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# Verification and application of resonance broadened quasi-linear (RBQ) model with multiple Alfvénic instabilities

## Abstract

The resonance broadened quasilinear (RBQ) model for the problem of relaxing the hot ion distribution function in constant-of-motion 3D space [Gorelenkov et al., Nucl. Fusion 58, 082016 (2018)] is presented with the self-consistent evolution of multiple Alfvén eigenmode amplitudes. The RBQ model represents the generalization of the earlier published model [Berk et al., Nucl. Fusion 35, 1661 (1995)] by carefully examining the wave particle interaction in the presence of realistic Alfvén eigenmode (AE) structures and pitch angle scattering with the help of the guiding center code ORBIT. One aspect of the generalization is that the RBQ model goes beyond the local perturbative-pendulumlike approximation for the wave particle dynamics near the resonance. An iterative procedure is introduced to account for eigenstructures varying within the resonances. It is found that a radially localized mode structure implies a saturation level 2–3 times smaller than that predicted by an earlier bump-on-tail quasilinear model that employed uniform mode structures. We apply the RBQ code to a DIII-D plasma with an elevated q-profile where the beam ion profiles exhibit stiff transport properties [Collins et al., Phys. Rev. Lett. 116, 095001 (2016)]. Finally, the properties of AE driven fast ion distribution relaxation are studied for validations ofmore »

- Authors:

- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- General Atomics, San Diego, CA (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1557588

- Alternate Identifier(s):
- OSTI ID: 1545413

- Grant/Contract Number:
- AC02-09CH11466; FC02-04ER54698

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 26; Journal Issue: 7; 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

```
Gorelenkov, N. N., Duarte, V. N., Collins, C. S., Podestà, M., and White, R. B. Verification and application of resonance broadened quasi-linear (RBQ) model with multiple Alfvénic instabilities. United States: N. p., 2019.
Web. doi:10.1063/1.5087252.
```

```
Gorelenkov, N. N., Duarte, V. N., Collins, C. S., Podestà, M., & White, R. B. Verification and application of resonance broadened quasi-linear (RBQ) model with multiple Alfvénic instabilities. United States. doi:10.1063/1.5087252.
```

```
Gorelenkov, N. N., Duarte, V. N., Collins, C. S., Podestà, M., and White, R. B. Mon .
"Verification and application of resonance broadened quasi-linear (RBQ) model with multiple Alfvénic instabilities". United States. doi:10.1063/1.5087252.
```

```
@article{osti_1557588,
```

title = {Verification and application of resonance broadened quasi-linear (RBQ) model with multiple Alfvénic instabilities},

author = {Gorelenkov, N. N. and Duarte, V. N. and Collins, C. S. and Podestà, M. and White, R. B.},

abstractNote = {The resonance broadened quasilinear (RBQ) model for the problem of relaxing the hot ion distribution function in constant-of-motion 3D space [Gorelenkov et al., Nucl. Fusion 58, 082016 (2018)] is presented with the self-consistent evolution of multiple Alfvén eigenmode amplitudes. The RBQ model represents the generalization of the earlier published model [Berk et al., Nucl. Fusion 35, 1661 (1995)] by carefully examining the wave particle interaction in the presence of realistic Alfvén eigenmode (AE) structures and pitch angle scattering with the help of the guiding center code ORBIT. One aspect of the generalization is that the RBQ model goes beyond the local perturbative-pendulumlike approximation for the wave particle dynamics near the resonance. An iterative procedure is introduced to account for eigenstructures varying within the resonances. It is found that a radially localized mode structure implies a saturation level 2–3 times smaller than that predicted by an earlier bump-on-tail quasilinear model that employed uniform mode structures. We apply the RBQ code to a DIII-D plasma with an elevated q-profile where the beam ion profiles exhibit stiff transport properties [Collins et al., Phys. Rev. Lett. 116, 095001 (2016)]. Finally, the properties of AE driven fast ion distribution relaxation are studied for validations of the applied RBQ model in DIII-D discharges. Initial results show that the model is robust, is numerically efficient, and can predict fast ion relaxation in present and future burning plasma experiments.},

doi = {10.1063/1.5087252},

journal = {Physics of Plasmas},

number = 7,

volume = 26,

place = {United States},

year = {2019},

month = {7}

}

*Citation information provided by*

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