Ion Motion in Self-Modulated Plasma Wakefield Accelerators

The effects of plasma ion motion in self-modulated plasma-based accelerators are examined. An analytical model describing ion motion in the narrow beam limit is developed and confirmed through multidimensional particle-in-cell simulations. It is shown that the ion motion can lead to the early saturation of the self-modulation instability and to the suppression of the accelerating gradients. This can reduce the total energy that can be transformed into kinetic energy of accelerated particles. For the parameters of future proton-driven plasma accelerator experiments, the ion dynamics can have a strong impact. Possible methods to mitigate the effects of the ion motion in future experiments are demonstrated.

Figure 1

Comparison between the ion density profile ($\Delta n=n_i-n_0$) analytical predictions (dashed lines) with 3D (a) and (b) and 2D (c)–(f) osiris PIC simulations (solid lines). (a), (c), (e) 3D on-axis plasma proton density profile. [(b),(d),(f)] Corresponding transverse density profiles at the $\xi$ of the vertical dashed lines.

Figure 2

2D cylindrically symmetric osiris simulations of a PDPWFA at $\tau =11450/{\omega }_p$ (6.1 m) in a hydrogen plasma. (a) Plasma electron density. The inset shows sample electron trajectories colored according to the initial radius. (b) Corresponding plasma ion density. The horizontal solid line represents the driving ion beam density profile. The arrow indicates the propagation direction. The vertical solid line is a lineout of $n_i$ at $\xi =640c/{\omega }_p$.

Figure 3

osiris simulation results of a PDPWFA at $\tau =11450/{\omega }_p$ (6.1 m). (a) and (b) Proton bunch density. (c) Plasma focusing force profile with mobile plasma ions. The solid line is a lineout at $r=0.5c/{\omega }_p$. The inset shows the evolution of the energy of $E_{\xi }$. (d) On axis accelerating gradients using mobile ${\mathrm{Ar}}^{+}$ and ${\mathrm{H}}^{+}$ ions.