that certain implementations described herein can achieve an energy spread of 1 pcV/pA (e.g., energy spread on the order of 100 pcV for an electron beam current of 100 pA), which represents an order-of-magnitude improvement over previous electron sources for EELS (e.g., for examining phenomena with energies of about 100 peV). The energy spread can be strongly linear with the electron beam current, so the energy spread can be further reduced by reducing the electron beam current. In addition, simulations also indicate that certain implementations described herein generate an electron beam with an emittance in a range of 10 nm-rad to 30 nm-rad, in a range of 1 nm-rad to 10 nm-rad, or of about 10 nm-rad, depending on how large the area from which current is drawn. The electron beam of certain implementations, being diffraction limited, can be focused to nanometer- sized spots, and can be used to examine phonon properties of MOSFETs under 5 nm, magnon phenomena in two-dimensional materials, and electron-phonon coupling giving rise to superconductivity in nanostructures such as Josephson junctions.

[0016] Previous studies of extracting photoelectrons from a cold jet of alkali gas with continuous wave (CW) lasers (see, e.g., Bommels (2001)) were limited by the computational power of the time, and each only investigated a single corresponding geometry (e.g., mostly aspect ratio 1 spheroids). In contrast, certain implementations described herein utilize a quasi-two-dimensional geometry that was not discussed or considered in past studies and that is less susceptible to electron scattering by space-charge effects.

[0017] Certain implementations described herein utilize a cold plasma cathode (CPC) configuration based on continuous, shaped, two-photon ionization of alkali gas in molecular flow. The ionization of a low-density gas by narrow bandwidth laser light allows for a near-uniform emission process (in the limit of a monochromatic laser ionizing a zero- density/infinite-spacing gas, the emission process would be entirely uniform). Certain implementations described herein produce an electron beam with a very narrow energy spread (e.g., approximately I pcV/pA. depending on the desired current and emittance) in which space-charge effects are reduced (e.g., minimized) by shaping the ionization region as well as by neutralizing the resulting ions.

[0018] FIG. 1 schematically illustrates an example energy level diagram for potassium gas atoms in accordance with certain implementations described herein. The potassium gas atoms are impinged in an ionization region of a vacuum chamber by photons from two laser light sources each having a predetermined wavelength. For two-photon ionization of potassium gas atoms, a pump laser can provide a pump beam of 770-nm photons and an ionizing laser can provide an ionization beam of 454-nm photons. For another example of two-photon ionization of rubidium gas atoms, a pump laser can provide a pump beam of 780-nm photons and an ionizing laser can provide an ionization beam of 480-nm photons. Other alkali gas atoms (e.g., sodium; cesium) can also be used in accordance with certain implementations described herein. While FIG. 1 schematically illustrates two-photon ionization through an excited p- state of alkali atoms, ionization out of another excited state (e.g., s-state; d-state) with a sufficiently high ionization cross-section is also compatible with certain implementations described herein.

[0019] FIG. 2A schematically illustrates a cross-sectional view of an example apparatus 100 for generating a beam of electrons 102 in accordance with certain implementations described herein. The apparatus 100 comprises a first surface 110 of a first electrically conductive element 112 and a second surface 120 of a second electrically conductive element 122, the second surface 120 substantially parallel to the first surface 110. The first and second elements 112, 122 are configured to apply an electric field in a region 130 between the first and second surfaces 110, 120. The apparatus 100 further comprises an atomic gas source 140 configured to direct an atomic gas beam 142 into the region 130. The atomic gas beam 142 propagates from the atomic gas source 140 to the region 130 through at least one orifice 114 of the first surface 110 and impinges the second surface 120. The apparatus 100 further comprises a first laser source 150 configured to direct a first laser beam 152 into the region 130, the first laser beam 152 having a first wavelength. The apparatus 100 further comprises a second laser source 160 configured to direct a second laser beam 162 into the region 130, the second laser beam 162 having a second wavelength different from the first wavelength. One of the first and second wavelengths is configured to excite atoms of the atomic gas beam 142 from a ground state to an excited state and another of the first and second wavelengths is configured to ionize atoms of the atomic gas beam 142 that are in the excited state. The first and second laser beams 152, 162 and at least a portion of the atomic gas beam 142 overlap one another in an ionization volume 170 within the region 130, the ionization volume 170 having a substantially planar shape that is substantially parallel to the first and second surfaces 110, 120.

[0020] In certain implementations, the first surface 110 comprises a substantially planar surface of the first electrically conductive (e.g., metallic) element 112 (e.g., plate; electrode) and the second surface 120 comprises a substantially planar surface of the second electrically conductive (e.g., metallic) element 122 (e.g., plate; electrode). In certain implementations, the first and second surfaces 110, 120 are spaced from one another by a distance D in a range of 1 millimeter to 3 centimeters, and the at least one orifice 114 has a width IT in a range of 1 millimeter to 1 centimeter. In certain implementations, the at least one orifice 1 14 is substantially circular, while in certain other implementations, the at least one orifice 114 has other shapes (c.g., rectangular; square; polygonal; oval; irregular).

[0021] FIG. 2A schematically illustrates the first electrically conductive element 112 as a plate having a single orifice 114 through which the atomic gas beam 142 and the first laser beam 152 propagate to the ionization volume 170 and through which the electrons 102 propagate from the ionization volume 170 and the region 130. FIG. 2A also schematically illustrates the second electrically conductive element 122 as a plate without an orifice. In certain other implementations, the first electrically conductive element 112 can comprise a plurality of orifices 114. For example, the first electrically conductive element 112 can comprise a grid of electrically conductive wires bounding a plurality of orifices 114 therebetween or an electrically conductive plate having multiple discrete orifices 114. In certain implementations, at least one of the electrons 102, the atomic gas beam 142, and the first laser beam 152 can propagate through a different orifice 114 than does at least one other of the electrons 102, the atomic gas beam 142, and the first laser beam 152. In certain other implementations, the second electrically conductive element 122 can comprise at least one orifice configured to allow a non-ionized portion of the atomic gas beam 142 and/or the ionized atoms to propagate out of the region 130. For example, the second electrically conductive element 122 can comprise a grid of electrically conductive wires bounding a plurality of orifices therebetween or an electrically conductive plate having a single orifice. In certain such implementations, the second electrically conductive element 122 can further comprise another surface configured to be impinged by and to neutralize the ionized atoms propagating through the at least one orifice of the second surface 120.

[0022] The first and second electrically conductive elements 112, 122 are configured to be in electrical communication with at least one electrical voltage supply (not shown) configured to apply an electrical voltage across the first and second electrically conductive elements 112, 122 to generate an electric field (not shown) within the region 130 between the first and second surfaces 110, 120 and within the ionization volume 170. For an example of electrical voltage supplies compatible with certain implementations described herein, see, P. Schury et al., “High-stability, high-voltage power supplies for use with multireflection time-of-flight mass spectrographs,” Rev. Sci. Instrum. Vol. 91, 014702 (2020). The electric field is configured to accelerate the electrons 102 photoionized from the ionized atoms such that the electrons 102 propagate along a propagation direction from the ionization volume 170 through the at least one orifice 114. For example, as schematically illustrated by FIG. 2A, the propagation direction of the electrons 102 can be substantially perpendicular to the first and second surfaces 110, 120. In certain implementations, the distance D and the width IF are configured such that the electric field within the ionization volume 170 is substantially uniform (e.g., in magnitude and direction) such that spatial variations of the electric field do not appreciably contribute to a broadening of the energy distribution of the electrons 102 propagating from the ionization volume 170 through the at least one orifice 114. For example, the electrons 102 emitted from the at least one orifice 114 can have an energy spread less than IpeV/pA.

[0023] In certain implementations, the atomic gas beam 142 comprises alkali gas atoms (e.g., selected from the group consisting of: lithium; sodium; potassium; rubidium; cesium). While sodium and cesium have only one stable isotope, other alkali atoms have multiple stable isotopes. The different ionization energies for different isotopes can cause the electrons 102 to be emitted with different energies. For example, the different isotopes of lithium can result in an ionization energy difference that is the same order of magnitude as the energy spread of the electrons 102 (e.g., about 100 peV). However, other alkali atoms have sufficiently low first ionization energy differences between isotopes such that the energy range of the electrons 102 is not significantly affected. Furthermore, the initial kinetic energy of the electrons 102 and the final energy spread of the electrons 102 can be broadened by doppler shifts due to the distribution of the velocity of the gas atoms in the atomic gas beam 142.

[0024] Various atomic gas sources 140 (e.g., getter sources; heated alkali metal; liquid metal ovens) configured to produce a collimated atomic gas beam 142 with sufficient atomic gas density are compatible to be used with certain implementations described herein. For example, the atomic gas source 140 can comprise an alkali atom getter source and a collimator (e.g., tube) configured to collimate alkali atoms propagating from the getter source towards the ionization volume 170, such that the atomic gas beam 142 comprises a substantially collimated alkali gas jet.

[0025] FIG. 3A schematically illustrates an example atomic gas source 140 comprising an elongate collimator (e.g., tube) having inner surfaces and a getter source (e.g., within the collimator). Alkali atoms from the getter source with trajectories that impinge the inner surfaces are deposited onto the inner surfaces, while other alkali atoms from the getter source with trajectories that do not impinge the inner surfaces propagate out of the collimator. Some alkali meters have a strong affinity for other metals (e.g., potassium has an affinity for steel; rubidium has an affinity to gold) and the alkali atoms will be deposited permanently on the metal surface. See, e.g., Peter D.D. Schwindt, “Magnetic Traps and Guides for Bose- Einstein Condensates on an Atom Chip: Progress toward a Coherent Atom Waveguide Beamsplitter,” Thesis, University of Colorado (2003); C. Slowe et al., “High flux source of cold rubidium atoms,” Rev. Sci. Instr. 76, 103101 (2005); D. Patterson et al., “Intense atomic and molecular beams via neon buffer-gas cooling,” New J. of Phys. 11, 055018 (2009). For example, cesium is absorbed strongly by poly crystalline graphite (see, e.g., N.D. Bhaskar et al., “Absorption of Cesium by Poly crystalline Graphite - Sticking Coefficient Studies,” Carbon, Vol 28, No. 1, pp. 71-78 (1990). In certain implementations, the first and second elements 112, 122 and/or the entire inner surface of the vacuum chamber are coated with polycrystalline graphite configured to absorb errant cesium atoms to significantly decrease gas scattering in the vacuum chamber and in proximity to the ionization volume 170. In certain implementations, an inner surface of the collimator is coated with polycrystalline graphite such that the alkali gas beam 142 is more collimated (see, e.g., FIG. 3A).

[0026] FIG. 3B schematically illustrates another example atomic gas source 140 comprising an elongate collimator (e.g., tube) having a backing-gas injection aperture and a getter source within the collimator. In certain such implementations, the back-pressure gas is cryogenic (e.g., cryogenic buffer gas beam source or CBGB source), while in certain other implementations, the back-pressure gas is non-cryogenic (e.g., similar to a CBGB source without cooled cells). For another example, collimation of the atomic beam 142 can be provided by optical molasses by which the transverse motion of the atoms is slowed by the introduction of laser light bouncing transversely at a small angle down the collimator (e.g., tube).

[0027] The atomic gas beam 142 of certain implementations propagates through the at least one orifice 114 to the ionization volume 170. For example, as schematically illustrated by FIG. 2A, the atomic gas beam 142 can propagate at a non-zero and nonperpendicular angle relative to the first and second surfaces 110, 120 (e.g., in a range of 30 to 85 degrees relative to the first and second surfaces 110, 120; in a range of 5 degrees to 60 degrees relative to the propagation direction of the electrons 102 and/or the electric field in the ionization volume 170).

[0028] In certain implementations, the atomic gas source 140 is configured to generate sufficient atomic flux to the ionization volume 170 such that the electrical current of the electrons 102 are sufficient for the application to which the electrons 102 are to be applied. For example, to generate sufficient electrical current for EELS (e.g., 100 pA), the atomic flux of the atomic gas beam 142 generated by the atomic gas source 140 can be in the range of 10 ¹⁴ to 10 ¹⁵ atoms/m ² s. In certain implementations, the atomic flux is within the molecular flow regime such that turbulent hydrodynamic concerns are minimal.

[0029] In certain implementations, the atomic gas beam 142 is directed towards the second surface 120 such that the momentum of the ionized atoms is also directed towards the second surface 120. Interaction of the ionized atoms with the second surface 120 can neutralize the ionized atoms by the second surface 120 providing electrons to the ionized atoms impinging the second surface 120. In certain implementations, the neutralized atoms can deposit onto the second surface 120. In addition, the electric field in the region 130 can also be configured to accelerate the positively charged ionized atoms (not shown) away from the ionization volume 170 towards the second surface 120. Thus, by neutralizing and/or removing the ionized atoms, certain implementations reduce (e.g., eliminate; prevent) coulomb forces from the ionized atoms from scattering the electrons 102 and substantially broadening the energy distribution of the electrons 102 emitted from the at least one orifice 114. Since the total scattering effect of the ionized atoms logarithmically diverges (e.g., as an integral over r ¹ dependence, with the coulomb force scaling as r ² and the number of ionized atoms scaling with r), neutralizing the ionized atoms otherwise removing their scattering effect on the electrons 102, certain implementations described herein provide sufficiently narrow energy spread for the beam of electrons 102 to be used as an EELS probe beam.

[0030] In certain implementations, the first laser source 150 comprises at least one laser diode and the second laser source 160 comprises at least one laser diode. Each of the first and second laser sources 150, 160 is configured to be tuned such that each of the first laser beam 152 and the second laser beam 162 has a linewidth sufficiently narrow (e.g., in GHz range) such that the first and second laser beams 152, 162 do not significantly affect the energy spread of the beam of electrons 102. In certain implementations, one of the first and second laser beams 152, 162 is a pump beam having a pump wavelength configured to excite atoms of the atomic gas beam 142 from a ground state to at least one excited state (c.g., to excite potassium gas atoms from the 45 state to the 47*3/2 state or the 47’1/2 state using a pump wavelength of 770 nm) and the other of the first and second laser beams 152, 162 is an ionization beam having an ionization wavelength configured to ionize atoms of the atomic gas beam 142 that are in the excited state (e.g., to ionize potassium gas atoms in the 47*3/2 state or the 4P1/2 state using an ionization wavelength of 454 nm). In certain implementations, the first laser beam 152 is the pump beam and the second laser beam 162 is the ionization beam, while in certain other implementations, the first laser beam 152 is the ionization beam and the second laser beam 162 is the pump beam. For rubidium gas atoms, the pump wavelength can be 780 nm and the ionization wavelength can be 480 nm. For both potassium and rubidium, the two-photon ionization process can be both more precise than the single-photon ionization process from the ground state (e.g., the laser light to directly ionize the alkali gas atoms is less precise) and more efficient than the single -photon ionization process from the ground state (e.g., the ionization cross-section out of the excited state is larger than the ionization crosssection out of the ground state) (see, e.g., O. Zatsarinny and S. S. Tayal, “Photoionization of potassium atoms from the ground and excited states,” Phys. Rev. A 81 (2010); J. R. Lowell et al., “Measurement of the photoionization cross section of the 5s 1/2 state of rubidium,” Phys. Rev. A 66(6) (2002)). The pumping process can be relatively easily saturated with commercially available mW-class CW lasers (see, e.g., T.G. Tiecke, “Properties of potassium,” Thesis, University of Amsterdam, January 2010). In certain implementations, using commercially available 454-nm or 480-nm diode lasers to generate the ionization beam provides an ionization efficiency in a range of 0.01% to 80% (e.g., approximately 50%), depending on the laser focused spot size.

[0031] As schematically illustrated by FIG. 2A, the first laser beam 152 can propagate at a non-zero and non-perpendicular angle relative to the first and second surfaces 110, 120. For example, the first laser beam 152 can propagate at an angle in a range of 30 to 85 degrees relative to the first and second surfaces 110, 120 (e.g., in a range of 5 degrees to 60 degrees relative to the propagation direction of the electrons 102 and/or the electric field in the ionization volume 170). In addition, as schematically illustrated by FIG. 2A, the second laser beam 162 can propagate substantially parallel to and spaced from the second surface 120. For another example, a center of the second laser beam 162 can be spaced from the second surface 120 by a distance d that is less than or equal to 10% of the distance D between the first and second surfaces 110, 120 (e.g., less than 3 millimeters; less than 1 millimeter; less than 10 microns; in a range of 1 micron to 5 microns). Other configurations of the first laser source 150 and the second laser source 160 in which the first laser beam 152 and the second laser beam 162 intersect with the atomic gas beam 142 in a flat (e.g., disk-like) region are also compatible with certain implementations described herein. For example, FIG. 2B schematically illustrates a perspective view of a portion of another example apparatus 100 in accordance with certain implementations described herein. In FIG. 2B, both the first laser beam 152 and the second laser beam 162 can propagate substantially parallel to and spaced from the second surface 120 (e.g., both the first laser beam 152 and the second laser beam 162 injected transversely).

[0032] The ionization volume 170 can be defined as the volume in which the first and second laser beams 152, 162 overlap one another and overlap the atomic gas beam 142. In certain implementations in which the atomic gas beam 142 overlaps the whole region in which the first and second laser beams 152, 162 overlap one another, at least one of the first and second laser beams 152, 162 has a cross-sectional shape that produces an ionization volume 170 that is substantially planar and substantially parallel to the first and second surfaces 110, 120. The electrons 102 can be extracted from the ionization volume 170 and accelerated out of the at least one orifice 114 by the electric field generated between the first and second surfaces 110, 120.

[0033] FIG. 4 schematically illustrate example first and second laser beams 152, 162 overlapping (e.g., intersecting) one another in accordance with certain implementations described herein. The atomic gas beam 142, not shown in FIG. 4, overlaps the whole region in which the first and second laser beams 152, 162 overlap one another. As schematically illustrated by FIG. 4, the first laser beam 152 can have a substantially circular cross-section in a plane substantially perpendicular to a propagation direction of the first laser beam 152, and the second laser beam can be substantially planar, such that the ionization volume 170 is substantially disk-shaped. For example, the ionization volume 170 can have a width (e.g., diameter) of less than 10 millimeters (e.g., about 6 millimeters) and a thickness of less than 25 microns (e.g., about 15 microns). Other cross-sectional shapes of the first laser beam 152 arc also compatible with certain implementations described herein.

[0034] In certain implementations, the first laser source 150 and/or the second laser source 160 comprises one or more beam-shaping optical elements (e.g., lenses; apertures; filters) configured to shape the first and/or second laser beams 152, 162. For example, the second laser source 160 can comprise a cylindrical lens configured to receive laser light having a substantially circular cross-section and to generate the substantially planar second laser beam 162. Other optical elements and/or filtering elements are also compatible with certain implementations described herein. While FIG. 4 schematically illustrates the first and second laser beams 152, 162 as being collimated, in certain implementations, at least one of the first and second laser beams 152, 162 is focused within the region 130. FIG. 5 schematically illustrates an optical set-up compatible with certain implementations described herein. FIG. 5 shows an example implementation in which the first laser beam 152 is reflected from the second surface 120, the reflected portion propagating out of the region 130 via the at least one orifice 114. In certain such implementations, the reflected portion can contribute to the substantially planar ionization volume 170 (e.g., which may have a shape of two overlapping disks), although this contribution is not shown in FIG. 4.

[0035] In certain implementations, the beam of electrons 102 is configured to be used as a probe beam for electron energy loss spectroscopy (EELS) providing an order-of- magnitude higher energy resolution than conventional EELS systems (see, e.g., J. Hachtel et al., “Exploring the capabilities of monochromated electron energy loss spectroscopy in the infrared regime,” Sci. Rep. 8: 5637 (2018)).

[0036] FIG. 6 schematically illustrates a cross-sectional view of another example apparatus 200 for generating a beam of electrons 202 in accordance with certain implementations described herein. The apparatus 200 comprises an electrically conductive enclosure 210 (e.g., Faraday cage) comprising a plurality of orifices 212 and an inner surface 214, the enclosure 210 substantially shielding a region 216 within the enclosure 210 from electric fields external to the enclosure 210. In certain implementations, the orifices 212 are as large as possible without affecting field uniformity within the region 216. The orifices 212 of certain implementations are sufficiently small to block externally-generated electric fields from entering the region 216 but do not electromagnetic waves. For example, the orifices 212 can have a size in a range of a few millimeters to 1 centimeter.

[0037] The apparatus 200 further comprises an atomic gas source 240 configured to direct an atomic gas beam 242 into the region 216 through at least one of the orifices 212 and configured to impinge the inner surface 214 of the enclosure 210. The atomic gas source 240 and the atomic gas beam 242 can have one or more of the same features as the atomic gas source 140 and/or the atomic gas beam 142 described herein.

[0038] The apparatus 200 further comprises an ionization laser source 250 (e.g., diode laser) configured to direct a substantially linearly polarized laser beam 252 into the region 216 through at least one of the orifices 212 (e.g., different from the at least one orifice 212 through which the atomic gas beam 242 propagates), the laser beam 252 configured to ionize atoms of the atomic gas beam 242 within the region 216. For example, the laser beam 252 can be polarized in the direction of electron transport (e.g., in a direction extending to the orifice 212 through which the electrons 202 propagate). At least some electrons 202 resulting from the ionization of the atomic gas beam 242 by the laser beam 252 propagate from the region 216 out of the enclosure 210 through at least one of the orifices 212 (e.g., different from one or both of the orifices 212 through which the atomic gas beam 242 and/or the laser beam 252 propagate). In certain implementations, the laser beam 252 is substantially planar in a plane substantially perpendicular to the direction of linear polarization (e.g., focused to a small spot with a lens then defocused in one direction with a cylindrical lens).

[0039] The apparatus 200 further comprises at least one electron optic element 260 configured to accelerate and/or focus the electrons 202 emitted from the enclosure 210 through at least a third orifice of the plurality of orifices 212. For example, the at least one electron optic element 260 can comprise a pair of electrically conductive substantially parallel plates 262, each having an opening 264 through which the electrons 202 from the enclosure 210 can propagate. For example, the third orifice can have a diameter of less than 1 centimeter and the walls of the enclosure 210 can have a thickness less than 1 centimeter.

[0040] In certain implementations, photoionization takes place is a substantially zero-field region 216 within the enclosure 210. Unlike the apparatus 100 described herein, in certain implementations, the apparatus 200 does not apply an external electric field to the region 216 in which ionization of the atomic gas beam 242 occurs. The photoionized electrons 202 can be launched from the atoms of the atomic gas beam 242 with substantial kinetic energy (c.g., 0-10 eV), which asymptotically approaches zero with distance by the substantially linearly polarized laser beam 252 (see, e.g., semiclassical ionization models, such as that of Engelen 2014). The electron can be launched with the ionization energy out of the p state (ionization threshold minus the p state energy) plus any excess energy (e.g., any amount of energy, determined by what laser is used and how far the laser energy is above the ionization threshold).

[0041] In certain implementations, the at least one electron optic element 260 is positioned sufficiently close (e.g., in a range of 1 centimeter to 10 centimeters) to the orifice 212 from which the electrons 202 propagate from the enclosure 210 that accelerating electrical and/or magnetic fields of the at least one electron optic element 260 are applied to the electrons 202 emitted from the orifice 212. In certain implementations, the electrons 202 emitted from the at least one electron optic element 260 have an energy spread that is less than an inherent lower limit of the energy spread from gas cathodes positioned in electric fields (e.g., inherent lower limit of the energy spread being substantially equal to the spatial spread of the atoms in the longitudinal direction AZ multiplied by the applied electric field E).

[0042] In certain implementations, the apparatus 200 has an ionization region (e.g., defined as the overlap of the atomic gas beam 242 and the laser beam 252) that is substantially planar (e.g., as described above with regard to the apparatus 100) and substantially perpendicular to a polarization direction of the laser beam. The apparatus 200 of certain implementations also neutralizes the ionized atoms using the inner surface 214 as described above with regard to the apparatus 100, but without suffering from the (E- AZ) inherent energy spread lower limit. The apparatus 200 of certain implementations uses a linearly polarized ionizing laser beam 252 (polarized in the direction of electron transport/longitudinal) to further enhance (e.g., increase the efficiency of) the photoionization and propagation of the photoelectrons towards the orifice 212 through which the electrons 202 propagate.

[0043] Although commonly used terms are used to describe the systems and methods of certain implementations for ease of understanding, these terms are used herein to have their broadest reasonable interpretations. Although various aspects of the disclosure are described with regard to illustrative examples and implementations, the disclosed examples and implementations should not be construed as limiting. Conditional language, such as, among others, "can," "could," "might," or "may," unless specifically stated otherwise, or otherwise understood within the context as used, is generally intended to convey that certain implementations include, while other implementations do not include, certain features, elements and/or steps. Thus, such conditional language is not generally intended to imply that features, elements and/or steps are in any way required for one or more implementations or that one or more implementations necessarily include logic for deciding, with or without user input or prompting, whether these features, elements and/or steps are included or are to be performed in any particular implementation. In particular, the terms “comprises” and “comprising” should be interpreted as referring to elements, components, or steps in a nonexclusive manner, indicating that the referenced elements, components, or steps may be present, or utilized, or combined with other elements, components, or steps that are not expressly referenced.

[0044] It is to be appreciated that the implementations disclosed herein are not mutually exclusive and may be combined with one another in various arrangements. In addition, although the disclosed methods and apparatuses have largely been described in the context of electron beam sources, various implementations described herein can be incorporated in a variety of other suitable devices, methods, and contexts.

[0045] Language of degree, as used herein, such as the terms “approximately,” “about,” “generally,” and “substantially,” represent a value, amount, or characteristic close to the stated value, amount, or characteristic that still performs a desired function or achieves a desired result. For example, the terms “approximately,” “about,” “generally,” and “substantially” may refer to an amount that is within ± 10% of, within ± 5% of, within ± 2% of, within ± 1% of, or within ± 0.1% of the stated amount. As another example, the terms “generally parallel” and “substantially parallel” refer to a value, amount, or characteristic that departs from exactly parallel by ± 10 degrees, by ± 5 degrees, by ± 2 degrees, by ± 1 degree, or by ± 0.1 degree, and the terms “generally perpendicular” and “substantially perpendicular” refer to a value, amount, or characteristic that departs from exactly perpendicular by ± 10 degrees, by ± 5 degrees, by ± 2 degrees, by ± 1 degree, or by ± 0.1 degree. The ranges disclosed herein also encompass any and all overlap, sub-ranges, and combinations thereof. Language such as “up to,” “at least,” “greater than,” less than,” “between,” and the like includes the number recited. As used herein, the meaning of “a,” “an,” and “said” includes plural reference unless the context clearly dictates otherwise. Also, as used in the description herein, the meaning of “in” includes “into” and “on,” unless the context clearly dictates otherwise.

[0046] While the methods and systems are discussed herein in terms of elements labeled by ordinal adjectives (e.g., first, second, etc.), the ordinal adjective are used merely as labels to distinguish one element from another (e.g., one laser source from another), and the ordinal adjective is not used to denote an order of these elements or of their use.

[0047] The invention described and claimed herein is not to be limited in scope by the specific example implementations herein disclosed, since these implementations are intended as illustrations, and not limitations, of several aspects of the invention. Any equivalent implementations are intended to be within the scope of this invention. Indeed, various modifications of the invention in form and detail, in addition to those shown and described herein, will become apparent to those skilled in the art from the foregoing description. Such modifications are also intended to fall within the scope of the claims. The breadth and scope of the invention should not be limited by any of the example implementations disclosed herein, but should be defined only in accordance with the claims and their equivalents.