Starting from the eikonal approximation (geometrical optics), a set of nonlinear quantum plasma fluid equations to describe the quantum free-electron laser (FEL) is presented. Subsequently, by using these fluid equations for a relativistic electron beam, interacting with stimulated radiation and an optical wiggler field, a general dispersion relation for quantum FEL instability is derived taking into account the beam space-charge mode modulated by the ponderomotive potential well. It is shown that the saturation time for the quantum FEL instability can be estimated from the solutions of three-wave coupled equations which describe the FEL dynamics in the fluid model.

Using a quantum fluid model, the linear dispersion relation for FEL pumped by a short wavelength laser wiggler is deduced. Subsequently, a new quantum corrected resonance condition is obtained. It is shown that, in the limit of low energy electron beam and low frequency pump, the quantum recoil effect can be neglected, recovering the classical FEL resonance condition, ks=4kwγ2. On the other hand, for short wavelength and high energy electron beam, the quantum recoil effect becomes strong and the resonance condition turns into ks=2kw/ƛcγ3/2, with ƛc being the reduced Compton wavelength. As a result, a set of nonlinear coupled equations, which describes the quantum FEL dynamics as a three-wave interaction, is obtained. Neglecting wave propagation effects, this set of equations is solved numerically and results are presented.

A hydrodynamic description is used to investigate the generation of ion-sound waves by intense neutrino beams in a dense plasma. The excited ion-sound waves can mediate the transfer of energy and momentum from the neutrinos to the plasma environment of Type II supernova. Since the growth rate of the neutrino-driven ion-sound waves is proportional to G 2/3 F , where G F (≡10 −49 erg cm −3 ) is the Fermi coupling constant, it is likely that they can contribute to enhance the stalled supernova shock front.

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