### Abstract

Parametric instabilities of finite amplitude, circularly polarized, parallel propagating Alfvén waves in a homogeneous plasma is discussed analytically, taking into account the ion Landau damping and the ion finite Larmor radius (FLR) effects. A hybrid kinetic fluid model is systematically derived from one-dimensional Vlasov equation for longitudinal ion motion and the FLR-Hall magnetohydrodynamic (MHD) equations for transverse directions. The longitudinal kinetic effects are retained in the model, whereas transverse kinetic effects such as ion cyclotron damping is neglected. Validity of the model is justified as far as the collisionless damping is concerned, since the ion cyclotron damping for typical quasi-parallel Alfvén waves in the solar wind is considered to be negligibly small. As already shown in a number of past studies, inclusion of the kinetic effects let some new instabilities emerge, while that reduces the growth rates of fluid instabilities in general. Damping rates computed by a model using collision-like (local) damping terms deviate from results of the present model, suggesting the importance of using the exact Landau-type interactions. Furthermore, as a consequence of the FLR effects, the growth rates of the fluid decay and beat instabilities of the left-hand (right-hand) polarized mode are reduced more strongly (weakly) in the FLR-Hall-MHD model (FHM model) than in the Hall-MHD model (HM model). A hybrid simulation is carried out to confirm that the FHM model is in better agreement than the HM model with the simulation results. When the initial parent wave amplitude is relatively small, the simulation results quantitatively agree with the linear analysis. Furthermore, some arguments are given to the observed ion relaxation and the energy oscillation of the parent waves observed in the hybrid simulations. Here again, quantitatively better explanation is obtained by using the FHM model rather than the HM model, suggesting that it is important to include the FLR effects for correctly describing the Alfvén wave parametric instabilities in finite ion beta plasmas, such as the solar wind near the Earth and the foreshock plasma.

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

Article number | A10107 |

Journal | Journal of Geophysical Research: Space Physics |

Volume | 112 |

Issue number | 10 |

DOIs | |

Publication status | Published - Oct 1 2007 |

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### Cite this

**Consequences of finite ion temperature effects on parametric instabilities of circularly polarized Alfvén waves.** / Nariyuki, Y.; Hada, Tohru.

Research output: Contribution to journal › Article

*Journal of Geophysical Research: Space Physics*, vol. 112, no. 10, A10107. https://doi.org/10.1029/2007JA012373

}

TY - JOUR

T1 - Consequences of finite ion temperature effects on parametric instabilities of circularly polarized Alfvén waves

AU - Nariyuki, Y.

AU - Hada, Tohru

PY - 2007/10/1

Y1 - 2007/10/1

N2 - Parametric instabilities of finite amplitude, circularly polarized, parallel propagating Alfvén waves in a homogeneous plasma is discussed analytically, taking into account the ion Landau damping and the ion finite Larmor radius (FLR) effects. A hybrid kinetic fluid model is systematically derived from one-dimensional Vlasov equation for longitudinal ion motion and the FLR-Hall magnetohydrodynamic (MHD) equations for transverse directions. The longitudinal kinetic effects are retained in the model, whereas transverse kinetic effects such as ion cyclotron damping is neglected. Validity of the model is justified as far as the collisionless damping is concerned, since the ion cyclotron damping for typical quasi-parallel Alfvén waves in the solar wind is considered to be negligibly small. As already shown in a number of past studies, inclusion of the kinetic effects let some new instabilities emerge, while that reduces the growth rates of fluid instabilities in general. Damping rates computed by a model using collision-like (local) damping terms deviate from results of the present model, suggesting the importance of using the exact Landau-type interactions. Furthermore, as a consequence of the FLR effects, the growth rates of the fluid decay and beat instabilities of the left-hand (right-hand) polarized mode are reduced more strongly (weakly) in the FLR-Hall-MHD model (FHM model) than in the Hall-MHD model (HM model). A hybrid simulation is carried out to confirm that the FHM model is in better agreement than the HM model with the simulation results. When the initial parent wave amplitude is relatively small, the simulation results quantitatively agree with the linear analysis. Furthermore, some arguments are given to the observed ion relaxation and the energy oscillation of the parent waves observed in the hybrid simulations. Here again, quantitatively better explanation is obtained by using the FHM model rather than the HM model, suggesting that it is important to include the FLR effects for correctly describing the Alfvén wave parametric instabilities in finite ion beta plasmas, such as the solar wind near the Earth and the foreshock plasma.

AB - Parametric instabilities of finite amplitude, circularly polarized, parallel propagating Alfvén waves in a homogeneous plasma is discussed analytically, taking into account the ion Landau damping and the ion finite Larmor radius (FLR) effects. A hybrid kinetic fluid model is systematically derived from one-dimensional Vlasov equation for longitudinal ion motion and the FLR-Hall magnetohydrodynamic (MHD) equations for transverse directions. The longitudinal kinetic effects are retained in the model, whereas transverse kinetic effects such as ion cyclotron damping is neglected. Validity of the model is justified as far as the collisionless damping is concerned, since the ion cyclotron damping for typical quasi-parallel Alfvén waves in the solar wind is considered to be negligibly small. As already shown in a number of past studies, inclusion of the kinetic effects let some new instabilities emerge, while that reduces the growth rates of fluid instabilities in general. Damping rates computed by a model using collision-like (local) damping terms deviate from results of the present model, suggesting the importance of using the exact Landau-type interactions. Furthermore, as a consequence of the FLR effects, the growth rates of the fluid decay and beat instabilities of the left-hand (right-hand) polarized mode are reduced more strongly (weakly) in the FLR-Hall-MHD model (FHM model) than in the Hall-MHD model (HM model). A hybrid simulation is carried out to confirm that the FHM model is in better agreement than the HM model with the simulation results. When the initial parent wave amplitude is relatively small, the simulation results quantitatively agree with the linear analysis. Furthermore, some arguments are given to the observed ion relaxation and the energy oscillation of the parent waves observed in the hybrid simulations. Here again, quantitatively better explanation is obtained by using the FHM model rather than the HM model, suggesting that it is important to include the FLR effects for correctly describing the Alfvén wave parametric instabilities in finite ion beta plasmas, such as the solar wind near the Earth and the foreshock plasma.

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U2 - 10.1029/2007JA012373

DO - 10.1029/2007JA012373

M3 - Article

AN - SCOPUS:37249072353

VL - 112

JO - Journal of Geophysical Research

JF - Journal of Geophysical Research

SN - 0148-0227

IS - 10

M1 - A10107

ER -