Whistler Mode Wave-particle Interactions Research Articles

Computer simulations of relativistic whistler-mode wave–particle interactions

Whistler-mode wave–electron interactions constitute an important physical mechanism in the Earth’s magnetosphere and the radiation belts of the magnetized planets. From linear theory, an analytical result for the growth rate of electromagnetic R-mode (whistler-mode) waves in a relativistic bi-Maxwellian plasma with given temperature anisotropy is obtained. In order to test the linear theory, a one-dimensional self-consistent electromagnetic particle simulation is performed with a newly developed fully relativistic code. A major background component of isotropic cold electrons and a minor component of anisotropic hot electrons in a uniform magnetic field are assumed. Driven by the temperature anisotropy of the hot relativistic electrons, the whistler-mode waves grow initially linearly, and then nonlinearly to a level at which saturation takes place. Saturation occurs due to a combination of nonlinear trapping of resonant electrons and quasilinear relaxation of the temperature anisotropy. The initial wave growth rate obtained from the particle simulation agrees well with the growth rate predicted from linear theory. In order to reduce electrostatic fluctuations and achieve accuracy in the simulation, a large number of superparticles must be used.

Stochastic pitch angle diffusion due to electron-whistler wave–particle interactions

In the Earth’s magnetosphere, electron–whistler mode wave–particle interactions are a candidate mechanism for auroral precipitation via electron phase space diffusion. Of particular interest are stochastic interactions between relativistic electrons and (as often observed) waves of more than one wave number. It can be shown that the interaction between electrons and two oppositely directed monochromatic whistlers is stochastic. Once a threshold is exceeded, stochastic trajectories exist in addition to regular orbits (Kolmogorov–Arnold–Moser, or KAM, surfaces) near resonance, and here their corresponding pitch angle diffusion is estimated. The treatment is extended to consider broad band whistler wave packets and it is shown that the stochastic diffusion mechanism is again present for interactions with one or two wave packets. The pitch angle diffusion coefficient is estimated from the dynamics of stochastic electrons. For wave amplitudes consistent with planetary magnetospheres, such as at the Earth and Jupiter, pitch angle diffusion due to stochastic interactions occurs on fast (millisecond) time scales resulting in significant increases in the pitch angle diffusion coefficient.

Enhanced phase space diffusion due to chaos in relativistic electron–whistler mode wave particle interactions with applications to Jupiter

Using numerical solutions of single-particle dynamics, we consider a chaotic electron–whistler interaction mechanism for enhanced diffusion in phase space. This process, when applied to parameters consistent with the Jovian magnetosphere, is a candidate mechanism for pitch angle scattering in the Io torus, thus providing a source of auroral precipitating electrons. We initially consider the interaction between two oppositely directed monochromatic whistler mode waves. We generalize previous work to include relativistic effects. The full relativistic Lorentz equations are solved numerically to permit application to a more extensive parameter space. We use this simplified case to study the underlying behaviour of the system. For large-amplitude monochromatic waves the system is stochastic, with strong diffusion in phase space. We extend this treatment to consider two oppositely directed, broad band whistler wave packets. Using Voyager 1 data to give an estimate of the whistler wave amplitude at the Io torus at Jupiter, we calculate the degree of pitch angle scattering as a function of electron energy and initial pitch angle. We show that for relatively wide wave packets, significant pitch angle diffusion occurs (up to ±25°), on millisecond timescales, for electrons with energies from a few keV up to a few hundred keV.

Whistler mode wave coupling effects on electron dynamics in the near Earth magnetosphere

Nonlinear electron whistler mode wave particle interactions in the near earth magnetosphere suggest several candidate mechanisms for phase space diffusion of electrons into the loss cone to provide a source of auroral precipitating electrons. A unidirectional whistler mode wave propagating parallel to the background magnetic field and interacting with an electron can be shown to produce resonance (trapping of electrons) but the process is not stochastic. Chaos can be introduced by resonance between electrons that mirror many times in the earth's field, and a whistler wavefield. Here, we show that an electron interacting with two oppositely directed, parallel propagating whistler mode waves exhibits stochastic behaviour in addition to resonance. The background field is uniform, so that stochasticity arises solely due to the presence of the wavefield without requiring bounce motion of electrons between mirror points. Stochasticity first appears for wave amplitudes not inconsistent with observations at disturbed times in the near earth magnetosphere and therefore may contribute to pitch angle diffusion.

Lightning-induced electron precipitation

The broadband very low frequency (VLF, 0.3–30 kHz) radiation from lightning propagates in the Earth–ionosphere cavity as impulsive signals (spherics) and in the dispersive plasma regions of the ionosphere and magnetosphere it propagates as tones of descending or rising frequency (whistlers)1. VLF radio waves propagating in the magnetospheric plasma scatter energetic electrons by whistler-mode wave–particle interactions (cyclotron resonance) into the atmosphere2–6. These electrons, through collisions with the atmospheric constituents, cause localized ionization, conductivity enhancement, visual and ultraviolet light emissions, and brems-strahlung X rays. We have reported previously on the precipitation of energetic electrons from the radiation belts by the controlled injection from the ground of VLF radio waves7,8. Here we report the first satellite measurements of electron precipitation by lightning. The measured energy deposition of these conspicuous lightning-induced electron precipitation (LEP) bursts (∼ 10−3 erg cm−2) is sufficient to deplete the Earth's radiation belts and to alter subionospheric radiowave propagation (≲1 MHz). A one-to-one correlation is found between ground-based measurements of VLF spherics and whistlers at Palmer, Antarctica, and low-altitude satellite (S81-1) measurements of precipitating energetic electrons.

Two types of phase bunching in the whistler mode wave-particle interaction.

Importance of the “phase bunching” of resonant electrons in the whistler mode (WM) wave-particle interactions was pointed out by Brice. In this paper, we call attention on the point that there are two different types of phase bunching with two physically distinct phasing mechanisms in the case of the WM wave-particle interaction. One is a longitudinal phase bunching (the Brice type) which is caused by a longitudinal acceleration, while the other is a transverse phase bunching which is caused by a transverse acceleration. The both types are considered separately and examined mathematically and physically. In order to visualize the different characteristics of the two, numerical results on the phasing patterns and the resultant resonant current are shown by computing the nonlinear motion of electrons in a monochromatic WM wave with various initial velocities (36 different initial phase angles ×15 different speed |υ|).