Beam plasma electromagnetic instabilities in a smooth density gradient: Application to the fast ignition scenario

Abstract

The integrated growth rate of various relativistic beam∕plasma instabilities in a weakly varying plasma density gradient is calculated using a WKB-like approximation. It is proven that such an assumption can be made in fast ignition scenario conditions. The formalism is applied to the two-stream, the filamentation, and the two-stream∕filamentation instabilities, the latter instability being a mixture of the former two, and is the fastest growing one. The results are restricted to collisionless plasmas and nonrelativistic beam and plasma temperatures. Filamentation instability is reduced by the density gradient and eventually does not develop in the core, whereas two-stream and two-stream∕filamentation instabilities should saturate even before they feel the gradient. Various effects connected to the density gradient are discussed. It is found they should be negligible as long as these later instabilities remain in their respective linear regime.

The effect of density gradient on the growth rate of relativistic Weibel instability

“…The pellet core is denser than its side by four orders of magnitude, so that the beam makes its way through an important density gradient. [11][12][13][14][15] The energy deposition of a relativistic electron beam in a plasma can be managed through sufficiently steep plasma density gradients. These beams then deposit most of their energy in a reasonably short flat density region.…”

A Shock Wave Instability Induced on a Periodically Disturbed Interface With Plasma

“…The similarity effect (7) was numerically verified using simulations for the shock perturbation profiles performed for different combinations of the interface disturbance amplitude and wavelength but keeping the small ratio λ A same (corresponding to the same curvature). The results for several sets of parameters (A/λ) including (0.1/1.0), (0.2/2.0), (0.3/3.0), (0.4/4.0), (0.5/5.0) returned the curves of identical shapes thus confirming the above conclusions.…”

“…toward or off their symmetry axes. The Mach number components along the normal to the interface M 1n and M 2n are defined through the corresponding velocity components [7] and their ratio accounts for the losses due to the shock reflections off the interface [13]. In the equations below, the interaction time…”

“…However, the possibility of this kind of reorganization of the steady-state flow can be limited in the case of a stronger refraction effect resulting in the front overstretching and decay via degeneration of the shock into a sonic wave [9]. This can occur because, while the shape of the perturbation remains similar in accordance to the law (7), the perturbation's absolute value is still dependent on the disturbance amplitude through the interaction time…”

The density gradient effect on quantum Weibel instability

“…The pellet core is denser than its side by four orders of magnitude so that the beam makes its way through an important density gradient. [15][16][17][18][19][20][21][22] The purpose of the present work is to investigate the influence of the density gradient of fuel dense and plasma degeneracy quantum effects on Weibel instability.…”