Non-equilibrium effects in a relativistic plasma sheath model

Abstract

Plasma sheaths characterized by electrons with relativistic energies and far from thermodynamic equilibrium are governed by a rich and largely unexplored physics. A reliable kinetic description of relativistic non-equilibrium plasma sheaths-besides its interest from a fundamental point of view-is crucial to many application, from controlled nuclear fusion to laser-driven particle acceleration. Sheath models proposed in the literature adopt either relativistic equilibrium distribution functions or non-relativistic non-equilibrium distribution functions, making it impossible to properly capture the physics involved when both relativistic and non-equilibrium effects are important. Here we tackle this issue by solving the electrostatic Vlasov-Poisson equations with a new class of fully-relativistic distribution functions that can describe non-equilibrium features via a real scalar parameter. After having discussed the general properties of the distribution functions and the resulting plasma sheath model, we establish an approach to investigate the effect of non-equilibrium solely. Then, we apply our approach to describe laser-plasma ion acceleration in the target normal sheath acceleration scheme. Results show how different degrees of non-equilibrium lead to the formation of sheaths with significantly different features, thereby having a relevant impact on the ion acceleration process. We believe that this approach can offer a deeper understanding of relativistic plasma sheaths, opening new perspectives in view of their applications.2 In a kinetic description, an equilibrium plasma state is any stationary state that cancels out the collision integral in the transport equation (or, equivalently, that makes the entropy production rate vanish) and is solution of the transport equation itself. Any other state-even if stationary-is of non-equilibrium.

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