The instability resulting from the interaction of a weak, monoenergetic electron beam with a magnetoplasma (ω≳ω C E ) has been studied experimentally. A calculation, using the dispersion relation appropriate to the experiment, shows that the interaction may take the form of convective or absolute instability, depending on plasma temperature. This is in qualitative and quantitative agreement with the experiment. The convective mode has spatially amplified waves which are steady state in time. Saturation is due to beam trapping, and agrees quantitatively with a trapping calculation which includes cyclotron damping. After saturation the wave damps, which is attributed to untrapping of the beam by relatively low‐level amplified plasma noise. The absolute instability is a feedback oscillation due to the negative group velocity in the plasma. It rises suddenly to large amplitude near the electron gun and has a short over‐all length. There are two nonlinear states: one is steady state in time, and agrees with a beam trapping calculation for absolute instability; the second has temporal quenching, or relaxation oscillations. This is attributed to the interaction of several oscillation modes strongly coupled by the nonlinear beam dynamics. This effect may limit wave amplitudes below the value predicted by trapping theory.

Nonlinear development of absolute and convective instabilities

Generation of harmonic Langmuir modes during beam–plasma interaction is studied by means of nonlinear theoretical calculations and computer simulations. The present Vlasov simulation of multiple harmonic Langmuir modes (up to 12th harmonics), generalizes the previously available simulations which were restricted to the second harmonic only. The frequency-wave-number spectrum obtained by taking the Fourier transformation of simulated electric field both in time and space shows an excellent agreement with the theoretical nonlinear dispersion relations for harmonic Langmuir waves. The saturated wave amplitude features a quasi-power-law spectrum which reveals that the harmonic generation process may be an integral part of the Langmuir turbulence.

/pdf/harmonic-langmuir-waves-iii-vlasov-simulation-21b8utlzid.pdf

Harmonic Langmuir waves. III. Vlasov simulation

Strong electrostatic double layers were produced with a triple plasma configuration in the large plasma chamber (5 m long, 2·5 m diameter) at IPM in Freiburg, Federal Republic of Germany. Owing to relatively low densities (1011 1012m−3), Debye lengths of a few centimetres and layer thicknesses of the order of a metre were obtained. Layers both with and without magnetic fields were studied. Analysis of particle spectra prove that wave-particle interactions play a minor role in maintaining the strong electric field. The three-dimensional potential distribution is measured and is qualitatively discussed in terms of particle budget. For cases with a magnetic field it tends to agree with observations above the aurora. Comparisons are made with double-layer theory and computer experiments, and general agreement is found as far as the available results allow.

Studies of strong laboratory double layers and comparison with computer simulation

Although the beam-plasma discharge (BPD) represents one of the first plasma physics phenomena, investigated as early as 1960, many of the quantitative aspects of the problem are only now beginning to emerge. This can be attributed partly to the fact that the understanding of the energization processes of the ambient plasma interacting with energetic electron beams required the theoretical development of strong turbulence, which was not accomplished till the middle 1970’s, and partly to the importance of BPD, for active electron beam experiments in space. On a superficial level BPD is nothing more than an R-F discharge, with the exception that the excited waves are electrostatic and near the ambient plasma frequency (ωe). This difference has profound consequences in the resulting absorption of the wave energy by the plasma particles. Under collisionless circumstances the energy absorption is by a few (VL%) electrons which are thus accelerated to high energies (~100’s eV). The ionization process is then dominated by the suprathermal tails rather than by the heating of the mainbody of the electrons. A proper description of BPD requires the following information: 

(1)

The deposition rate of the beam energy to plasma waves, and the accompanying beam energy relaxation length.




(2)

The ratio of wave energy heating electrons by electron neutral collisions, and creating suprathermal tails by collapse (i.e., turbulent acceleration).




(3)

The physics and time scale of axial and radial confinement of the cold, energetic electrons and beam electrons (i.e., electrostatic, collisional or anomalous diffusion, vehicle motion, etc.).

Theory of Beam Plasma Discharge

The Langmuir wave turbulence generated by a beam–plasma interaction has been studied since the early days of plasma physics research. In particular, mechanisms which lead to the quasi-power-law spectrum for Langmuir waves have been investigated, since such a spectrum defines the turbulence characteristics. Meanwhile, the generation of harmonic Langmuir modes during the beam–plasma interaction has been known for quite some time, and yet has not been satisfactorily accounted for thus far. In paper I of this series, nonlinear dispersion relations for these harmonics have been derived. In this paper (paper II), generalized weak turbulence theory which includes multiharmonic Langmuir modes is formulated and the self-consistent particle and wave kinetic equations are solved. The result shows that harmonic Langmuir mode spectra can indeed exhibit a quasi-power-law feature, implying multiscale structure in both frequency and wave number space spanning several orders of magnitude.

/pdf/harmonic-langmuir-waves-ii-turbulence-spectrum-34ei5jxzo7.pdf

Harmonic Langmuir waves. II. Turbulence spectrum

The Cerenkov interaction of a weak electron beam with a plasma is studied numerically. Three parts of the nonlinear evolution of the convective instability are discussed. In the first part the understanding of the saturation amplitude of the initial wave and its harmonics is extended. In the second part it is shown that a quasi‐linear‐like cascade process is responsible for the simutaneous appearance of beam particles and waves which move slower than the original beam velocity. These modes destroy the trapped particle oscillations of the initial wave. The third part of the instability is the development of fast waves whose phase velocities are greater than the original velocity of the beam. It is shown that these waves arise due to a mode coupling mechanism.

Numerical simulation of the weak beam‐plasma interaction

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 electrostatic instability in a magnetoplasma, omega > omega /sub ce/ , excited by a weak electron beam is found to be either convectively unstable (amplifying) or absolutely unstable (oscillating) depending upon effective plasma electron temperature and beam density. Measurements of the transition between the two types agree with caculations.

Transition from Absolute to Convective Instability in a Beam-Plasma System

Plasma simulation models have been developed which replicate the fundamental features of the convective and oscillating instability in the nonlinear weak beam regime The oscillating instability is characterized in this regime by a randomly fluctuating electric field which is caused by the presence of a fresh, strong beam in a region of space in which the electric field is large Nonlinear behavior of the background plasma need not be present during the production of the oscillating instability The convective instability develops into a quasilinear quiescent state during its nonlinear evolution because the nonlinear behavior of the system is confined to a diffused beam

Numerical simulation of the nonlinear convective and oscillating instabilities in a beam plasma system

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