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Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid
Nuclear Inst. and Methods in Physics Research, A xxx (xxxx) xxx
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Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid D. Kim a ,∗, H.L. Andrews a , B.K. Choi b , R.L. Fleming a , C.-K. Huang a , T.J.T. Kwan a , J.W. Lewellen a , K. Nichols a , V. Pavlenko a , E.I. Simakov a a b
Los Alamos National Laboratory, Los Alamos, 87545, USA Cheju Halla University, Jeju-si, 63092, South Korea
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Keywords: Diamond field-emitter array Cathode Divergence Emittance
ABSTRACT This paper reports the results of a divergence study and emittance measurements for an electron beam emitted from a single diamond pyramid in a sparse diamond field-emitter array (DFEA) cathode. DFEA cathodes are arrays of micrometer scale diamond pyramids with nanometer scale tips. A single diamond pyramid produces currents as high as 10 μA from a small surface area. DFEA cathodes are expected to be a good beam source for compact dielectric laser accelerators. For the electron beam divergence experiment, we have designed and assembled a test stand consisting of a DFEA cathode, a mesh anode, and a screen. We measured current and the size of the beam on the screen as functions of the distance between the cathode and the anode, the size of a pyramid’s base, and applied voltage on the cathode. In order to perform beam emittance measurements, we designed and fabricated a magnetic lens to be placed between the mesh and the screen. By measuring the size of the beam for different distances between the lens and the screen, we estimate the beam’s emittance. We also simulated the electron beam dynamics with Computer Simulation Technology Studio and General Particle Tracer codes. Experimentally measured divergence angles and normalized transverse emittance show good agreement with simulations.
1. Introduction Compact dielectric laser accelerators (DLA) have been extensively studied in particular in the frame work of the accelerator on a chip international program (ACHIP) collaboration [1]. The goal of the ACHIP collaboration is to demonstrate an ‘‘accelerator in a shoebox’’. If successful, DLAs will find numerous applications in national security, medical imaging, and basic research. In recent years, high acceleration gradients in excess of several hundred MV/m for relativistic electrons have been demonstrated using dielectric grating structures [2–6]. The DLA consists of three major components: first is an electron emitter (cathode), second is a dielectric accelerator microstructure, and third is a near-infrared laser with the wavelength (≥800 nm) that provides electromagnetic energy to accelerate the electrons (see detailed explanation in ref. [7]). Due to the typical wavelength and dimensions of the structure, the cathodes must have nanometer size emitting areas (so-called needle cathodes) [8,9]. Two examples of the needle cathodes are a tungsten wire coated with diamond [10] and a silicon tip [11]. At Los Alamos National Laboratory (LANL), we have proposed to use diamond pyramids that are the base unit of a diamond fieldemitter array (DFEA) cathode as an electron source for a DLA [12].
DFEA cathodes have sharp nanometer scale tips (nanotips) on top of micrometer scale diamond pyramids. One of our fabricated cathode samples, Mo-25, is shown in Fig. 1. A diamond cathode (black) in shape of a 5.0 mm square was brazed on a polished molybdenum substrate [Fig. 1(a)]. Within the diamond square is a 5 × 5 array of 25 diamond pyramids [Fig. 1(b)]. Each pyramid in Fig. 1(b) has 20 μm base, and the spacing between pyramids is 200 μm [Fig. 1(b, c)]. On the top of each pyramid, there is an exquisitely sharp tip having a 10–20 nm radius [Fig. 1(d)]. DFEAs were invented at Vanderbilt University [13–16]. It has been reported that DFEA cathodes produce high per-tip current (≥15 μA) with low emittance (<1 μm rad) via field emission [14]. Currently, we have established capabilities to fabricate DFEAs at LANL [12,17]. After fabrication, we test the samples in a field emission regime to determine the emission uniformity and the number of emitting tips. The cathodes then undergo the conditioning process [18]. During conditioning and subsequent field emission studies [18,19], we observe beam divergence that characterizes the change of the size of the electron beam as a function of the distance from the nanotip. It includes effects of the beam’s emittance, but also geometrical effects of the cathode, and anode mesh defocusing effects. We conducted a study
∗ Corresponding author. E-mail address: [email protected] (D. Kim).
https://doi.org/10.1016/j.nima.2019.163055 Received 25 October 2019; Accepted 26 October 2019 Available online xxxx 0168-9002/Published by Elsevier B.V.
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
D. Kim, H.L. Andrews, B.K. Choi et al.
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Fig. 1. (a) A photograph of a polished molybdenum substrate with brazed diamond cathode. (b) Scanning electron microscope (SEM) image of a 5 × 5 array of diamond pyramids with a 200 μm spacing. (c) SEM image of a single pyramid with a 20 μm base. (d) SEM image of an exquisitely sharp tip on the top of the pyramid.
Fig. 2. (a) The layout of the experimental setup for divergence study. (b) The photograph of the test stand and (c) the photograph of the mesh anode with 100 wires per inch mounted on steel plate.
of the electron beam divergence and also estimated the emittance of an electron beam produced by the diamond pyramid cathode. In this paper, we first present the results of the electron beam divergence measurement in a direct current (DC) test stand. We study dependencies of the beam divergence on the base size of pyramids, anode–cathode (AK) gaps, and voltages applied to the cathode. Second, the focusing magnet and a collimator are added between the mesh and the AZO screen, and the transverse beam emittance is measured. We compare experimental results with simulations using Computer Simulation Technology (CST) Studio [20] and General Particle Tracer (GPT) [21] codes.
the tungsten mesh is mounted on a movable stage (Stage 1) and has a 9.52 mm (0.375-inch) aperture mesh at the center [Fig. 2(c)]. The mesh is welded to the back of the anode plate and has 100 lines per inch with 20 μm diameter wires. The AK gap can be varied remotely by moving Stage 1. This gap is initially set at 15.0 mm and decreased to increase electric field on the cathode and produce field emission. The screen is a conductive luminescent ZnO:Al2 O3 (AZO) coated sapphire substrate and is used to visualize the electron beam and measure its size and current. In this experiment, we studied two DFEA samples with different sizes of pyramid’s bases, Mo-25 and Mo-30. Both cathodes were 5 × 5 sparse arrays of 25 tips. Mo-25 has 20 μm base tips with 200 μm spacing, and Mo-30 has 10 μm base tips with 400 μm spacing. The experiment was conducted in the following order: first, we fixed the AK gap at 4 mm for Mo-25 and 3.6 mm for Mo-30, next, we moved the screen from 6 to 14 mm with 0.5 mm increments. With both samples, we observed emission from 2 separate tips. We measured the beam current and recorded the images of the beam on the AZO screen for each position of the screen. Several recorded images at a fixed position enabled us to obtain average sizes of electron beamlets. Second, we varied the voltage between the cathode and the mesh anode from 34 to 44 kV at 4.0 mm for Mo-25 and 3.6 mm for Mo-30 and repeated measurements of the beam size on the screen for different screen positions.
2. Detailed experimental setup for beam divergence The experimental setup for divergence studies is illustrated in Fig. 2(a) and (b). The relevant parameters of the experiment are summarized in Table 1. The test stand consists of the three parts: the cathode, the mesh anode, and the screen. The negative voltage of 40 kV is applied to the cathode through a 20 MΩ resistor that limits the current. The cathode is held in a clamp and is installed on an aluminum bracket. The cathode clamp is electrically isolated from the bottom of the chamber by four alumina (Al2 O3 ) rods. The mesh anode and the conductive screen are connected together to ground through a 20 kΩ resistor, allowing us to measure total emitted current that reached the anode and the screen from the cathode. A stainless steel plate with 2
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Table 1 Parameters for the divergence experiment. Parameters for the electron divergence experiment
Value
Applied voltage on the cathode Base size of the pyramids
34 kV to 44 kV 20 μm 10 μm 200 μm 400 μm 3.5 mm to 6.0 mm 3.2 mm to 4.2 mm 9.52 mm 0.635 mm 20 μm, 100 lines/inch 6 mm to 14 mm
Mo-25 Mo-30 Spacing between pyramids Mo-25 Mo-30 Distance from the mesh anode to the cathode Mo-25 Mo-30 Diameter of the mesh anode aperture Thickness of the mesh anode Diameter of the mesh wire and number of wires per inch Distance from the mesh anode to the screen
(0.5 mm intervals from 6.0 to 14.0 mm of the mesh-to-screen distance). The slope determines the divergence angle. Results of the measured divergence angles for the sample Mo-25 with 20 μm base pyramids (red circles) and the sample Mo-30 with 10 μm base pyramids (blue squares) are shown in Fig. 5. We observed that divergence angles were dependent on the AK gap and the size of pyramids. For the 20 μm base pyramids, the divergence angle was 2.61◦ at 3.5 mm AK gap. The angle decreased as the AK gap increased to 6 mm with constant voltage of 40 kV [Fig. 5(a)]. For the 10 μm base pyramids, the divergence data looked very similar. However, we could not measure the divergence for the AK gaps larger than 4.5 mm because the electron beam was unstable on the screen at low electric field for small pyramids. In the next test, we fixed the AK gap at 4 mm for Mo-25 and 3.6 mm for Mo-30 and measured the divergence angle as a function of the applied voltages. The results are shown in Fig. 5(b). We discovered that the divergence angle had very little dependence on the applied voltage. This must be due to the fact that the ratio of the longitudinal component of the electric field (Ez ) to the transverse component of the electric field (Ex and Ey ) does not change with voltage. The 20 μm base pyramid with 4.0 mm AK gap produced a beam with an approximately 2.4◦ divergence angle. Whereas the 10 μm base pyramid with 3.6 mm AK gap produced the beam with a smaller divergence angle of 2.0◦ despite a closer AK gap.
Fig. 3. A schematic of the beam divergence process in the experiment with a mesh anode. A red solid line illustrates the beam divergence when the mesh anode is not present. A blue dashed line shows the beam divergence after passing through the mesh. An additional contribution to divergence is introduced by the mesh.
4. Simulations of the beam divergence and comparison to the experiment A simulation of the beam divergence was performed using CST Studio and GPT. The CST model closely reproduced the experimental setup, as shown in Fig. 6. The model consisted of a single pyramid cathode on a metal plate, a mesh anode, and a conductive screen. The mesh anode was composed of a 20 μm diameter wire with 100 mesh lines per inch. A distance from the mesh anode to the cathode was varied from 3.0 mm to 7.0 mm. The cathode was held at a negative voltage, and both the mesh and the screen were at ground. The emitters were modeled with 10 and 20 μm pyramid base sizes and an opening angle of 70.6◦ , as shown in Fig. 6(b). On the top of the pyramid, we placed a nanowire with the height of 250 nm and a hemisphere apex with a radius of 10 nm [Fig. 6(c)] which is close to the average measured values for fabricated diamond pyramids. The electric field was modeled using the electrostatic solver in CST Studio. The parameters of the simulation are summarized in Table 2. We defined extremely fine mesh at both the emitter tip and the mechanical mesh area with the step sizes of 1 nm and 10 μm, respectively. This simulation produced electric field (Ex and Ez ) profiles which are plotted along the electron’s trajectory as shown in Fig. 6(d). In this figure, the electric field is plotted along a horizontal line that is offset by 5 nm from the x and 𝑦-axis, and the applied field is 8.5 MV/m with a 4 mm AK gap. Because of an extremely sharp nanotip at the top of the pyramid, the magnitudes of both Ex and Ez were approximately 2 GV/m at the tip, corresponding to the field enhancement by about a factor of 200. Simulations show that Ex component only exists near the nanotip region, and we believe it is mostly responsible for divergence. On the other hand, Ez component exists through the entire AK gap. Fig. 7(a) shows the initial uniform distribution of the electrons in GPT over the tip of the nanowire shown in Fig. 6(c). The electric field profile was exported to GPT which was used to simulate propagation of the electron beam. The results of the GPT simulations are shown in Fig. 7(b). Electrons travel on parabolic trajectories of a certain curvature in the AK gap and are spreading at an angle that becomes constant after passing through the mesh anode. The beam divergence angle was calculated and plotted as a function of AK gap and applied voltage for different sizes of pyramids. Red solid and blue dashed lines in Fig. 5 show the results for the 20 μm and 10 μm base pyramids, respectively. We determined
Fig. 3 illustrates the divergence process for the beam emitted from a single pyramid and passing through the mesh anode. In the experiment with the mesh anode, the divergence angle has a contribution from the mesh, given by [22] ℎ (A) 8𝑅 where 𝛿𝜃 is the contribution of mesh wire, h is the size of a single cell of the mesh, and R is the AK gap. In our experimental setup, the estimated contribution of the mesh varied between 0.52◦ for the AK gap of 3.2 mm and 0.28◦ for the AK gap of 6 mm. 𝛿𝜃 ∼
3. Experimental measurements of beam divergence Fig. 4(a) shows photographs of the luminescent spots produced by an electron beam hitting the AZO screen for the sample Mo-25 at the voltage of 40 kV. The typical electron emission patterns recorded by the camera (Canon EOS REBEL SL2 with EF 180 mm f/3.5 L Macro USM) placed behind the AZO screen are shown at different mesh-to-screen distances with the AK gap fixed at 4.0 mm. Each image consists of two beamlets because two tips were emitting. The beamlets are circled with white circles in Fig. 4(a). We analyzed images for one emitting tip [right beamlet in Fig. 4(a)]. The data analysis line is shown with a yellow dotted line in Fig. 4(a). As the screen was moved further away from the mesh anode, the size of the electron beamlet on the luminescent screen increased and the brightness decreased. To compute the size of the electron beam, images were first converted to grayscale. Next, the intensity of the image was normalized between 0 (black) and 1 (white) and integrated along each line of pixels to obtain the beam profile as shown in Fig. 4(b). A calibration of pixels to millimeters was performed, and the horizontal axis in Fig. 4(b) shows the distance along the screen in millimeters. We discovered that each beamlet had current distribution resembling a flat-top as opposed to a Gaussian distribution. Therefore, the size of the beam was computed at 90% of the full height of the distribution curve. Fig. 4(c) shows the average values of each beamlet’s radius with error bars at different positions of the screen 3
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Fig. 4. (a) Emission images on the AZO screen at different mesh-to-screen distances. White circles indicate two beamlets produced by emitting tips. (b) Normalized intensity of the right beamlet of the image shown in Fig. 4(a) for the mesh-to-screen distance of 6 mm plotted along a central line of pixels. (c) Calculated average beam radius as a function of the mesh-to-screen distance. The data was taken for the sample Mo-25 at a voltage of 40 kV.
Fig. 5. Measured and calculated divergence angles at different AK gaps and applied voltages. (a) The applied voltage was fixed at 40 kV, and the AK gap was varied. (b) The AK gap was fixed at 4.0 mm for Mo-25 and 3.6 mm for Mo-30, and the applied voltage was varied from 34 kV to 44 kV.
that smaller base emitter is expected to produce slightly smaller divergence angle. As shown in Fig. 5(a), each simulated divergence angle is expected to decrease in proportion to 1/(AK gap) for fixed voltage. This is in good agreement with the experimental data. Even though we changed the nanowire height from 250 nm to 100 nm, the corresponding variation of the divergence angle was small. As shown in
Fig. 5(b), simulated divergence angles were independent of the applied voltage that also agreed with the experiment results. We observed the same divergence angles even if the voltage between the cathode and the anode was increased to 100 kV in simulation. 4
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Fig. 6. (a) The CST model for the beam divergence simulation. (b) The CST model of a single pyramid. (c) Close up view of the CST model of the tip of the pyramid. (d) x (blue dashed line), y (green dotted line), and z (red solid line) components of the electric field profile with a 4.0 mm AK gap and 34 kV voltage across the gap as computed by the CST Studio. Purple and green dashed vertical lines indicate the front surface of the mesh plane and the location of mesh wires, respectively.
Fig. 7. (a) 25,000 electrons uniformly distributed along the emitting tip in GPT. (b) The simulated GPT DC beam trajectories are shown by overlaid snapshots of the particles at each time step. Table 2 Parameters for divergence simulation. Design parameters for the beam divergence simulation
Value
Applied voltage on the cathode Base size of the pyramids Distance from the mesh anode to the cathode Diameter of the mesh anode aperture Thickness of the mesh anode Diameter of the mesh wire Distance from the mesh anode to the screen Opening angle of the pyramid Length of the nanowire Radius of the emitter tip
34 kV to 44 kV 20 μm and 10 μm 3 mm to 7 mm 9.52 mm 0.635 mm 20 μm 14 mm 70.6◦ 250 nm 10 nm
focusing lens, including a collimator and two permanent ring magnets. A distance between two magnets was 5.3 mm, and measured maximum magnetic field strength along z axis was about 0.11 T. The collimating copper plate was located at the center of the ring magnets and had a 1 mm aperture to reduce the current and emittance. We assume that the position of the lens is at z = 0. The parameters of the focusing experiment are summarized in Table 3. The conductive screen was connected to ground through a 20 kΩ resistor to allow us to measure the beam current past the focusing lens. We moved the screen between the distances of 20 mm and 32 mm from the magnetic center of the lens. The electron beam energy and magnetic field strength were constant while performing the focusing experiments. Transfer matrices satisfy the following equation required to calculate the beam emittance using measurements of the beam spot size [22]
5. Estimates of beam emittance from spot-size measurements
2 𝜎𝑥,𝑛 = 𝜀𝑅211,𝑛 𝛽𝑜 − 2𝜀𝑅11,𝑛 𝑅12,𝑛 𝛼𝑜 + 𝜀𝑅212,𝑛
To estimate the transverse beam emittance for a single beamlet produced by the DFEA cathode, we employed the multiple wire measurement method along the beamline, separated by drift spaces [23,24]. As shown in Fig. 8(a), we placed two permanent ring magnets between the mesh anode and the conductive screen. These magnets formed a lens that focused the electron beam [25]. The lens and the mesh anode were grounded. Fig. 8(b) shows the detailed design for the
𝜀 with 𝜀 = 𝑁 , 𝛽𝛾
1 + 𝛼𝑜2 𝛽𝑜
(B) (C)
where 𝜎𝑥,𝑛 is the measured beam size on the nth measurement, 𝜀 is the unnormalized emittance, 𝑅𝑖𝑗 are the transfer matrix elements, 𝛼0 and 𝛽0 are Twiss parameters, 𝜀𝑁 is the normalized emittance, 𝛽 is the electron velocity divided by the speed of light c, and 𝛾 is the Lorentz factor. The 5
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Fig. 8. (a) Experimental setup for the electron beam emittance measurement using a focusing lens. (b) A detailed schematic drawing of the components (not to scale).
Fig. 9. Emission images on the AZO screen at different lens-to-screen distances.
general transfer matrix for the drift of length 𝐿𝑛 is [ ] 1 𝐿𝑛 𝑅= . 0 1
Table 3 Parameters for focusing study.
(D)
Design parameters for the beam focusing simulation
Value
(E)
Applied voltage on the cathode Base size of the pyramid (Mo-25) Distance from the mesh anode to the cathode Diameter of the collimator Distance from the mesh to the collimator Separation between two ring magnets Maximum magnetic field strength in z direction Distance from the mesh to the center of the magnet Distance from the center of the magnet to the screen
40 kV 20 μm 4.5 mm 1 mm 43.03 mm 5.3 mm 0.11 T 43.03 mm 20 mm to 32 mm
For the free space beam drift after the lens, Eq. (B) becomes: 2 𝜎𝑥,𝑛 = 𝜀𝛽𝑜 − 2𝜀𝛼𝑜 𝐿𝑛 + 𝜀
1 + 𝛼𝑜2 𝛽𝑜
𝐿2𝑛
The set of Eq. (E) written for multiple beam positions, 𝐿1 , 𝐿2 , . . . 𝐿𝑛 can be presented in matrix form as: 2 ⎤ ⎡𝜎𝑥,1 ⎡1 ⎢𝜎 2 ⎥ ⎢ ⎢ 𝑥,2 ⎥ = ⎢1 ⎢ ⋮ ⎥ ⎢⋮ ⎢ 2 ⎥ ⎢ ⎣𝜎𝑥,𝑛 ⎦ ⎣1
2𝐿1 2𝐿2 ⋮ 2𝐿𝑛
𝐿21 ⎤ ⎡ 𝛽𝑜 ⎤ ⎥⎢ ⎥ 𝐿22 ⎥ ⎢ −𝛼𝑜 ⎥ 𝜀 2 1 + 𝛼 ⎥ ⎢ ⋮ 𝑜⎥ ⎥ ⎥⎢ 𝐿2𝑛 ⎦ ⎣ 𝛽𝑜 ⎦
(F) of focusing lens. Also, as the screen moved from 20 mm to 32 mm, images of the electron beam on the screen slightly moved to the bottom left which was probably due to misalignment of focusing lens on the camera. The total shift of the center of the beamlet was about 0.3 mm (59 pixels, 1 pixel ≈ 5 μm) in both x and y directions.
Using Eq. (F) and at least three measurements of the beam spot sizes, we can determine the beam emittance and Twiss parameters. We conducted the experiment moving the screen between 20 mm and 32 mm from the lens and taking beam images. Fig. 9 shows the images of one single beamlet recorded at three various positions of the screen for the DFEA cathode Mo-25. The electron beam is unfocused at the screen position of 20 mm, close to being focused at 26 mm, and unfocused again at 32 mm. The beam size was again measured at 90% of the full height, same as in previous analysis in divergence study. The measured minimum beam radius was 60.0 μm at 26 mm from the center
Fig. 10 shows the measured beam radius in the transverse y-plane at different lens-to-screen distances. Using Eq. (F), the Twiss parameters and the emittance were calculated. The normalized transverse beam emittance computed from these experimental measurements was 0.689 μm rad. The total current measured on the conductive screen varied between 1.1 μA and 1.5 μA. 6
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Table 4 Results of the minimum beam radius and normalized transverse emittance.
Experiment Simulation with no offset Simulation with 1.15 mm offset
Minimum beam radius (μm)
Normalized transverse emittance (μm rad)
60.0 5.90 17.5
0.689 0.046 0.147
divergence angle. In addition, the divergence angles remained the same with reasonable variation of the applied voltage across the AK gap. We determined that the experimental results of the beam divergence were in good agreement with the results of the beam dynamics simulations. We designed permanent magnet lens to focus the beam and measured the transverse beam emittance. The experimentally measured beam emittance was slightly larger than the GPT simulation result. Currently we are working to improve the beam alignment and focusing. We also conduct the measurements of the focused beam size using knife edge scanner. We plan to demonstrate focusing of the electron beam into a spot that is a few micrometers in diameter. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors gratefully acknowledge the support of Los Alamos National Laboratory (LANL), USA Laboratory Directed Research and Development (LDRD), USA program. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Los Alamos National Laboratory (Contract DEAC52-06NA25396) and Sandia National Laboratories, USA (Contract DE-NA-0003525).
Fig. 10. Measured and computed beam spot size as a function of the lens-to-screen distance. The experimentally measured beam size was taken at 90% of the full height.
References We also performed GPT simulation of the beam propagation using the parameters shown in Table 3. The permanent ring magnets were simulated by POISSON [26], and the two-dimensional field map was exported to GPT. The maximum simulated magnetic field strength along z direction was 0.115 T. The results of the experiment and the simulation are summarized in Table 4. An initial simulation result is plotted with the red solid line in Fig. 10, with the focused beam radius of about 5.90 μm at 27.5 mm of lens-to-screen distance and the normalized emittance of about 0.046 μm rad. We conducted another simulation considering the misalignment of the focusing lens and the collimator observed in the experiment. We offset the magnetic lens in x and y axis at GPT by 1.15 mm. The results of the second simulation are shown with a blue dashed line in Fig. 10. In the second simulation, the beam spot size and the normalized emittance were 17.5 μm and 0.147 μm rad, respectively, much closer to measured values. We believe that a discrepancy between the experiment and simulation was mostly due to the spherical aberration of the lens and inaccurate measurements of the beam size on the AZO screen. In addition, focusing of the camera on the screen was controlled by hand in the experiment. Especially near the focal length, it was problematic to capture the clear spot image focused on the screen because of the extremely small size of the electron beamlet.
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6. Conclusions In this paper, we have reported the results of studying the electron beam divergence and measurements of the beam emittance for a diamond pyramid cathode. We conditioned two diamond arrays with two emitting tips each. One sample had pyramids with 20 μm base (Mo25), and the other one had pyramids with 10 μm base (Mo-30). We conducted measurements and simulations with CST Studio and GPT. In divergence study, we found that the experimentally measured and simulated divergence angles were dependent on the anode–cathode distance and on the size of the pyramid. We confirmed that the divergence angle decreased as the AK gap increased with fixed voltage. We observed that a larger base size of the pyramid resulted in a larger 7
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Nuclear Inst. and Methods in Physics Research, A xxx (xxxx) xxx [20] Computer Simulation Technology, Dassault Systemes, https://www.cst.com/. [21] General Particle Tracer, Pulsar Physics, http://www.pulsar.nl/gpt/. [22] J. Feng, J. Nasiatka, W. Wan, T. Vecchione, H.A. Padmore, A novel system for measurement of the transverse electron momentum distribution from photocathodes, Rev. Sci. Instrum. 86 (2015). [23] M.G. Minty, F. Zimmermann, Measurement and Control of Charged Particle Beams, Springer, 2003, pp. 99–116. [24] K. McDonald, D. Russell, Methods of Emittance Measurement, Springer, 1989, pp. 122–132. [25] R.L. Fleming, H.L. Andrews, K.A. Bishofberger, D. Kim, J.L. Lewellen, K. Nichols, D.Y. Shchegolkov, E.I. Simakov, A simple variable focus lens for field-emitter cathodes, in: Proc. 2018 Adv. Accel. Concepts Work. Breckenridge, CO, Unisted States, 2018, pp. 1–5. [26] POISSON, https://laacg.lanl.gov/laacg/services/download_sf.phtml.
[15] J.D. Jarvis, B.K. Choi, A.B. Hmelo, B. Ivanov, C.A. Brau, Emittance measurements of electron beams from diamond field emitter arrays, J. Vac. Sci. Technol. B Nanotechnol. Microelectron. Mater. Process. Meas. Phenom. 30 (2012) 042201. [16] P. Piot, C.A. Brau, B.K. Choi, B. Blomberg, W.E. Gabella, B. Ivanov, J. Jarvis, M.H. Mendenhall, D. Mihalcea, H. Panuganti, P. Prieto, J. Reid, Operation of an ungated diamond field-emission array cathode in a L-band radiofrequency electron source, Appl. Phys. Lett. 104 (2014). [17] D. Kim, H.L. Andrews, B.K. Choi, E.I. Simakov, Fabrication of micron-scale diamond field emitter arrays for dielectric laser accelerators, in: Proc. 2018 Adv. Accel. Concepts Work. Breckenridge, CO, Unisted States, 2018, pp. 2–4. [18] D. Kim, H.L. Andrews, R.L. Fleming, J.L. Lewellen, K. Nichols, V. Pavlenko, D.Y. Shchegolkov, E.I. Simakov, Study of the beam divergence in diamond field emitter array cathodes, in: Proc. 2018 Adv. Accel. Concepts Work. Breckenridge, CO, Unisted States, 2018, pp. 1–4. [19] H.L. Andrews, B.K. Choi, R.L. Fleming, D. Kim, J.W. Lewellen, K. Nichols, D.Y. Shchegolkov, E.I. and Simakov, An investigation of electron beam divergence from a single DFEA emitter tip, in: Proc. 9th International Particle Accelerator Conference, Vancouver, Canada, 2018, pp. 4662-4664.
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Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid D. Kim a ,∗, H.L. Andrews a , B.K. Choi b , R.L. Fleming a , C.-K. Huang a , T.J.T. Kwan a , J.W. Lewellen a , K. Nichols a , V. Pavlenko a , E.I. Simakov a a b
Los Alamos National Laboratory, Los Alamos, 87545, USA Cheju Halla University, Jeju-si, 63092, South Korea
ARTICLE
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Keywords: Diamond field-emitter array Cathode Divergence Emittance
ABSTRACT This paper reports the results of a divergence study and emittance measurements for an electron beam emitted from a single diamond pyramid in a sparse diamond field-emitter array (DFEA) cathode. DFEA cathodes are arrays of micrometer scale diamond pyramids with nanometer scale tips. A single diamond pyramid produces currents as high as 10 μA from a small surface area. DFEA cathodes are expected to be a good beam source for compact dielectric laser accelerators. For the electron beam divergence experiment, we have designed and assembled a test stand consisting of a DFEA cathode, a mesh anode, and a screen. We measured current and the size of the beam on the screen as functions of the distance between the cathode and the anode, the size of a pyramid’s base, and applied voltage on the cathode. In order to perform beam emittance measurements, we designed and fabricated a magnetic lens to be placed between the mesh and the screen. By measuring the size of the beam for different distances between the lens and the screen, we estimate the beam’s emittance. We also simulated the electron beam dynamics with Computer Simulation Technology Studio and General Particle Tracer codes. Experimentally measured divergence angles and normalized transverse emittance show good agreement with simulations.
1. Introduction Compact dielectric laser accelerators (DLA) have been extensively studied in particular in the frame work of the accelerator on a chip international program (ACHIP) collaboration [1]. The goal of the ACHIP collaboration is to demonstrate an ‘‘accelerator in a shoebox’’. If successful, DLAs will find numerous applications in national security, medical imaging, and basic research. In recent years, high acceleration gradients in excess of several hundred MV/m for relativistic electrons have been demonstrated using dielectric grating structures [2–6]. The DLA consists of three major components: first is an electron emitter (cathode), second is a dielectric accelerator microstructure, and third is a near-infrared laser with the wavelength (≥800 nm) that provides electromagnetic energy to accelerate the electrons (see detailed explanation in ref. [7]). Due to the typical wavelength and dimensions of the structure, the cathodes must have nanometer size emitting areas (so-called needle cathodes) [8,9]. Two examples of the needle cathodes are a tungsten wire coated with diamond [10] and a silicon tip [11]. At Los Alamos National Laboratory (LANL), we have proposed to use diamond pyramids that are the base unit of a diamond fieldemitter array (DFEA) cathode as an electron source for a DLA [12].
DFEA cathodes have sharp nanometer scale tips (nanotips) on top of micrometer scale diamond pyramids. One of our fabricated cathode samples, Mo-25, is shown in Fig. 1. A diamond cathode (black) in shape of a 5.0 mm square was brazed on a polished molybdenum substrate [Fig. 1(a)]. Within the diamond square is a 5 × 5 array of 25 diamond pyramids [Fig. 1(b)]. Each pyramid in Fig. 1(b) has 20 μm base, and the spacing between pyramids is 200 μm [Fig. 1(b, c)]. On the top of each pyramid, there is an exquisitely sharp tip having a 10–20 nm radius [Fig. 1(d)]. DFEAs were invented at Vanderbilt University [13–16]. It has been reported that DFEA cathodes produce high per-tip current (≥15 μA) with low emittance (<1 μm rad) via field emission [14]. Currently, we have established capabilities to fabricate DFEAs at LANL [12,17]. After fabrication, we test the samples in a field emission regime to determine the emission uniformity and the number of emitting tips. The cathodes then undergo the conditioning process [18]. During conditioning and subsequent field emission studies [18,19], we observe beam divergence that characterizes the change of the size of the electron beam as a function of the distance from the nanotip. It includes effects of the beam’s emittance, but also geometrical effects of the cathode, and anode mesh defocusing effects. We conducted a study
∗ Corresponding author. E-mail address: [email protected] (D. Kim).
https://doi.org/10.1016/j.nima.2019.163055 Received 25 October 2019; Accepted 26 October 2019 Available online xxxx 0168-9002/Published by Elsevier B.V.
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Fig. 1. (a) A photograph of a polished molybdenum substrate with brazed diamond cathode. (b) Scanning electron microscope (SEM) image of a 5 × 5 array of diamond pyramids with a 200 μm spacing. (c) SEM image of a single pyramid with a 20 μm base. (d) SEM image of an exquisitely sharp tip on the top of the pyramid.
Fig. 2. (a) The layout of the experimental setup for divergence study. (b) The photograph of the test stand and (c) the photograph of the mesh anode with 100 wires per inch mounted on steel plate.
of the electron beam divergence and also estimated the emittance of an electron beam produced by the diamond pyramid cathode. In this paper, we first present the results of the electron beam divergence measurement in a direct current (DC) test stand. We study dependencies of the beam divergence on the base size of pyramids, anode–cathode (AK) gaps, and voltages applied to the cathode. Second, the focusing magnet and a collimator are added between the mesh and the AZO screen, and the transverse beam emittance is measured. We compare experimental results with simulations using Computer Simulation Technology (CST) Studio [20] and General Particle Tracer (GPT) [21] codes.
the tungsten mesh is mounted on a movable stage (Stage 1) and has a 9.52 mm (0.375-inch) aperture mesh at the center [Fig. 2(c)]. The mesh is welded to the back of the anode plate and has 100 lines per inch with 20 μm diameter wires. The AK gap can be varied remotely by moving Stage 1. This gap is initially set at 15.0 mm and decreased to increase electric field on the cathode and produce field emission. The screen is a conductive luminescent ZnO:Al2 O3 (AZO) coated sapphire substrate and is used to visualize the electron beam and measure its size and current. In this experiment, we studied two DFEA samples with different sizes of pyramid’s bases, Mo-25 and Mo-30. Both cathodes were 5 × 5 sparse arrays of 25 tips. Mo-25 has 20 μm base tips with 200 μm spacing, and Mo-30 has 10 μm base tips with 400 μm spacing. The experiment was conducted in the following order: first, we fixed the AK gap at 4 mm for Mo-25 and 3.6 mm for Mo-30, next, we moved the screen from 6 to 14 mm with 0.5 mm increments. With both samples, we observed emission from 2 separate tips. We measured the beam current and recorded the images of the beam on the AZO screen for each position of the screen. Several recorded images at a fixed position enabled us to obtain average sizes of electron beamlets. Second, we varied the voltage between the cathode and the mesh anode from 34 to 44 kV at 4.0 mm for Mo-25 and 3.6 mm for Mo-30 and repeated measurements of the beam size on the screen for different screen positions.
2. Detailed experimental setup for beam divergence The experimental setup for divergence studies is illustrated in Fig. 2(a) and (b). The relevant parameters of the experiment are summarized in Table 1. The test stand consists of the three parts: the cathode, the mesh anode, and the screen. The negative voltage of 40 kV is applied to the cathode through a 20 MΩ resistor that limits the current. The cathode is held in a clamp and is installed on an aluminum bracket. The cathode clamp is electrically isolated from the bottom of the chamber by four alumina (Al2 O3 ) rods. The mesh anode and the conductive screen are connected together to ground through a 20 kΩ resistor, allowing us to measure total emitted current that reached the anode and the screen from the cathode. A stainless steel plate with 2
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Table 1 Parameters for the divergence experiment. Parameters for the electron divergence experiment
Value
Applied voltage on the cathode Base size of the pyramids
34 kV to 44 kV 20 μm 10 μm 200 μm 400 μm 3.5 mm to 6.0 mm 3.2 mm to 4.2 mm 9.52 mm 0.635 mm 20 μm, 100 lines/inch 6 mm to 14 mm
Mo-25 Mo-30 Spacing between pyramids Mo-25 Mo-30 Distance from the mesh anode to the cathode Mo-25 Mo-30 Diameter of the mesh anode aperture Thickness of the mesh anode Diameter of the mesh wire and number of wires per inch Distance from the mesh anode to the screen
(0.5 mm intervals from 6.0 to 14.0 mm of the mesh-to-screen distance). The slope determines the divergence angle. Results of the measured divergence angles for the sample Mo-25 with 20 μm base pyramids (red circles) and the sample Mo-30 with 10 μm base pyramids (blue squares) are shown in Fig. 5. We observed that divergence angles were dependent on the AK gap and the size of pyramids. For the 20 μm base pyramids, the divergence angle was 2.61◦ at 3.5 mm AK gap. The angle decreased as the AK gap increased to 6 mm with constant voltage of 40 kV [Fig. 5(a)]. For the 10 μm base pyramids, the divergence data looked very similar. However, we could not measure the divergence for the AK gaps larger than 4.5 mm because the electron beam was unstable on the screen at low electric field for small pyramids. In the next test, we fixed the AK gap at 4 mm for Mo-25 and 3.6 mm for Mo-30 and measured the divergence angle as a function of the applied voltages. The results are shown in Fig. 5(b). We discovered that the divergence angle had very little dependence on the applied voltage. This must be due to the fact that the ratio of the longitudinal component of the electric field (Ez ) to the transverse component of the electric field (Ex and Ey ) does not change with voltage. The 20 μm base pyramid with 4.0 mm AK gap produced a beam with an approximately 2.4◦ divergence angle. Whereas the 10 μm base pyramid with 3.6 mm AK gap produced the beam with a smaller divergence angle of 2.0◦ despite a closer AK gap.
Fig. 3. A schematic of the beam divergence process in the experiment with a mesh anode. A red solid line illustrates the beam divergence when the mesh anode is not present. A blue dashed line shows the beam divergence after passing through the mesh. An additional contribution to divergence is introduced by the mesh.
4. Simulations of the beam divergence and comparison to the experiment A simulation of the beam divergence was performed using CST Studio and GPT. The CST model closely reproduced the experimental setup, as shown in Fig. 6. The model consisted of a single pyramid cathode on a metal plate, a mesh anode, and a conductive screen. The mesh anode was composed of a 20 μm diameter wire with 100 mesh lines per inch. A distance from the mesh anode to the cathode was varied from 3.0 mm to 7.0 mm. The cathode was held at a negative voltage, and both the mesh and the screen were at ground. The emitters were modeled with 10 and 20 μm pyramid base sizes and an opening angle of 70.6◦ , as shown in Fig. 6(b). On the top of the pyramid, we placed a nanowire with the height of 250 nm and a hemisphere apex with a radius of 10 nm [Fig. 6(c)] which is close to the average measured values for fabricated diamond pyramids. The electric field was modeled using the electrostatic solver in CST Studio. The parameters of the simulation are summarized in Table 2. We defined extremely fine mesh at both the emitter tip and the mechanical mesh area with the step sizes of 1 nm and 10 μm, respectively. This simulation produced electric field (Ex and Ez ) profiles which are plotted along the electron’s trajectory as shown in Fig. 6(d). In this figure, the electric field is plotted along a horizontal line that is offset by 5 nm from the x and 𝑦-axis, and the applied field is 8.5 MV/m with a 4 mm AK gap. Because of an extremely sharp nanotip at the top of the pyramid, the magnitudes of both Ex and Ez were approximately 2 GV/m at the tip, corresponding to the field enhancement by about a factor of 200. Simulations show that Ex component only exists near the nanotip region, and we believe it is mostly responsible for divergence. On the other hand, Ez component exists through the entire AK gap. Fig. 7(a) shows the initial uniform distribution of the electrons in GPT over the tip of the nanowire shown in Fig. 6(c). The electric field profile was exported to GPT which was used to simulate propagation of the electron beam. The results of the GPT simulations are shown in Fig. 7(b). Electrons travel on parabolic trajectories of a certain curvature in the AK gap and are spreading at an angle that becomes constant after passing through the mesh anode. The beam divergence angle was calculated and plotted as a function of AK gap and applied voltage for different sizes of pyramids. Red solid and blue dashed lines in Fig. 5 show the results for the 20 μm and 10 μm base pyramids, respectively. We determined
Fig. 3 illustrates the divergence process for the beam emitted from a single pyramid and passing through the mesh anode. In the experiment with the mesh anode, the divergence angle has a contribution from the mesh, given by [22] ℎ (A) 8𝑅 where 𝛿𝜃 is the contribution of mesh wire, h is the size of a single cell of the mesh, and R is the AK gap. In our experimental setup, the estimated contribution of the mesh varied between 0.52◦ for the AK gap of 3.2 mm and 0.28◦ for the AK gap of 6 mm. 𝛿𝜃 ∼
3. Experimental measurements of beam divergence Fig. 4(a) shows photographs of the luminescent spots produced by an electron beam hitting the AZO screen for the sample Mo-25 at the voltage of 40 kV. The typical electron emission patterns recorded by the camera (Canon EOS REBEL SL2 with EF 180 mm f/3.5 L Macro USM) placed behind the AZO screen are shown at different mesh-to-screen distances with the AK gap fixed at 4.0 mm. Each image consists of two beamlets because two tips were emitting. The beamlets are circled with white circles in Fig. 4(a). We analyzed images for one emitting tip [right beamlet in Fig. 4(a)]. The data analysis line is shown with a yellow dotted line in Fig. 4(a). As the screen was moved further away from the mesh anode, the size of the electron beamlet on the luminescent screen increased and the brightness decreased. To compute the size of the electron beam, images were first converted to grayscale. Next, the intensity of the image was normalized between 0 (black) and 1 (white) and integrated along each line of pixels to obtain the beam profile as shown in Fig. 4(b). A calibration of pixels to millimeters was performed, and the horizontal axis in Fig. 4(b) shows the distance along the screen in millimeters. We discovered that each beamlet had current distribution resembling a flat-top as opposed to a Gaussian distribution. Therefore, the size of the beam was computed at 90% of the full height of the distribution curve. Fig. 4(c) shows the average values of each beamlet’s radius with error bars at different positions of the screen 3
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Fig. 4. (a) Emission images on the AZO screen at different mesh-to-screen distances. White circles indicate two beamlets produced by emitting tips. (b) Normalized intensity of the right beamlet of the image shown in Fig. 4(a) for the mesh-to-screen distance of 6 mm plotted along a central line of pixels. (c) Calculated average beam radius as a function of the mesh-to-screen distance. The data was taken for the sample Mo-25 at a voltage of 40 kV.
Fig. 5. Measured and calculated divergence angles at different AK gaps and applied voltages. (a) The applied voltage was fixed at 40 kV, and the AK gap was varied. (b) The AK gap was fixed at 4.0 mm for Mo-25 and 3.6 mm for Mo-30, and the applied voltage was varied from 34 kV to 44 kV.
that smaller base emitter is expected to produce slightly smaller divergence angle. As shown in Fig. 5(a), each simulated divergence angle is expected to decrease in proportion to 1/(AK gap) for fixed voltage. This is in good agreement with the experimental data. Even though we changed the nanowire height from 250 nm to 100 nm, the corresponding variation of the divergence angle was small. As shown in
Fig. 5(b), simulated divergence angles were independent of the applied voltage that also agreed with the experiment results. We observed the same divergence angles even if the voltage between the cathode and the anode was increased to 100 kV in simulation. 4
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Fig. 6. (a) The CST model for the beam divergence simulation. (b) The CST model of a single pyramid. (c) Close up view of the CST model of the tip of the pyramid. (d) x (blue dashed line), y (green dotted line), and z (red solid line) components of the electric field profile with a 4.0 mm AK gap and 34 kV voltage across the gap as computed by the CST Studio. Purple and green dashed vertical lines indicate the front surface of the mesh plane and the location of mesh wires, respectively.
Fig. 7. (a) 25,000 electrons uniformly distributed along the emitting tip in GPT. (b) The simulated GPT DC beam trajectories are shown by overlaid snapshots of the particles at each time step. Table 2 Parameters for divergence simulation. Design parameters for the beam divergence simulation
Value
Applied voltage on the cathode Base size of the pyramids Distance from the mesh anode to the cathode Diameter of the mesh anode aperture Thickness of the mesh anode Diameter of the mesh wire Distance from the mesh anode to the screen Opening angle of the pyramid Length of the nanowire Radius of the emitter tip
34 kV to 44 kV 20 μm and 10 μm 3 mm to 7 mm 9.52 mm 0.635 mm 20 μm 14 mm 70.6◦ 250 nm 10 nm
focusing lens, including a collimator and two permanent ring magnets. A distance between two magnets was 5.3 mm, and measured maximum magnetic field strength along z axis was about 0.11 T. The collimating copper plate was located at the center of the ring magnets and had a 1 mm aperture to reduce the current and emittance. We assume that the position of the lens is at z = 0. The parameters of the focusing experiment are summarized in Table 3. The conductive screen was connected to ground through a 20 kΩ resistor to allow us to measure the beam current past the focusing lens. We moved the screen between the distances of 20 mm and 32 mm from the magnetic center of the lens. The electron beam energy and magnetic field strength were constant while performing the focusing experiments. Transfer matrices satisfy the following equation required to calculate the beam emittance using measurements of the beam spot size [22]
5. Estimates of beam emittance from spot-size measurements
2 𝜎𝑥,𝑛 = 𝜀𝑅211,𝑛 𝛽𝑜 − 2𝜀𝑅11,𝑛 𝑅12,𝑛 𝛼𝑜 + 𝜀𝑅212,𝑛
To estimate the transverse beam emittance for a single beamlet produced by the DFEA cathode, we employed the multiple wire measurement method along the beamline, separated by drift spaces [23,24]. As shown in Fig. 8(a), we placed two permanent ring magnets between the mesh anode and the conductive screen. These magnets formed a lens that focused the electron beam [25]. The lens and the mesh anode were grounded. Fig. 8(b) shows the detailed design for the
𝜀 with 𝜀 = 𝑁 , 𝛽𝛾
1 + 𝛼𝑜2 𝛽𝑜
(B) (C)
where 𝜎𝑥,𝑛 is the measured beam size on the nth measurement, 𝜀 is the unnormalized emittance, 𝑅𝑖𝑗 are the transfer matrix elements, 𝛼0 and 𝛽0 are Twiss parameters, 𝜀𝑁 is the normalized emittance, 𝛽 is the electron velocity divided by the speed of light c, and 𝛾 is the Lorentz factor. The 5
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
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Fig. 8. (a) Experimental setup for the electron beam emittance measurement using a focusing lens. (b) A detailed schematic drawing of the components (not to scale).
Fig. 9. Emission images on the AZO screen at different lens-to-screen distances.
general transfer matrix for the drift of length 𝐿𝑛 is [ ] 1 𝐿𝑛 𝑅= . 0 1
Table 3 Parameters for focusing study.
(D)
Design parameters for the beam focusing simulation
Value
(E)
Applied voltage on the cathode Base size of the pyramid (Mo-25) Distance from the mesh anode to the cathode Diameter of the collimator Distance from the mesh to the collimator Separation between two ring magnets Maximum magnetic field strength in z direction Distance from the mesh to the center of the magnet Distance from the center of the magnet to the screen
40 kV 20 μm 4.5 mm 1 mm 43.03 mm 5.3 mm 0.11 T 43.03 mm 20 mm to 32 mm
For the free space beam drift after the lens, Eq. (B) becomes: 2 𝜎𝑥,𝑛 = 𝜀𝛽𝑜 − 2𝜀𝛼𝑜 𝐿𝑛 + 𝜀
1 + 𝛼𝑜2 𝛽𝑜
𝐿2𝑛
The set of Eq. (E) written for multiple beam positions, 𝐿1 , 𝐿2 , . . . 𝐿𝑛 can be presented in matrix form as: 2 ⎤ ⎡𝜎𝑥,1 ⎡1 ⎢𝜎 2 ⎥ ⎢ ⎢ 𝑥,2 ⎥ = ⎢1 ⎢ ⋮ ⎥ ⎢⋮ ⎢ 2 ⎥ ⎢ ⎣𝜎𝑥,𝑛 ⎦ ⎣1
2𝐿1 2𝐿2 ⋮ 2𝐿𝑛
𝐿21 ⎤ ⎡ 𝛽𝑜 ⎤ ⎥⎢ ⎥ 𝐿22 ⎥ ⎢ −𝛼𝑜 ⎥ 𝜀 2 1 + 𝛼 ⎥ ⎢ ⋮ 𝑜⎥ ⎥ ⎥⎢ 𝐿2𝑛 ⎦ ⎣ 𝛽𝑜 ⎦
(F) of focusing lens. Also, as the screen moved from 20 mm to 32 mm, images of the electron beam on the screen slightly moved to the bottom left which was probably due to misalignment of focusing lens on the camera. The total shift of the center of the beamlet was about 0.3 mm (59 pixels, 1 pixel ≈ 5 μm) in both x and y directions.
Using Eq. (F) and at least three measurements of the beam spot sizes, we can determine the beam emittance and Twiss parameters. We conducted the experiment moving the screen between 20 mm and 32 mm from the lens and taking beam images. Fig. 9 shows the images of one single beamlet recorded at three various positions of the screen for the DFEA cathode Mo-25. The electron beam is unfocused at the screen position of 20 mm, close to being focused at 26 mm, and unfocused again at 32 mm. The beam size was again measured at 90% of the full height, same as in previous analysis in divergence study. The measured minimum beam radius was 60.0 μm at 26 mm from the center
Fig. 10 shows the measured beam radius in the transverse y-plane at different lens-to-screen distances. Using Eq. (F), the Twiss parameters and the emittance were calculated. The normalized transverse beam emittance computed from these experimental measurements was 0.689 μm rad. The total current measured on the conductive screen varied between 1.1 μA and 1.5 μA. 6
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
D. Kim, H.L. Andrews, B.K. Choi et al.
Nuclear Inst. and Methods in Physics Research, A xxx (xxxx) xxx
Table 4 Results of the minimum beam radius and normalized transverse emittance.
Experiment Simulation with no offset Simulation with 1.15 mm offset
Minimum beam radius (μm)
Normalized transverse emittance (μm rad)
60.0 5.90 17.5
0.689 0.046 0.147
divergence angle. In addition, the divergence angles remained the same with reasonable variation of the applied voltage across the AK gap. We determined that the experimental results of the beam divergence were in good agreement with the results of the beam dynamics simulations. We designed permanent magnet lens to focus the beam and measured the transverse beam emittance. The experimentally measured beam emittance was slightly larger than the GPT simulation result. Currently we are working to improve the beam alignment and focusing. We also conduct the measurements of the focused beam size using knife edge scanner. We plan to demonstrate focusing of the electron beam into a spot that is a few micrometers in diameter. Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors gratefully acknowledge the support of Los Alamos National Laboratory (LANL), USA Laboratory Directed Research and Development (LDRD), USA program. This work was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science by Los Alamos National Laboratory (Contract DEAC52-06NA25396) and Sandia National Laboratories, USA (Contract DE-NA-0003525).
Fig. 10. Measured and computed beam spot size as a function of the lens-to-screen distance. The experimentally measured beam size was taken at 90% of the full height.
References We also performed GPT simulation of the beam propagation using the parameters shown in Table 3. The permanent ring magnets were simulated by POISSON [26], and the two-dimensional field map was exported to GPT. The maximum simulated magnetic field strength along z direction was 0.115 T. The results of the experiment and the simulation are summarized in Table 4. An initial simulation result is plotted with the red solid line in Fig. 10, with the focused beam radius of about 5.90 μm at 27.5 mm of lens-to-screen distance and the normalized emittance of about 0.046 μm rad. We conducted another simulation considering the misalignment of the focusing lens and the collimator observed in the experiment. We offset the magnetic lens in x and y axis at GPT by 1.15 mm. The results of the second simulation are shown with a blue dashed line in Fig. 10. In the second simulation, the beam spot size and the normalized emittance were 17.5 μm and 0.147 μm rad, respectively, much closer to measured values. We believe that a discrepancy between the experiment and simulation was mostly due to the spherical aberration of the lens and inaccurate measurements of the beam size on the AZO screen. In addition, focusing of the camera on the screen was controlled by hand in the experiment. Especially near the focal length, it was problematic to capture the clear spot image focused on the screen because of the extremely small size of the electron beamlet.
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6. Conclusions In this paper, we have reported the results of studying the electron beam divergence and measurements of the beam emittance for a diamond pyramid cathode. We conditioned two diamond arrays with two emitting tips each. One sample had pyramids with 20 μm base (Mo25), and the other one had pyramids with 10 μm base (Mo-30). We conducted measurements and simulations with CST Studio and GPT. In divergence study, we found that the experimentally measured and simulated divergence angles were dependent on the anode–cathode distance and on the size of the pyramid. We confirmed that the divergence angle decreased as the AK gap increased with fixed voltage. We observed that a larger base size of the pyramid resulted in a larger 7
Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.
D. Kim, H.L. Andrews, B.K. Choi et al.
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[15] J.D. Jarvis, B.K. Choi, A.B. Hmelo, B. Ivanov, C.A. Brau, Emittance measurements of electron beams from diamond field emitter arrays, J. Vac. Sci. Technol. B Nanotechnol. Microelectron. Mater. Process. Meas. Phenom. 30 (2012) 042201. [16] P. Piot, C.A. Brau, B.K. Choi, B. Blomberg, W.E. Gabella, B. Ivanov, J. Jarvis, M.H. Mendenhall, D. Mihalcea, H. Panuganti, P. Prieto, J. Reid, Operation of an ungated diamond field-emission array cathode in a L-band radiofrequency electron source, Appl. Phys. Lett. 104 (2014). [17] D. Kim, H.L. Andrews, B.K. Choi, E.I. Simakov, Fabrication of micron-scale diamond field emitter arrays for dielectric laser accelerators, in: Proc. 2018 Adv. Accel. Concepts Work. Breckenridge, CO, Unisted States, 2018, pp. 2–4. [18] D. Kim, H.L. Andrews, R.L. Fleming, J.L. Lewellen, K. Nichols, V. Pavlenko, D.Y. Shchegolkov, E.I. Simakov, Study of the beam divergence in diamond field emitter array cathodes, in: Proc. 2018 Adv. Accel. Concepts Work. Breckenridge, CO, Unisted States, 2018, pp. 1–4. [19] H.L. Andrews, B.K. Choi, R.L. Fleming, D. Kim, J.W. Lewellen, K. Nichols, D.Y. Shchegolkov, E.I. and Simakov, An investigation of electron beam divergence from a single DFEA emitter tip, in: Proc. 9th International Particle Accelerator Conference, Vancouver, Canada, 2018, pp. 4662-4664.
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Please cite this article as: D. Kim, H.L. Andrews, B.K. Choi et al., Divergence study and emittance measurements for the electron beam emitted from a diamond pyramid, Nuclear Inst. and Methods in Physics Research, A (2019) 163055, https://doi.org/10.1016/j.nima.2019.163055.