Einar Mjølhus

On the modulational instability of hydromagnetic waves parallel to the magnetic field

The stability of circularly polarized waves of finite amplitude propagating parallel to the magnetic field is studied. A set of equations for slowly varying waves of arbitrary amplitude is obtained. A discussion of the stability of the waces is based on this set of equations. Earlier results are confirmed; in addition we find that finite amplitude always promotes stability. An amplitude dependent stability condition for long waves, previously obtained by the author, is confirmed.

Coupling to Z mode near critical angle

The transmission and reflexion coefficients are calculated for the coupling of an ordinary polarized wave to the Z mode when the angle of incidence is near the critical angle.

Numerical test of the weak turbulence approximation to ionospheric Langmuir turbulence

The standard weak Langmuir turbulence approach to explain the artificial plasma line in ionospheric radio modification experiments is examined. We compare solutions of a weak turbulence approximation (WTA) derived from a version of the one-dimensional driven and damped Zakharov system of equations (ZSE) with solutions to the same full ZSE. The electromagnetic pump field is modeled as a long-wavelength parametric driving term. We found that from a certain distance below the O mode reflection level the wave number saturation spectra computed from the WTA agree qualitatively with those from the ZSE for weak driving strengths, in the sense that the number of cascade lines increases with increasing pump strength. However, in general, the number of cascades apparent in the WTA solutions is larger than that predicted from the full ZSE. At higher intensities of the driver the saturation spectra from the ZSE differ from the WTA cascade spectra, in that a truncation of the cascade sets in, with a subsequent filling in of the bands between the cascades. This truncation takes place far before the ZSE cascade spectra reach the so-called “Langmuir condensate,”; contrary to earlier conjectures based mainly on dimensional analysis arguments. In the reflection region a qualitatively different process takes place: temporal cycles of large ensembles of localized events; nucleation of cavitons, collapse, and burnout constitute the basic elements of the turbulence in this region of space. No WTA exists for this region. Our findings are discussed with respect to the experiments performed at Arecibo and Tromso, the conclusion being that the ZSE yields results closer to observations than does the WTA, in all regions of space.

Radiation from electromagnetically driven Langmuir turbulence

A two-level model for the interaction between the electromagnetic pump wave and the electrostatic turbulence is formulated for ionospheric radio modification experiments. On the local level, the Zakharov equations, or similar models, apply. The interaction with the global electromagnetic level is represented by a second-order current density averaged over the local spatial variable. The energy exchange between the local and global level is represented by a Joulean product involving this second-order current density. The global generation problem is solved in the simplest cases. The escaping energy flux in the sideband ω is shown to be represented as a folding between the power spectrum of the local source and a squared Airy function. This power spectrum has been calculated from numerical simulations of electromagnetically driven Langmuir turbulence, using a one-dimensional model of the Zakharov type, for varying values of the parameters. For parameters in the cascade range, narrow line structured spectra were obtained, while for parameters in the cavitation range, very broad featureless spectra were obtained. Comparison with recent experimental stimulated electromagnetic emissions data did not confirm a signature for the existence of cavitation in the experiments.

Nonlinear Landau damping of weakly dispersive circularly polarized MHD waves

The combined effect of modulational instability and nonlinear Landau damping on a circularly polarized MHD wave is studied. When the wave gets modulated, the magnetic mirror force as well as the parallel electric field associated with the modulations, transfer energy to the charged particles with velocity near the Alfven velocity, to cause a nonlinear Landau damping. Our mathematical model is a DNLS equation extended with a nonlocal term representing the resonant particles. This irreversible model allows a conservation law which in a slowly varying wave train limit corresponds to conservation of wave action. In addition to the modulational instability already known from the DNLS model, the Landau damping term introduces a modulational instability in the wave number range where the wave would otherwise be stable. We present numerical studies of the development of the instabilities and the subsequent wave damping in both ranges. One of our principal findings is that the wave frequency decreases in the same proportion as the energy density. This can be understood in terms of the conservation of action law.

Cavitating Langmuir turbulence in the terrestrial aurora.

Langmuir cavitons have been artificially produced in Earths ionosphere, but evidence of naturally occurring cavitation has been elusive. By measuring and modeling the spectra of electrostatic plasma modes, we show that natural cavitating, or strong, Langmuir turbulence does occur in the ionosphere, via a process in which a beam of auroral electrons drives Langmuir waves, which in turn produce cascading Langmuir and ion-acoustic excitations and cavitating Langmuir turbulence. The data presented here are the first direct evidence of cavitating Langmuir turbulence occurring naturally in any space or astrophysical plasma.

Parametric instabilities of trapped upper-hybrid oscillations

Parametric instabilities of upper-hybrid oscillations trapped in a plasma density depletion across an ambient magnetic field are investigated. Approximate dispersion relations are derived, which lead to the identification of two parametric instabilities of the localized upper-hybrid bounded wave structure. Both are related to trapped upper-hybrid oscillation resonances. The first is a decay to a frequency of a trapped wave resonance, downshifted from the applied frequency, where the downshift must be slightly larger than the lower-hybrid frequency. The second instability can exist when the applied frequency is slightly below the arithmetic mean of the frequencies of two trapped oscillation resonances; then the antiStokes component of one is in resonance with the Stokes component of the other. Both slab and two-dimensional geometries are considered.

Velocity–amplitude relationships and polarizations in families of MHD solitary waves

Plausible observations of MHD solitons by means of the Cluster system have recently been reported. The present paper addresses the theory of stationary wave forms obtained from MHD-type equations extended with Hall dispersion. Two aspects will be discussed: (i) the solitary wave solutions come in families, characterized by their velocity–amplitude relationship. The metamorphosis of these relationships will be described, starting with their form for small amplitude models (the KdV equation, the MKdV equation, the DNLS equation, and the triple-degenerate DNLS model), going through the cold plasma model, warm plasma scalar pressure model, and concluding with studies of models with anisotropic pressure. (ii) The predicted wave forms have a series of robust signatures well fitted for experimental tests. These include the polarization of the magnetic field through the structures (i.e., the magnetic hodograph), the relation between magnetic pressure and density perturbation, and the relation between the pressure components in the anisotropic models. These are also characterized in various families and models.

The effect of resonant particles on Alfvén solitons

Abstract The effect of resonant particles on an Alfven soliton is studied. Soliton perturbation theory based on the inverse scattering data formalism is applied to an extended DNLS equation, including a term which represents resonant particles. The results are compared with a numerical solution of the same equation. The numerical results show that when the initial soliton state is in the normal regime, the perturbation method gives an adequate description of the evolution, while the discrepancy between numerical and perturbation results increases as the initial soliton state is moved into the anomalous regime. Both approaches indicate that the solitons generally develop into the normal regime, and that the effective damping takes place around the transition from the anomalous to the normal regime.

Significance of short-scale irregularities for radar diagnostics of HF-driven Langmuir turbulence in the ionosphere

In experiments where ground-based VHF/UHF radars are used to diagnose Langmuir turbulence driven by powerful HF waves transmitted from the ground into the ionosphere, there has been a severe observability aspect: The excited Langmuir wave vector spectrum must contain a component satisfying the actual radar Bragg condition. In order to explain earlier observations, in particular those made by the Arecibo facility, it was proposed long ago that the actual wave number spectra were widened by refraction in small-scale irregularities, or ducts. This mechanism of improved observability is discussed in a broad approach in this paper. The main contribution is a mathematical derivation of the theory of parametric decay instability in the presence of magnetic-field-aligned ducts. This implies that the decay is into discrete duct modes. The threshold is slightly higher and the growth rate is slightly lower than for a corresponding homogeneous medium. Moreover, this tendency is more pronounced for the higher duct modes, which are those that may satisfy conditions for observability. The mathematical derivation is based on the driven and damped Zakharov model with ducts included. The model is run numerically, confirming the approximate decay instability theory and demonstrating improved observability. The numerics also demonstrate higher Langmuir energy density inside the ducts than outside.