Electromagnetic Beam Breakup: Multiple Filaments, Single Beam Equilibria, and Radiation [Phys. Rev. Lett 77, 1282 (1996)]

Abstract

We are indebted to Dr. Luc Berge who has brought to our attention the fact that we carelessly reproduced a trivial error of Zakharov et al. [1]. The correct quantity to be varied about its minimum is, of course, H 1 lN and not 2H 1 lN (as we wrote) nor the quantity H 2 lN given previously [1].[1] V. E. Zakharov, V. V. Sobolev, and V. C. Synakh, Zh. Eksp. Teor. Fiz. 60, 136 (1971) [Sov. Phys. JETP 33, 77 (1971]. 48520031-9007͞96͞77(23)͞4852(1)$10.00

Laser-plasma filamentation and the spatially periodic nonlinear Schrödinger equation approximation

“…͑The variable u is used here instead of the earlier 1 E to avoid confusion with the unnormalized electric field.͒ Here we specialize as before 1 to a further subset of GNLSE, which we term SNLSE ͑S is for saturation͒, being the analytic models for which the nonlinearity function f (uu*) saturates, which is to say that f (uu*) remains bounded as the square of the field modulus (ϭuu*) tends to infinite values. While most previous analyses of filament behavior have been applied ͑i͒ to obtaining steady-state filaments ͑CNLSE can evade collapse only in one-dimensional Cartesian geometry but a stable radial filament is possible for two-dimensional transverse geometry in SNLSE͒ and ͑ii͒ to perturbation analysis of those steady states, progress has been made recently 1 in using some general SNLSE features to understand more complicated and nonlinear filament dynamics in two transverse dimensions ͑2-D͒.…”

Stationary laser beam filaments in a semicollisional plasma

“…Following the previous studies of the NLS equation with a local nonlinearity, 8 we consider dimensionless coordinates by normalizing the radial coordinates by the electron skin depth, c/ pe , and the axial length by 2k 0 c 2 / pe 2 , where pe is the unperturbed electron plasma frequency. The density perturbation is defined by the acoustic-type equation…”

LLE Quarterly Report (July-September 1999)[Library for Laser Energetics]

“…(7) into the definition of the imprint amplitude gives %;; = 0. ) '%(0'+08$i)sinA '8) where a Equation (8) shows that in the presence of the mass ablation, the imprint amplitude has an oscillatory dependence on the mode number. For modes with Aa c 1, the oscillation period and amplitude are determined by the velocity and acceleration perturbation growth reduced by the dynamic overpressure and the mass ablation [the first two terms in Eq.…”