The earlier interpretation of the Zebra patterns by the concept of double resonance is examined for a realistic magneto-hydrostatic model of a coronal condensation over a bipolar spot group. It appears that the frequency drift of the Zebra stripes over a longer time can scarcely be explained by a change of state of the plasma as done till now. The proposed modified mechanism is based on a helical beam of electrons forming fronts that excite radiation at places of double resonance. Considering the field and density configuration conditions are found which produce drifting Zebra stripes. Structures of longer duration and absorptions arise from more or less overlapping stripe segments, which are excited by the fronts following one another in a beam of sufficient great length. The second stripe system of other drift direction found by Slottje (1972a) arises from lateral splitting of the beam.

Interpretation of patterns of drifting Zebra stripes

A recently proposed very general dynamic model for the interpretation of Zebra patterns (Mollwo, 1983) traces back the observed dynamic spectra to a warm helical electron beam travelling through the magnetically confined plasma of a coronal condensation. Supposing a two-dimensional field configuration it is shown that Zebra patterns with two crossing stripe systems supply an adequate number of parameters to calculate the most essential field quantities for the emitting region. The found magnitude of the magnetic field B is in accordance with the results of potential field calculations (cf. Dulk and McLean, 1978). Four events with very different values of the frequency drift of the Zebra stripes among them one with a typical braided Zebra pattern yield rather similar results. It is pointed out that special variants of the mechanism may account for fiber bursts and perhaps also type III b-bursts. Considerations on the continuation of the field configuration beyond the region of the Zebra pattern yield some basic approaches to treat the field of an unipolar sunspot.

The magneto-hydrostatic field in the region of zebra patterns in solar type IV dm-bursts

Ionosphere Feedback to Electron Scattering by Equatorial Whistler Mode Waves

The linear theory of a mono−energetic electron beam interacting with a cylindrical, homogeneous, Maxwellian magnetoplasma is investigated numerically. Using standard criteria the instability of the upper branch (ω ≳ ωce; ω ∼ kzV) is shown to be either convective or absolute depending on the specific beam and plasma parameters. In the weak beam limit, nb ≪ np, a cubic dispersion equation is derived to describe the same system. The cubic equation is analyzed to show that the instability is convective when the group velocity of the plasma wave is positive. The instability is absolute when the group velocity of the plasma wave is negative and when the beam density exceeds a threshold density.

Convective and absolute instabilities in beam−plasma systems

The beam‐plasma instability in a strong magnetic field, (ωce≳ωpe), has been studied experimentally. Although the electron plasma waves have positive group velocity, oscillating instabilities are observed when reflections become important. The amplifying (convective) instability has waves which grow in space and saturate due to beam trapping. After saturation, the spectrum broadens and the beam spread increases due to nonlinear generation of sidebands. When reflective feedback is sufficiently strong, an oscillating instability appears. It has large amplitude near the electron gun, and also saturates by trapping for a weak beam. For stronger beams, several oscillating modes are present and quenching occurs, due to interactions between modes. The difference between amplifying and oscillating modes, quiescent broad spectrum versus quenching, is similar to the absolute instability observations, which occur for (ωce<ωpe, ω).

Comparison of amplifying modes and feedback oscillations in a beam‐plasma experiment

The dispersion equation corresponding to the interaction of an electron beam with a Maxwellian plasma has been solved in quasistatic and infinite geometry approximations. Two representative beams are considered: a parallel beam with isotropic velocity spread and a helical beam with different longitudinal and transverse temperatures. The aim of the work is to predict the frequency, growth rate, and wavenumbers of the most unstable waves as functions of the basic beam and the plasma parameters. The results of the calculations are presented in graphs suitable for comparison with the experiments. The effect of plasma and beam temperatures on the spectrum of the instabilities is discussed in detail. It is shown that the plasma temperature reduces the growth rate of the instabilities at cyclotron harmonic frequencies while a velocity spread in the helical beam suppresses the instabilities everywhere, except in the vicinity of the cyclotron harmonics.

M. Seidl

Papers

Temperature Effects on High‐Frequency Beam Plasma Interaction