Wakefield Acceleration in a Layered Plasma Waveguide

TL;DR

The paper addresses the challenge of stable, high-gradient transport of drive and witness bunches in plasma wakefield accelerators by proposing a layered plasma wake accelerator (LPWA), where a low-density inner plasma is embedded in a surrounding dense plasma to form a layered waveguide supporting a surface TM mode. Analytical wakefield solutions in the quasi-linear regime predict a single TM-mode resonance with the drive bunch, a Langmuir shock in the inner column, and the possibility of simultaneous acceleration and focusing for both electron and positron witnesses; a resonant eigenfrequency $f_1$ is obtained from the dispersion relation and a density ratio yielding $f_s/f_{p(1)}\approx 3$ is used. PIC simulations with a single drive bunch and with a resonant train of four drive bunches confirm that comparable wakefield amplitudes can be excited and that witness bunches can be accelerated while being focused, with $E_z$ dominated by the TM-mode and $W_r$ by Langmuir-type focusing near the interface. The results indicate LPWA as a promising route for robust, high-gradient electron/positron acceleration, while further work is needed to quantify beam quality metrics over longer propagation distances and optimize layer densities and bunch patterns.

Abstract

Plasma wakefield accelerators (PWFA) represent one of the promising new accelerator concepts that are now being developed intensively for future applications in high-energy physics and industry. Among the unresolved problems of practical implementation of PWFA there are maintaining the required quality (emittance, size, energy spread of bunches) and stable transportation of drive and accelerated (witness) bunches over long acceleration distances. For improving the bunch transport, we propose to fill the bunch transport channel with the background plasma, the density of which is lower than the main plasma density building up an accelerating wake wave. We call this waveguide structure a layered plasma waveguide (LPW). The wakefield excitation by a regular sequence of electron bunches in the LPW of cylindrical configuration has been explored both analytically and numerically. The layered plasma has been modeled as a combination of a tubular plasma and a plasma column of significantly different densities. The plasma column has a lower density. The dispersion dependencies of the TM-modes of the LPW was obtained and analyzed, and it was found that there was a single TM wave resonant with the electron bunch. Based on the obtained analytical expressions, the structures of the axial and radial wakefield amplitudes have been numerically investigated for the cases of a single drive bunch and a regular train of bunches. It is shown that for certain density ratios of the outer and inner plasmas, it is possible both to accelerate and focus simultaneously the drive and witness bunches. The 2.5D particle-in-cell code was used to simulate the witness acceleration of an electron bunch by a wakefield created by drive electron bunches in a two-layer plasma wakefield accelerator. The simulation showed good agreement with the results of analytical calculations.

Figures (13)

• Figure 1: General view of the cylindrical plasma waveguide. Metal coating, layered plasma, drive and witness bunches are shown schematically. The drive and witness bunches move along to the waveguide axis without an offset.
• Figure 2: Tubular plasma density versus resonant eigenfrequency of the layered plasma waveguide. The waveguide dimensions are given in Tab. \ref{['tab:01']}. Plasma density in the plasma column region (1) is $n_{p(1)}=4.93\cdot 10^{14}\rm cm^{-3}$.
• Figure 3: Dispersion dependence of the layered plasma waveguide. Parameters of the waveguide and the plasma density in the plasma column region $n_{p(1)}$ are presented in Tab. \ref{['tab:01']}. The tubular plasma density (region 2) is $n_{p(2)}=1.53\cdot 10^{16}\rm cm^{-3}$. The dash-dotted red line is the Cherenkov line $2\pi f=k_zv_0$, the dashed blue line $f=f_{p(1)}$ shows the Langmuir oscillations. Among the multitude of electromagnetic $TM_{0n}$-waves (solid black lines) there exists only one slow $TM_{01}$ wave, resonant with the relativistic electron bunch ($W_b=5\,GeV$). The bunch resonance with the Langmuir wave $\omega_{p(1)}=k_zv_0$ describes the quasistatic waves responsible for focusing the accelerated bunches (the first summands in the expressions (\ref{['eq:02']})-(\ref{['eq:05']})).
• Figure 4: Two-dimensional distributions of the longitudinal $E_z$ and traverse $W_r$ wakefields excited by a single drive electron bunch. Drive bunch head is located at $\xi = vt - z = 0$. In the plasma column region (1) ($r<a=0.3\,mm$) the period of the transverse wakefield $W_r$, focusing the drive and witness bunches is equal to the Langmuir wave period $\approx 1.5\,\rm mm$. In the same region, the basic period of the longitudinal wakefield $E_z$, that accelerates the witness bunches, is equal to the period of the $TM_{01}$ wave $\approx 0.5\,\rm mm$.
• Figure 5: Axial structure of the longitudinal (black solid line) and radial (dash-dot red line) wakefields behind the single drive electron bunch with a charge of $2\,\rm nC$. The fill areas show the position and current of the drive bunch (blue ground-color) and possible positions for accelerating the electron (grey ground-color) and positron (pink ground-color) witness bunches. The witness bunches centers are found in the peak of the accelerating field.