# Algorithm for Wave-Particle Resonances in Fluid Codes - Final Report

## Abstract

We review the work performed under LDRD ER grant 98-ERD-099. The goal of this work is to write a subroutine for a fluid turbulence code that allows it to incorporate wave-particle resonances (WPR). WPR historically have required a kinetic code, with extra dimensions needed to evolve the phase space distribution function, f(x, v, t). The main results accomplished under this grant have been: (1) Derivation of a nonlinear closure term for 1D electrostatic collisionless fluid; (2) Writing of a 1D electrostatic fluid code, ''es1f,'' with a subroutine to calculate the aforementioned closure term; (3) derivation of several methods to calculate the closure term, including Eulerian, Euler-local, fully local, linearized, and linearized zero-phase-velocity, and implementation of these in es1f; (4) Successful modeling of the Landau damping of an arbitrary Langmuir wave; (5) Successful description of a kinetic two-stream instability up to the point of the first bounce; and (6) a spin-off project which uses a mathematical technique developed for the closure, known as the Phase Velocity Transform (PVT) to decompose turbulent fluctuations.

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., CA (US)

- Sponsoring Org.:
- USDOE Office of Defense Programs (DP) (US)

- OSTI Identifier:
- 792770

- Report Number(s):
- UCRL-ID-138116

TRN: US0300431

- DOE Contract Number:
- W-7405-Eng-48

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 3 Mar 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; DISTRIBUTION FUNCTIONS; ELECTROSTATICS; LANDAU DAMPING; PHASE SPACE; PHASE VELOCITY; TURBULENCE; TWO-STREAM INSTABILITY; FLOW MODELS; E CODES

### Citation Formats

```
Mattor, N.
```*Algorithm for Wave-Particle Resonances in Fluid Codes - Final Report*. United States: N. p., 2000.
Web. doi:10.2172/792770.

```
Mattor, N.
```*Algorithm for Wave-Particle Resonances in Fluid Codes - Final Report*. United States. doi:10.2172/792770.

```
Mattor, N. Fri .
"Algorithm for Wave-Particle Resonances in Fluid Codes - Final Report". United States. doi:10.2172/792770. https://www.osti.gov/servlets/purl/792770.
```

```
@article{osti_792770,
```

title = {Algorithm for Wave-Particle Resonances in Fluid Codes - Final Report},

author = {Mattor, N},

abstractNote = {We review the work performed under LDRD ER grant 98-ERD-099. The goal of this work is to write a subroutine for a fluid turbulence code that allows it to incorporate wave-particle resonances (WPR). WPR historically have required a kinetic code, with extra dimensions needed to evolve the phase space distribution function, f(x, v, t). The main results accomplished under this grant have been: (1) Derivation of a nonlinear closure term for 1D electrostatic collisionless fluid; (2) Writing of a 1D electrostatic fluid code, ''es1f,'' with a subroutine to calculate the aforementioned closure term; (3) derivation of several methods to calculate the closure term, including Eulerian, Euler-local, fully local, linearized, and linearized zero-phase-velocity, and implementation of these in es1f; (4) Successful modeling of the Landau damping of an arbitrary Langmuir wave; (5) Successful description of a kinetic two-stream instability up to the point of the first bounce; and (6) a spin-off project which uses a mathematical technique developed for the closure, known as the Phase Velocity Transform (PVT) to decompose turbulent fluctuations.},

doi = {10.2172/792770},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Mar 03 00:00:00 EST 2000},

month = {Fri Mar 03 00:00:00 EST 2000}

}