S. Cuperman

Nonlinear development of the ion-cyclotron electromagnetic instability

Cornwall et al. (1970) suggested that if the ring current protons penetrated the plasmapause, intense resonant electromagnetic ion cyclotron turbulence would lead to their rapid precipitation loss. IN this paper we present a computer simulation study of the electromagnetic ion -cyclotron instability in a homogeneous plasma consisting of protons and electrons embedded in a static magnetic field, B 0x . The plasma parameters used are and Effects such as sources and losses or space non-uniformities are not considered here. The predictions of the linear theory for the fast build-up of unstable left-hand (proton-like) electromagnetic ion-cyclotron waves are fully confirmed.

Theory and computer simulation of electron beam-plasma interactions in unbounded systems

Computer simulation experiments of linear and nonlinear collisionless interactions between electron beams and background plasmas, for conditions relevant to active magnetospheric experiments, were carried out. Both electrostatic and electromagnetic interactions were simultaneously considered. The beam-plasma systems were infinite and homogeneous. The relative beam concentrations considered were e ≡ n b / n p , = 1, 0·1 and 0·01. In all cases, the background plasma (1 eV thermal energy) was penetrated by an electron beam of 1 keV streaming energy and 5 % thermal spread in the streaming direction. The paper presents a full description of the results and a brief discussion of their relevance to magnetospheric active experiments. The off-angle propagation case in unmagnetized plasmas is also briefly discussed.

A temperature-anisotropy instability for electromagnetic waves propagating across a static magnetic field

The instability of electromagnetic waves propagating across a static magnetic field in the presence of a thermal anisotropy ( T ∥ > T ⊥ ) is investigated. The marginal stabifity criterion as well as the rate of growth of the instability are derived. When compared with the fire hose instability (of electromagnetic waves propagating along the static magnetic field) it is found that higher electron pressures are required for this new instability to be set up; however, the maximal rate of growth is much larger than in the fire hose case. The interplanetary plasma is stable to this thermal anisotropy instability; high β plasma devices may be unstable. The T ⊥ = 0 case treated by Hamasaki is recovered.

Nonlinear equilibrium and stability analysis of rippled, partially neutralized, magnetically focused electron beams

In the first part of this work a higher-order solution of the anharmonic oscillator equation describing the nonlinear rippled equilibrium state of magnetically focused, partially neutralized electron beams is given. Thus, using the method of harmonic balance, we derive a ripple-l coupling of fast-fast, slow-slow and slow-fast waves is considered. The growth rates and band widths for different possible wave couplings are derived and compared.

Three component non-symmetric counter-streaming instabilities: longitudinal electron plasma modes

The counter-streaming instabilities arising in three-component electron plasmas are investigated analytically and numerically in the general non-symmetric case, i.e. when Here n 1 n 2 and n a represent the electron particle density in the first and second beams and in the background (ambient) stationary plasma, respectively; U 1 and U 2 represent the streaming velocities of the two counter-streaming electron beams. No magnetic or temperature effects are considered; consequently the three components interact only through the electric collective fields and only longitudinal modes are present. The positive ions here represent a stationary neutralizing background. Combined analytical and numerical solutions of the dispersion equation indicate that the basic properties of the unstable plasma modes may change significantly, depending on the values of the dimensionless parameters e, a and g. Thus, the standing wave spectrum (Re ω = 0) which occurs in the symmetric case (e = a = 1) without background (gr = 0) may be replaced by a mixed travellingstanding wave spectrum having a rather complex structure; the maximum growth rate could be also strongly affected. The transformation of the instability from ‘absolute’ into mixed ‘convective and absolute’ may have significant physical implications, especially for finite size plasma systems or finite length unstable interaction regions. The results are relevant for laboratory and (especially) astrophysical situations in which counter-streaming electron beams having unequal streaming velocities (and particle densities) penetrate plasma regions with significant relative particle concentration.

Non-symmetric two-stream instability

A theoretical investigation is performed concerning the instability spectrum of quasi-electrostatic waves at shifted half-odd-integer values of the cyclotron frequency due to nonsymmetric counterstreaming electron beams. The beam velocities parallel and perpendicular to the static magnetic field are represented by double Dirac delta functions with no imposition of parameter limitations. Systematic consideration is given to the coupling between plasma modes and cyclotron modes as well as the coupling between cyclotron modes of the two beams that result in shifted half-odd-integer multiples of the cyclotron frequency. The general dispersion equation for quasi-electrostatic waves is analyzed, and plasma-cyclotron coupling in the nonsymmetric case is treated by deriving approximate analytical expressions for maximum growth rates and marginal stability. Exact numerical solutions in both frequency and wavenumber space are obtained and compared with the analytical expressions. Cyclotron-cyclotron coupling modes are treated in the same way, and the results for both types of coupling are compared. It is found that certain modes may be weakened or completely suppressed when the Bessel functions for specific plasma parameters vanish.

Stability analysis of sheared non-neutral relativistic cylindrical electron beams in applied magnetic fields

A self-consistent stability analysis of relativistic non-neutral cylindrical electron flows propagating along applied magnetic fields is considered within the framework of the macroscopic cold-fluid-Maxwell equations. The full influence of the equilibrium self-electric and self-magnetic fields is retained. Then the E x B drift (E being the radial electric field created by the uncompensated charge) generates a radial shear, v z (r) and v 0 (r) . The effect of the shear in the axial velocity component, as reflected in the relative axial motion of adjacent concentric layers of beam particles, is investigated. The self-consistent treatment of the problem thus shows that the equilibrium state considered in this paper is unstable.

Three-component non-symmetric counter-streaming instabilities: oblique propagation case

The effects of the background plasma as well as of the non-resonant plasma-cyclotron and cyclotron–cyclotron interactions on the oblique unstable electrostatic waves generated by resonant plasma–cyclotron (P–C) and cyclotron–cyclotron (C–C) interactions in magnetized non-symmetric two-stream plus background plasma systems are theoretically investigated. Two main effects are reported: (a) preferential increase or decrease of the maximum growth rates of certain m −modes for appropriate plasma parameters and (b) an additional contribution to the frequency shift from the integer multiple values of half the cyclotron frequency. Closed analytical expressions for the maximum growth rates and frequency shifts of both plasma-cyclotron and cyclotron–cyclotron unstable interactions are presented and discussed. The theoretical results obtained in this paper are supported by recent experimental results on electron counter-streaming instabilities in the presence of significant background plasma concentrations in which dominant electric field emissions at 3Ω e /2 have been observed to occur.

Effect of thermal anisotrophy on the loss-cone produced high-frequency quasi-electrostatic ion cyclotron waves in mixed warm-cold plasmas

We show that in the case of generalized loss-cone distribution functions characterized by loss-cone index l , parallel thermal velocity α ∥ and perpendicular spread α ⊥ sufficiently large anisotropy, (α ∥ /α ⊥ ), may stabilize the high-frequency electrostatic ion cyclotron instability. The discussion refers to the oblique propagation and includes also a second, cold, ion component (besides warm isotropic electrons). Electromagnetic corrections to the quasi-electrostatic dispersion relation are also considered. Simple analytical expressions for the growth rates are derived and discussed.