Suppression of the Laser Hosing Instability in a Parabolic Plasma Channel

Abstract

We present an analytical stability analysis of the laser hosing instability in a parabolic channel in the weakly relativistic regime. We employ a variational principle approach to derive a set of coupled equations describing laser dynamics in a transversely inhomogeneous plasma. The quadratic Lagrangian formalism is applied to perform a stability analysis and to derive the growth rates for hosing in both long- and short-wavelength regimes. We find that a parabolic channel suppresses the long-wavelength hosing mode completely, for any channel depth, and that the unstable band of the short-wavelength mode is bounded below by a cutoff wavenumber set by the ratio of the channel frequency to the hosing coupling. A steeper channel narrows the unstable band and lowers the short-wavelength growth rate, but cannot stabilize the mode, since the dispersion relation forbids damping identically. The analysis is accompanied by two-dimensional particle-in-cell simulations, which reproduce the prediction in the nonlinear regime: the long-wavelength mode is absent in a channel, the surviving modulation shortens as the channel steepens, and its amplitude falls with channel depth. Further, our simulation results demonstrate the sensitivity of off-axis laser propagation to the plasma channel and distinguish the hosing instability from laser oscillations due to off-axis laser propagation in a plasma channel.