All-metal wakefield accelerator: Two-dimensional periodic surface lattices for charged particle acceleration

Interest in “all-metal” surface periodic structures to control charged particle beam dynamics and properties, and to generate coherent radiation in the THz frequency range has recently risen exponentially. While such structures have the benefits of metal, they are capable of providing similar properties to a dispersive dielectric. All-metal structures allow good temperature and space charge management. Transportation of high energy charge particle beams in the vicinity of the structure without risking material degradation makes them very attractive for particle acceleration and terahertz radiation generation applications. Here, the results of theoretical studies (via numerical modeling) of the electron beam dynamics and wakefield excitation and evolution along the cylindrical two-dimensional periodic surface structure will be presented, and the properties of the wakefields generated will be discussed. The wakefield acceleration of the witness bunch in the potential reaching $1\mathrm{GV}/\mathrm{m}$ will be demonstrated. The challenges will be identified and discussed, and the concept of the cascade accelerator based on such all-metal wakefield accelerator (AMWA) structures will be presented.

Figure 1

(a) 3D model basic cell of the 2D periodic surface lattice generated using cst mw studio with the period of the lattice $d_z$ indicated, (b) photograph (left figure) of the copper, cylindrical, 2D periodic surface lattice, which single cell can be approximated by the “square element” shown in Fig. 1, with shallow sine corrugation constructed using 3D printing technique and 3D model (right figure) of the 2D PSL with shallow square wave corrugation build using 3D PiC code magic, with a single cell similar to one shown in Fig. 1. Such a structure can be considered as a periodic composition of such elements along azimuthal ($\overline{m}$ periods) and longitudinal coordinates. (c) Numerical model $(x,y)$ and $(r,z)$ views of the periodic structure with driver and witness bunches, the insets on the right figure are zoom-in of the driver and witness bunches and contour plot of the amplitude of the $E_z$ field component in front of the driver bunch.

Figure 2

Results of numerical studies using 3D PiC code magic. Distributions of the electrons inside the driver bunch in $(x,y)$ (first column) and $(r,z)$ cross sections measured at different moments of times (a) and (b) 2.74 (solid blue dots) and 18.77 ps (hollow orange dots); (c) and (d) 18.77 (hollow orange dots) and 50.84 ps (hollow green dots); (e) and (f) 50.84 (hollow green dots) and 80.9 ps (solid red dots). The 2.74 and 80.9 ps are corresponding to injection in and exit from the AMWA structure, while dashed lines in Figs. 2 and 2 show the entrance and exit of the AMWA.

Figure 3

Results of the numerical studies using 3D PiC code magic. The time dependences of the wakefield driver bunch depletion (a) and the amplitude of the wakefield (b) as the electron bunches propagate through the structure. The results observed for different values of the bunch grating separations $\mathrm{\Delta }{r}_b=1\mathrm{mm}$ (dotted line); $\mathrm{\Delta }{r}_b=0.9\mathrm{mm}$ (short-dashed line); $\mathrm{\Delta }{r}_b=0.8\mathrm{mm}$ (dashed line); $\mathrm{\Delta }{r}_b=0.6\mathrm{mm}$ (dash-dotted line); $\mathrm{\Delta }{r}_b=0.4\mathrm{mm}$ (solid line). The graphs in Figs. 3and 3are observed for the same bunches and illustrate the wakefield amplitude drops in all cases at approximately 50 ps indicating that electron loss and radial dispersion of the bunch are responsible for the amplitude decay. (c) The dependence of the amplitude of the $E_z$ field component of the wakefield inside the periodic structure [waveform (left axis)] taken at two different times $t_1=31.9 \mathrm{ps}$ (dashed blue line) and $t_2=36.4 \mathrm{ps}$ (solid orange line) induced by the high intensity (20 nC, 2 ps, injected bunch CM energy 7 MeV) electron bunch which positions at different times, in respect to the wakefield, are also shown (solid blue/orange dots). The electron energy distribution shown on the right axis of the figure.

Figure 4

Results of numerical studies using 3D PiC code magic. Dependences of the witness bunch (WB) energies: (top lines) maximum (max.) single electron (${\mathrm{SE}}_{\max }$); (middle lines) CM; (bottom lines) minimum (min.) single electron (${\mathrm{SE}}_{\min }$) on the witness bunch transient through the structure time. The results observed for DW-pair separations (a) 1.35 (solid lines) and 0.8 ps (dashed lines) and (b) 3.5 (dashed lines) and 4.0 ps (solid lines). The inset to (a) shows the dependence of the single electron maximum energy in the witness bunch on the DW-pair separation. The inset to (b) shows WB energies as functions of the WB length: (top line) ${\mathrm{SE}}_{\max }$ maximum energy; (middles line) CM; ${\mathrm{SE}}_{\min }$ minimum energy (c) illustration of the WB electron density and energy distributions for long (1.25 ps, blue dots) and short (0.05 ps, red dots) at the exit from AMWA structure of 12-mm length.

Figure 5

(a) Schematic illustration of the AMWA cascade accelerator. (b) Results of numerical simulations using 3D PiC code magic. An example of acceleration of the witness bunch from 7 MeV (CM) to above 14 MeV (CM) in three stages. Figure 5is to illustrate two main challenges in the realization of the AMWA cascade accelerator concept: driver depletion (needs for three sections) and witness bunch energy spread at the exit of the AMWA section. The dependences of the WB energies on the bunch transient time in stages are shown by the top dashed line (${\mathrm{SE}}_{\max }$—maximum energy), solid line (CM), dotted line (${\mathrm{SE}}_{\min }$—minimum energy).