# Nonlinear theory of collisionless trapped ion modes

## Abstract

A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level {delta}n/n{sub 0} is lower than the conventional mixing length estimate, {Delta}r/L{sub n} (ii) the ion temperature fluctuation level {delta}T{sub i}/T{sub i} significantly exceeds the density fluctuation level {delta}n/n{sub 0}; and (iii) the parallel ion velocity fluctuation level {delta}v{sub i}{sub {parallel}}/v{sub Ti} is expected to be negligible.

- Authors:

- Publication Date:

- Research Org.:
- Princeton Univ., NJ (United States). Plasma Physics Lab.

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 206969

- Report Number(s):
- PPPL-3143

ON: DE96007064; TRN: 96:009459

- DOE Contract Number:
- AC02-76CH03073

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: [1996]

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION; TFTR TOKAMAK; TRAPPED-PARTICLE INSTABILITY; THERMAL DIFFUSIVITY; KINETIC EQUATIONS; NONLINEAR PROBLEMS; ION TEMPERATURE

### Citation Formats

```
Hahm, T.S., and Tang, W.M.
```*Nonlinear theory of collisionless trapped ion modes*. United States: N. p., 1996.
Web. doi:10.2172/206969.

```
Hahm, T.S., & Tang, W.M.
```*Nonlinear theory of collisionless trapped ion modes*. United States. doi:10.2172/206969.

```
Hahm, T.S., and Tang, W.M. Fri .
"Nonlinear theory of collisionless trapped ion modes". United States.
doi:10.2172/206969. https://www.osti.gov/servlets/purl/206969.
```

```
@article{osti_206969,
```

title = {Nonlinear theory of collisionless trapped ion modes},

author = {Hahm, T.S. and Tang, W.M.},

abstractNote = {A simplified two field nonlinear model for collisionless trapped-ion-mode turbulence has been derived from nonlinear bounce-averaged drift kinetic equations. The renormalized thermal diffusivity obtained from this analysis exhibits a Bohm-like scaling. A new nonlinearity associated with the neoclassical polarization density is found to introduce an isotope-dependent modification to this Bohm-like diffusivity. The asymptotic balance between the equilibrium variation and the finite banana width induced reduction of the fluctuation potential leads to the result that the radial correlation length decreases with increasing plasma current. Other important conclusions from the present analysis include the predictions that (i) the relative density fluctuation level {delta}n/n{sub 0} is lower than the conventional mixing length estimate, {Delta}r/L{sub n} (ii) the ion temperature fluctuation level {delta}T{sub i}/T{sub i} significantly exceeds the density fluctuation level {delta}n/n{sub 0}; and (iii) the parallel ion velocity fluctuation level {delta}v{sub i}{sub {parallel}}/v{sub Ti} is expected to be negligible.},

doi = {10.2172/206969},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Mar 01 00:00:00 EST 1996},

month = {Fri Mar 01 00:00:00 EST 1996}

}