Abstract
A new formulation based on Hamiltonian reduction technique using the invariance of generalized canonical momentum is introduced for the study of relativistic Weibel-type instability. An example of application is given for the current filamentation instability resulting from the propagation of two counter-streaming electron beams in the relativistic regime of the instability. This model presents a double advantage. From an analytical point of view, the method is exact and standard fluid dispersion relations for Weibel or filamentation instabilies can be recovered. From a numerical point of view, the method allows a drastic reduction of the computational time. A 1D multi-stream Vlasov-Maxwell code is developed using such dynamical invariants in the perpendicular momentum space. Numerical comparison with a full Vlasov-Maxwell system has also been carried out to show the efficiency of this reduction technique.
Highlights
As a fundamental issue, the Weibel instability [1] or the current filamentation instability [2,3,4,5] are able to generate a magnetic field by extracting the free energy from an anisotropy velocity distribution in an unmagnetized plasma
An example of application is given for the current filamentation instability resulting from the propagation of two counterstreaming electron beams in the relativistic regime of the instability
Numerical comparison with a full VlasovMaxwell system has been carried out to show the efficiency of this reduction technique
Summary
The Weibel instability [1] or the current filamentation instability [2,3,4,5] are able to generate a magnetic field by extracting the free energy from an anisotropy velocity distribution in an unmagnetized plasma. The propagation of a hot electron beam in a plasma induces a return current in the background plasma to keep current neutralization of the beam-plasma system, resulting in the current filamentation instability (CFI). Such a scenario is met and relevant to the concept of the fast ignitor [6] of laser inertial confinement fusion. Numerical comparisons of our kinetic multi-stream Vlasov model with the standard 1D2V full-kinetic Vlasov-Maxwell are shown in section 4 for a symetric case of CFI and section 5 is reserved for the conclusions and discussion
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