Mitigation of the Onset of Hosing in the Linear Regime through Plasma Frequency Detuning

The hosing instability poses a feasibility risk for plasma-based accelerator concepts. We show that the growth rate for beam hosing in the linear regime (which is relevant for concepts that use a long driver) is a function of the centroid perturbation wavelength. We demonstrate how this property can be used to damp centroid oscillations by detuning the plasma response sufficiently early in the development of the instability. We also develop a new theoretical model for the early evolution of hosing. These findings have implications for the general control of an instability’s growth rate.

Figure 1

(a) Hosing growth factor at $z=k_{\beta }^{-1}$ versus wave number of an initial sinusoidal perturbation, according to theory (blue curve) and simulations (red cross symbols). (b) Theoretical hosing growth spectrum along $z$. The horizontal dashed line corresponds to the blue lineout in (a).

Figure 2

(a) Initial centroid (black) and average transverse force (blue) for three different seed wave numbers, obtained from 2D osiris simulations at $z=0$. (b) Phase shift between the initial $y_c$ and $⟨F_y⟩$ as a function of the perturbation wave number, obtained from theory (blue curve) and simulations (red cross symbols).

Figure 3

Comparison of the series model truncated at $n$ terms (colored curves) with a 3D osiris simulation (black curves), (a) along $\zeta$ at $z=2k_{\beta }^{-1}$ and (b) along $z$ at $\zeta =30k_p^{-1}$.

Figure 4

Transverse energy of the bunch relative to the initial value along the plasma (integrated over the simulation domain): plasma at $n_0$ (gray), with two density steps (red), and with four density steps (blue). Results from 3D osiris. Inset: plasma density profiles of the two density step configurations. The vertical dash-dotted lines indicate the boundaries of each density step.