Warm Plasma Theory Research Articles

The effect of electron and ion temperature on the refractive index surface of 1–10 kHz whistler mode waves in the inner magnetosphere

AbstractWhistler mode waves in the magnetosphere play an important role in the energy dynamics of the Earth's radiation belts. Previous theoretical work has been extended to include ions in the fully adiabatic warm plasma theory. Using a finite electron and ion temperature of 1 eV, refractive index surfaces are calculated for 1–10 kHz whistler mode waves in the inner magnetosphere (L ≲ 2.5). For the frequencies of interest, a finite ion temperature is found to have a greater effect on the refractive index surface than the electron temperature and the primary effect is to close an otherwise open refractive index surface. Including a finite ion temperature is especially important when the wave frequency is just above the local lower hybrid resonance frequency. For wave frequencies more than ∼1 kHz above the local lower hybrid resonance frequency, including the ion temperature has a negligible effect on the refractive index surface calculation. The results are used to assess previous conclusions on whether in situ whistler mode sources can be realistically used to precipitate energetic electrons. It is found that the number of in situ sources needed to illuminate the inner plasmasphere (L≲2.5) with whistler mode energy may be greater than previously predicted.

THEMIS observations and modeling of multiple ion species and EMIC waves: Implications for a vanishing He+ stop band

Observations of left‐hand polarized electro‐magnetic ion cyclotron (EMIC) waves with significant wave power across fHe+ are presented. Concurrent field and particle measurements reveal pitch angle scattering of thermal ions during the interval of maximum wave power. The observations suggest the presence of multiple cold ion species (H+, He+) at this time, below the sum of spacecraft potential and minimum energy of the ion instrument (i.e., <∼20 eV). Fortuitously, immediately following the most intense wave activity, the ambient plasma flow velocity became sufficiently large such that cold ions can be accelerated into the energy range of the particle instrument. Thus, two low energy ion components are revealed in the particle measurements at energies consistent with cold protons and He+. Maxwellian fits provide approximations of these cold ion species component densities and temperatures. The linear dispersion relation of parallel propagating EMIC waves for the observed conditions shows a vanishing cold plasma He+ stop band, consistent with the wave measurements during this interval. These results provide the first observational evidence of the importance of the cool ion species temperature/density in controlling linear wave growth through the heavy ion stop bands in warm plasma theory.

Behaviour of a low frequency wave in a FRC plasma

A low frequency torsional Alfven wave (angular frequency ω ∼ 0.3ωci0, ωci0; ion gyro frequency in vacuum) is induced in an extremely high beta (beta = plasma pressure/pressure of confining magnetic field) plasma with the field reversed configuration (FRC) by an external antenna. When the wave is introduced from outside towards the magnetic axis of the FRC plasma, not only the Alfven velocity vA but also the local ion gyro frequency ωci decreases as the density increases and the magnetic field decreases. The spatial structure of the wave is examined in the region between the separatrix and the location near the O-point. Near the former location, the plasma is tenuous and the magnetic field has nearly external value so that ω ∼ 0.3ωci0, and near the latter location, the beta value is large and ω > 0.7ωci. The observed amplitude of the toroidal component of the magnetic disturbance has a broad peak around the radial location of the resonance position obtained from the cold plasma theory, although the cold plasma theory yields a sharper spatial structure. The polarization of the magnetic disturbance component perpendicular to the static magnetic field is left-handed outside the theoretical resonance position and right-handed deep in the plasma. The measured perpendicular wave number kr is small except for the region near the resonance position where the kinetic Alfven wave is expected to have a large wave number. This behaviour will be interpreted as, with the help of the warm plasma theory, the torsional Alfven wave evolves into the kinetic Alfven wave and is then converted to the compressional wave with a smaller wave number when the wave propagates inside the plasma.

Extraordinary mode resonance cones in the Uranian magnetosphere?

A theory is introduced for previously unidentified waveforms involving decreasing frequency with time that were picked up in the Voyager 2 flyby of Uranus. They are identified as a possible band of extraordinary waves detected on resonance cone surfaces. Because of the resonance cone phenomenon, certain frequencies are only observed at certain angles from the source, and the frequency decreases as the angle decreases. The homogeneous plasma theory is shown to predict an almost linear drop in frequency with time. In principle one can use the wave frequency with time to estimate the distance and angle of the source for the homogeneous case. Inhomogeneities in the plasma are shown to produce a substantial variation on that and give the waveforms an important fine structure. They give arches to the waveform and can explain sudden drops in the frequency and changes in the slope of the waveforms at certain times, as is observed in the data. Inhomogeneities from a plasma wave (possibly an Alfvén wave) near the spacecraft are shown to explain the modulation in one of the waveforms. A decreasing magnetic field of growing negative slope can independently account for the arching over of the waveform and the decreasing modulation frequency. The multiple peaks in the frequency observed for given times in the waveform may be caused by the multiple peaks from the resonance cone interference structure, which are predicted in the warm plasma theory of resonance cones.

Propagation of electromagnetic waves in a warm plasma-filled cylindrical waveguide in the presence of an external magnetic field

The propagation of electromagnetic waves in a plasma-filled cylindrical waveguide in the presence of a constant external magnetic field is investigated using warm plasma theory. It is found that the waves cannot be separated into transverse magnetic and transverse electric modes; only hybrid modes are propagated. Dispersion relations are derived for zero, finite and infinite magnetic fields. Frequency shifts for the wave propagation in the case of a small magnetic field are calculated.

High power heating in the ion cyclotron range of frequencies in the Wisconsin Tokapole II

Fast wave heating at the second, third and fourth harmonics of the ion cyclotron resonance, and slow wave heating at the fundamental in a single ion species hydrogen plasma, are found to be in good agreement with warm plasma theory at RF power levels <or=130 kW. Ion heating is negligible off an eigenmode. Ion body temperatures are more than doubled to 75 eV from the 35 eV ohmically heated case with tails comprising 8% of the plasma at 320 eV. No deleterious effects except a non-disruptive 10% shortening of the discharge length caused by impurity influx are noted. A passive mode tracking technique allows approximately=40% increase in power deposition in a passing eigenmode over that of a fixed frequency RF source. Ion temperatures are limited by charge exchange due to the <50 eV central temperature and the small 13 cm radius current channel.

A study of plasma filled parallel plate waveguide with one boundary corrugated

Warm plasma theory is used to investigate the propagation of electromagnetic waves in a plasma filled parallel plate waveguide with one boundary plate corrugated. Dispersion relations for TE- and TM-modes are derived and it is found that the propagation of TE-modes is unaffected by corrugation of one boundary plane while the propagation of TM-modes is affected by it. For TM-modes the wave numberk depends on the frequency ta as well as on the distance through which the wave is propagated.

Stimulated plasma waves in the ionosphere

The results of 15 years of plasma resonance observations from rocket‐ and satellite‐borne topside sounders are summarized. The major resonances are observed at the electron plasma frequency ƒN, the electron cyclotron frequency ƒH, the upper hybrid frequency ƒT = (ƒ2N+ƒ2H)1/2, the harmonics 2ƒT and nƒH with n &gt; 1, and two series of resonances that appear between nƒH∶ the ƒQn resonances observed above ƒT (at the maximum frequency of the Bernstein modes) and the ƒDn resonances observed below ƒT (called the diffuse resonances). Most of the resonances can be interpreted in terms of the reception of longitudinal plasma waves stimulated by the sounder pulse. In some cases these waves, which travel with low group velocity (of the order of the electron thermal velocity or less) are received after being reflected in the nearby medium (within a distance of several kilometers). The reflections are due to the extreme sensitivity of the dispersion curves near the resonant frequencies to small changes in electron density (for the ƒN and ƒT resonances) or to small changes in magnetic field strength (for the lower‐order nƒH resonances). In other cases (ƒQn resonances and the higher‐order nƒH resonances) the signal reception is due to the matching of a component of the wave group velocity to the satellite velocity rather than to a wave reflection process. The ƒDn resonances involve a sounder‐stimulated electron temperature anisotropy leading to the Harris instability of the Bernstein modes and a nonlinear coupling between these wave‐modes. Since the interpretation of all of the resonances depends on warm plasma theory, the observations can be used to obtain the electron temperature T⊥ and T∥ (corresponding to electron motions perpendicular and parallel to the ambient magnetic field direction, respectively) as well as the electron density and the magnetic field intensity. These measurements pertain to a large volume (hundreds of meters to kilometers) around the antenna and thus are not seriously affected by spacecraft/plasma interactions. The results of the investigations of artificially stimulated plasma waves by sounder pulses have been applied to the interpretation of naturally occurring wave phenomena such as the (n+1/2)ƒH magnetospheric VLF emissions, the terrestrial kilometric radiation, and the Jovian decametric radiation. Among the major unexplained plasma resonance phenomena are the resonances observed at ƒH and 2ƒT, and the numerous ion effects associated with the electron plasma resonances. The advent of the Space Shuttle with subsatellites will enable active‐controlled experiments to be conducted with highly flexible radio‐frequency instrumentation in order to investigate problems of interest to many geophysical and astrophysical phenomena such as wave mode coupling and the evolution of nonlinear and plasma wave instability processes.

Lower Hybrid Instability Driven by a Spiraling Ion Beam

A lower-hybrid instability with ion cyclotron harmonics is observed to be resonantly driven by an ion beam injected obliquely to the confining magnetic field, in agreement with a linear, warm-plasma theory. Quasilinear velocity-space diffusion of the beam is observed.

Monopole and Dipole Antennas in a Nonlinear Isotropic Plasma

The theoretical nonlinear response of a plasma is studied for the case of two RF signals simultaneously applied to the terminals of thin-wire monopole and dipole antennas of arbitrary length. Distributed nonlinear sources of charge density and current density are identified and used to calculate induced open-circuit antenna terminal voltages at harmonic, sum, difference, and intermodulation frequencies and at d.c. (rectification). The importance of the antenna as a field scatterer is identified for the calculation of radiation fields and higher-order near fields. Experiments on the terminal properties of a monopole antenna were performed in a laboratory gas discharge and quantitative agreement with cold-plasma theory is demonstrated for frequencies above about half the plasma frequency; lower frequency response closely resembles earlier predictions using warm-plasma theory. Experiments and theory for a constant RF input current indicate that the plasma frequency can be identified and therefore that the antenna system is useful for electron-density diagnostics. Experiments indicate a complex form of signal limiting or saturation, but below this level there exist situations where the nonlinear response is high enough to be classified as interference in practical systems.

Electron density and temperature measurements in the lower ionosphere as deduced from the warm plasma theory of the h.f. quadrupole probe

The frequency response of the h.f. quadrupole probe is calculated to be used as a diagnostic tool for measurements of electron density and temperature. In §2 the magnetic field is assumed to be zero, and ion motions are neglected. For a Maxwellian plasma, the so-called ‘Landau wave approximation’ is compared with various more sophisticated treatments, such as numerical integration or super-Cauchy and multiple water-bag models. The range of validity of this approximation is shown to be large, and the results can be applied to the most interesting parts of the experimental observations. All results previously established are recovered with greater speed. Having studied various disturbances (collisions, inhomogeneity and relative motion of the probe with respect to the plasma), it is deduced that the best way to determine the electron temperature is to use the anti-resonances due to beating between the Landau wave and the cold plasma field. In § 3 we describe the quadrupole probe, launched in December 1971 as part of the CISASPE rocket experiment. To deduce the electron density and temperature from these measurements, it is necessary to consider the influence of a static magnetic field, such as the earth's magnetic field. The general case could be treated by numerical integration, though with great difficulty, but it is shown that in most ionospheric conditions, in the vicinity of the upper hybrid frequency ωT the above treatment is again possible, the plasma frequency simply being replaced by ωT, and the thermal velocity slightly modified. These assumptions are used to deduce the electron density and temperature profiles.

Excitation: Summary Report

Three short papers were read after the review paper by T. W. Johnston.P. E. Vandenplas (Ecole Royale Militaire, Brussels, Belgium) gave a survey concerning resonances observed in laboratory plasma capacitors. For such a capacitor with plate distance l and plates covered with rarified sheaths, cold plasma theory gives the main resonance of an infinite plane capacitor as a serial one at a frequency ƒN (1 − a/l)1/2, where a is the thickness of the (homogeneous) plasma sheath between the plates. In warm plasma theory apart from a correction term of the order λDe2/a2(λDe is electron Debye‐length) this resonance splits up into a narrow series of successive resonances, the distance of which is controlled by the same parameter. Furthermore, since the ‘warm’ dispersion equation is of fourth order now, other eigenvalues lead to new resonances of another type, which have been found in the laboratory also.

Resonance Cones in the Field Pattern of a Radio Frequency Probe in a Warm Anisotropic Plasma

An experimental and theoretical investigation of the angular distribution of the electric field of a short radio frequency probe in a plasma in a magnetic field is described. The field is observed to become very large along a resonance cone whose axis is parallel to the static magnetic field and whose opening angle is observed to vary with incident probe frequency, cyclotron frequency, and plasma frequency in agreement with simple cold plasma dielectric theory. The relationship of these cones to the limiting phase- and group-velocity cones which appear in the theory of plane wave propagation is discussed. The addition of electron thermal velocities (warm plasma effects) is examined in the limit of a large static magnetic field. A fine structure appears inside the cones and is shown to result from an interference between a fast electromagnetic wave and a slow plasma wave. This interference structure is observed experimentally and measurements of the angular interference spacing are shown to agree with the warm plasma theory. The use of measurements of the resonance cones and structure as a diagnostic tool to determine the plasma density and electron temperature in a plasma in a magnetic field is discussed.

Beam-Plasma Interaction with Transverse Modulation

This paper describes experimental observations of electron beam-plasma interaction in low-pressure mercury-vapor discharges. Comprehensive data have been obtained of rf growth, phase velocity, axial and radial electric field profiles in the interaction region, and Faraday rotation, for the case of transverse modulation, i.e., for growth in the first azimuthally-varying mode (m = 1). The work complements previous parallel studies of the axisymmetric mode (m = 0) made with axial modulation. The results are compared with cold- and warm-plasma theories of the interaction. It is concluded that the warm-plasma theory gives a satisfactory approximation to the experimental results, and that the remaining discrepancies are due to lack of sharpness of the experimental beam edge.

Electron-Beam-Probing Studies of Beam—Plasma Interactions

This paper describes experimental observations of electron-beam—plasma amplification in a low-pressure, beam-produced, mercury-vapor discharge. A nonperturbing probing technique, employing a fine auxiliary electron beam, was used to measure rf growth, phase velocity, and axial and radial electric-field profiles in the interaction region. The comprehensive data obtained have been compared with predictions based on cold- and warm-plasma theories of beam—plasma amplification. It is concluded that the experimental growth rates and electric-field profiles are approached more closely by warm-plasma theory, but that the measured phase velocities are somewhat slower than either theory suggests. The electric-field profiles are smoother than expected, probably owing to the beam boundary being less sharp in practice than is assumed in the theories.

On the resonant frequencies of a reactive structure coupled to a warm plasma

The resonant frequencies of a v.h.f. Lecher line coupled to a mercury arc plasma via a split-cylinder coupler have been measured as a function of electron density. Two strong resonances have been found for every value of electron density. The higher frequency resonance may be described as circuit resonance perturbed by the plasma, the lower one as plasma resonance influenced by the circuit. Cold plasma theory predicts qualitatively many of the observed properties of these resonances, including the appearance of upper and lower frequencies. It also predicts a forbidden frequency gap between the lower and upper frequency curves. It fails to predict the behaviour of the lower branch curves near their horizontal asymptote. Experimentally the curves approach this asymptote from above, whereas cold plasma theory predicts that the asymptote should be approached from below. Since the average transit time of thermal electrons is comparable with the period of the v.h.f. oscillations in this experiment, the results have been compared with warm plasma theory. It was found that warm plasma theory gives the correct behaviour near the lower branch asymptotes, and compares well with the experimentally measured resonant frequencies.

Comments on a paper by T. L. Dutt on the low-frequency dielectric constant of a plasma

The bound-electron concept is compared with the warm-plasma theory. The two theories are found to be approximately equivalent for phenomena associated with the main resonance. As the bound-electron concept fails to predict the higher-order (Tonks-Dattner) resonances, it is suggested that the recently observed discrepancies between free-electron cold-plasma theory and experiment are due to finite temperature effects and not to elastic restoring forces.