We present results from numerical studies of whistler mode wave propagation in the Earth's magnetosphere. Numerical simulations, based on the novel algorithm, solving one‐dimensional electron‐MHD equations in the dipole coordinate system, demonstrate that the amplitude (and power) of the whistler mode waves generated by the ground‐based transmitter can be significantly increased in some particular location along the magnetic field line (for example, at the equatorial magnetosphere) by the frequency modulation of the transmitted signal. The location where the amplitude of the signal reaches its maximum is defined by the time delay between different frequency components of the signal. Simulations reveal that a whistler mode wave with a discrete frequency modulation (where the frequency changes by a finite step) in the range from 1 to 3 kHz can be compressed as efficiently as a signal with a continuous frequency modulation when the frequency difference between components of the discrete‐modulated signal is not greater than 100 Hz.
Wave-particle interaction plays a crucial role in the dynamics of the Earth’s radiation belts. Cyclotron resonance between coherent whistler mode electromagnetic waves and energetic electrons of the radiation belts is often called a coherent instability. Coherent instability leads to wave amplification/generation and particle acceleration/scattering. The effect of wave on particle’s distribution function is a key component of the instability. In general, whistler wave amplitude can grow over threshold of quasi-linear (linear) diffusion theory which analytically tracks the time-evolution of a particle distribution. Thus, a numerical approach is required to model the nonlinear wave induced perturbations on particle distribution function. A backward test particle model is used to determine the energetic electrons phase space dynamics as a result of coherent whistler wave instability. The results show the formation of a phase space features with much higher resolution than is available with forward scattering models. In the nonlinear regime the formation of electron phase space holes upstream of a monochromatic wave is observed. The results validate the nonlinear phase trapping mechanism that drives nonlinear whistler mode growth. The key differences in phase-space perturbations between the linear and nonlinear scenarios are also illustrated. For the linearized equations or for low (below threshold) wave amplitudes in the nonlinear case, there is no formation of a phase-space hole and both models show features that can be characterized as linear striations or ripples in phase-space.
This book is intended to provide a general introduction to plasma phenomena at a level appropriate for advanced undergraduate students or beginning graduate students. The reader is expected to have had exposure to basic electromagnetic principles including Maxwell's equations and the propagation of plane waves in free space. Despite its importance in both science and engineering the body of literature on plasma physics is often not easily accessible to the non-specialist, let alone the beginner. The diversity of topics and applications in plasma physics has created a field that is fragmented by topic-specific assumptions and rarely presented in a unified manner with clarity. In this book we strive to provide a foundation for understanding a wide range of plasma phenomena and applications. The text organization is a successive progression through interconnected physical models, allowing diverse topics to be presented in the context of unifying principles. The presentation of material is intended to be compact yet thorough, giving the reader the necessary tools for further specialized study. We have sought a balance between mathematical rigor championed by theorists and practical considerations important to experimenters and engineers. Considerable effort has been made to provide explanations that yield physical insight and illustrations of concepts through relevent examples from science and technology.
Numerical raytracing is an important technique that is being used to determine the trajectory of whistler mode waves in the magnetosphere. Previous whistler mode raytracing techniques were developed by assuming cold magnetospheric plasma. In this work we analyze the effect of finite electron and ion temperature on the whistler mode wave trajectories.
A data set from the Siple experiments (Siple Station Antartica) generated on December 8, 1986. A brief explanation of the data: We investigated one particular 35.5 second record that shows the repeated generation of sidebands. This record, occurring on December 8, 1986 during 14:24:29.30 UT -14:24:64.80 UT was triggered by the transmission of a constant amplitude and constant frequency “key down” tone at 2.7 kHz which, remarkably, was observed as 17 individual ∼2 second packets with sidebands and triggered free running emissions in the conjugate region. To open the data, you will need the files - matGetVariable.m AND matGetHeader.m.
Abstract Experimental observations of very low frequency (VLF) triggered emissions are an important resource in investigation of nonlinear wave‐particle interactions between whistler mode waves and energetic electrons in the Earth's radiation belts. Magnetospherically generated whistler mode sidebands observed during the Siple Station wave injection experiment are analyzed using a mixed modulation model and the MINUIT minimization package. The observed sidebands are found to exhibit features of both amplitude and frequency modulation of the input carrier wave with frequency modulation becoming more prominent as the observed amplitudes of the carrier and sidebands increase. A nonlinear whistler mode wave growth formulation based on phase bunching of counterstreaming electrons within a well‐defined phase trap is shown to reproduce the salient features of the sideband observations. Whistler mode sideband amplitude is shown to be affected by the shape and uniformity of the trap.
<p>Ground-based VLF transmitters located around the world generate signals that leak through the bottom side of the ionosphere in the form of whistler mode waves.&#160; Wave and particle measurements on satellites have observed that these man-made VLF waves can be strong enough to scatter trapped energetic electrons into low pitch angle orbits, causing loss by absorption in the lower atmosphere.&#160; This precipitation loss process is greatly enhanced by intentional amplification of the whistler waves in the ionosphere using a newly discovered process called Rocket Exhaust Driven Amplification (REDA).&#160; Satellite measurements of REDA have shown between 30 and 50 dB intensification of VLF waves in space using a 60-second burn of the 150 g/s thruster on the Cygnus satellite that services the International Space Station (ISS) [Bernhardt et al. 2021; Bernhardt 2021].&#160; This controlled amplification process is adequate to deplete the energetic particle population in the radiation belts in a few minutes rather than the multi-day period it would take naturally.&#160; Numerical simulations of the pitch angle diffusion for radiation belt particles use the UCLA quasi-linear Fokker Planck model (QLFP) to assess the impact of REDA on radiation belt remediation (RBR) of newly injected energetic electrons [Bernhardt et al., 2022].&#160; The simulated precipitation fluxes of energetic electrons are applied to models of D-region electron density and bremsstrahlung x-rays for predictions of the modified environment that can be observed with satellite and ground-based sensors.&#160;&#160;&#160;</p><p>References:</p><p>Bernhardt, P.A., et al., Strong Amplification of ELF/VLF Signals in Space Using Neutral Gas Injections from a Satellite Rocket Engine (2021), Radio Science, 56(2), e2020RS007207, https://doi.org/10.1029/ 2020RS007207.</p><p>Bernhardt, P.A., The Whistler Traveling Wave Parametric Amplifier (WTWPA) Driven by an Ion Ring-Beam Distribution from a Neutral Gas Injection in Space Plasmas (2021), IEEE Transactions on Plasma Science. 49, 6, 1983-1996, DOI: 10.1109/TPS.2021.3079130.</p><p>Bernhardt, P.A., et al., Active Precipitation of Radiation Belt Electrons using Rocket Exhaust Driven Amplification (REDA) of Man-Made Whistlers, Submitted to the Journal of Geophysical Research, 2022.</p>
The Russian `Alpha' transmitters broadcast alternating pulses between 11-15 kHz for navigation. A fraction of the VLF energy escapes into the magnetosphere, is guided by ducts, amplified by interaction with radiation belt particles, and observed at the geomagnetic conjugate point. We analyze VLF data from Adelaide, Australia, conjugate to Komsomolsk transmitter. An automated detection scheme separates the subionospheric and magnetospheric signals. We track availability of ducts at L=1.9 and find them present often. We correlate to geomagnetic conditions and assess the role of wave growth and triggering from wave-particle interactions, and compare to DEMETER satellite measurements.
'/%3e%3c/defs%3e%3cpath fill='%23012169' d='M0 0h10080v5040H0z'/%3e%3cpath stroke='%23fff' stroke-width='.6' d='m0 0 6 3m0-3L0 3' clip-path='url(%23b)' transform='scale(840)'/%3e%3cpath stroke='%23e4002b' stroke-width='.4' d='m0 0 6 3m0-3L0 3' clip-path='url(%23c)' transform='scale(840)'/%3e%3cpath stroke='%23fff' stroke-width='840' d='M2520 0v2520M0 1260h5040'/%3e%3cpath stroke='%23e4002b' stroke-width='504' d='M2520 0v2520M0 1260h5040'/%3e%3cg fill='%23fff'%3e%3cuse xlink:href='%23d' x='2520' y='3780'/%3e%3cuse xlink:href='%23a' x='7560' y='4200'/%3e%3cuse xlink:href='%23a' x='6300' y='2205'/%3e%3cuse xlink:href='%23a' x='7560' y='840'/%3e%3cuse xlink:href='%23a' x='8680' y='1869'/%3e%3cuse xlink:href='%23e' x='8064' y='2730'/%3e%3c/g%3e%3c/svg%3e)