Nonlinear Stability of the Extraordinary Wave in a Plasma

Engel, Robert

doi:10.1063/1.1761338

Cited by 22 publications

(3 citation statements)

References 11 publications

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“…The modified operator Q _ k resulting from these replacements is GHAUG and PEARLSTEIff. l6 " ,ENGSL , 17 KEUlffiL and PBTSCHEK, 14 (18 } DRUMMOKlA ' and others for these modes may be easily obtained.…”

Section: •Amentioning

confidence: 99%

Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field

Kennel

Engelmann

1966

The Physics of Fluids

985

893

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The quasi-linear velocity space diffusion is considered for waves of any oscillation branch propagating at an arbitrary angle to a uniform magnetic field in a spatially uniform plasma. The space-averaged distribution function is assumed to change slowly compared to a gyroperiod and characteristic times of the wave motion. Nonlinear mode coupling is neglected. An H-like theorem shows that both resonant and nonresonant quasi-linear diffusion force the particle distributions towards marginal stablity. Creation of the marginally stable state in the presence of a sufficiently broad wave spectrum in general involves diffusing particles to infinite energies, and so the marginally stable plateau is not accessible physically, except in special cases. Resonant particles with velocities much larger than typical phase velocities in the excited spectrum are scattered primarily in pitch angle about the magnetic field. Only particles with velocities the order of the wave phase velocities or less are scattered in energy at a rate comparable with their pitch angle scattering rate.

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Section: •Amentioning

confidence: 99%

Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field

Kennel

Engelmann

1966

The Physics of Fluids

985

893

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“…In a complete nonlinear theory for a closed system, the anisotropy is destroyed as the wave grows to its final equilibrium amplitude. An analysis of this problem has been given by Engel [1965]. The linear theory used here is adequate because the wave energy density is much less than the particle energy density.…”

Section: The Propagation Medium Is Assumed To Consistmentioning

confidence: 99%

Cyclotron-resonance amplification of VLF and ULF whistlers

Liemohn¹

1967

J. Geophys. Res.

159

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Electromagnetic signals that propagate through the magnetosphere exchange energy with nonthermal charged particles by the cyclotron‐resonance mechanism. The interaction is due to a Doppler shift of the propagation frequency ω to the cyclotron frequency ωc of the charged particle that allows the particle to resonate with the electromagnetic fields. The dominant exchange is between electrons around 1 kev and VLF whistlers that propagate in the right‐hand mode and between protons around 1 kev and ULF whistlers (Pc 1 geomagnetic micropulsations) that propagate in the left‐hand mode. The complex wave number k(ω) = kr + iki for propagation in a hot uniform plasma parallel to a static magnetic field is assumed to describe whistler properties locally in the magnetosphere. The power transfer function A(ω), which relates the input and output power spectrums, is determined by the path integral of ki along a geomagnetic flux tube. Spectrums of A for both VLF and ULF whistlers have been evaluated for a variety of energy and pitch‐angle distributions of the form E−n sinm α. In general, A has an amplification maximum just below a sharp absorption cutoff, which is consistent with observations. The detailed input‐output spectrums of whistlers that are necessary to test the theory are not available yet. When these spectrums are measured, this interaction may provide a possible method for mapping the phase space distribution of nonthermal particles in the magnetosphere.

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“…Nonlinearities of a similar sort are familiar in plasma physics, where they were first studied analytically by Drummond and Pines [1962] for longitudinal (electrostatic) plasma oscillations. More recently, JOI-IN M. CORNWALL nonlinearities for transverse cyclotron instabilities have been discussed by Chang and Pearlstein [1965], and by Engel [1965]. The analysis of these nonlinearities for the earth's magnetosphere is given in section 3, and two interesting results emerge.…”

Section: Introductionmentioning

confidence: 96%

Micropulsations and the outer radiation zone

Cornwall¹

1966

J. Geophys. Res.

150

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Recently the present author and others have suggested that Pc 1 micropulsations (hydromagnetic waves of frequency 0.1–5 cps) are generated in the outer radiation zone (L > 4) by low‐energy protons via a cyclotron instability. Several points are discussed in the present paper; the first concerns the interpretation of ground‐based experimental data in the light of the above model. A simple formula is given for the highest emitted frequency on a given field line, which formula is in good agreement with the data. Secondly, it is observed that the combined processes of cyclotron instabilities and pitch‐angle scattering give rise to upper limits on both the energy density of trapped particles and of Pc 1 wave fields. This saturation effect may account for the remarkable stability of the low‐energy proton population against fluctuations associated with the source mechanism. Finally, it is pointed out that the wave periods are in quasi‐resonance with the bounce periods of moderately energetic electrons, and this leads to radial diffusion of such electrons.

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Nonlinear Stability of the Extraordinary Wave in a Plasma

Cited by 22 publications

References 11 publications

Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field

Velocity Space Diffusion from Weak Plasma Turbulence in a Magnetic Field

Cyclotron-resonance amplification of VLF and ULF whistlers

Micropulsations and the outer radiation zone

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