## This content will become publicly available on December 3, 2020

# Collisional resonance function in discrete-resonance quasilinear plasma systems

## Abstract

In this paper, a method is developed to analytically determine the resonance broadening function in quasilinear theory from first principles, due to either Krook or Fokker-Planck scattering collisions of marginally unstable plasma systems where discrete resonance instabilities are excited without any mode overlap. It is demonstrated that a quasilinear system that employs the calculated broadening functions reported here systematically recovers the growth rate and mode saturation levels for near-threshold plasmas previously calculated from nonlinear kinetic theory. The distribution function is also calculated, which enables precise determination of the characteristic collisional resonance width.

- Authors:

- Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
- Univ. of Texas, Austin, TX (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1580577

- Alternate Identifier(s):
- OSTI ID: 1576864

- Grant/Contract Number:
- AC02-09CH11466

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 26; 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

```
Duarte, V. N., Gorelenkov, N. N., White, R. B., and Berk, H. L. Collisional resonance function in discrete-resonance quasilinear plasma systems. United States: N. p., 2019.
Web. doi:10.1063/1.5129260.
```

```
Duarte, V. N., Gorelenkov, N. N., White, R. B., & Berk, H. L. Collisional resonance function in discrete-resonance quasilinear plasma systems. United States. doi:10.1063/1.5129260.
```

```
Duarte, V. N., Gorelenkov, N. N., White, R. B., and Berk, H. L. Tue .
"Collisional resonance function in discrete-resonance quasilinear plasma systems". United States. doi:10.1063/1.5129260.
```

```
@article{osti_1580577,
```

title = {Collisional resonance function in discrete-resonance quasilinear plasma systems},

author = {Duarte, V. N. and Gorelenkov, N. N. and White, R. B. and Berk, H. L.},

abstractNote = {In this paper, a method is developed to analytically determine the resonance broadening function in quasilinear theory from first principles, due to either Krook or Fokker-Planck scattering collisions of marginally unstable plasma systems where discrete resonance instabilities are excited without any mode overlap. It is demonstrated that a quasilinear system that employs the calculated broadening functions reported here systematically recovers the growth rate and mode saturation levels for near-threshold plasmas previously calculated from nonlinear kinetic theory. The distribution function is also calculated, which enables precise determination of the characteristic collisional resonance width.},

doi = {10.1063/1.5129260},

journal = {Physics of Plasmas},

number = 12,

volume = 26,

place = {United States},

year = {2019},

month = {12}

}

Free Publicly Available Full Text

This content will become publicly available on December 3, 2020

Publisher's Version of Record

DOI: 10.1063/1.5129260

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

##
Stability of Plasma

journal, February 1961

- Vedenov, A. A.; Velikhov, E. P.; Sagdeev, Roal'd Z.
- Soviet Physics Uspekhi, Vol. 4, Issue 2

##
Resonance broadening due to particle scattering and mode coupling in the quasi-linear relaxation of electron beams

journal, June 2014

- Bian, Nicolas H.; Kontar, Eduard P.; Ratcliffe, Heather
- Journal of Geophysical Research: Space Physics, Vol. 119, Issue 6

##
Prediction of nonlinear evolution character of energetic-particle-driven instabilities

journal, March 2017

- Duarte, V. N.; Berk, H. L.; Gorelenkov, N. N.
- Nuclear Fusion, Vol. 57, Issue 5

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

journal, July 2019

- Gorelenkov, N. N.; Duarte, V. N.; Collins, C. S.
- Physics of Plasmas, Vol. 26, Issue 7

##
Line broadened quasi-linear burst model [fusion plasma]

journal, December 1995

- Berk, H. L.; Breizman, B. N.; Fitzpatrick, J.
- Nuclear Fusion, Vol. 35, Issue 12

##
On the Shape of Collision-Broadened Lines

journal, April 1945

- Van Vleck, J. H.; Weisskopf, V. F.
- Reviews of Modern Physics, Vol. 17, Issue 2-3

##
Collisional enhancement of energetic particle Alfvénic resonance width in tokamaks

journal, March 2019

- White, R. B.; Duarte, V. N.; Gorelenkov, N. N.
- Physics of Plasmas, Vol. 26, Issue 3

##
Nonlinear Splitting of Fast Particle Driven Waves in a Plasma: Observation and Theory

journal, December 1998

- Fasoli, A.; Breizman, B. N.; Borba, D.
- Physical Review Letters, Vol. 81, Issue 25

##
Nonlinear evolution of a single coherent mode in a turbulent plasma

journal, April 2014

- Mendonça, J. T.; Galvão, R. M. O.; Smolyakov, A. I.
- Plasma Physics and Controlled Fusion, Vol. 56, Issue 5

##
Nonlinear Dynamics of a Driven Mode near Marginal Stability

journal, February 1996

- Berk, H. L.; Breizman, B. N.; Pekker, M.
- Physical Review Letters, Vol. 76, Issue 8

##
Resonance processes in magnetic traps

journal, January 1960

- Chirikov, B. V.
- Journal of Nuclear Energy. Part C, Plasma Physics, Accelerators, Thermonuclear Research, Vol. 1, Issue 4

##
Time-dependent critical layers in shear flows on the beta-plane

journal, May 1984

- Hickernell, Fred J.
- Journal of Fluid Mechanics, Vol. 142

##
Observation of Critical-Gradient Behavior in Alfvén-Eigenmode-Induced Fast-Ion Transport

journal, February 2016

- Collins, C. S.; Heidbrink, W. W.; Austin, M. E.
- Physical Review Letters, Vol. 116, Issue 9

##
Critical nonlinear phenomena for kinetic instabilities near threshold

journal, May 1997

- Breizman, B. N.; Berk, H. L.; Pekker, M. S.
- Physics of Plasmas, Vol. 4, Issue 5

##
Quasilinear Diffusion of an Axisymmetric Toroidal Plasma

journal, January 1972

- Kaufman, Allan N.
- Physics of Fluids, Vol. 15, Issue 6

##
A Perturbation Theory for Strong Plasma Turbulence

journal, January 1966

- Dupree, T. H.
- Physics of Fluids, Vol. 9, Issue 9

##
Theory of the pressure broadening and shift of spectral lines

journal, June 1981

- Peach, G.
- Advances in Physics, Vol. 30, Issue 3

##
Coulomb collision effects on linear Landau damping

journal, May 2014

- Callen, J. D.
- Physics of Plasmas, Vol. 21, Issue 5

##
A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems

journal, May 1954

- Bhatnagar, P. L.; Gross, E. P.; Krook, M.
- Physical Review, Vol. 94, Issue 3

##
Theory and observation of the onset of nonlinear structures due to eigenmode destabilization by fast ions in tokamaks

journal, December 2017

- Duarte, V. N.; Berk, H. L.; Gorelenkov, N. N.
- Physics of Plasmas, Vol. 24, Issue 12

##
Analytical nonlinear collisional dynamics of near-threshold eigenmodes

journal, February 2019

- Duarte, V. N.; Gorelenkov, N. N.
- Nuclear Fusion, Vol. 59, Issue 4

##
Fundamental statistical descriptions of plasma turbulence in magnetic fields

journal, April 2002

- Krommes, John A.
- Physics Reports, Vol. 360, Issue 1-4

##
Comparing the line broadened quasilinear model to Vlasov code

journal, March 2014

- Ghantous, K.; Berk, H. L.; Gorelenkov, N. N.
- Physics of Plasmas, Vol. 21, Issue 3