Dielectric Tensor of Weakly Relativistic Electron Distributions Separable in Momentum and Pitch Angle

The dielectric tensor of a weakly relativistic, magnetized plasma is derived for distributions separable in momentum and pitch angle by using an expansion in powers of the Larmor radius. The results are initially expressed in terms of an integral over the electron pitch angle distribution which is itself unrestricted apart from a single symmetry condition. These results include relativistic and finite Larmor radius effects contributed by harmonics s with - 2 .;;; s .;;; 2 for all propagation angles and thus provide a useful framework for both numerical and analytical investigation of electron cyclotron phenomena (propagation and absorption of waves, maser action, current drive etc.) in a wide variety of isotropic and anisotropic plasmas. Explicit results are presented for the dielectric properties of isotropic, loss cone, anti-loss cone and hollow beam distributions, and for wave propagation perpendicular to the magnetic field. In these cases the pitch angle integrals are performed in terms of functions related to the standard plasma dispersion function.

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Comparison between CNA and energetic electron precipitation: simultaneous observation by Poker Flat Imaging Riometer and NOAA satellite

Annales Geophysicae ◽

10.5194/angeo-23-1555-2005 ◽

2005 ◽

Vol 23 (5) ◽

pp. 1555-1563 ◽

Cited By ~ 4

Author(s):

Y.-M. Tanaka ◽

M. Ishii ◽

Y. Murayama ◽

M. Kubota ◽

H. Mori ◽

...

Keyword(s):

Pitch Angle ◽

Electron Flux ◽

Energetic Electron ◽

Energetic Particles ◽

Electron Precipitation ◽

Angle Distribution ◽

Pitch Angle Distribution ◽

Loss Cone ◽

Isotropic Pitch ◽

Trapped Electron

Abstract. The cosmic noise absorption (CNA) is compared with the precipitating electron flux for 19 events observed in the morning sector, using the high-resolution data obtained during the conjugate observations with the imaging riometer at Poker Flat Research Range (PFRR; 65.11° N, 147.42° W), Alaska, and the low-altitude satellite, NOAA 12. We estimate the CNA, using the precipitating electron flux measured by NOAA 12, based on a theoretical model assuming an isotropic pitch angle distribution, and quantitatively compare them with the observed CNA. Focusing on the eight events with a range of variation larger than 0.4dB, three events show high correlation between the observed and estimated CNA (correlation coefficient (r0)>0.7) and five events show low correlation (r0<0.5). The estimated CNA is often smaller than the observed CNA (72% of all data for 19 events), which appears to be the main reason for the low-correlation events. We examine the assumption of isotropic pitch angle distribution by using the trapped electron flux measured at 80° zenith angle. It is shown that the CNA estimated from the trapped electron flux, assuming an isotropic pitch angle distribution, is highly correlated with the observed CNA and is often overestimated (87% of all data). The underestimate (overestimate) of CNA derived from the precipitating (trapped) electron flux can be interpreted in terms of the anisotropic pitch angle distribution similar to the loss cone distribution. These results indicate that the CNA observed with the riometer may be quantitatively explained with a model based on energetic electron precipitation, provided that the pitch angle distribution and the loss cone angle of the electrons are taken into account. Keywords. Energetic particles, precipitating – Energetic particles, trapped – Ionosphere-magnetosphere interactions

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Loss-cone index in distribution function in a hot magnetized plasma

Journal of Plasma Physics ◽

10.1017/s0022377806004491 ◽

2007 ◽

Vol 73 (2) ◽

pp. 207-214 ◽

Cited By ~ 2

Author(s):

R. P. SINGHAL ◽

A. K. TRIPATHI

Keyword(s):

Distribution Function ◽

Growth Rates ◽

Particle Distribution ◽

Distribution Functions ◽

Magnetized Plasma ◽

Dielectric Tensor ◽

Loss Cone ◽

Bernstein Waves ◽

Cone Index

Abstract.The components of the dielectric tensor for the distribution function given by Leubner and Schupfer have been obtained. The effect of the loss-cone index appearing in the particle distribution function in a hot magnetized plasma has been studied. A case study has been performed to calculate temporal growth rates of Bernstein waves using the distribution function given by Summers and Thorne and Leubner and Schupfer. The effect of the loss-cone index on growth rates is found to be quite different for the two distribution functions.

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Exact dielectric tensor for relativistic magnetized plasma with loss-cone and field-aligned drift

Journal of Plasma Physics ◽

10.1017/s002237780001429x ◽

1989 ◽

Vol 42 (2) ◽

pp. 193-204 ◽

Cited By ~ 9

Author(s):

Peter H. Yoon ◽

Tom Chang

Keyword(s):

Distribution Function ◽

External Field ◽

Field Line ◽

Maxwell Equations ◽

Exact Result ◽

Magnetized Plasma ◽

Dielectric Tensor ◽

Exact Form ◽

Loss Cone ◽

Equilibrium Function

An exact form of the dielectric tensor for a wide variety of relativistic magnetized plasmas is derived from the fully relativistic linearized Vlasov-Maxwell equations. The equilibrium function chosen incorporates a loss-cone in perpendicular momentum space, and a net drift along the external field-line. This choice of distribution function is fully relativistic, and the resulting form of the dielectric tensor is valid for arbitrary value of temperature, arbitrary degrees of loss-cone, and arbitrary drift velocity along the field-line. The exact result is simplified in several limiting cases relevant to various physical applications.

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Early-Time Non-Equilibrium Pitch Angle Diffusion of Electrons by Whistler-Mode Hiss in a Plasmaspheric Plume Associated with BARREL Precipitation

Frontiers in Astronomy and Space Sciences ◽

10.3389/fspas.2021.776992 ◽

2021 ◽

Vol 8 ◽

Author(s):

R. M. Millan ◽

J.-F. Ripoll ◽

O. Santolík ◽

W. S. Kurth

Keyword(s):

Phase Space ◽

Pitch Angle ◽

Particle Interaction ◽

Phase Space Density ◽

Angle Distribution ◽

Loss Cone ◽

Linear Diffusion ◽

Whistler Mode ◽

Space Density ◽

Van Allen Probes

In August 2015, the Balloon Array for Radiation belt Relativistic Electron Losses (BARREL) observed precipitation of energetic (<200 keV) electrons magnetically conjugate to a region of dense cold plasma as measured by the twin Van Allen Probes spacecraft. The two spacecraft passed through the high density region during multiple orbits, showing that the structure was spatial and relatively stable over many hours. The region, identified as a plasmaspheric plume, was filled with intense hiss-like plasma waves. We use a quasi-linear diffusion model to investigate plume whistler-mode hiss waves as the cause of precipitation observed by BARREL. The model input parameters are based on the observed wave, plasma and energetic particle properties obtained from Van Allen Probes. Diffusion coefficients are found to be largest in the same energy range as the precipitation observed by BARREL, indicating that the plume hiss waves were responsible for the precipitation. The event-driven pitch angle diffusion simulation is also used to investigate the evolution of the electron phase space density (PSD) for different energies and assumed initial pitch angle distributions. The results show a complex temporal evolution of the phase space density, with periods of both growth and loss. The earliest dynamics, within the ∼5 first minutes, can be controlled by a growth of the PSD near the loss cone (by a factor up to ∼2, depending on the conditions, pitch angle, and energy), favored by the absence of a gradient at the loss cone and by the gradients of the initial pitch angle distribution. Global loss by 1-3 orders of magnitude (depending on the energy) occurs within the first ∼100 min of wave-particle interaction. The prevalence of plasmaspheric plumes and detached plasma regions suggests whistler-mode hiss waves could be an important driver of electron loss even at high L-value (L ∼6), outside of the main plasmasphere.

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Electron cyclotron absorption for oblique propagation in loss-cone plasmas

Journal of Plasma Physics ◽

10.1017/s002237780002674x ◽

1988 ◽

Vol 39 (3) ◽

pp. 431-446 ◽

Cited By ~ 11

Author(s):

L. F. Ziebell

Keyword(s):

Electron Distribution ◽

Relativistic Effects ◽

Larmor Radius ◽

Dielectric Tensor ◽

Full Account ◽

Loss Cone ◽

Oblique Propagation ◽

Wave Parameters ◽

Cyclotron Absorption

The components of the dielectric tensor for a plasma described by a relativistic loss-cone electron distribution are written in a simple way, which takes full account of relativistic effects, harmonics and Larmor radius, for perpendicular and oblique propagation. For sufficiently oblique propagation and temperatures in the thermonuclear range, a still simpler form of the dielectric tensor is derived. The role of the wave parameters in the absorption is discussed, and some comments are made about the weakly relativistic and non-relativistic approaches. A numerical example is given for both the extraordinary and ordinary modes.

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Spatial absorption of a magnetosonic wave in a dusty magnetized plasma

Journal of Plasma Physics ◽

10.1017/s0022377800008448 ◽

2000 ◽

Vol 64 (1) ◽

pp. 57-74 ◽

Cited By ~ 13

Author(s):

M. C. de JULI ◽

R. S. SCHNEIDER

Keyword(s):

Dusty Plasma ◽

Second Order ◽

Magnetized Plasma ◽

Dust Particles ◽

Magnetosonic Wave ◽

Larmor Radius ◽

Dielectric Tensor ◽

Finite Larmor Radius ◽

Magnetized Dusty Plasma ◽

Electrons And Ions

The dielectric tensor for a multicomponent magnetized dusty plasma, including the effect of capture of plasma electrons and ions by the dust particles, is rewritten in order to provide expressions more suitable for applications. We use this tensor to study the spatial absorption of a magnetosonic wave, including effects up to second order in the Larmor radius. We analyse the absorption of the wave due to the presence of dust particles with variable charge and the modification of this absorption due to finite-Larmor-radius effects.

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Search for low-altitude acceleration mechanisms during an auroral substorm

Canadian Journal of Physics ◽

10.1139/p68-115 ◽

1968 ◽

Vol 46 (8) ◽

pp. 911-921 ◽

Cited By ~ 8

Author(s):

I. B. McDiarmid ◽

E. E. Budzinski

Keyword(s):

Pitch Angle ◽

Magnetic Moments ◽

Angular Distributions ◽

Angle Distribution ◽

Particle Interactions ◽

Pitch Angle Distribution ◽

Loss Cone ◽

Black Brant ◽

Auroral Substorm ◽

Low Altitude

Two Black Brant rockets were fired simultaneously from Fort Churchill during an auroral substorm. Electron spectra and angular distributions were examined at altitudes up to 800 km in an attempt to observe the effects of acceleration or loss mechanisms acting on the particles at low altitudes. In particular, the variation of the pitch-angle distribution in the loss cone for electrons with energies greater than 40 keV and near 10 keV was examined as a function of altitude. It was found that the distributions within the loss cone at higher altitudes decreased more slowly with pitch angle than expected on the basis of the observed distributions at low altitudes if no forces other than the earth's magnetic field act on the particles. The discrepancy was larger for 10-keV electrons than for 40-keV electrons. It is concluded that mechanisms exist at altitudes below 800 km which can alter the magnetic moments and/or the energies of the particles. No satisfactory explanation of the observed discrepancy has been found. An attempt was made to interpret the results in terms of wave-particle interactions which could give rise to pitch-angle diffusion, but the magnetic-wave amplitude required is at least two orders of magnitude larger than observed values.

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New representations of dielectric tensor elements in magnetized plasma

Journal of Plasma Physics ◽

10.1017/s0022377800011363 ◽

1986 ◽

Vol 35 (2) ◽

pp. 319-331 ◽

Cited By ~ 37

Author(s):

I. P. Shkarofsky

Keyword(s):

Functional Expression ◽

Relativistic Plasma ◽

Magnetized Plasma ◽

Dispersion Function ◽

Dielectric Tensor ◽

Relativistic Case ◽

Plasma Dispersion ◽

Derivatives Of

Each of the dielectric tensor elements in a Maxwellian magnetoplasma is expressed in terms of various derivatives of a single functional expression. The relationships for all the elements are given, first for the general case of a relativistic plasma, then for the slightly relativistic case, and finally for the non-relativistic case, when the perpendicular wavenumber is either large or small. We also derive new relations useful for the computation of the slightly relativistic plasma dispersion function.

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