High efficiency uniform positron beam loading in a hollow channel plasma wakefield accelerator

We propose a novel positron beam loading regime in a hollow plasma channel that can efficiently accelerate $e^{+}$ beam with a high gradient and narrow energy spread. In this regime, the $e^{+}$ beam coincides with the drive $e^{-}$ beam in time and space and their net current distribution determines the plasma wakefields. By precisely shaping the beam current profile and loading phase according to explicit expressions, three-dimensional particle-in-cell (PIC) simulations show that the acceleration for $e^{+}$ beam of $\sim \mathrm{nC}$ charge with $\sim \mathrm{GV}/\mathrm{m}$ gradient, $\lesssim 0.5\%$ induced energy spread, and $\sim 50\%$ energy transfer efficiency can be achieved simultaneously. Besides, only tailoring the current profile of the more tunable $e^{-}$ beam instead of the $e^{+}$ beam is enough to obtain such favorable results. A theoretical analysis considering both linear and nonlinear plasma responses in hollow plasma channels is proposed to quantify the beam loading effects. This theory agrees very well with the simulation results and verifies the robustness of this beam loading regime over a wide range of parameters.

Figure 1

(a–c) Plasma wakes in hollow plasma channels driven by 2 nC $e^{-}$ beams. From (a) to (c) the rms bunch durations are 625, 167, and 104 fs and plasma densities are $1.26\times {10}^{15}$, $1.77\times {10}^{16}$, $4.52\times {10}^{16}{\mathrm{cm}}^{-3}$ correspondingly so that the normalized bunch length, size, and plasma structures are constant. (d) The maximum normalized outward displacement of the plasma electron sheath and the corresponding maximum $E_z$ against plasma density. The blue asterisks denote $k_p{r}_m$ for simulations in (a–c). The red dotted line separates the linear and nonlinear regions where the peak $E_z$ field from linear theory is 50% larger than that in simulation.

Figure 2

(a–c) Beam loading effects when the $e^{+}$ beam is loaded behind the drive beam. The plasmas and electron beams are identical to that in Fig. 1. And the $e^{+}$ beam profile is chosen to obtain uniform acceleration according to the linear theory. The gray dashed line in (a) is the current profile of the beams. The orange line in (c) is the transverse lineout of $E_z$. (d) The induced energy spread of the $e^{+}$ beam for these situations.

Figure 3

Positron beam loading scenario when the $e^{+}$ and $e^{-}$ beams coincide. (a) A discontinuous net current case. (b) A continuous net current case. $E_z$ is calculated according to the linear theory.

Figure 4

The positron beam loading effects when two bunches coincide. (a–c) The plasma response and the corresponding wakefields for (a) $I_1=0.2\mathrm{kA}$, $Q_{\mathrm{net}}=56\mathrm{pC}$, (b) $I_1=1\mathrm{kA}$, $Q_{\mathrm{net}}=280\mathrm{pC}$ and (c) $I_1=5\mathrm{kA}$, $Q_{\mathrm{net}}=1.4\mathrm{nC}$. (d) The comparison of $E_z/I_1$ for three simulations and the linear theory. (e) The spectrum of the $e^{+}$ beam energy gain normalized to the linear theory predictions for three different situations.

Figure 5

Two other positron beam loading cases. The drive beam has (a) a piecewise linearly ramped and (b) a bi-Gaussian current profile. The $E_z$ fields are calculated according to the linear theory. (c, d) Simulated plasma responses and wakefields.

Figure 6

Theoretical analysis of the beam loading regime in a hollow plasma channel. (a) The plasma density and net charge density of the beams with identical parameters to Fig. 4. The black dashed line is the blowout radius obtained from the adiabatic approximation. (b) The radial distribution of $-(\rho -J_z/c)$ at $\xi =90\mu \mathrm{m}$ denoted by red line in (a). (c) The on-axis $E_z$ lineouts from the simulation, linear and nonlinear theory.