Harvey A. Rose

Statistical mechanics of the nonlinear Schrödinger equation

AbstractWe investigate the statistical mechanics of a complex fieldø whose dynamics is governed by the nonlinear Schrödinger equation. Such fields describe, in suitable idealizations, Langmuir waves in a plasma, a propagating laser field in a nonlinear medium, and other phenomena. Their Hamiltonian

Recent Trident single hot spot experiments: Evidence for kinetic effects, and observation of Langmuir decay instability cascade

H(\phi ) = \int_\Omega {[\frac{1}{2}|\nabla \phi |^2 - (1/p) |\phi |^p ] dx}

A self-consistent trapping model of driven electron plasma waves and limits on stimulated Raman scatter

is unbounded below and the system will, under certain conditions, develop (self-focusing) singularities in a finite time. We show that, whenΩ is the circle and theL2 norm of the field (which is conserved by the dynamics) is bounded byN, the Gibbs measureυ obtained is absolutely continuous with respect to Wiener measure and normalizable if and only ifp andN are such that classical solutions exist for all time—no collapse of the solitons. This measure is essentially the same as that of a one-dimensional version of the more realisitc Zakharov model of coupled Langmuir and ion acoustic waves in a plasma. We also obtain some properties of the Gibbs state, by both analytic and numerical methods, asN and the temperature are varied.

Numerical test of the weak turbulence approximation to ionospheric Langmuir turbulence

Abstract We study the nonlinear Schrodinger equation with an “attractive” linear potential: i ϕ t = -Δϕ + (V(x) − |ϕ| 2σ )ϕ, 0 (n−2) (NLS) , which arises in the mathematical description of phenomena in nonlinear optics and plasma physics. Nonlinear bound states are finite energy localized solutions which, if dynamically stable, play an important role in the structure of general solutions of NLS. We discuss the existence and nonlinear orbital stability of nonlinear ground states of NLS. In particular, if -Δ + V supports a linear bound state, then NLS has stable nonlinear ground states in the supercritical and critical cases (σ≥2/n), where blow-up (self-focusing or collapse) can occur. This is a phenomenon not present in the case where V≡0. In addition, islands of stability in the regime of large H1 norm exist.

Nonlinear saturation of stimulated Raman scattering in laser hot spots

Single hot spot experiments offer several unique opportunities for developing a quantitative understanding of laser-plasma instabilities. These include the ability to perform direct numerical simulations of the experiment due to the finite interaction volume, isolation of instabilities due to the nearly ideal laser intensity distribution, and observation of fine structure due to the homogeneous plasma initial conditions. Experiments performed at Trident in the single hot spot regime have focused on the following issues. First, the intensity scaling of stimulated Raman scattering (SRS) for classically large damping regimes (kλD=0.35) was examined, and compared to classical SRS theory. SRS onset was observed at intensities much lower than expected (2×1015 W/cm2), from which nonclassical damping is inferred. Second, Thomson scattering was used to probe plasma waves driven by SRS, and structure was observed in the scattered spectra consistent with multiple steps of the Langmuir decay instability. Finally, sca...

Laser beam deflection by flow and nonlinear self-focusing

A quantitative theory of laser hot spots, which control plasma instabilities in real laser–plasma interactions, is presented in the case of random phase plate (RPP) optics. It is shown that the probability density of intense hot spots with intensity I, Phot(I), is given by Phot(I)∼(I/I02)exp(−I/I0) where I0 is the average intensity, and that the detailed amplitude and phase variation of the laser field in the vicinity of an intense hot spot is uniquely specified by the optics and is deterministic. These hot spots may be the source of below threshold stimulated Raman scattering (SRS) and its variation with I0 is shown to be super exponential. A brief preview of a quantitative nonlinear theory of hot‐spot‐induced laser filamentation is presented.

Evidence of plasma fluctuations and their effect on the growth of stimulated Brillouin and stimulated Raman scattering in laser plasmas

A Vlasov equation based model is used to determine various regimes of electron plasma wave response to a source appropriate to stimulated scatter in a laser hot spot. It incorporates trapped particle effects such as the standard nonlinear frequency shift, extended beyond the weak regime, and a reduction of damping a la Zakharov and Karpman [V. E. Zakharov and V. I. Karpman, JETP 16, 351 (1963)]. The results are consistent with those of Holloway and Dorning [J. P. Holloway and J. J. Dorning, Phys. Rev. A 44, 3856 (1991)] for small amplitude Bernstein–Greene–Kruskal modes. This leads to the prediction that as long as kλD⩾0.53 for a background Maxwellian distribution function, e.g., a 5 keV plasma with ne/nc⩽0.075, anomalously large backward stimulated Raman scatter can be excluded. A similar analysis leads to density limits on stimulated Brillouin scatter.

Symmetry experiments in gas‐filled hohlraums at NOVA

The standard weak Langmuir turbulence approach to explain the artificial plasma line in ionospheric radio modification experiments is examined. We compare solutions of a weak turbulence approximation (WTA) derived from a version of the one-dimensional driven and damped Zakharov system of equations (ZSE) with solutions to the same full ZSE. The electromagnetic pump field is modeled as a long-wavelength parametric driving term. We found that from a certain distance below the O mode reflection level the wave number saturation spectra computed from the WTA agree qualitatively with those from the ZSE for weak driving strengths, in the sense that the number of cascade lines increases with increasing pump strength. However, in general, the number of cascades apparent in the WTA solutions is larger than that predicted from the full ZSE. At higher intensities of the driver the saturation spectra from the ZSE differ from the WTA cascade spectra, in that a truncation of the cascade sets in, with a subsequent filling in of the bands between the cascades. This truncation takes place far before the ZSE cascade spectra reach the so-called “Langmuir condensate,”; contrary to earlier conjectures based mainly on dimensional analysis arguments. In the reflection region a qualitatively different process takes place: temporal cycles of large ensembles of localized events; nucleation of cavitons, collapse, and burnout constitute the basic elements of the turbulence in this region of space. No WTA exists for this region. Our findings are discussed with respect to the experiments performed at Arecibo and Tromso, the conclusion being that the ZSE yields results closer to observations than does the WTA, in all regions of space.