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A qualitative account is presented of collisionless shock theory in relation to the problem of upstream waves and particles. Particular attention is given to parallel shocks in high-beta plasmas, the relation of upstream phenomena to local shock structure, and Fermi acceleration.
Hydromagnetic wave-charged particle resonant interaction described by diffusion equation in momentum space, deriving diffusion coefficients and time evolution ultrarelativistic particle energy spectrum
While Galactic Cosmic Rays (GCR) represent a long-term cancer risk to deep space human missions, Solar Energetic Particles (SEP) represent a significant acute radiation hazard to human spaceflight. This work investigates wave-particle interactions caused by the incidence of a beam of energetic protons, representing a notional SEP event, onto a cloud of ions representing a notional ion thruster plume. The resulting electromagnetic ion/ion instability is developed to investigate the degree to which energetic protons can be scattered out of the initial beam. This work includes investigations of deflection rate dependences on incident SEP energy and flux, ion thruster power and orientation relative to SEP incidence, plume ion species, and background plasma. Also investigated are the spectrum and angular distribution of electromagnetic radiation resulting from the wave-particle interactions. The primary objective of this investigation is to develop a technique for active mitigation of SEP radiation threats to spacecraft and crew, by exploring the wave-particle interaction of a SEP event with the plasma plume expelled from an ion thruster. Since the cost in expended fuel restricts this technique to intermittent use during interplanetary flights, effective prediction of when a SEP event might impact the mission is still important, and the observation of conditions that might lead to SEP events, human-in-the-loop space weather analyses, and development of SEP prediction models remain essential to crew safety, spacecraft function, and mission success.
A description is presented of the results of a computer simulation involving a study of the particle precipitation induced by coherent VLF waves in the magnetosphere. The results of a computation for a 10 picoweber/sq m wave amplitude are shown in a graph. The precipitated flux for three different energies is given in a table. For 1.5 keV the energy deposition rate is about 0.8 erg/sq cm-sec, almost as intense as a moderate aurora. It is concluded that significant energy is deposited by a wave of 10 picoweber/sq m intensity. Such a wave amplitude is representative of highly coherent VLF wave types that are found in the magnetosphere. On the basis of the considered results it appears that controlled VLF wave injection in the magnetosphere could be an important and useful tool to study the coupling processes between the atmosphere and magnetosphere.
During geomagnetic disturbances when the ring current interacts intensely with the plasmasphere, the plasma of this region undergoes a strong heating due to an ion cyclotron instability. This is followed by the transfer of heat along geomagnetic field lines from the heating region to the ionosphere. One of the results of this process is the formation of non-isothermal region (in which T(sub e) greater than 3.4 T(sub i) at ionospheric heights) caused by a rapid cooling the H(+) ions due to their resonant charge exchange with neutral hydrogen. Heat transfer from the top of the flux tube to the ionosphere is investigated using a hydrodynamic model for the ionosphere-plasmasphere coupling. Field-aligned currents, present in the topside ionosphere, are often accompanied by ion sound turbulence. The turbulence scatters electrons, increasing the total electron collision frequency through wave-particle effects. The influence of wave-particle interactions introduces an anomalous component to the total collision frequency, which modifies substantially the heat conduction coefficient of the plasma. As a result, the plasma is heated more intensely above than below this region of ion sound turbulence.
Solutions are presented for the dispersion relation of waves propagating parallel to the ambient magnetic field, in a plasma having an arbitrary ratio of thermal to magnetic pressure, beta. Previous results applicable only to wave frequencies much lower than the ion cyclotron frequency are extended to include all frequencies lower than the electron cyclotron frequency. The cyclotron turnovers are found to occur at significantly lower frequencies in finite beta plasmas. Cyclotron damping is significant for small wavelength waves. These results show that in energetic particle scattering by electromagnetic turbulence in a plasma with beta value greater than 40, scattering by waves with wave frequencies greater than the ion cyclotron frequency can be neglected. This condition is satisfied in many astrophysical plasmas.
The kinetic wave equation which describes the nonlinear wave-particle interaction in a plasma is considered, and a method which uses the picture of quantized plasmons interacting with particles for the description of nonlinear wave-particle interactions is briefly described. In this method an assumption is made of the Markoffian character of the equation. It is shown that the Markoffian assumption can be justified at least for the case when the plasma is close to a stable stationary state. The diagram method developed by Nishikawa (1966) is used to derive an explicit expression for the kinetic equation. The application of the result to the case of interaction between an electron-wave and an ion-wave is discussed.
Past studies of the properties of Alfven waves in the solar wind have indicated that (1) the amplitude of the velocity fluctuations is almost always smaller than expected on the basis of the amplitude of the field fluctuations, even when the anisotropy of the plasma is taken into account, and (2) the alpha particles do not participate in the wave motions because they 'surf' on the waves carried by the proton fluid. Ulysses data are used to demonstrate that (1) the discrepancy between the velocity and field fluctuations is greater at high heliographic latitudes than in the ecliptic plane, and (2) the alphas do participate in the waves, being either in phase or out of phase with the proton motions depending on whether the differential flow speed between the alphas and protons is greater than or less than the 'observed' wave speed, B(sub o)(delta v squared / delta B squared)exp 1/2, as determined from the ratio of the amplitudes of the velocity and magnetic fluctuations. It is proposed that the modification of Alfven wave propagation speed is due to pressure anisotropies resulting from asymmetric distributions of interstellar pickup ions. If the proposed explanation is correct, it indicates that scattering of pickup ions onto a (bi)spherical shell may not be as complete as generally supposed.
Past studies of the properties of Alfven waves in the solar wind have indicated that the amplitude of the velocity fluctuations is almost always smaller than expected on the basis of the amplitude of the field fluctuations, even when plasma anisotropy is taken into account. Also, the alpha particles often do not participate in the wave motions because they "surf" on the proton fluid waves.
The origin of whistler mode radiation in the plasmasphere is examined from three years of plasma wave observations from the Dynamics Explorer and three years from the Imager for Magnetopause-to-Aurora Global Exploration (IMAGE) spacecraft. These data are used to construct plasma wave intensity maps of whistler mode radiation in the plasmasphere. The highest average intensities of the radiation in the wave maps show source locations and/or sites of wave amplification. Each type of emission is classified based on its magnetic latitude and longitude rather than any spectral feature. Equatorial electromagnetic (EM) emissions (approx. 30-330 Hz), plasmaspheric hiss (approx. 330 Hz - 3.3 kHz), chorus (approx. 2 kHz - 6 kHz), and VLF transmitters (approx. 10-50 kHz) are the main types of waves that are clearly delineated in the plasma wave maps. Observations of the equatorial EM emissions show that the most intense region is on or near the magnetic equator in the afternoon sector and that during times of negative B(sub z) (interplanetary magnetic field),the maximum intensity moves from L values of 3 to less than 2. These observations are consistent with the origin of this emission being particle-wave interactions in or near the magnetic equator. Plasmaspheric hiss shows high intensity at high latitudes and low altitudes (L shells from 2 to 4) and in the magnetic equator over L values from 2 to 3 in the early afternoon sector. The longitudinal distribution of the hiss intensity (excluding the enhancement at the equator) is similar to the distribution of lightning: stronger over continents than over the ocean, stronger in the summer than winter, and stronger on the dayside than nightside. These observations strongly support lightning as the dominant source for plasmaspheric hiss, which through particle-wave interactions, maintains the slot region in the radiation belts. The enhancement of hiss at the magnetic equator is consistent with particle-wave interactions. The chorus emissions are most intense on the morning side as previously reported. At frequencies from approx. 10-50 kHz VLF transmitters dominate the spectrum. The maximum intensity of the VLF transmitters is in the late evening or early morning with enhancements all along L shells from 1.8 to 3.
Analysis of VLF emissions that have been observed near 3/2, 5/2, and 7/2 f sub H by Ogo 5 in the magnetosphere (f sub H is the electron cyclotron frequency) in the light of the mechanism used for the diffuse plasma resonance f sub Dn observed by Alouette 2 and Isis 1. The VLF emission is considered to be generated by nonlinear coupling mechanisms in certain portions of the observation as the f sub Dn is enhanced by its association with nonlinear wave-particle interaction of the electrostatic electron cyclotron harmonic wave, including the instability due to the nonlinear inverse Landau damping mechanism in the turbulence. The difference between the two observations is in the excitation mechanism of the turbulence; the turbulence in the plasma trough detected by Ogo 5 is due to natural origins, whereas the ionospheric topside sounder makes the plasma wave turbulence artificially by submitting strong stimulation pulses. Electron density values in the plasma trough are deduced by applying the f sub Dn-f sub N/f sub H relationship obtained from the Alouette 2 experiment as well as by applying the condition for the wave-particle nonlinear interactions. The electron density values reveal good agreement with the ion density values observed simultaneously by the highly sensitive ion mass spectrometer.
A study is made of electrons in the drift and bounce loss cones of the magnetospheric slot region. It is observed that discrete events account for the arrival of most electrons in the 100-400 keV range into the drift loss cone. Most such events originate from a high power level VLF transmitter. Calculations of the loss rate caused by the events indicate that the electron flux in the slot region may decrease by as much as 50% per day. It is likely that wave-particle interaction occurs low on the field line due to the particular particle energies and wave frequencies. In order to transport particles to the lower interaction region, additional near-equator scattering, via power-line harmonic emissions or ELF hiss, may be required.
A model which explains the nonresonant waves which produce the diffuse resonance observed near 3/2 f(H) by the Alouette and Isis topside sounders, where f(H) is the ambient electron cyclotron frequency, is presented. These waves are the result of plasma wave instabilities driven by anisotropic electron velocity distributions initiated by the high-power short-duration sounder pulse. Calculations of the nonlinear wave-particle coupling coefficients show that the diffuse resonance wave can be maintained by nonlinear Landau damping of the sounder-stimulated 2f(H) wave which is observed with a time duration longer than that of the diffuse resonance wave. The time duration of the diffuse resonance is determined by the transit time of the instability-generated and nonlinearly maintained diffuse resonance wave from the remote short-lived hot region back to the antenna. The model is consistent with the Alouette/Isis observations and it demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.
Two-dimensional electrostatic particle simulations are presented which incorporate the effect of quasi-static electric fields on particle dynamics as well as effects associated with wave-particle interactions induced by the accelerated particles. The properties of the soft and hard X-ray and microwave emissions from such systems are examined. In particular, it is shown that acceleration by quasi-static electric fields and heating via wave-particle interactions produces electron distributions with a broken-power law, similar to those inferred from hard X-ray spectra. Also, heating of the ambient plasma gives rise to a region of hot plasma propagating down to the chromosphere at about the ion sound speed.
Charge particle motion and radiation in strong plane and spherical electromagnetic waves with nonthermal astrophysical applications
A model is presented to explain the non-resonant waves which give rise to the diffuse resonance observed near 3/2 f sub H by the Alouette and ISIS topside sounders, where f sub H is the ambient electron cyclotron frequency. In a strictly linear analysis, these instability driven waves will decay due to Landau damping on a time scale much shorter than the observed time duration of the diffuse resonance. Calculations of the nonlinear wave particle coupling coefficients, however, indicate that the diffuse resonance wave can be maintained by the nonlinear Landau damping of the sounder stimulated 2f sub H wave. The time duration of the diffuse resonance is determined by the transit time of the instability generated and nonlinearly maintained diffuse resonance wave from the remote short lived hot region back to the antenna. The model is consistent with the Alouette/ISIS observations, and clearly demonstrates the existence of nonlinear wave-particle interactions in the ionosphere.
Charged particle acceleration in the Earth inner magnetosphere is believed to be mainly due to the local resonant wave-particle interaction or particle transport processes. However, the Van Allen Probes have recently provided interesting evidence of a relatively slow transverse heating of eV ions at distances about 2-3 Earth radii during quiet times. Waves that are able to resonantly interact with such very cold ions are generally rare in this region of space, called the plasmasphere. Thus, non-resonant wave-particle interactions are expected to play an important role in the observed ion heating. We demonstrate that stochastic heating by random transverse electric field fluctuations of whistler (and possibly electromagnetic ion cyclotron) waves could explain this weak and slow transverse heating of H+ and O+ ions in the inner magnetosphere. The essential element of the proposed model of ion heating is the presence of trains of random whistler (hiss) wave packets, with significant amplitude modulations produced by strong wave damping, rapid wave growth, or a superposition of wave packets of different frequencies, phases, and amplitudes. Such characteristics correspond to measured characteristics of hiss waves in this region. Using test particle simulations with typical wave and plasma parameters, we demonstrate that the corresponding stochastic transverse ion heating reaches 0.07-0.2 eV/h for protons and 0.007-0.015 eV/h for O+ ions. This global temperature increase of the Maxwellian ion population from an initial Ti approx. 0.3 eV could potentially explain the observations.
Expressions are derived for transport by weak electrostatic microfluctuations driven unstable by a density gradient perpendicular to a uniform magnetic field in a Vlasov plasma. These expressions, which are evaluated for the universal and lower-hybrid density drift instabilities, provide improved physical interpretations for various wave-particle exchange frequencies previously reported. It is demonstrated that wave-particle effects generally reduce the free energy driving these instabilities, and that some forms of steady-state distribution functions are inappropriate for nonlinear theory.