# Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks

## Abstract

Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly for each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.

- Authors:

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

- Publication Date:

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

- Sponsoring Org.:
- USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)

- OSTI Identifier:
- 1377823

- Alternate Identifier(s):
- OSTI ID: 1348951

- Grant/Contract Number:
- AC02-76CH03073

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 3; 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; banana-drift transport; momentum dissipation; plasmas; stability

### Citation Formats

```
Park, Jong-Kyu, and Logan, Nikolas C.
```*Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks*. United States: N. p., 2017.
Web. doi:10.1063/1.4977898.

```
Park, Jong-Kyu, & Logan, Nikolas C.
```*Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks*. United States. doi:10.1063/1.4977898.

```
Park, Jong-Kyu, and Logan, Nikolas C. Wed .
"Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks". United States.
doi:10.1063/1.4977898. https://www.osti.gov/servlets/purl/1377823.
```

```
@article{osti_1377823,
```

title = {Self-consistent perturbed equilibrium with neoclassical toroidal torque in tokamaks},

author = {Park, Jong-Kyu and Logan, Nikolas C.},

abstractNote = {Toroidal torque is one of the most important consequences of non-axisymmetric fields in tokamaks. The well-known neoclassical toroidal viscosity (NTV) is due to the second-order toroidal force from anisotropic pressure tensor in the presence of these asymmetries. This work shows that the first-order toroidal force originating from the same anisotropic pressure tensor, despite having no flux surface average, can significantly modify the local perturbed force balance and thus must be included in perturbed equilibrium self-consistent with NTV. The force operator with an anisotropic pressure tensor is not self-adjoint when the NTV torque is finite and thus is solved directly for each component. This approach yields a modified, non-self-adjoint Euler-Lagrange equation that can be solved using a variety of common drift-kinetic models in generalized tokamak geometry. The resulting energy and torque integral provides a unique way to construct a torque response matrix, which contains all the information of self-consistent NTV torque profiles obtainable by applying non-axisymmetric fields to the plasma. This torque response matrix can then be used to systematically optimize non-axisymmetric field distributions for desired NTV profiles. Published by AIP Publishing.},

doi = {10.1063/1.4977898},

journal = {Physics of Plasmas},

number = 3,

volume = 24,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}