The two-plasmon instability in warm inhomogeneous plasma for a normally incident pump is considered. The complex eigenfrequencies of the absolute instability are obtained by reducing the linearized fluid equations to a Schrödinger equation in wavenumber space. These eigenvalues are obtained in several ways. One is by combining a perturbation expansion in powers of the reciprocal scale length with WKB theory. The resulting algebraic equations are solved by three analytical approximations and by direct numerical solution. A second way is by analysis of the Schrödinger equation using an interactive WKB computer code. A third way is by the use of a shooting code. These methods are all used and compared for threshold curves and growth rates above threshold. Some eigenfunction forms are also obtained. The threshold is near (v0/ve)2k0 L =3, and varies weakly with β≂v4e/v20c2, rising from near 2 to about 4 over six decades of variation of β. The corresponding critical value of (ky/k0)2 is near 0.2/β over this range. Above threshold, there is a smooth variation of the growth rate with (ky/k0)2, peaking at some intermediate value. The perturbation method is in good agreement there with more exact calculations. Experimental implications of these results are discussed.
One- and two-dimensional simulations and supporting analysis of nonlinear ion acoustic waves as might be associated with the saturation of stimulated Brillouin backscattering (SBBS) are presented. To simulate ion wave phenomena efficiently, while retaining a fully kinetic representation of the ions, a Boltzmann fluid model is used for the electrons, and a particle-in-cell representation is used for the ions. Poisson’s equation is solved in order to retain space-charge effects. We derive a new dispersion relation describing the parametric instability of ion waves, evidence for which is observed in our simulations. One- and two-dimensional simulations of plasma with either initially cold or warm ions (and multi-species ions) exhibit a complex interplay of phenomena that influence the time evolution and relaxation of the amplitude of the excited ion wave: ion trapping, wave steepening, acceleration, heating and tail formation in the ion velocity distribution, parametric decay into longer wavelength ion waves, modulational and filamentation instabilities, and induced scattering by ions. The additional degrees of freedom in two dimensions allow for a more rapid relaxation of the primary ion wave. One-dimensional electrostatic simulations with externally driven ion waves agree qualitatively with electromagnetic simulations in one dimension in which the ponderomotive driving potential is computed self-consistently by solving a Schroedinger-like equation for the electromagnetic waves and calculating the low-frequency ponderomotive force on the electrons.
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Articles you may be interested inEffects of ion-ion collisions and inhomogeneity in two-dimensional kinetic ion simulations of stimulated Brillouin backscattering Phys. Plasmas 13, 022705 (2006); An analysis of the effects of ion trapping on ion acoustic waves excited by the stimulated Brillouin scattering of crossing intense laser beams is presented. Ion trapping alters the dispersion of ion acoustic waves by nonlinearly shifting the normal mode frequency and by reducing the ion Landau damping. This in turn can influence the energy transfer between two crossing laser beams in the presence of plasma flows such that stimulated Brillouin scattering ͑SBS͒ occurs. The same ion trapping physics can influence the saturation of SBS in other circumstances. A one-dimensional analytical model is presented along with reasonably successful comparisons of the theory to results from particle simulations and laboratory experiments. An analysis of the vulnerability of the National Ignition Facility Inertial Confinement Fusion point design ͓S. W. Haan et al., Fusion Sci. Technol. 41, 164 ͑2002͔͒ is also presented.
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