# Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes

## Abstract

Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEM peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.

- Authors:

- Univ. of California, San Diego, CA (United States)
- General Atomics, San Diego, CA (United States)

- Publication Date:

- Research Org.:
- General Atomics, San Diego, CA (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE)

- OSTI Identifier:
- 1438438

- Alternate Identifier(s):
- OSTI ID: 1411993

- Grant/Contract Number:
- FG02-95ER54309; FC02-08ER54977

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 12; Journal ID: ISSN 1070-664X

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY

### Citation Formats

```
Bass, Eric M., and Waltz, R. E.
```*Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes*. United States: N. p., 2017.
Web. doi:10.1063/1.4998420.

```
Bass, Eric M., & Waltz, R. E.
```*Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes*. United States. doi:10.1063/1.4998420.

```
Bass, Eric M., and Waltz, R. E. Fri .
"Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes". United States.
doi:10.1063/1.4998420.
```

```
@article{osti_1438438,
```

title = {Nonlinear verification of a linear critical gradient model for energetic particle transport by Alfven eigenmodes},

author = {Bass, Eric M. and Waltz, R. E.},

abstractNote = {Here, a “stiff transport” critical gradient model of energetic particle (EP) transport by EPdriven Alfven eigenmodes (AEs) is verified against local nonlinear gyrokinetic simulations of a well-studied beam-heated DIII-D discharge 146102. A greatly simplifying linear “recipe” for the limiting EP-density gradient (critical gradient) is considered here. In this recipe, the critical gradient occurs when the AE linear growth rate, driven mainly by the EP gradient, exceeds the ion temperature gradient (ITG) or trapped electron mode (TEM) growth rate, driven by the thermal plasma gradient, at the same toroidal mode number (n) as the AE peak growth, well below the ITG/TEM peak n. This linear recipe for the critical gradient is validated against the critical gradient determined from far more expensive local nonlinear simulations in the gyrokinetic code GYRO, as identified by the point of transport runaway when all driving gradients are held fixed. The reduced linear model is extended to include the stabilization from equilibrium E×B velocity shear. The nonlinear verification unambiguously endorses one of two alternative recipes proposed in Ref. 1: the EP-driven AE growth rate should be determined with rather than without added thermal plasma drive.},

doi = {10.1063/1.4998420},

journal = {Physics of Plasmas},

number = 12,

volume = 24,

place = {United States},

year = {Fri Dec 08 00:00:00 EST 2017},

month = {Fri Dec 08 00:00:00 EST 2017}

}