### Abstract

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

Article number | 052114 |

Number of pages | 7 |

Journal | Physics of Plasmas |

Volume | 23 |

Issue number | 5 |

DOIs | |

Publication status | Published - 19 May 2016 |

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### Keywords

- electron trapping
- Fermi-Dirac distribution
- electrostatic wave

### Cite this

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**On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas.** / Schamel, Hans; Eliasson, Bengt.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the correct implementation of Fermi-Dirac statistics and electron trapping in nonlinear electrostatic plane wave propagation in collisionless plasmas

AU - Schamel, Hans

AU - Eliasson, Bengt

PY - 2016/5/19

Y1 - 2016/5/19

N2 - Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional (3D) Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes the holes become of cnoidal wave type and the electron density is shown to be described by a phi(x)^{1/2} rather than a phi(x) expansion, where phi(x) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of phi(x) and the nonlinear dispersion relation, which describes their phase velocity.

AB - Quantum statistics and electron trapping have a decisive influence on the propagation characteristics of coherent stationary electrostatic waves. The description of these strictly nonlinear structures, which are of electron hole type and violate linear Vlasov theory due to the particle trapping at any excitation amplitude, is obtained by a correct reduction of the three-dimensional (3D) Fermi-Dirac distribution function to one dimension and by a proper incorporation of trapping. For small but finite amplitudes the holes become of cnoidal wave type and the electron density is shown to be described by a phi(x)^{1/2} rather than a phi(x) expansion, where phi(x) is the electrostatic potential. The general coefficients are presented for a degenerate plasma as well as the quantum statistical analogue to these steady state coherent structures, including the shape of phi(x) and the nonlinear dispersion relation, which describes their phase velocity.

KW - electron trapping

KW - Fermi-Dirac distribution

KW - electrostatic wave

U2 - 10.1063/1.4949341

DO - 10.1063/1.4949341

M3 - Article

VL - 23

JO - Physics of Plasmas

JF - Physics of Plasmas

SN - 1070-664X

IS - 5

M1 - 052114

ER -