Adiabatic invariants for the nonconservative Kepler's problem

This paper considers adiabatic invariants for the classical Kepler problem with resisting forces. The analysis is based on the theory of integrating factors and theory of adiabatic invariants in the Krylov-Bogoliubov-Mitropolski variables. The adiabatic invariants are series with respect to a small parameter. Also, for every particular case of nonconservative forces, it is shown that, with a complete set of adiabatic invariants, an approximate solution of the problem can be obtained. Four problems are analyzed in detail where approximate solutions are compared with numerical.     

Adiabatic plasma convection in the tail plasma sheet

We investigate the transport process of electrons in the tail plasma sheet by convection electric fields, under the assumption of conservation of the first two adiabatic invariants. The variation of the electron distribution function, and hence the bulk parameters with distance from the Earth are calculated. The results show that the electron distribution has a pressure anisotropy with p/p< 1 in the plasma sheet. Finally, the effects of the pressure anisotropy are qualitatively considered in terms of the modification of the geomagnetic field structure in the tail plasma sheet and instabilities due to wave-particle interactions.     

Gnevyshev peaks in geomagnetic indices

Sunspots have a major 11-year cycle, but the years near the maximum show two or more peaks called Gnevyshev peaks. It was noticed that in cycle 23, the double peaks in sunspot numbers are reflected in the electromagnetic radiations and coronal mass ejections (CMEs) in the solar atmosphere. But, in the interplanetary space, the ICMEs (interplanetary CMEs) show peaks not all coinciding with the peaks of sunspot numbers. Also, there are stream interaction regions (SIR), including co-rotating interaction regions (CIR), which evolve quite differently from sunspot numbers. In the geomagnetic indices, the peaks are related mainly to the peaks in SIRs, indicating that geomagnetic indices have no direct relationship with most of the phenomena at the Sun but are responding only to the interplanetary blobs due to SIRs, which are more predominant in the declining phase of sunspot activity.     

Current-driven plasma turbulence in a magnetic flux tube

The behaviour of a multi-component anisotropic plasma in a magnetic flux tube is studied in the presence of current-driven electrostatic ion-cyclotron turbulence. The plasma transport is considered in both parallel and perpendicular directions with respect to the given tube. As one of the sources of the parallel electric field, the anomalous resistivityof the plasma caused by the turbulence is taken into account. The acceleration and heating processes of the plasma are simulated numerically. It is found that at the upper boundary of the nightside auroral ionosphere, the resonant wave-particle interactions are most effective in the case of upward field-aligned currents with densities of a few 10^—6 A/m². The occurring anomalous resistivity maycause differences of the electric potential along the magnetic field lines of some kV. Further it is shown that the thickness of the magnetic flux tube and the intensity of the convection strongly influence the turbulent plasma heating.     

Rotational discontinuities in an anisotropic plasma

A general theory of rotational discontinuities is developed and the changes in the components of the plasma pressure, p_| and p, and in the magnetic induction, B, are found. For a given value of λ=(p_| − p) 4πμ/B² upstream only a limited range of downstream anisotropies are possible. If λ>0.6 upstream then isotropy is not possible downstream. Some special solutions are analysed and the identification of rotational discontinuities is the solar wind is discussed.     

Adiabatic plasma convection in a dipole field: Variation of plasma bulk parameters with L

We here investigate the motion of particles in a dipole magnetic field under the assumption of conservation of the first two adiabatic invariants. The results are then combined with Liouville's theorem to obtain the variation of the distribution function, and hence the plasma bulk parameters with L-shell. A comparison of the numerical results with recently published analytical approximations is made. Finally, the results are used to describe the structure of the ring current plasma in the outer radiatoin zone, the effects of the Alfvén layers being quantitatively evaluated for a simple electric field model.     

Theory of radiation in an anisotropic plasma

We follow up the work of Fung and Young (1982) to derive explicit expressions for the power emitted and the power observed per unit solid angle along the direction of the group velocity in an anisotropic plasma. We have deduced the ratio of the time interval during which the energy is emitted and the corresponding time interval during which the energy is received in this anisotropic case. Our result obtained is consistent to the basic well-known concept of group-ray propagation in a plasma.     

Electromagnetic instability in collisionless anisotropic plasma contrastreams

The electromagnetic instability in collisionless, anisotropic magnetized plasma contrastreams for perturbations propagating normally to the ambient magnetic field is investigated. It is found that the parallel temperature stabilizes the configuration forT _‖≤T _⊥ while it shows destabilizing effect forT _‖>T _⊥. A comparative study of the growth rates associated with various coexisting modes reveals that the electromagnetic instability may, under certain conditions, be associated with larger growth rates than the electrostatic instability.     

Electromagnetic instabilities in an anisotropic loss-cone plasma

A form of general dispersion relation for electromagnetic waves in a fully ionized anisotropic plasma with loss-cone that explicates the contribution of the loss-cone to the dispersion relation is developed. By initially ignoring effects due to anisotropy, it is shown by means of Nyquist diagram technique that an isotropic loss-cone distribution can be unstable to EM waves corresponding to the whistler mode (0<< _e ). The growth rate is then determined analytically for this distribution, assuming cyclotron resonance between the waves in the whistler mode and particles in the high energy tail of the velocity distribution. By including the effects of anisotropy, a general growth rate is obtained which is found to depend on the anisotropy, the size of the loss-cone, the softness of the energy spectrum, and the fraction of the particles which are resonant with the wave. For particular distributions the relative contributions of the anisotropy and of the loss-cone to the growth rate have been determined. It is seen that loss-cone effects, which depend on the size of the loss-cone as well as the softness of the energy spectrum, can be a significant factor in the determination of the growth rate. For the Lorentzian distribution, the half-width of unstable waves is considerably broadened and the growth rates are somewhat more severe as compared to a two-temperature Maxwellian. The threshold frequency is which confirms the presence of unstable EM waves in the magnetospheric plasma leading to turbulence.     

Field solution in an anisotropic plasma imbedded in a moving dielectric medium

Wave equations in an anisotropic plasma imbedded in a moving dielectric medium have been derived through Maxwell-Minkowski relations. These are solved for longitudinal and transverse cases of propagation. The dispersion relation within the medium has been deduced through which the nature of splitting may be understood.     

Analytical treatment of the force acting on a relativistic electron beam spreading in dense gas plasma by the ohmic plasma channel

A method is described for the analytical evaluation of the force acting on a relativistic electron beam spreading in dense gas plasma by the ohmic plasma channel. This is useful for the solution of the general definitions for the force of the beam plasma interactions in the case of an arbitrary displacement of the symmetry axis of the plasma channel relative to the corresponding axis of the beam. The accuracy of these procedures is tested and their efficiency illustrated with practical applications, including the computation of the tracking force exerting on a relativistic electron beam by the ohmic plasma channel.     

Radiation from a dipole in an anisotropic plasma medium containing time-varying irregularities

The expression for power radiated from a dipole within an anisotropic plasma has been obtained in presence of a current source and time-varying irregularities. This may be useful for numerical computation in lossy media.     

Electrostatic ion cyclotron waves in an anisotropic plasma

In the solar wind, electrostatic ion cyclotron waves can be excited, by electrons or ions when the flow velocity becomes supersonic. The instability of these waves is investigated for a situation in which ions are streaming in opposite directions along the interplanetary magnetic field in a uniform background of relatively stationary electrons. Many modes become unstable under the existing conditions. It is conjectured that the excitation of this instability may lead to a steady state electrostatic turbulence in the solar wind.     

Thermal-convective instability of a composite rotating plasma in a stellar atmosphere with finite larmor radius

Thermal-convective instability of a hydromagnetic, composite, rotating, inviscid and infinitely conducting plasma in a stellar atmosphere has been studied in the presence of finite Larmor radius. It is found that the criterion for monotonic instability holds good in the presence of the effects due to rotation and finite Larmor radius.     

Nonlinear coherent four‐wave interaction in space plasma

According to a widespread point of view, intensive electrostatic structures in the E‐region of the auroral ionosphere can be a consequence of the excitation of the modified two‐stream or Farley‐Buneman (FB) plasma turbulence. But in spite of the successes of the theoretical and experimental research of the auroral radar scattering, it is impossible to explain the existence of auroral echoes with large aspect angles (> 2 deg.), the wave propagation perpendicular to the electron drift velocity and wave scales less than 1 m. In this paper the coherent nonlinear interactions of three and four electrostatic FB‐waves are considered analytically and numerically. The evolution of the nonlinear waves is described by a system of magnetohydrodynamic equations. 1) It is shown that the interaction of three and four coherent waves is the main physical mechanism which leads to the saturation of the FB‐instability. 2) If no dissipative and dispersive effects occur, an explosive instability may be excited. 3) The main result of the interaction of coherent waves is the generation of nonlinear waves and nonlinear structures when the waves are damped linearly and propagate perpendicular to the electron drift velocity. This region corresponds to large aspect angles of the small‐scale waves. 4) Further, the wave interaction causes a nonlinear stabilization of the growth of the high‐frequency waves and a formation of local density structures of the charged particles. The results of the numerical models allow to analyse the possibility of scenarios of the two‐stream plasma instability in the collisional auroral E‐region.     

Exchange and correlation interactions in electron-positron plasma

The effect of particle-particle interaction on the adiabatic index γ for an electron-positron plasma is considered. An improved method for numerically calculating the Hartree-Fock exchange integral is presented and its relativistic asymptotics is determined. An approximation formula is derived for the correlation part of the interaction in the low-density limit. This formula includes degeneracy and the positron component.