# 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:

- 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
- 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
- AX Division, L-038, Lawrence Livermore National Laboratory, PO Box 808, Livermore, CA 94551-0808 (United States). E-mail: berger5@llnl.gov
- 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}

}