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Wave-particle interactions are fundamental to all collisionless plasmas, from the instabilitites generating the waves to the resonant interactions which cause pitch-angle scattering, particle energy diffusion and cross-field diffusion of particles.
Plasma wave particle interactions in outer magnetosphere, magnetosheath and solar wind, noting role of AC electric fields
Three different wave-particle interaction processes are investigated: (1) the pickup of newborn ions by the solar wind, (2) the cyclotron maser mechanism, and (3) a special wave-particle interaction process which generalizes the conventional concept of the wave-particle interaction process. It is demonstrated on the basis of these three cases that wave-particle interactions can play an indispendable role in certain physical phenomena associated with space plasmas, whose nature is such as to preclude conventional hydrodynamic characterization. Wave-particle interactions can also generate such anomalous transport processes as spatial diffusion, anomalous heating, absorptions of radiation, etc., which also have significant consequence in space plasmas.
Wave-particle interactions in solar wind
The EXOS-B/Siple Station joint experiment on the triggering of VLF emissions by man-made signals causing some form of wave-particle interactions in the magnetosphere is presented, and results concerning wave-particle correlations are reported. In situ measurements of both energetic electron flux and VLF waves were made near the meridian connecting Siple Station, Antarctica with Roberval, Quebec, Canada in campaigns during July through September, 1979 and December 1979 through January 1980 at times of VLF transmission from Siple. Strong observed signals were found to be well correlated with a pancake pitch angle distribution of 0.3 to 6.9-keV electrons, and to exhibit a positive linear growth rate. Artificially stimulated emissions were observed to be accompanied by large electron fluxes in all energy channels in the equatorial interaction region, although the measured pitch angle distribution was not highly anisotropic. Results may be interpreted by the amplification of Siple signals by the cyclotron instability due to high pitch angle anisotropy (pancake distribution) and the triggering of emissions in the presence of high electron fluxes with some anisotropy and a sufficiently strong signal.
Space experiments with particle accelerators (SEPAC) flew on Spacelab 1 in November and December 1983. SEPAC included an accelerator which emitted electrons into the ionospheric plasma with energies up to 5 keV and currents up to 300 mA. The SEPAC equipment also included an energetic plasma generator, a neutral gas generator, and an extensive array of diagnostics. The diagnostics included plasma wave detectors, and energetic electron analyzer, a photometer, a high sensitivity television camera, a Langmuir probe and a pressure gage. Twenty-eight experiments were performed during the mission to investigate beam-plasma interactions, electron beam dynamics, plasma beam propagation, and vehicle charging. The wave-particle interactions were monitored by the plasma wave instrumentation, by the energetic electron detector and by the optical detectors. All show evidence of wave-particle interactions, which are described in this paper.
Magnetic field observations made by satellites in the earth's magnetic field reveal a wide variety of ULF waves. These waves interact with the ambient particle populations in complex ways, causing modulation of the observed particle fluxes. This modulation is found to be a function of species, pitch angle, energy and time. The characteristics of this modulation provide information concerning the wave mode and interaction process. One important characteristic of wave-particle interactions is the phase of the particle flux modulation relative to the magnetic field variations. To display this phase as a function of time a dynamic cross spectrum program has been developed. The program produces contour maps in the frequency time plane of the cross correlation coefficient between any particle flux time series and the magnetic field vector. This program has been utilized in several studies of ULF wave-particle interactions at synchronous orbit.
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A theory for the spatial development of linearly unstable, coupled waves is presented in which both quasi-linear and mode coupling effects are treated in a self-consistent manner. Steady state excitation of two waves is assumed at the boundary x = 0, the plasma being homogeneous in the y and z directions. Coupled equations are derived for the x dependence of the amplitudes of the primary waves and the secondary waves, correct through second order terms in the wave amplitude, but without usual approximation of small growth rates. This general formalism is then applied to the case of coupled ion acoustic waves driven unstable by an ion beam streaming in the direction of the x axis. If the modifications of the ion beam by the waves (quasi-linear effects) are ignored, explosive instabilities (singularities in all of the amplitudes at finite x) are found, even when all of the waves have positive energy. If these wave-particle interactions are included, the solutions are no longer singular, and all of the amplitudes have finite maxima.
The averaged-Lagrangian method is applied to nonlinear wave-particle interactions in an infinite, homogeneous, magnetic-field-free plasma. The specific example of Langmuir waves is considered, and the combined effects of four-wave interactions and wave-particle interactions are treated. It is demonstrated how the latter lead to diffusion in velocity space, and the quasilinear diffusion equation is derived. The analysis is generalized to the random phase approximation. The paper concludes with a summary of the method as applied in Parts 1-3 of the paper.
Wave-particle interactions play a crucial role in energetic particle dynamics in the Earths radiation belts. However, the relative importance of different wave modes in these dynamics is poorly understood. Typically, this is assessed during geomagnetic storms using statistically averaged empirical wave models as a function of geomagnetic activity in advanced radiation belt simulations. However, statistical averages poorly characterize extreme events such as geomagnetic storms in that storm-time ultralow frequency wave power is typically larger than that derived over a solar cycle and Kp is a poor proxy for storm-time wave power.
A theory for the spatial development of linearly unstable, coupled waves is presented in which both quasilinear and mode-coupling effects are treated in a self-consistent manner. Steady-state excitation of two waves is assumed at the boundary x = 0, the plasma being homogeneous in the y and z directions. Coupled equations are derived for the x dependence of the amplitudes of the primary waves and the secondary waves, correct through terms of second order in the wave amplitude, but without the usual approximation of small growth rates. This general formalism is then applied to the case of coupled ion-acoustic waves driven unstable by an ion beam streaming in the direction of the x axis. If the modifications of the ion beam by the waves (quasilinear effects) are ignored, explosive instabilities (singularities in all of the amplitudes at finite x) are found even when all of the waves have positive energy. If these wave-particle interactions are included, the solutions are no longer singular, and all of the amplitudes have finite maxima.
A general procedure for understanding plasma behaviour when resonant wave–particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principal results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas, narrow collisional boundary layers must be retained for resonant wave–particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear processes.
The physical concepts of wave-particle interactions in a collisionless plasma are developed from first principles. Using the Lorentz force, starting with the concepts of gyromotion, particle mirroring and the loss-cone, normal and anomalous cyclotron resonant interactions, pitch-angle scattering, and cross-field diffusion are developed.
A general procedure for understanding plasma behavior when resonant wave-particle interactions are the sole destabilizing and transport mechanism or only heating and/or current drive source is highlighted without recourse to involved numerical or analytical treatments. These phenomena are characterized by transport that appears to be collisionless even though collisions play a central role in narrow collisional boundary layers. The order of magnitude estimates, which include nonlinear effects, are shown to provide expressions in agreement with the principle results of recent toroidal Alfvén eigenmode (TAE), toroidal magnetic field ripple, and heating and current drive treatments. More importantly, the retention of nonlinearities leads to new estimates of the alpha particle energy diffusivity at saturation for TAE modes, and the ripple threshold at which superbanana plateau evaluations of alpha particle transport are modified by nonlinear radial drift effects. In addition, the estimates indicate when quasilinear descriptions for heating and current drive will begin to fail. The phenomenological procedure demonstrates that in magnetic fusion relevant plasmas narrow collisional boundary layers must be retained for resonant wave-particle interactions as they enhance the role of collisions, and make stochastic particle motion unlikely to be more important than other nonlinear process.
Kinetic effects due to wave-particle interactions and suprathermal electrons have been suggested in the literature as possible solar wind acceleration mechanisms. Ion cyclotron resonant heating, in particular, has been associated with some qualitative features observed in the solar wind. In terms of solar wind acceleration, however, it is interesting to compare the kinetic effects of suprathermal electrons with those due to the wave-particle interactions. The combined effects of the two acceleration mechanisms on the fast solar wind have been studied by Tam and Chang (1999a,b). In this study. we investigate the role of the suprathermal electron population in the acceleration of the solar wind. Our model follows the global kinetic evolution of the fast solar wind under the influence of ion cyclotron resonant heating, while taking into account Coulomb collisions, and the ambipolar electric field that is consistent with the particle distributions themselves. The kinetic effects due to the suprathermal electrons, which we define to be the tail of the electron distributions, can be included in the model as an option. By comparing the results with and without the inclusion of the suprathermal electron effects, we determine the relative importance of suprathermal electrons and wave-particle interactions in driving the solar wind. We find that although suprathermal electrons enhance the ambipolar electric potential in the solar wind considerably, their overall influence as an acceleration mechanism is relatively insignificant in a wave-driven solar wind.
The Voyager 2 encounter of Uranus has provided observations of plasma waves in and near the magnetosphere. These data, while the first from Uranus, will also be the only direct information on wave-particle interactions at this planet for many years to come. The observations include electrostatic waves upstream of the bow shock, turbulence in the shock, Bernstein emissions and whistler mode waves in the magnetosphere, broadband electrostatic noise in the magnetotail, and a number of the other types of plasma waves which have yet to be clearly identified. Each of these types of waves exist in a plasma environment which both supports the growth of the waves and is modified by interactions with the waves. Wave-particle interactions provide the channels through which the waves can accelerate, scatter, or thermalize the plasmas. The most spectacular example in the case of Uranus is the extremely intense whistler mode activity in the inner magnetosphere which is the source of strong pitch angle diffusion. The resulting electron precipitation is sufficient to produce the auroral emissions observed by Voyager. The strong diffusion, however, presents the problem of supplying electrons in the range of 5 to 40 keV in order to support the losses to the atmosphere.
The Voyager 2 encounter of Uranus has provided observations of plasma waves in and near the magnetosphere. These data, while the first from Uranus, will also be the only direct information on wave-particle interactions at this planet for many years to come. The observations include electrostatic waves upstream of the bow shock, turbulence in the shock Bernstein emissions and whistler mode waves in the magnetosphere, broadband electrostatic noise in the magnetotail, and a number of the other types of plasma waves which have yet to be clearly identified. Each of these types of waves exist in a plasma environment which both supports the growth of the waves and is modified by interactions with the waves. Wave-particle interactions provide the channels through which the waves can accelerate, scatter, or thermalize the plasmas. The most spectacular example in the case of Uranus is the extremely intense whistler mode activity in the inner magnetosphere which is the source of strong pitch angle diffusion. The resulting electron precipitation is sufficient to produce the auroral emissions observed by Voyager. The strong diffusion, however, presents the problem of supplying electrons in the range of 5 to 40 keV in order to support the losses to the atmosphere.