### Abstract

The matrix elements for nonlinear wave-particle scattering (nonlinear Landau damping) are obtained in explicit form for electrostatic waves from the Vlasov-Maxwell equations. The waves are allowed to propagate at arbitrary angles to the magnetic field, and no restrictions are imposed upon the Larmor radius or the frequencies. In the case k _{⊥}≫k _{∥}, the symmetry relations for mode-mode coupling are demonstrated by appropriate manipulations of the matrix elements. This allows one to cast the nonlinear Landau damping coefficients in a particularly simple form. The conditions for explosive instabilities are obtained, and a possible stabilization mechanism for these instabilities is pointed out. In the limit of either perpendicular or parallel propagation to the magnetic field, a comparison is made with previous results. The nonlinear stability of two types of velocity anisotropy instabilities are examined. Explosive instabilities are found to exist both for Harris modes and upper hybrid loss-cone modes. In addition, recent experimental results on nonlinear decay (induced scattering) of waves are discussed in the light of the present theory.

Original language | English |
---|---|

Pages (from-to) | 283-296 |

Number of pages | 14 |

Journal | Physics of Fluids |

Volume | 15 |

Issue number | 2 |

Publication status | Published - 1972 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Physics and Astronomy(all)
- Mechanics of Materials
- Computational Mechanics
- Fluid Flow and Transfer Processes

### Cite this

*Physics of Fluids*,

*15*(2), 283-296.

**Instabilities and induced scattering due to nonlinear Landau damping of longitudinal plasma waves in a magnetic field.** / Porkolab, M.; Chang, Robert P. H.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 15, no. 2, pp. 283-296.

}

TY - JOUR

T1 - Instabilities and induced scattering due to nonlinear Landau damping of longitudinal plasma waves in a magnetic field

AU - Porkolab, M.

AU - Chang, Robert P. H.

PY - 1972

Y1 - 1972

N2 - The matrix elements for nonlinear wave-particle scattering (nonlinear Landau damping) are obtained in explicit form for electrostatic waves from the Vlasov-Maxwell equations. The waves are allowed to propagate at arbitrary angles to the magnetic field, and no restrictions are imposed upon the Larmor radius or the frequencies. In the case k ⊥≫k ∥, the symmetry relations for mode-mode coupling are demonstrated by appropriate manipulations of the matrix elements. This allows one to cast the nonlinear Landau damping coefficients in a particularly simple form. The conditions for explosive instabilities are obtained, and a possible stabilization mechanism for these instabilities is pointed out. In the limit of either perpendicular or parallel propagation to the magnetic field, a comparison is made with previous results. The nonlinear stability of two types of velocity anisotropy instabilities are examined. Explosive instabilities are found to exist both for Harris modes and upper hybrid loss-cone modes. In addition, recent experimental results on nonlinear decay (induced scattering) of waves are discussed in the light of the present theory.

AB - The matrix elements for nonlinear wave-particle scattering (nonlinear Landau damping) are obtained in explicit form for electrostatic waves from the Vlasov-Maxwell equations. The waves are allowed to propagate at arbitrary angles to the magnetic field, and no restrictions are imposed upon the Larmor radius or the frequencies. In the case k ⊥≫k ∥, the symmetry relations for mode-mode coupling are demonstrated by appropriate manipulations of the matrix elements. This allows one to cast the nonlinear Landau damping coefficients in a particularly simple form. The conditions for explosive instabilities are obtained, and a possible stabilization mechanism for these instabilities is pointed out. In the limit of either perpendicular or parallel propagation to the magnetic field, a comparison is made with previous results. The nonlinear stability of two types of velocity anisotropy instabilities are examined. Explosive instabilities are found to exist both for Harris modes and upper hybrid loss-cone modes. In addition, recent experimental results on nonlinear decay (induced scattering) of waves are discussed in the light of the present theory.

UR - http://www.scopus.com/inward/record.url?scp=0039208533&partnerID=8YFLogxK

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M3 - Article

VL - 15

SP - 283

EP - 296

JO - Physics of Fluids

JF - Physics of Fluids

SN - 0031-9171

IS - 2

ER -