Pitch angle and energy diffusion coefficients from resonant interactions with ion–cyclotron and whistler waves

1974 ◽  
Vol 12 (3) ◽  
pp. 417-432 ◽  
Author(s):  
Lawrence R. Lyons
Keyword(s):  
Wave Energy ◽  
Diffusion Coefficients ◽  
Pitch Angle ◽  
Whistler Waves ◽  
Linear Diffusion ◽  
Resonant Interactions ◽  
Ion Cyclotron ◽  
Diffusion Rates ◽  
General Relations ◽  
Wave Normal

General relations for quasi-linear diffusion coefficients in pitch angle and energy are applied to resonant particle interactions with ion–cyclotron and whistler waves. Expressions for the diffusion coefficients, valid for any distribution of wave energy with frequency and wave normal angle, are derived and normalized to be independent of the ambient magnetic field intensity and the electron density. The results illustrate how resonant particle diffusion rates vary with pitch angle and energy, and how the diffusion rates depend upon the distribution of wave energy.

General relations for resonant particle diffusion in pitch angle and energy

1974 ◽  
Vol 12 (1) ◽  
pp. 45-49 ◽  
Author(s):  
Lawrence R. Lyons
Keyword(s):  
Wave Energy ◽  
Diffusion Coefficients ◽  
Pitch Angle ◽  
Diffusion Theory ◽  
Plasma Turbulence ◽  
Particle Diffusion ◽  
Linear Diffusion ◽  
Resonant Interactions ◽  
General Relations ◽  
Wave Normal

By applying quasi-linear diffusion theory, general expressions are obtained for particle diffusion coefficients in both pitch angle and energy. The results are valid for resonant interactions with any mode of weak plasma turbulence, with wave energy distributed over any range of frequencies and wave normal angles. Simple relations are found between the diffusion coefficients, these relations reflecting the geometry of the diffusion surfaces for resonant particles.

Unmagnetized diffusion for azimuthally symmetric wave and particle distributions

1988 ◽  
Vol 40 (1) ◽  
pp. 179-198 ◽  
Author(s):  
P. B. Dusenbery ◽  
L. R. Lyons
Keyword(s):  
Magnetic Field ◽  
Diffusion Coefficients ◽  
Pitch Angle ◽  
Particle Distribution ◽  
Ion Beam ◽  
Distribution Model ◽  
Sound Waves ◽  
Linear Diffusion ◽  
Particle Distributions ◽  
Diffusion Rates

The general equations describing the quasi-linear diffusion of charged particles from resonant interactions with a spectrum of electrostatic waves are given, assuming the wave and particle distributions to be azimuthally symmetric. These equations apply when a magnetic field organizes the wave and particle distributions in space, but when the local interaction between the waves and particles can be evaluated assuming that no magnetic field is present. Such diffusion is, in general, two-dimensional and is similar to magnetized diffusion. The connection between the two types of diffusion is presented. In order to apply the general quasi-linear diffusion coefficients in pitch angle and speed, a specific particle-distribution model is assumed. An expression for the unmagnetized dielectric function is derived and evaluated for the assumed particle distribution model. It is found that slow-mode ion-sound waves are unstable for the range of plasma parameters considered. A qualitative interpretation of unmagnetized diffusion is presented. The diffusion coefficients are then evaluated for resonant ion interactions with ion-sound waves. The results illustrate how resonant ion diffusion rates vary with pitch angle and speed, and how the diffusion rates depend upon the distribution of wave energy in k–space. The results of this study have relevance for ion beam heating in the plasma-sheet boundary layer and upstream of the earth's bow shock.

Electron pitch-angle diffusion driven by oblique whistler-mode turbulence

1971 ◽  
Vol 6 (3) ◽  
pp. 589-606 ◽  
Author(s):  
L. R. Lyons ◽  
R. M. Thorne ◽  
C. F. Kennel
Keyword(s):  
Wave Energy ◽  
Diffusion Coefficients ◽  
Pitch Angle ◽  
High Energy ◽  
Harmonic Number ◽  
General Description ◽  
Linear Diffusion ◽  
Whistler Mode ◽  
Angle Scattering ◽  
Cyclotron Harmonic

A general description of cyclotron harmonic resonant pitch-angle scattering is presented. Quasi-linear diffusion coefficients are prescribed in terms of the wave normal distribution of plasma wave energy. Numerical computations are performed for the specific case of relativistic electrons interacting with a band of low frequency whistler-mode turbulence. A parametric treatment of the wave energy distribution permits normalized diffusion coefficients to be presented graphically solely as a function of the electron pitch-angle.The diffusion coefficients generally decrease with increasing cyclotron harmonic number. Higher harmonic diffusion is insignificant at very small electron pitch-angles, but becomes increasingly important as the pitch-angle increases. One thus expected the rate of pitch-angle scattering to decrease with increasing electron energy, since the resonant value of the latter varies proportionately with harmonic number. This indicates that, in mirror-type magnet field geometrics, such as the Earth's radiation belts, the diffusion losses of high energy electrons are likely to be appreciably slower than those at low energy. Integration of the diffusion rates along a complete bounce orbit will be required to clarify this point, however, since the high-energy particles will be subject to more rapid first harmonic diffusion near their mirror points.

Pitch-angle diffusion of relativistic electrons due to resonant interactions with whistler waves

1999 ◽  
Vol 6 (12) ◽  
pp. 4597-4606 ◽  
Author(s):  
Rodica Ciurea-Borcia ◽  
Gilles Matthieussent ◽  
Jacques Solomon ◽  
Edouard Le Bel ◽  
Françoise Simonet
Keyword(s):  
Pitch Angle ◽  
Relativistic Electrons ◽  
Whistler Waves ◽  
Resonant Interactions

scholarly journals Pitch-angle diffusion coefficients from resonant interactions with electrostatic electron cyclotron harmonic waves in planetary magnetospheres

2011 ◽  
Vol 29 (2) ◽  
pp. 321-330
Author(s):  
A. K. Tripathi ◽  
R. P. Singhal ◽  
K. P. Singh
Keyword(s):  
Diffusion Coefficients ◽  
Pitch Angle ◽  
Wave Amplitude ◽  
Radial Distance ◽  
Resonant Interaction ◽  
Electron Cyclotron ◽  
Harmonic Waves ◽  
Resonant Interactions ◽  
Cyclotron Harmonic ◽  
Strong Diffusion

Abstract. Pitch-angle diffusion coefficients have been calculated for resonant interaction with electrostatic electron cyclotron harmonic (ECH) waves in the magnetospheres of Earth, Jupiter, Saturn, Uranus and Neptune. Calculations have been performed at two radial distances of each planet. It is found that observed wave electric field amplitudes in the magnetospheres of Earth and Jupiter are sufficient to put electrons on strong diffusion in the energy range of less than 100 eV. However, for Saturn, Uranus and Neptune, the observed ECH wave amplitude are insufficient to put electrons on strong diffusion at any radial distance.

Modulation of Ion Pitch Angle in the Presence of Large-amplitude, Electromagnetic Ion Cyclotron (EMIC) Waves: 1-D Hybrid Simulation

2021 ◽  
Author(s):  
Shuo Ti ◽  
Tao Chen ◽  
Jiansheng Yao
Keyword(s):  
Large Amplitude ◽  
Pitch Angle ◽  
Hybrid Simulation ◽  
Bulk Velocity ◽  
Ion Energy ◽  
Ion Cyclotron ◽  
Angle Modulation ◽  
Wave Normal ◽  
Ion Species ◽  
Emic Waves

<p>Large-amplitude electromagnetic ion cyclotron (EMIC) waves induce unique dynamics of charged particle movement in the magnetosphere. In a recent study, modulation of the ion pitch angle in the presence of large-amplitude EMIC waves is observed, and there lacks a good explanation for this phenomenon. We investigate this modulation primarily via a 1-D hybrid simulation model and find that the modulation is caused by the bulk velocity triggered by large-amplitude EMIC waves. Affected by the bulk velocity, the number density of ions will enhance around pitch angle . Beyond that, the ion pitch angle is also modulated by the EMIC waves, and the modulation period is half of the EMIC waves' period. In addition, parameters that affect ion pitch angle modulation, including the wave amplitude, ion energy, ion species, and wave normal angle, are studied in our work.</p>

scholarly journals Resonant enhancement of relativistic electron fluxes during geomagnetically active periods

1999 ◽  
Vol 17 (5) ◽  
pp. 631-638 ◽  
Author(s):  
I. Roth ◽  
M. Temerin ◽  
M. K. Hudson
Keyword(s):  
Magnetic Field ◽  
Relativistic Electron ◽  
Pitch Angle ◽  
Adiabatic Invariant ◽  
Similar Process ◽  
Strong Increase ◽  
Relativistic Electrons ◽  
Whistler Waves ◽  
Resonant Interactions ◽  
The Magnetic Field

Abstract. The strong increase in the flux of relativistic electrons during the recovery phase of magnetic storms and during other active periods is investigated with the help of Hamiltonian formalism and simulations of test electrons which interact with whistler waves. The intensity of the whistler waves is enhanced significantly due to injection of 10-100 keV electrons during the substorm. Electrons which drift in the gradient and curvature of the magnetic field generate the rising tones of VLF whistler chorus. The seed population of relativistic electrons which bounce along the inhomogeneous magnetic field, interacts resonantly with the whistler waves. Whistler wave propagating obliquely to the magnetic field can interact with energetic electrons through Landau, cyclotron, and higher harmonic resonant interactions when the Doppler-shifted wave frequency equals any (positive or negative) integer multiple of the local relativistic gyrofrequency. Because the gyroradius of a relativistic electron may be the order of or greater than the perpendicular wavelength, numerous cyclotron, harmonics can contribute to the resonant interaction which breaks down the adiabatic invariant. A similar process diffuses the pitch angle leading to electron precipitation. The irreversible changes in the adiabatic invariant depend on the relative phase between the wave and the electron, and successive resonant interactions result in electrons undergoing a random walk in energy and pitch angle. This resonant process may contribute to the 10-100 fold increase of the relativistic electron flux in the outer radiation belt, and constitute an interesting relation between substorm-generated waves and enhancements in fluxes of relativistic electrons during geomagnetic storms and other active periods.Key words. Magnetospheric physics (energetic particles · trapped; plasma waves and instabilities; storms and substorms)

An Overview of the Interdiffusion Studies in Mo-Si and W-Si Systems

2014 ◽  
Vol 354 ◽  
pp. 79-83
Author(s):  
Soumitra Roy ◽  
Soma Prasad ◽  
Aloke Paul
Keyword(s):  
Crystal Structures ◽  
Atomic Number ◽  
Diffusion Coefficients ◽  
Relative Increase ◽  
The Other ◽  
Reactive Diffusion ◽  
Refractory Elements ◽  
Other Hand ◽  
Two Systems ◽  
Diffusion Rates

The growth of phases by reactive diffusion in Mo-Si and W-Si systems are compared. The crystal structures of MSi2 and M5Si3 phases (M = Mo, W) are similar in these two systems. However, the diffusion rates of the components change systematically with a change in the atomic number. Integrated diffusion coefficients in both phases increase with an increasing atomic number of refractory elements i.e. from Mo to W. On the other hand, the ratio of diffusivities of the components decreases. This indicates a relative increase in the diffusion rates of the metal components with increasing atomic number and a difference in defects concentrations in these two systems.

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