Hosing Instability in the Blow-Out Regime for Plasma-Wakefield Acceleration

The electron hosing instability in the blow-out regime of plasma-wakefield acceleration is investigated using a linear perturbation theory about the electron blow-out trajectory in Lu et al. [in Phys. Rev. Lett. 96, 165002 (2006)]. The growth of the instability is found to be affected by the beam parameters unlike in the standard theory Whittum et al. [Phys. Rev. Lett. 67, 991 (1991)] which is strictly valid for preformed channels. Particle-in-cell simulations agree with this new theory, which predicts less hosing growth than found by the hosing theory of Whittum et al.

Figure 1

(a) A 2D slice of the beam (moving to the left) and plasma density after the beam has propagated 0.52 m, illustrating the three regions of behavior. (b) The beam centroid $|x_b|$ (lower red curve) in the simulation (the asymmetry in this curve is due to beam centroid aligning to the axis at region I) and from the standard theory prediction (upper blue curve). The growth in the simulation is 1 order of magnitude smaller than the standard theory prediction.

Figure 2

The beams (red, moving to the left) and the plasma (blue) in (a) the adiabatic nonrelativistic regime, (b) the adiabatic relativistic regime, (c) the nonadiabatic nonrelativistic regime, (d) the nonadiabatic relativistic regime. Left-hand (white) and right-hand (gray) arrows denote where tilts are added and the centroids are measured.

Figure 3

Hosing growth in four regimes. $x_{b0}$ is the initial displacement of the beam centroid. We assume ${\Delta }_s=0.1r_0$, ${\Delta }_L=1c/{\omega }_p$ for the analytic curve in case (d). The slightly slower hosing growth in simulation (d) is caused by nonlinearity in beam-channel centroid coupling.