Hydrodynamic approach to the free electron laser instability

Abstract

Starting from the Vlasov-Maxwell system, an exact relativistic hydrodynamic closure for a special type water bag distributions satisfying the Vlasov equation has been derived. It has been shown that the hydrodynamic equations are fully equivalent to the original Vlasov-Maxwell equations. The linear stability of the exact hydrodynamic closure has been studied as well. It has been shown that all basic features of the small signal gain can be derived from the fluid dynamic description developed here. Satisfactory agreement with previously reported results has been also found.

Nonlinear waves and coherent structures in quasi-neutral plasmas excited by external electromagnetic radiation

“…This remarkable simplification, i.e., exact closure of the hydrodynamic equations with the first two velocity moments is a consequence of the fact that the heat flow can be shown to be zero 21 for the class of relativistic water-bag distribution functions. It is worth be pointed out that Eqs.…”

“…21 manner by expressing the source terms entering the corresponding wave equations for the electromagnetic potentials as functions of n a , V a and Γ a . Using the Lorentz gauge…”

“…21, it is possible to introduce hydrodynamic variables n a , V a and Γ a for each plasma species. Omitting details, which can be reproduced in a straightforward manner, we state here the final result.…”

“…Following Ref. 21, we reduce in Section III the VlasovMaxwell system to an exact closure of relativistic warm fluid dynamic equations for the plasma species, which are coupled to the wave equations for the radiation field. The fact that this reduction leads to an exact hydrodynamic closure, makes it extremely valuable simplification for the description of the underlying processes governed by the Vlasov-Maxwell system.…”

Nonlinear low-frequency collisional quantum Buneman instability

“…Also, in the near future the development of coherent brilliant X-ray radiation sources [11] and keV free-electron lasers [12] will provide experimental access to the quantum nature of plasmas under extreme conditions. Some of the most recent developments in the field are the analysis of wave breaking in quantum plasmas [13], the characteristics of bounded quantum plasmas including electron exchange correlation effects [14], the development of a quantum single-wave theory for nonlinear coherent structures in quantum plasmas [15], the discussion of waves in quantum dusty plasmas [16], the prediction of a fundamental size limit for plasmonic devices due to the quantum broadening of the transition layer [17], as well as the inclusion of spin [18] and relativistic [19] effects in quantum plasma modeling. Finally, we note the usefulness of quantum plasma techniques to other, closely related problems, such as the treatment of nonlinear wave propagation in gravitating Bose-Einstein condensates [20].…”