PHYSICS OF PLASMAS 21, 023110 (2014)
Numerically optimized structures for dielectric asymmetric dual-grating laser accelerators A. Aimidula,1,2,3 M. A. Bake,1 F. Wan,1 B. S. Xie,1,a) C. P. Welsch,2,3 G. Xia,2,4 O. Mete,2,4 M. Uesaka,5 Y. Matsumura,5 M. Yoshida,6 and K. Koyama6
1 Key Laboratory of Beam Technology and Materials Modification of the Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China 2 Cockcroft Institute, Daresbury Sci-Tech, Warrington WA44AD, United Kingdom 3 Physics Department, University of Liverpool, Liverpool, United Kingdom 4 School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 5 Department of Nuclear Engineering and Management, The University of Tokyo, Tokai 319-1188, Japan 6 High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305-0801, Japan
(Received 6 January 2014; accepted 5 February 2014; published online 20 February 2014) Optical scale dielectric structures are promising candidates to realize future compact, low cost particle accelerators, since they can sustain high acceleration gradients in the range of GeV/m. Here, we present numerical simulation results for a dielectric asymmetric dual-grating accelerator. It was found that the asymmetric dual-grating structures can efficiently modify the laser field to synchronize it with relativistic electrons, therefore increasing the average acceleration gradient by 10% in comparison to symmetric structures. The optimum pillar height which was determined by simulation agrees well with that estimated analytically. The effect of the initial kinetic energy of injected electrons on the acceleration gradient is also discussed. Finally, the required laser C 2014 parameters were calculated analytically and a suitable laser is proposed as energy source. V AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4866020] I. INTRODUCTION
Novel accelerators based on lasers are considered to have great potential to substitute current accelerators based on conventional radio-frequency technology in order to substantially reduce the size and associated costs of future accelerators. Development of ultra short intense laser technology has led to remarkable achievements in recent laser-plasma acceleration experiments.1,2 However, in these schemes, the phase velocity of the accelerating mode is less than the speed of light. This leads to a dephasing between the accelerating wave and the relativistic particles.3,4 Consequently, the particles can only be accelerated over a short distance and the maximum attainable energies are limited. Micro-fabricated dielectric laser accelerators (DLAs) are an alternative, attractive approach5–10 due to the high damage threshold of dielectric materials and because they offer continuous acceleration to relativistic11 as well as nonrelativistic12 charged particles. DLAs are also able to deliver nm-beams of sub-fs pulses, since the transverse dimensions of the acceleration channel are on the operating laser wavelength scale. These beams have unique advantages for investigating basic radiobiology processes as they are able to target single DNA strands.13 There are currently three candidates for DLAs: the dualgrating structure,14–17 photonic crystal fibers,18,19 and the woodpile structure.20 The dual-grating type accelerator has a simpler structure geometry than the other types of DLAs and does not suffer from the before-mentioned group-velocity limitations. Dual-grating structures also allow a much higher overlapping efficiency of the laser field with the electron a)
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beam than semi-open accelerator structures.21 In principle, the power coupling efficiency to the particle bunches is 10%, with optimal efficiency at bunch charges of 1 to 20 fC.22 A successful proof-of-principle experiment has demonstrated the acceleration of electrons for very high gradients, 250 MeV/m and greater in a fused silica dual-grating structure.11 In addition, development of lithographic techniques has enabled the fabrication of DLAs with nanometer precision and at lower cost.23,24 In this paper, we study the properties of a fiber laser based dielectric asymmetric dual-grating accelerator structure. This structure is a modification from the original design from Plettner et al.,14 where the grating supporting walls at the laser input and output side have been removed. In practice, this makes it easier to establish a high vacuum inside the sub-micron size narrow acceleration tunnel that is critical for low energy electron acceleration. The basic working principle of this structure is based on decreasing the phase velocity of the electric field, thereby synchronizing it with relativistic or nonrelativistic electrons. II. STRUCTURE GEOMETRIES AND ACCELERATION MECHANISM
The proposed structure cross section geometry and dimensions are shown in Fig. 1(a). A represents the length of the dielectric pillar, and B represents the length of the vacuum gap. The lattice length A þ B is equal to the wavelength of the operating laser, k0. And A ¼ k0 =2 Dh, where 0 Dh k0 =2 describes the asymmetry level of the structure. The optimum parameters of the vacuum channel width C, pillar height L, and Dh are determined by simulations. Electrons move in the vacuum channel (along the Z axis), while laser pulses are
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FIG. 1. (a) Dielectric dual-grating structure overview and dimensions. A, B, C, and L represent dielectric pillar length, vacuum length, vacuum channel width, and pillar height, respectively; A þ B ¼ k0 was selected for all simulations, A ¼ k0 =2 Dh ð0 Dh k0 =2Þ. (b) The working principle of dual-grating dielectric structure.
fed perpendicular to the direction of electron movement from the two facing outward surfaces (along the X axis). Fig. 1(b) illustrates the working principle of the dualgrating accelerator structure. As the plane wave of a linearly polarized laser light passes through the structure, the speed of light in the dielectric grating pillar is lower than that in the adjacent vacuum space. This produces the desired p-phase-delay and a periodic standing-wave-like electric field distribution inside the vacuum channel along the longitudinal beam axis. Electrons are accelerated along the vacuum channel perpendicular to the laser. This is a fundamental difference as compared to dielectric laser waveguide acceleration,18,20 where the electrons move in the same direction as the laser propagation. A wavelength of 1550 nm as emitted by an erbium-fiber laser was used in our simulation. Silica (SiO2, refractive index of n ¼ 1.528 [Ref. 25]) was chosen as the dual-grating accelerator structure material for its favorable properties of transparency, electric field damage threshold, thermal conductivity, nonlinear optical coefficients, and chemical stability. III. NUMERICAL EVALUATION METHOD AND SIMULATION RESULTS
The electric and magnetic fields are calculated using CST Microwave Studio,26 then a DC current is applied to
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calculate the maximum energy gain. The current was set low enough so that wakefield and space charge effects were negligible. Laser input surfaces are separated by one laser wavelength from the structure to avoid numerical errors. Open boundary conditions (equal to a fully absorbing boundary) were used at both laser input and output faces. Electric boundary conditions (Ex ¼ Ey ¼ 0) are used on both the outer surfaces in the Z direction, to represent the periodic characteristics of this structure. The electric and magnetic field distributions in the Y direction were considered to be uniform, with magnetic boundary conditions (Hx ¼ Hz ¼ 0) used at both outer surfaces in the Y direction. A hexahedral mesh type was used, as it matches the geometry of the structures. The mesh size was chosen to be much smaller than the operating laser wavelength to increase accuracy. The mesh density is determined by three parameters: lines per wavelength, lower mesh limit, and mesh line ratio limit. They were set at 80:80:50, respectively. Fig. 2 shows the Z-component of the electric field peak distribution on the XZ plane, where the Z-axis corresponds to the direction of electrons travel, and the X-axis corresponds to the direction in which the laser propagates. Note that all structure lengths are normalized by the operating laser wavelength k0, and all field strengths are normalized by the maximum electric field strength of the operating laser pulse E0 at the entry surface. Periodic field reversal can be seen along the vacuum channel, where regions of opposite polarity are separated by k0/2. Consequently, relativistic electrons are synchronous to and accelerated by the oscillating electric field which has a phase velocity equal to the speed of light in vacuum. The accelerating field gradient was determined by particle tracking simulations with CST Particle Studio. The resulting average gradient is 2.6 GV/m for a threshold electric field of Eth 10 GV/m. About 1/4 of the maximum electric field can hence used for particle acceleration. Taking a safety factor as Eth/Emax ¼ 2 into account, so that the maximum laser field strength Emax in the dielectric structure is less than half of the threshold value Eth, then the achievable average acceleration gradient would be 1.3 GV/m. At a wavelength of k0 ¼ 1550 nm, the damage threshold of a silica
FIG. 2. Simulation result of the Z-component of the peak electric field on the XZ plane normalized by the maximum electric field strength of the operating laser pulse E0. Colors represent field strength and directions; A ¼ B ¼ k0/2, C ¼ 0.24 k0, L ¼ 0.9 k0, Dh ¼ 0, and n ¼ 1.528 was used for this simulation.
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dual-grating structure has been measured to be 2 J/cm2 (Ref. 27). Fig. 3 shows the average accelerating gradient for different structure dimensions. Fig. 3(a) shows that a maximum gradient with a value close to 0.95 E0 can be achieved when the vacuum channel width C 0.24 k0. In this calculation, the pillar height L was 0.9 k0. The optimum dielectric pillar height L can be estimated analytically as follows: tv t0 ¼ L þk0 =2 tp t0 ¼ L; where, tv and tp are the phase velocities of light in vacuum and in the dielectric pillar, respectively, t0 is the pulse propagating time in a dielectric pillar of height L. tp/tv ¼ 1/n, where n is the refractive index of the dielectric material L¼
k0 : 2ðn 1Þ
The optimum pillar height L for silica can be easily calculated from the equation above as L 0.94 k0. Note that nonlinear effects were not taken into account in these simulations. Fig. 3(b) shows that the average accelerating gradient depends not only on the pillar height L, but is also affected by the asymmetry level Dh of the dielectric pillar length A. In these simulations, the vacuum channel width C was 0.24
FIG. 3. (a) Relationship between normalized average acceleration gradient and vacuum channel width; A ¼ B ¼ k0/2, L ¼ 0.9 k0, Dh ¼ 0, n ¼ 1.528. (b) Normalized average acceleration gradient as a function of pillar height with different asymmetric pillar parameters. A þ B ¼ k0, A ¼ k0/2 – Dh, C ¼ 0.24 k0, n ¼ 1.528.
k0. One can see that as the pillar height L increases, several peaks appear periodically on the average accelerating gradient plot. The maximum gradient appears at L ¼ 0.91 k0, 0.93 k0, 0.94 k0, and 0.96 k0 for different asymmetry levels Dh ¼ 0, 0.04 k0, 0.044 k0, and 0.048 k0, respectively. It was found that a maximum average gradient of 1.05 E0 can be reached at an asymmetry level of 0.044 k0 for a pillar height of 0.94 k0, as predicted analytically. Fig. 4(a) shows the Z-component of the peak electric field on the central axis along the vacuum channel. The region within the dielectric pillars at 0.25 k0 and 0.75 k0 is indicated by dashed lines. The pillar height L and vacuum channel width C are 0.94 k0 and 0.24 k0. The red line represents a symmetric structure (Dh ¼ 0), the black line represents an asymmetric structure (Dh ¼ 0.044 k0). One can see that the periodic electric field distribution region is asymmetric for the symmetric structures (A ¼ B ¼ k0/2), i.e., the negative field region is larger than k0/2, and the positive field region is smaller than k0/2. This will negatively affect the phase synchronization and decrease the overall energy gain. In the asymmetric structure case, the oscillating periodic field region is equally divided into two parts, i.e., each region
FIG. 4. (a) Z-component of the peak electric field on the central axis along the vacuum channel; red line A ¼ B ¼ k0/2, black line A þ B ¼ k0, A ¼ k0/2 – Dh. Here, Dh ¼ 0 for symmetric structure (red line); Dh ¼ 0.044k0 for asymmetric structure (black line); vacuum channel width C and pillar height L have been set to 0.24 k0 and 0.94 k0, respectively. (b) X-component of the electric field peak distribution along the X direction, perpendicular to the electron beam direction of travel. Black and red lines denote Ex at phase 0 and p. Vacuum channel width C, pillar height L, and Dh have been set to 0.24 k0, 0.94 k0, and 0.044 k0, respectively.
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is k0/2. The plot shows that the electric field is zero when the normalized Z-value is 1/4 k0 and 3/4 k0. This ensures that electrons are in phase with the field and are being accelerated. The maximum field strength in the dielectric region (0:25 k0 Z 0:75 k0 ) of the asymmetric structure is decreased by 4% as compared to the symmetric structure, but the field in the vacuum region is increased by 50%. This compensation is the reason why the average accelerating gradient in asymmetric structures is higher than in symmetric structures under the same conditions. Another advantage is that a reduction in maximum field strength also protects the structure from the strong laser field. Fig. 4(b) shows the peak transverse electric field along the X-direction in the vicinity of the dielectric edge. The transverse field is induced, via side-feeding of two lasers, symmetrically with respect to the Z-axis, where it provides alternating focusing and defocusing sections.
IV. REQUIREMENTS FOR INITIAL PARTICLE ENERGY AND LASER PARAMETERS
Since the longitudinal length of a standing wave in the vacuum channel is equal to the wavelength of the operating laser, the requisite bunch duration is on the attosecond scale in order for successive bunches to sit in the accelerating phase of the wave. Needle-tip emitters are available to generate optically microbunched attosecond scale beams by field emission with requisite charge and emittance.28–30 The phase velocity of the accelerating field is identical to the speed of light in a vacuum, when the structure lattice constant is equal to one laser wavelength. In other words, the structure presented here requires that the electrons to be accelerated are initially highly relativistic. Fig. 5 shows average acceleration gradient as a function of initial electron energy. It can be seen that electron bunches at energies higher than 500 keV are well synchronized with the acceleration field. The laser can be focused on the structure by a lens, whilst it must be ensured that the maximum field strength Emax in the structure is kept below the damage threshold Eth. In order to decrease the required laser energy, Plettner et al.14 proposed that a short laser pulse should be divided into many segments and introduced into the accelerator through a properly tuned optical phase delay. Table I shows
Phys. Plasmas 21, 023110 (2014) TABLE I. Required laser parameters. Laser characteristics Pulse energy Average power Pulse width Repetition rate
Required parameters 2 mJ 2 kW 30 ps 1 MHz
the required laser parameters to pump a 1 cm long and one laser wavelength high structure with consideration of a safety factor of 2, assuming a 30 ps quasi-rectangular pulse. It can be seen that fiber lasers are ideally suited as a light source due to their unique advantages in terms of compactness, stability, no need for cooling, high repetition rate, and relatively low cost. The requirements described in Table I are readily available in widely used commercial fiber lasers. Since the main structure parameters are scaled against the operating laser wavelength, a long wavelength laser is favorable to make fabrication easier and allows for a wider beam tunnel. Also, the damage threshold value of a silica grating will be higher when operated with an erbium fiber laser, rather than a shorter wavelength laser.27 V. CONCLUSIONS
The numerical studies presented in this article show that an asymmetric dual-grating laser accelerator structure made from silica can generate high acceleration gradients greater than 1.3 GeV/m, using structure safety factor of 2. The asymmetry of the dielectric pillar length and adjacent vacuum length distribution helps to optimize the field distribution in the acceleration tunnel and decreases the maximum value of the focused laser field in this structure. The optimum structure dimensions for vacuum channel width C, pillar height L, and asymmetry level Dh, were determined in simulations to be 0.24 k0, 0.94 k0, and 0.044 k0, respectively. Considering the safety factor, it was found that a laser system with an average pulse energy of 2 mJ would be suitable to pump a 1 cm long structure and yield a 13 MeV energy increase. In the current design, electron bunches with an initial energy of more than 500 keV can be synchronized to the electric field in the structure. The geometry of the structure is simple enough to enable further modifications to allow acceleration of nonrelativistic electrons. ACKNOWLEDGMENTS
This work was supported by the EU under Grant Agreement No. 289191, the STFC Cockcroft Institute core Grant No. ST/G008248/1, KAKENHI, Grant-in-Aid for Scientific Research (C) 24510120, the National Natural Science Foundation of China (NSFC) under Grant Nos. 11175023, 11305010, and 11335013, and partially by the Fundamental Research Funds for the Central Universities (FRFCU). FIG. 5. Average accelerating gradient as function of initial electron energy; Vacuum channel width C, pillar height L, and Dh were 0.24 k0, 0.94 k0, and 0.044 k0, respectively.
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