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We analyze energy and momentum exchange associated with Landau damping of hydromagnetic waves, from a macroscopic viewpoint, and compare the conclusions with those of the resonant quasi-linear theory. It is found that the heating of protons and electrons is correctly given by the resonant theory, but that the momentum exchange is not correctly described by the resonant theory.
Demonstration that large-amplitude linearly or elliptically polarized Alfven waves propagating parallel to the average magnetic field can be dissipated by nonlinear Landau damping. The damping is due to the longitudinal electric field associated with the ion sound wave which is driven (in second order) by the Alfven wave. The damping rate can be large even in a cold plasma (beta much less than 1, but not zero), and the mechanism proposed may be the dominant one in many plasmas of astrophysical interest.
The Vlasov-fluid model of Freidberg (1972) is used to study the resonance heating of a sharp-boundary screw pinch. The analysis provides the first treatment of the magnetoacoustic heating of a cylindrical plasma by means of ion Landau damping, which was identified as a viable dissipative mechanism for the conversion of magnetoacoustic wave energy into ion thermal energy. In addition, local and global energy conservation are considered, and formulae and numerical results for the thermal energy doubling time and the associated induced rf electric fields are presented. It is shown that collisionless absorption can provide a heating mechanism when an equilibrium plasma column is pumped by oscillations of the confining magnetic field at a frequency near the oblique magnetoacoustic frequency.
Recent measurements by the Pioneer 10 and Helios 1 spacecraft show that the leading edge of a corotating structure spreads as it moves from 0.3 AU to the orbit of the earth and steepens again farther out. By including Landau damping effects in the dynamical behavior of the streams, the above qualitative features can be accounted for.
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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.
The equations of motion for a particle in resonance with a small finite amplitude wave are solved approximately, using secularity free perturbation theory. The wave propagates at an arbitrary angle to a uniform background magnetic field in an infinite collisionless plasma. The wave fields include a longitudinal electrostatic component and elliptically polarized transverse electric and magnetic components. The trajectories of trapped and resonant untrapped particles are described, for each of the possible wave-particle resonances. These trajectories are used to construct an estimate of the nonlinear time dependent Landau damping rate of the wave.
Unducted VLF signals produced by lightning activity can form a population of magnetospherically reflected (MR) whistlers in the inner magnetosphere. It has been suggested recently that in the absence of significant attenuation such waves could merge into a broadband continuum with sufficient intensity to account for plasmaspheric hiss. To test this conjecture we have evaluated the path-integrated attenuation of MR whistlers along representative ray paths using the HOTRAY code. Using a realistic plasma distribution modeled on in-situ data, we find that the majority of MR waves experience significant damping after a few transits across the equator. This is primarily due to Landau resonance with suprathermal (0.1-1 keV) electrons. The attenuation is most pronounced for waves that propagate through the outer plasmasphere; this can readily account for the infrequent occurrence of multiple-hop MR waves for L greater than or equal to 3.5. Selected waves that originate at intermediate latitudes (15 deg is less than or equal to lambda is less than or equal to 35 deg) and whose ray paths are confined to the inner plasma- sphere may experience up to 10 magnetospheric reflections before substantial attentuation occurs. These waves should form the population of observed MR waves. Wave attenuation becomes more pronounced at higher frequencies; this can account for the absence of multiple-hop waves above 5 kHz. Weakly attenuated MR waves tend to migrate outward to the L shell, where their frequency is comparable to the equatorial lower hybrid frequency. The enhanced concentration of waves due to a merging of ray paths would produce a spectral feature that rises in frequency at lower L. This is quite distinct from the reported properties of plasmaspheric hiss, which maintains a constant frequency band throughout the entire plasmasphere. Furthermore, in the absence of mode conversion, waves below 500 Hz, which often form an important if not dominant part of the spectral properties of hiss, are unable to escape from the topside ionosphere in the whistler mode. Consequently, we conclude that unducted lightning signals cannot account for the origin of plasmaspheric hiss.
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The Fourier-Hermite expansion is used to follow the time development of a non-analytic initial perturbation of the linearized Vlasov-Poisson system. The calculations differ from some previous applications of the Fourier-Hermite expansion in that they relax certain symmetry conditions on the distribution functions and in that many coefficients are required to describe the initial conditions. The results confirm Weitzner's prediction of the asymptotic t to the -3rd time dependence for this problem, and exhibit the way in which this behavior develops. An appendix outlines the way in which the initial conditions are expanded in Hermite functions.
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A numerical procedure is derived for the solution of the Vlasov-Poisson system of equations in two phase-space variables. Derivatives with respect to the phase-space variables are approximated by a weighted sum of the values of the distribution function at property chosen neighboring points. The resulting set of ordinary differential equations is then solved by using an appropriate time intergration scheme. The accuracy of the proposed method is tested with some simple model problems. The results for the free streaming case, linear Landau damping, and nonlinear Landau damping are investigated and compared with those of the splitting scheme. The proposed method is found to be very accurate and efficient.
The present reexamination of the problem of ISM heating via the damping of plasma irregularities responsible for interstellar scintillations of radio sources gives attention to the effects of recent observational results on the hot plasma of the irregularities and on developments of in the theory of MHD waves. The damping mechanisms considered are linear Landau damping, ion-neutral collisional damping, nonlinear steepening of wave packets, a parametric decay instability, and nonlinear Landau damping. The heat input from all damping mechanisms can be accommodated by the 'fluctifer' region containing the irregularities, if it has features similar to the extended H II envelopes.
Even though solar wind, as a collisionless plasma, is properly described by the kineticMaxwell-Vlasov description, it can be argued that much of our understanding of solar wind observational data comes from an interpretation and numerical modeling which is based on a fluid description of magnetohydrodynamics. In recent years, there has been a significant interest in better understanding the importance of kinetic effects, i.e. the differences between the kinetic and usual fluid descriptions. Here we concentrate on physical properties of oblique kinetic Alfvn waves (KAWs), which are often recognized as one of the key ingredients in the solar wind turbulence cascade. We use three different fluid models with various degrees of complexity and calculate polarization and magnetic compressibility of oblique KAWs (propagation angle q = 88), which we compare to solutions derived from linear kinetic theory. We explore a wide range of possible proton plasma b = [0.1,10.0] and a wide range of length scales krL = [0.001,10.0]. It is shown that the classical isotropic two-fluid model is very compressible in comparison with kinetic theory and that the largest discrepancy occurs at scales larger than the proton gyroscale. We also show that the two-fluid model contains a large error in the polarization of electric field, even at scales krL 1. Furthermore, to understand these discrepancies between the two-fluid model and the kinetic theory, we employ two versions of the Landau fluid model that incorporate linear low-frequency kinetic effects such as Landau damping and finite Larmor radius (FLR) corrections into the fluid description. It is shown that Landau damping significantly reduces the magnetic compressibility and that FLR corrections (i.e. nongyrotropic contributions) are required to correctly capture the polarization.We also show that, in addition to Landau damping, FLR corrections are necessary to accurately describe the damping rate of KAWs. We conclude that kinetic effects are important even at scales which are significantly larger than the proton gyroscale krL 1.
Several years of work have combined plasma measurements in a laboratory Hall thruster and r-z numerical simulations with Hall2De to isolate the spatial variation of the anomalous collision frequency needed in Ohm’s law to produce the observed thruster behavior. This numerical solution is used here to test the validity of a first-principles model of the anomalous transport in these devices before such model is implemented self-consistently in r-z fluid codes like Hall2De. The first-principles model employs quasi-linear theory and is based on the hypothesis that the Electron Cyclotron Drift Instability (ECDI) excites ion acoustic turbulence that, in turn, enhances the effective collision frequency in these devices. We find that a model of the ECDI that assumes Maxwellian velocity distributions for electrons and singly-charged, main-beam, cold ions (Ti=0.07 eV) is insufficient to explain the expected variation of the anomalous collision frequency both in the interior and exterior of the acceleration channel. When warm ions (~0.5-3 eV) are accounted for, the ECDI model in the channel interior appears more promising but fails by orders of magnitude in the near plume region due to the much higher Landau damping of the ion acoustic waves there. This implies that either (a) some process allows the ECDI instability to remain uninhibited by classical Landau damping or, (b) that a different instability (or instabilities) altogether, also insusceptible to Landau damping, is/are active in this region. A previous hypothesis, that convection of wave energy generated by the ECDI in the channel plays a significant role in the near plume, is not supported by the results of the simulations.