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Finite ion and electron temperature effect on ion cyclotron waves generated by Stix coil, and subsequent plasma ion heating in magnetic beaches
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Cyclotron waves in collisionless plasma column, finding three distinct waves with resonances at/near electron cyclotron frequency
A gyrating electron beam supports negative energy modes near the harmonics of electron-cyclotron frequency. An electromagnetic wave passing through such a beam parametrically up-converts into high-frequency electromagnetic modes separated from the pump frequency by the electron-cyclotron harmonics. The growth rate for this process varies directly as the oscillatory velocity of beam electrons caused by the pump and as square root of the beam density. It has a maximum at values of scattering angle close to 180 deg and is also implicitly dependent on the beam veocity and the cyclotron frequency of electrons. The effect of a cold electron component is to reduce the growth rate.
In the present paper, we have calculated electron pitch angle diffusion coefficients due to resonant interactions with whistler mode lower band chorus (LBC), upper band chorus (UBC), and electrostatic electron cyclotron harmonic (ECH) waves. Calculations have been performed at two values of the ratio of electron plasma frequency to gyro-frequency and thirteen representative values of electron energies for the plasma sheet electrons. The numerical data of diffusion coefficients have been fitted to simple analytical expressions for each wave mode. These analytical expressions allow for simple evaluation of pitch angle diffusion coefficients for the arbitrary pitch angle, energy, the ambient magnetic field, the wave amplitude, and the ratio of plasma frequency to gyro-frequency. In the case of LBC waves, the analytical coefficients are generally within a factor of two to the numerical coefficients, except at higher pitch angles where the numerical coefficients drop to show negligible values. Likewise, also for UBC waves, the analytical coefficients are generally within a factor of two to the numerical coefficients. The analytical coefficients for ECH waves are generally in agreement with numerical coefficients. However, the analytical expressions developed for ECH waves do not reproduce sharp fluctuations, dips, and gaps, the so-called banded structure observed in the data of numerical coefficients. The effect of the shape variation on the profile of the wave spectral intensity and the effect of cold temperature on the numerical coefficients are also investigated. Applications of the analytical expressions of diffusion coefficients are discussed.
Strongly peaked electrostatic emissions near 10.0 kHz and electromagnetic emissions near 0.56 kHz have been observed by the VLF wave detector on board Imp 6 on crossings from the earth's magnetosphere into the polar cusp during the occurrence of large magnetospheric substorms. The electrostatic emissions were observed to be closely confined to the cusp-magnetosphere interface. The electromagnetic emissions were of somewhat broader spatial extent and were seen on higher-latitude field lines within the cusp. Using these plasma wave observations and additional information provided by plasma, magnetometer and particle measurements made simultaneously on Imp 6, theories are constructed to explain each of the two classes of emission. The electromagnetic waves are modeled as whistlers, and the electrostatic waves as electron-cyclotron harmonics. The resulting growth rates predict power spectra similar to those observed for both emission classes. The electrostatic waves may play a significant role via enhanced diffusion in the relaxation of the sharp substorm time cusp-magnetosphere boundary to a more diffuse quiet time boundary.
Under the conditions at which auroral kilometric radiation (AKR) is known to be produced by a plasma sheet electron region, relativistic effects of the dispersion of extraordinary-mode waves near the electron cyclotron frequency are found to be very significant. The application of linear theory and computer simulation to a model distribution indicates that an extraordinary mode of a particular Reynolds number dominated the radiation emission due to the cyclotron maser instability, suggesting that hot electrons determine the propagation characteristics of AKR and that larger growth rates are possible for direct amplification of extraordinary waves in the auroral region than had been predicted by calculations employing cold plasma dispersion.
Research conducted from 1975 through 1978 on magnetospheric plasma waves generated in or passing through the magnetospheres of the earth and Jupiter is reviewed. Attention is given to bow shock whistlers and electrostatic waves, electromagnetic wave packets in the magnetosheath ('lion roars'), nonthermal continuum radiation apparently associated with energetic electrons in the outer radiation zone, electrostatic and magnetic noise and PI2 pulsations in the magnetotail and plasma sheet and polar cusp phenomena. Plasma waves in the auroral zone, including VLF hiss and saucers, electrostatic wave turbulence and kilometric radiation are treated, together with MHD waves and magnetic pulsations, ion cyclotron waves, VLF chorus and hiss and electrostatic electron cyclotron harmonic radiation in and beyond plasmapause, plasmaspheric hiss, whistlers, power line harmonic radiation and controlled wave generation experiments. Observations of plasmasphere and auroral zone phenomena in the ionosphere are discussed, and escaping and trapped plasma waves in the magnetospheres of Jupiter and other planets are considered. Planned future magnetospheric research for the next four years is outlined.
Wave normal and Poynting vector measurements from the Cassini radio and plasma wave instrument (RPWS) are used to examine the propagation characteristics of various plasma waves during the Earth flyby on August 18, 1999. Using the five-channel waveform receiver (WFR), the wave normal vector is determined using the Means method for a lightning-induced whistler, equatorial chorus, and a series of low-frequency emissions observed while Cassini was in the magnetosheath. The Poynting vector for these emissions is also calculated from the five components measured by the WFR. The propagation characteristics of the lightning-induced whistler were found to be consistent with the whistler wave mode of propagation, with propagation antiparallel to the magnetic field (southward) at Cassini. The sferic associated with this whistler was observed by both Cassini and the Stanford VLF group at the Palmer Station in Antarctica. Analysis of the arrival direction of the sferic at the Palmer Station suggests that the lightning stroke is in the same sector as Cassini. Chorus was observed very close (within a few degrees) to the magnetic equator during the flyby. The chorus was found to propagate primarily away from the magnetic equator and was observed to change direction as Cassini crossed the magnetic equator. This suggests that the source region of the chorus is very near the magnetic equator. The low-frequency emission in the magnetosheath has many of the characteristics of lion roars. The average value of the angle between the wave normal vector and the local magnetic field was found to be 16 degrees, and the emissions ranged in frequency from 0. 19 to 0.75 f(sub ce), where f(sub ce) is the electron cyclotron frequency. The wave normal vectors of these waves were primarily in one direction for each individual burst (either parallel or antiparallel to the local field) but varied in direction throughout the magnetosheath. This suggests that the sources of the emissions are far from the spacecraft and that there are multiple source regions.
The two ARTEMIS probes observe significant precursor activity upstream from the Moon, when magnetically connected to the dayside lunar surface. The most common signature consists of high levels of whistler wave activity near half of the electron cyclotron frequency. This precursor activity extends to distances of many thousands of km, in both the solar wind and terrestrial magnetosphere. In the magnetosphere, electrons reflect from a combination of magnetic and electrostatic fields above the lunar surface, forming loss cone distributions. In the solar wind they generally form conics, as a result of reflection from an obstacle moving with respect to the plasma frame (just as at a shock). The anisotropy associated with these reflected electrons provides the free energy source for the whistlers, with cyclotron resonance conditions met between the reflected source population and Moonward-propagating waves. These waves can in turn affect incoming plasma, and we observe significant perpendicular electron heating and plasma density depletions in some cases. In the magnetosphere, we also observe broadband electrostatic modes driven by beams of secondary electrons and/or photoelectrons accelerated outward from the surface. We also occasionally see waves near the ion cyclotron frequency in the magnetosphere. These lower frequency waves, which may result from the presence of ions of lunar origin, modulate the whistlers described above, as well as the electrons. Taken together, our observations suggest that the presence of the Moon leads to the formation of an upstream region analogous in many ways to the terrestrial electron foreshock.
The electron distribution functions measured by the Dynamics Explorer 1 satellite during an auroral pass in 1981 are used in a linear instability analysis of low-frequency electromagnetic and electrostatic waves near and below the hydrogen gyrofrequency. It is suggested that the low-frequency electric and magnetic noise in the auroral zone might be explained by O and H electromagnetic ion cyclotron waves excited by energetic electron beams. An instability analysis suggests that upward and downward streaming electrons throughout the central plasma sheet region provide the free energy for heating oxygen ion through oxygen electrostatic ion cyclotron waves.
Results of both a linear and a nonlinear study of oxygen cyclotron waves and the associated oxygen heating are presented. Linear theory predicts that oxygen cyclotron waves will have smaller growth rates than hydrogen cyclotron waves. Results of a simulation study in which the free energy source is an initial drifting electron distribution indicate that oxygen cyclotron waves only grow to small amplitudes, while the hydrogen cyclotron waves achieve larger amplitudes. In an attempt to model more realistically the continuous ionospheric outflow, a simulation model is used, in which the electron velocity distribution is maintained by a constant flow of electrons. This latter model predicts that the oxygen waves grow to amplitudes much larger than the hydrogen waves resulting in the preferential heating of the heavier ions.
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.
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Magnetic holes in the solar wind, which are characterized by isolated local depressions in the magnetic field magnitude, have been observed previously. The Unified Radio and Plasma Wave (URAP) instrument of Ulysses has found that within such magnetic structures, electrostatic waves at kHz frequency and ultralow frequency electromagnetic waves are often excited and seen as short duration wave bursts. Most of these bursts occur near the ambient electron plasma frequency, which suggests that the waves are Langmuir waves. Such waves are usually excited by electron streams. Some evidence of the streaming of energetic electrons required for exciting Langmuir waves has been observed. These electrons may have originated at sources near the Sun, which would imply that the magnetic structures containing the waves would exist as long channels formed by field and plasma conditions near the Sun. On the other hand, the electrons could be suprathermal 'tails' from wave collapse processes occurring near the spacecraft. In either case, the Langmuir waves excited in the magnetic holes provide a measurement of the plasma density inside the holes. Low frequency electromagnetic waves, having frequencies of a fraction of the local electron cyclotron frequency, sometimes accompany the Langmuir waves observed in magnetic holes. Waves excited in this frequency range are very likely to be whistler-mode waves. They may have been excited by an electron temperature anisotropy which has been observed in the vicinity of the magnetic holes or generated through the decay of Langmuir waves.
An account is given of the waves and instabilities occurring at collisionless shocks, with attention to the mechanisms responsible for the generation of these waves. The transition region of the shock usually involves an abrupt broadband burst of electrostatic noise that extends from below the lower hybrid resonance to near the electron plasma frequency, and by a broadband burst of whistler mode EM noise below the electron cyclotron frequency. Electrostatic lower hybrid waves are also noted. Upstream of the shock, electron plasma oscillations, ion acoustic waves, and intense ULF MHD waves are often observed. The region downstream of the shock is usually very chaotic; electrostatic waves often extend long distances into the downstream region, together with whistler mode emissions.
Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.
Electron pitch angle (D (alpha)) and momentum (D(pp)) diffusion coefficients have been calculated due to resonant interactions with electrostatic electron cyclotron harmonic (ECH) and whistler mode chorus waves. Calculations have been performed at two spatial locations L = 4.6 and 6.8 for electron energies 10 keV. Landau (n = 0) resonance and cyclotron harmonic resonances n = +/-1, +/-2,...+/-5 have been included in the calculations. It is found that diffusion coefficient versus pitch angle (alpha) profiles show large dips and oscillations or banded structures. The structures are more pronounced for ECH and lower band chorus (LBC) and particularly at location 4.6. Calculations of diffusion coefficients have also been performed for individual resonances. It is noticed that the main contribution of ECH waves in pitch angle diffusion coefficient is due to resonances n = +1 and n = +2. A major contribution to momentum diffusion coefficients appears from n = +2. However, the banded structures in D alpha and Dpp coefficients appear only in the profile of diffusion coefficients for n = +2. The contribution of other resonances to diffusion coefficients is found to be, in general, quite small or even negligible. For LBC and upper band chorus waves, the banded structures appear only in Landau resonance. The Dpp diffusion coefficient for ECH waves is one to two orders smaller than D alpha coefficients. For chorus waves, Dpp coefficients are about an order of magnitude smaller than D alpha coefficients for the case n does not = 0. In case of Landau resonance, the values of Dpp coefficient are generally larger than the values of D alpha coefficients particularly at lower energies. As an aid to the interpretation of results, we have also determined the resonant frequencies. For ECH waves, resonant frequencies have been estimated for wave normal angle 89 deg and harmonic resonances n = +1, +2, and +3, whereas for whistler mode waves, the frequencies have been calculated for angle 10 deg and Landau resonance. Further, in ECH waves, the banded structures appear for electron energies (is) greater than1 keV, and for whistler mode chorus waves, structures appear for energies greater than 2 keV at L = 4.6 and above 200 eV for L = 6.8. The results obtained in the present work will be helpful in the study of diffusion curves and will have important consequences for diffuse aurora and pancake distributions.