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Title: Simulating time-dependent energy transfer between crossed laser beams in an expanding plasma

Abstract

A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conducted in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift.

Authors:
 [1];  [2];  [3];  [4]
  1. Center for Applied Scientific Computing, L-561, Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94551-0808 (United States). E-mail: hittinger1@llnl.gov
  2. Center for Applied Scientific Computing, L-561, Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94551-0808 (United States). E-mail: dorr1@llnl.gov
  3. AX Division, L-038, Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94551-0808 (United States). E-mail: berger5@llnl.gov
  4. AX Division, L-038, Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94551-0808 (United States). E-mail: williams16@llnl.gov
Publication Date:
OSTI Identifier:
20687263
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 209; Journal Issue: 2; Other Information: DOI: 10.1016/j.jcp.2005.03.024; PII: S0021-9991(05)00194-4; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; BRILLOUIN EFFECT; COMPARATIVE EVALUATIONS; ENERGY TRANSFER; LASERS; NEWTON METHOD; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; PARAMETRIC INSTABILITIES; PLASMA; REFRACTION; TIME DEPENDENCE; WAVE EQUATIONS

Citation Formats

Hittinger, J.A.F., Dorr, M.R., Berger, R.L., and Williams, E.A. Simulating time-dependent energy transfer between crossed laser beams in an expanding plasma. United States: N. p., 2005. Web. doi:10.1016/j.jcp.2005.03.024.
Hittinger, J.A.F., Dorr, M.R., Berger, R.L., & Williams, E.A. Simulating time-dependent energy transfer between crossed laser beams in an expanding plasma. United States. doi:10.1016/j.jcp.2005.03.024.
Hittinger, J.A.F., Dorr, M.R., Berger, R.L., and Williams, E.A. Tue . "Simulating time-dependent energy transfer between crossed laser beams in an expanding plasma". United States. doi:10.1016/j.jcp.2005.03.024.
@article{osti_20687263,
title = {Simulating time-dependent energy transfer between crossed laser beams in an expanding plasma},
author = {Hittinger, J.A.F. and Dorr, M.R. and Berger, R.L. and Williams, E.A.},
abstractNote = {A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conducted in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift.},
doi = {10.1016/j.jcp.2005.03.024},
journal = {Journal of Computational Physics},
number = 2,
volume = 209,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}
  • A coupled mode system is derived to investigate a three-wave parametric instability leading to energy transfer between co-propagating laser beams crossing in a plasma flow. The model includes beams of finite width refracting in a prescribed transverse plasma flow with spatial and temporal gradients in velocity and density. The resulting paraxial light equations are discretized spatially with a Crank-Nicholson-type scheme, and these algebraic constraints are nonlinearly coupled with ordinary differential equations in time that describe the ion acoustic response. The entire nonlinear differential-algebraic system is solved using an adaptive, backward-differencing method coupled with Newton's method. A numerical study is conductedmore » in two dimensions that compares the intensity gain of the fully time-dependent coupled mode system with the gain computed under the further assumption of a strongly-damped ion acoustic response. The results demonstrate a time-dependent gain suppression when the beam diameter is commensurate with the velocity gradient scale length. The gain suppression is shown to depend on time-dependent beam refraction and is interpreted as a time-dependent frequency shift.« less
  • The energy transfer between two crossed lasers (a high frequency high amplitude pump and a low frequency low amplitude probe beam) through the coupling with a difference frequency electrostatic mode/quasimode in a plasma is examined. The electrostatic mode in an unmagnetized plasma is a linearly damped acoustic mode, while in a magnetized plasma it is also taken to be a lower hybrid mode. It is driven by the ponderomotive force due to the pump and probe beams. The electron density perturbation associated with the electrostatic mode beats with the oscillatory velocities due to the lasers to produce nonlinear current densitiesmore » facilitating the energy transfer from the high frequency laser to the probe beam. Efficient energy transfer occurs when the phase matching conditions are satisfied. Even when a finite mismatch between the lasers and the low frequency mode/quasimode exists, a significant energy transfer is possible. The theoretical results for the unmagnetized plasma are in compliance with the published experimental results. In a magnetized plasma lower hybrid wave appears to be a potential contender for facilitating energy exchange between lasers.« less
  • Analytic results are obtained for power transfer among crossing, equal frequency, laser beams, each smoothed by a random phase plate, in a flowing homogeneous plasma. For beams with well-separated directions, interbeam coupling transfers power, while intrabeam coupling causes beam deflection. For any pair of such beams, the beam with the largest positive projection on the flow direction will drain power from the other. {copyright} {ital 1998 American Institute of Physics.}
  • This paper outlines new ways for separating the different channels of optical dephasing of molecules in beams. It is shown that both the population loss and the optical phase relaxation rates can be obtained under collisionless conditions (molecular beams). These dephasing rates, which measure directly the homogeneous width of the prepared resonance, can be obtained with an energy resolution of better than one part in 10/sup 8/. Under these conditions the solution of the density matrix equations of motion is given for effusive and nozzle beams which represent a statistically open ensemble. The results, which we applied to our recentmore » measurements of optical T/sub 1/ and T/sub 2/, are discussed in different limits of power broadening, beam geometry, detector characteristics, temperature of the oven (or material container), and the transit time the molecules of different velocities spend in the laser beam. Furthermore, we indicate that the treatment of coherent transients in beams utilizing conventional Bloch equations is not valid since there is a loss of optically excited molecules. Finally, we discuss possible differences between small and large molecules when they undergo radiationless (or reactive) processes following the selective laser excitation (approx.10 kHz--10 MHz).« less
  • The power transfer between crossed laser beams made possible by an ion-acoustic wave is studied. A simple formula is derived for the steady-state power transfer, which depends on two dimensionless parameters: the ratio of the incident beam intensities and the normalized beamwidth. Numerical simulations show that the transient power transfer is larger than the steady-state power transfer and usually oscillates in time. The convective depletion of the higher-frequency beam saturates the power transfer more quickly than the damping of the ion-acoustic wave. {copyright} {ital 1996 American Institute of Physics.}