Temperature effects on mixed two-stream/filamentation modes

Two-stream instability is a basic plasma phenomenon and has been investigated for many decades. Beam-plasma related instabilities, such as filamentation instability, recently undergone a renewed interest due to the Fast Ignition Scenario for Inertial Fusion in which a laser generated relativistic electron beam is to ignite to pre-compressed DT core of the target. In this regard, a systematic effort has been conducted to study beam-plasma instabilities all over the Fourier space and find the most unstable modes of the system. Various features have been unraveled so far such as the existence of a most unstable mode for a wave vector making an oblique angle with the beam [1] as well as the fact that the mode which is usually held responsible for beam filamentation may not be the correct one [2]. As far as beam or plasma temperatures are concerned, it can be proved that the maximum growth rate is found for a wave vector away from the main axis as soon as the beam is relativistic [3], even within a cold fluid model. Still, an investigation of temperatures effects on these oblique modes shows a number of interesting effects. 1) Normal temperatures, whether it be beam or plasma ones, prompt a critical angle in the k space in which waves are unstable at high k. Additionally, the critical angle separates in two when plasma parallel temperature is accounted for, as evidenced on Figures 1. Waves are quasi longitudinal for wave vectors located below the smallest critical angle and transverse beam temperature damp instabilities for wave vectors located beyond. 2) Plasma parallel temperature can play a very interesting role in turning the plasma Weibel unstable. The Weibel instability does not come from the interaction with the beam but from a strong plasma temperature anisotropy. Weibel modes are purely transverse and normal to the high temperature direction. When the plasma is too hot in the normal direction, Weibel modes appear on another branch of the dispersion equation [1]. But when the plasma is too hot in the parallel direction, Weibel modes appear on the very same branch than two-stream and filamentation instabilities, and thus for wave vectors normal to the beam. As long as plasma parallel temperature is low enough (Fig 1.a), the filamentation instability remains beam dependant and can be suppressed by transverse beam temperature. But when parallel temperature exceed a given threshold, the plasma turns Weibel unstable for wave vectors normal to the beam (Fig 1.b) so that filamentation instability enters a Weibel regime where it is disconnected from the beam. Once in this regime, its growth rate is independent of the beam density and transverse beam temperature can no longer suppress it. This work has been partially achieved under project FTN2003-00721 of the Spanish Ministerio de Educacion y Ciencia.