Electrostatic Electron Cyclotron Harmonic Waves Research Articles

Three‐dimensional ray tracing of electrostatic cyclotron harmonic waves and Z mode electromagnetic waves in the magnetosphere

Three dimensional ray tracing is made for electrostatic electron cyclotron harmonic waves and Z mode electromagnetic waves in the earth magnetosphere, using the hot plasma dispersion relation. For a large wave number region, the so‐called electrostatic approximation for the dispersion relation can be used to trace the ray paths. The necessary initial conditions for an electrostatic electron cyclotron harmonic mode wave to be continuously converted to a Z mode electromagnetic mode wave can be investigated by the electrostatic approximation. Only the waves generated in the very vicinity of the geomagnetic equatorial plane can propagate over a long distance. The waves can be converted to Z mode if the initial wave normal direction lies near the geomagnetic meridian plane. The algorithm of ray tracing using the full hot plasma dispersion relation is also developed. A complete traverse of the wave starting from the electrostatic electron cyclotron harmonic mode to the Z mode can only be confirmed by the ray tracing based on the full hot plasma dispersion relation. A possibility of conversion from the electrostatic mode finally to a free space electromagnetic mode can also be investigated by this ray tracing. These results are not contradictory with the conversion mechanism for the generation of escaping continuum radiation in the earth magnetosphere.

Nonlinear Interaction between Electrostatic Electron Cyclotron Harmonic Waves and Electrons

The nonlinear interaction of linearly stable electrostatic electron cyclotron harmonic waves and electrons due to the cyclotron damping is experimentally examined. As moderate amplitude waves are excited, the amplitude oscillation of the wave and the periodic oscillation of electrons trapped by the wave are observed, whose results are explained by the monochromatic wave approximation. As large amplitude waves are excited, wave number spectra of waves widen, and then, the amplitude oscillation of waves collapses due to the many wave-particle interaction. The results can be explained qualitatively in the quasilinear theory for a weak turbulent plasma.

Are equatorial electron cyclotron waves responsible for diffuse auroral electron precipitation?

On the basis of theoretical calculations of electron diffusion coefficients and of OGO 5 data, Lyons [1974] suggested that electrostatic electron cyclotron harmonic waves had amplitudes large enough to cause the strong pitch angle diffusion of plasma sheet keV electrons and to be responsible for diffuse auroral precipitation. However, recent measurements of the wave location and amplitude performed aboard the GEOS spacecraft have brought new pieces of information challenging these conclusions. Our calculations are based on the theoretical tool developed by Lyons [1974] but take into account the recently observed wave confinement within a few degrees from the magnetic equator. Under these conditions, we avoid the numerical averaging of the pitch angle diffusion coefficient over the whole line of force, and we can derive an analytical expression of the minimum wave amplitude required to cause strong pitch angle diffusion for plasma sheet electrons. This expression has the advantage to be easily tractable in further calculations, and permits us to evaluate the dependence of the results on parameters that are not reported by observations, such as the wave number spectrum. Our results are found to differ from Lyons's [1974] predictions by a factor of about 2.5, and typically, a wave amplitude of more than 2 mV m−1 is required to put 1‐keV electrons on strong diffusion. On the other hand, on the basis of a statistical analysis of electron cyclotron wave amplitudes measured in the nightside plasmasheet by the GEOS 2 spacecraft, we show that most of the time (>91 %), this typical value of 2 mV m−1 is not reached. This result appears inconsistent with the hypothesis that diffuse auroras, which are a permanent feature of the auroral zones, are due solely to electrostatic electron cyclotron waves. This leads us to the conclusion that these waves are not the only cause of diffuse electron precipitation. It is suggested that other mechanisms involving for instance the dynamics of the ions (such as field‐aligned currents) could play an important role.

Dayside electron cyclotron harmonic emissions

Observations of waves exhibiting an often complex frequency banding related to the electron gyrofrequency were first reported in 19701. Later observations2–5 showed that the spectral content of these electrostatic electron cyclotron harmonic waves is highly variable6,7, including single frequency emissions between the electron gyrofrequency Ωe and its first harmonic, multiple bands between consecutive harmonics of Ωe, and emissions in a single band far above the electron gyrofrequency8–10. These observations have led theorists to investigate both the linear instability which generates the waves11–15 and various wave–particle14,16 and wave–wave17–18 interactions in which they may be involved. The consensus seems to be that at least two plasma components with different temperatures are required to destablilize electron cyclotron harmonic waves. We adopt this view here and test our present knowledge of electron cyclotron harmonic instabilities against the observed reality. To do this we use simultaneous observations of wave spectra and electron distribution functions, available in the GEOS 1 data from 25 August 1977 (see ref. 15). From these we present the wave event and then use the measured particle fluxes to derive a model distribution function, providing the input to a computer program which solves the plasma dispersion relation. From the computed temporal growth rates and group velocities, the total amplification of waves which are unstable within a limited volume of space is estimated.

Nonlinear Amplitude Oscillations of Obliquely Propagating Bernstein Waves in a Plasma

Electrostatic electron cyclotron harmonic waves are observed to executed amplitude oscillations. Observed results are consistent with the expected periodic energy exchanges between the wave and trapped electron particles.

On the convective properties of magnetospheric Bernstein Waves

Recent observations of electrostatic electron cyclotron harmonic waves have been organized very well within the framework of magnetospheric Bernstein waves. A number of effects that result simply from convective properties of these waves are examined. The roles of wave trapping in plasma density depressions and partial trappings near the magnetic equator are considered. A number of future wave observations are suggested that can improve our understanding of this magnetospheric wave phenomenon.

Experimental Studies of Explosive Instability in an Electron Beam-Plasma System

The explosive instability due to nonlinear wave-particle interaction has been observed experimentally. The slow space charge wave of the electron beam and the obliquely propagating electrostatic electron cyclotron harmonic wave interact nonlinearly with the electron beam and grow simultaneously, satisfying the resonant condition ω 1 -ω 2 -( k //1 - k //2 ) v b =ω c . One wave is amplified exponentially by increasing the power of the other wave. The virtual wave has also been observed. The nonlinear wave-particle coupling coefficients are measured quantitatively from the spatial growth rate, and found to be in good agreement with theory.

Unstable electron cyclotron harmonic waves during the relaxation of a temperature anisotropy

Electrostatic electron cyclotron harmonic waves are driven by an excess electron kinetic energy perpendicular to the magnetic field. If the anisotropy of the velocity distribution is transient, the propagation characteristics of the anisotropy‐driven waves change in time. The long‐time behavior of the waves is determined by the dispersion relation corresponding to the final velocity distribution. A model case is studied, within the framework of linear theory, for 3/2 electron cyclotron harmonic waves in the relaxation stage of a bi‐Maxwellian velocity distribution. It is shown that the dominant propagation angle changes from about 60° in an unstable state to about 80° in an isotropic state. Because of strong Landau damping, the most unstable wave in the instability cannot be a dominant wave after the relaxation. Since this result may be true for other velocity distribution models, it implies that great care should be taken in considering a wave model which requires a long lifetime for some of the waves involved.

Observation of explosive instability in an electron beam-plasma system

We have observed experimentally the explosive instability of the slow space charge wave of the electron beam and the electrostatic electron cyclotron harmonic wave due to nonlinear wave-particle interaction. These waves interact nonlinearly with the electron beam and grow simultaneously.

Plasma flow hypothesis in the magnetosphere relating to frequency shift of electrostatic plasma waves

The frequency dynamic spectrum indicating a monotonic frequency shift of the electrostatic electron cyclotron harmonic wave emissions in the data of VLF electric field observations by Ogo 5 has been detected in the midnight and dawn meridians outside the plasmapause; the emissions are produced from turbulent areas in the plasma states that include the temperature anisotropy, loss cone velocity distribution, or the double hump in the velocity distribution function. The frequency shift is also observed for the case of the emissions in the magnetosheath near the subsolar point. These frequency shifts are interpreted on a hypothesis of the Doppler effects of the plasma waves due to the plasma flow with respect to the satellite frame. The speeds of the plasma flow are obtained and have a range from 150 to 300 km/s. Disruption of the plasma flow due to the magnetic field bumps may produce the turbulent source generating the Harris type or beam type instabilities that generate the electrostatic electron cyclotron harmonic waves.

Short-life mode of electrostatic electroncyclotron harmonic waves

Dispersion curves of electrostatic electron cyclotron harmonic waves with a phase exp {i(k. r – ωt)}, where ω and k are the angular frequency and wave vector, respectively, are calculated numerically for a case of real ω and complex k that is pertinent for a case of pulsed short dipole excitation of plasma waves. Oblique propagation with respect to the ambient magnetic field direction is considered. There are positive κi and negative κi modes, where k is the imaginary part of the wave number κ = ∣κ∣ in the solutions. The energy propagates in opposite directions in the two modes, and the waves are always subjected to thermal damping. The positive κi mode usually indicates a large κi value (i.e. a large attentuation rate); and it is here called the ‘short-life’ mode.

Turbulence of electrostatic electron cyclotron harmonic waves observed by Ogo 5

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.

Verification of Theory on Weak Turbulence Relating to the Sequence of Diffuse Plasma Resonances in Space

An interpretation of the sequence of diffuse plasma resonances observed by space probes (Alouette 2 and ISIS-1 satellites) is developed in terms of wave-particle nonlinear interaction in a weakly turbulent plasma including the electrostatic electron cyclotron harmonic wave instability. Observations and theory indicate that the center frequency fDn of the diffuse plasma resonance [nfH<fDn<(n+1)fH and fDn<fT] and the center frequency of the electrostatic wave resonance [nfH<fQn<(n+1)fH and fT<fQn] satisfy the condition of the wave-particle nonlinear interaction with the 2fH resonance according to the condition 2π[fH− ( fQn+2−fDn)]=[K(fQn+2)− k (fDn)]·v, where nfH, fT and v are the cyclotron harmonic frequency, the upper hybrid frequency, and the thermal velocity of the plasma, respectively; and k(f) is a wave vector as a function of a frequency f. The weaker diffuse plasma resonance branch observed at fDn1 (where fDn1>fDn) satisfies the condition 2π[fH− (fQn+1−fDn1)] = [k(fQn+1)−k(fDn)]·V. The longest time duration of the fDn resonance coincides with the most favorable condition for the electrostatic electron cyclotron harmonic wave instability which is obtained by solving the dispersion equation obtained for a linear approximation of the kinetic wave equation for the warm magnetoactive plasma. The electrostatic field due to the transmission of the intense rf pulse produces plasma turbulence involving nonlinear wave-wave interaction and temperature anisotropy which leads to the instability; this instability supplies energy to the turbulence. The fH and 2fH nonlinear wave-particle interactions in the turbulence heat the plasma to maintain the temperature anisotropy which lengthens the time over which the cyclotron harmonic wave instability conditions prevail; this process can be thought of as a feedback system. The results also indicate that the fH, 2fH and fQn waves are dependent on the fDn resonance generation.