A compact electron source for the dielectric laser accelerator

Benchtop-sized electron linear accelerators using dielectric laser accelerator (DLA) technology have been intensively investigated in recent years.^1–10 DLAs can generate accelerating gradients one to two orders of magnitude higher than conventional radio frequency accelerators, enabling a significant reduction in the size of linear accelerators.^1,2,11,12 To achieve the goal of a benchtop-sized accelerator, it is essential to miniaturize all accelerator components, including the electron injector system.^12–14 Previously, McNeur et al. proposed a DLA system where the length between the electron source and the DLA inlet is between 10 and 30 mm.¹⁵ Other implementations use a scanning electron microscope as the injector; the most compact system demonstrated thus far has roughly 200 mm between the cathode and the DLA structure.¹⁶ Additionally, compact ultrafast electron sources are extremely beneficial for electron diffraction or microscopy experiments, and this source has the potential to shrink the overall size and complexity of those systems considerably.^17–21 

In this Letter, we propose and demonstrate a compact, integrated electron source for a DLA beamline consisting of a photoassisted field emitter based on silicon nanotips²² and a compact electrostatic lens, also silicon-based. The final beam energy was chosen to be 30 keV, which was sufficient energy for a proof-of-concept with a DLA experiment.² This source provides electron currents up to 28 electrons/pulse at a repetition rate of 100 kHz. The electron bunch length was measured by cross correlation¹⁶ with a 220 fs pulsed laser beam and was sub-picosecond for all the measured currents, with a minimum bunch length of 540 ± 50 fs at 0.012 electron/pulse. The lens working distance was measured to be 20 mm, providing a minimum RMS spot size of 0.40 μm with the corresponding RMS divergence angle of 0.45 mrad. An acceleration experiment with a single-grating DLA²³ was performed to demonstrate that this lens unit can serve as an injector for the DLA. This integrated, few-cm scale source is nearly an order of magnitude smaller in size compared to previous electron sources with built-in focusing at 30 keV or higher energies and has excellent beam parameters for a variety of ultrafast electron applications.^16,17,20,24

A single-aperture electrostatic lens design was chosen for the DLA electron source due to its simple structure. This design consists of a cathode, a focusing electrode, and an anode (see Fig. 1). When different potential gradients exist across the focusing electrode, a focusing or defocusing electrostatic field is formed around the focusing electrode according to the Davisson–Calbick formula given by the following equation:²⁵ 

where ϕ is the axial potential at the focusing electrode relative to the cathode potential, E₁ is the electric field between the cathode and the focusing electrode, and E₂ is the electric field between the focusing electrode and the anode. According to Eq. (1), the working distance can be reduced by reducing ϕ and/or increasing |E₁ − E₂|. Additionally, the length of the reduced field region between the cathode and the focusing electrode should be minimized to suppress unfavorable broadening of the electron bunch length.²⁶ 

Figure 1(a) shows the schematic of the experimental setup, which consists of the lens unit, a single grating DLA, knife edges, a microchannel plate (MCP) detector, and an illuminating laser. The detailed dimensions of the electrostatic lens are shown in Fig. 1(b) and Table I. The nanotip emitter was illuminated at an angle of 33° relative to the xy-plane.

In this work, we use two sets of lenses, which have the same essential structure but slightly varied dimensions. A polished, highly doped 0.4 mm thick Si wafer was used as the electrode material. The apertures were laser cut and then mechanically polished to be much larger than the electron beam diameter, allowing all electrons emitted from the cathode to be collected. The silicon nanotip was fabricated from a 1–5 Ω cm phosphorus-doped silicon wafer as shown in Fig. 1(c). This nanotip was fabricated using maskless photolithography and subsequent isotropic etching and oxidative sharpening.²² As shown in Table I, the tip radius and height for configuration #1 were 22 nm and 430 nm and 8.5 nm and 300 nm for #2, respectively. The cathode, insulator plate and focusing electrode were attached to a stainless-steel jacket [Fig. 1(d)]. The cathode potential was −30 kV, and the working distance was adjusted by varying the focusing electrode potential. Typically, bias voltages of −3.5 kV for configuration #1 and −1.5 kV for #2 relative to the cathode (−33.5 and −31.5 kV to ground, respectively) were applied to obtain a working distance of 20 mm. The gaps from the focusing electrode to the anode were 4 mm for #1 and 3 mm for #2, and thus, the average field strengths were 8.4 kV/mm and 10.5 kV/mm, respectively.

Both the cathode and the DLA structure were driven by a mid-infrared optical parametric amplifier (Light Conversion Orpheus-HP pumped by a Light Conversion Pharos Laser) with a center wavelength of 1960 nm and a full width at half maximum (FWHM) pulse duration of 220 fs at a repetition rate of 100 kHz. The electrons from the cathode were produced by multi-photon emission, which reduced the effective tip trigger pulse length to approximately 100 fs. The expected multi-photon order for 1960 nm illumination was 8–9 based on previous measurements.²² An optical delay line was used to adjust the timing offset between the DLA drive pulse and the cathode pulse. The laser was focused to 32 μm (1/e² radius) on the cathode and 48 μm (1/e² radius) on the DLA. The peak laser intensities ranged up to 2.8 × 10¹⁰ W/cm² (local electric field value: 0.46 GV/m) for the cathode and 5.6 × 10¹⁰ W/cm² (0.65 GV/m) for the DLA device. The electron bunch length was measured by cross correlation with the 220 fs DLA drive pulse.^16,23,27 When driven by a pulsed laser beam, the silicon DLA grating [260 nm wide, 410 nm tall, 380 nm spacing, and 25 μm overall length, see Fig. 1(e)] creates evanescent fields with a temporal envelope of 220 fs, which modulates the electron beam energy as it passes over the grating, providing the cross correlation signal for the pulse length measurement.¹⁶ 

The focused spot size and divergence of the electron beam were measured by a knife edge scan, using knife edges made of cleaved Si wafers. The knife edges were located 20 mm and 170 mm from the cathode [see Fig. 1(a)]. The electron beam was scanned along the x-axis, across the knife edge, by magnetic deflection coils [see Fig. 1(a)], and the spot size was analyzed by the recorded transmission current as a function of deflection distance.

The electron beam was observed using a Photonics Advanced Long-Life two-stage microchannel plate (MCP) detector with a P47 phosphor screen. The MCP was placed 280 mm from the cathode. Electron currents less than one electron/pulse (<100 000 electrons/s) were measured by electron counting on the MCP, and larger currents were measured using a Faraday cup and picoammeter.

To confirm the electron beam trajectory within the lens unit, we first calculated electrostatic field maps using a finite element solver (COMSOL Multiphysics). We then used a fifth order Runge–Kutta particle tracking code (General Particle Tracer) to analyze the beam trajectory. Reasonably close agreement was found between the simulated and experimental electrostatic focusing voltages and electron beam parameters.

Figures 2(a) and (b) show the unfocused electron beam profiles on the MCP screen for configurations #1 and #2 (parameters listed in Table I). In configuration #1, a Gaussian beam profile was observed. In configuration #2, a ring-shaped beam was observed. The difference in the beam profile derives from differences in the geometry of the silicon nanotip emitter and the resulting localized enhancement of the drive laser fields.^19,22 The ring beam results from electron emission slightly off from the apex of the sharper tip, whereas the Gaussian beam results from on-axis emission from the larger radius tip.²² The off-apex emission of a ring beam provides higher emission currents but results in a larger emittance beam with stronger spherical aberrations in the immersion lens focus. We characterized the focusing performance of the different lens configurations by measuring the beam diameter, divergence, and bunch length. The electron beams were focused at 20 mm from the cathode. Figures 2(c) and 2(d) show typical profiles for the first and second knife edges. The measured 10%–90% diameter (D_10–90) was converted to the RMS diameter (D_RMS) using D_10–90 = 2.56 D_RMS. A typical cross correlation measurement of the electron bunch length is shown in Fig. 2(e). In this figure, the FWHM of the Gaussian fit was 660 fs. The electron bunch length was then calculated by deconvolution of the 660 fs Gaussian with the 220 × $2$ fs electric field envelope of the DLA fields, also Gaussian. Finally, we calculated 5D brightness using the emittance and bunch length.²⁸ 

Table II shows the characterization results of the focused electron beams at a working distance of 20 mm. We measured both configurations #1 and #2 at currents ≪1 electron/pulse, where space charge effects can be neglected. Due to the larger tip radius of configuration #1, this cathode had much less emission efficiency than that of #2 and thus required higher laser intensity. To avoid laser damage, we measured #1 in a lower current regime. The RMS beam diameter and divergence were 0.4 μm and 0.45 mrad for #1 at 0.012 electrons/pulse and 1.2 μm and 1.0 mrad for #2 at 0.025 electrons/pulse. The measured divergences implied that the electron beam with #1 had smaller initial emission angle distribution than that with #2. An electron beam with a larger divergence angle is more strongly affected by spherical aberration in the electron lens, and therefore, configuration #1 achieved a smaller focused spot compared to #2. The normalized emittance was 62 pm-rad with a maximum 5D brightness of 2.4 × 10¹² A/(m² rad²) at a FWHM electron bunch length of 540 ± 50 fs for configuration #1. This meets the 100 pm-rad emittance requirement for an alternating phase confinement scheme for the DLA.¹³ 

For configuration #2, the electron beam was characterized at a higher current of up to 28 electrons/pulse. In all current conditions for #2, the RMS beam diameters had similar values, 1.1 to 1.3 μm. The beam divergence remained constant at 1.0 mrad as current increased as shown in Table II. The normalized emittance increased from 397 pm-rad in the single electron regime to 436 pm-rad at 28 electrons per laser pulse. The bunch length gradually increased with increasing current (see Table II), likely due to space charge causing broadening of the electron bunch length in the multiple electrons/pulse regime.²⁹ In our simulations, the space charge effects measurably increased the bunch length for more than 5 electrons/pulse. The 5D brightness increased upon increasing beam current up to a maximum of 6.8 × 10¹³ A/(m² rad²) for 28 electrons/pulse in a 700 ± 80 fs FWHM electron bunch.

We observed in both configurations that the measured electron bunch lengths were larger than the effective trigger pulse length used for cathode excitation. The photoelectrons have initial angle and energy distributions, which causes the variation in the trajectory length and electron speed across the ensemble of emitted electrons. We confirmed that the nonzero angle and energy spread increase the measured final bunch length in simulation. Energy spread could be reduced in future experiments by using lower photon-order excitation.¹⁷ 

In summary, we have developed a compact, integrated electron lens unit with a silicon based, two-element electrostatic lens and a silicon nanotip photocathode. Our lens produces a 30 keV electron beam focused to a sub-micrometer spot size of 20 mm from the cathode. We also demonstrate that this electron beam is suitable as a source for the DLA by conducting a DLA experiment, which we use to measure the electron bunch length. This source also has potential to be used for a variety of ultrafast electron microscopy, diffraction, and point projection applications, including imaging and diffraction of material phase transitions and biological structural changes.^17–21 The minimum bunch length in the <1 electron/pulse regime was limited by initial energy and angular spread of the photoelectrons. In the multiple electrons/pulse regime, space charge effects also increase the bunch length. Higher current regimes are accessible by increasing the excitation laser power up to the laser damage threshold of the silicon nanotips, optimizing the silicon tip geometry for a given excitation wavelength or increasing the laser repetition rate. The working distance shown here (20 mm) is the shortest yet produced as an electron focusing system for the DLA, one order of magnitude smaller than previous experiments,¹⁶ which enables a dramatic reduction in the total length of a benchtop sized linear accelerator or compact ultrafast electron microscopy and diffraction applications.

This work was funded by the Gordon and Betty Moore Foundation (No. GBMF4744). We wish to thank Professor P. Hommelhoff and Professor O. Solgaard for fruitful discussion.