George Schmidt

Nonadiabatic Particle Motion in Axialsymmetric Fields

The motion of charged particles in electromagnetic fields under extremely nonadiabatic conditions is investigated. This is the case, e.g., if the particle passes through a region of vanishing magnetic field, either in space or in time. In fields of axial symmetry, the constancy of the canonical angular momentum lends the tool for this investigation. Strict laws for flux conservation are derived including rapid changes of fields in space and time. Particle injection into cusped geometries is studied and compared to experimental results. Particle motion under magnetic‐field reversal in time is investigated and compared to findings in θ‐pinch experiments under field reversal. A simple self‐consistent model for such a particle motion is developed leading to the automatic formation of an E layer as a consequence of field reversal.

Filamentation instability in magneto plasmas

It is shown that the filamentation of ordinary‐mode pumps propagating at an arbitrary angle with respect to the magnetic field has to be magnetic field‐aligned, but not for extraordinary‐mode pumps. A general dispersion relation is derived including the effects of magnetic field and collisions, and the nonlinear effects of ponderomotive force, thermal focusing force, and the beating currents. Threshold field and growth rates are obtained and compared to the results of the unmagnetized and collisionless case. Applications of these results to ionospheric modifications are discussed.

Fractal diagrams for Hamiltonian stochasticity

Abstract A new diagrammatic representation is presented for Hamiltonian systems with three phase space dimensions. These fractal diagrams permit an easy way to find KAM boundaries and island in the Poincare mapping and lead thereby to a complete description of the geography of the mapping. In addition a qualitative insight is gained into the diffusion problem. The standard mapping is used for demonstration.

Parametric instabilities with finite wavelength pump

The general problem of parametric instabilities driven by a finite wavelength pump is investigated. For the particular case of a Langmuir wave pump, it is shown that resonant decay instabilities (forward or backward scattering in the one‐dimensional case), with thresholds which vanish in the colisionless limit, can occur only for pump wavenumber k0 greater than the critical value [(m/M)1/2/γ]kD, where m and M are the electron and the ion mass, respectively, and γ is the specific heat ratio. For smaller wavenumbers, there is always a nonzero threshold, the instability being of modulation character at long wavelengths and almost pure growing for short wavelengths. Frequency locking for small k0 and wavenumber locking for large k0 are demonstrated. The results are generalized to the case where the coupled waves satisfy arbitrary dispersion relations and simple physical interpretations of the instabilities are given.

Three wave backscatter interactions in a finite region

The space‐time, three wave, coupled mode equations are numerically integrated for a backscatter process in a finite region, with zero‐reflection boundary conditions. It is found that only spatially aperiodic steady states are stable. Effects of damping on the scattered waves are investigated.

Stability of a Steady, Large Amplitude Whistler Wave

The behavior of weak electrostatic waves in a collisionless magnetoplasma supporting a steady large amplitude whistler wave has been studied. All waves are assumed to propagate parallel to a uniform backgound magnetic field B0. In the presence of the whistler wave fields each particle executes an oscillatory motion parallel to B0, in addition to a translation along B0 and transverse motions. This oscillation causes the Landau resonance to be replaced by a series of new resonances between particles and the electrostatic modes. A distribution function for the perturbed plasma is constructed by solving the Vlasov equation, linearized in the electrostatic wave amplitudes. A dispersion relation is obtained and solved approximately for the growth/damping rate of the perturbations. Growing electrostatic modes are found to be approximately uncoupled. Trapped particles have a strong influence on the stability of the system.

Mixing windows in discontinuous cavity flows

Abstract The presence of islands, in particular those generated by P-1 points, are major obstacles to chaotic mixing. We study discontinuous cavity flow mixing systems, where the form of P-1 orbits are known as a combination of two segments of streamlines caused by the motion of the top and bottom walls, respectively. P-1 islands are born and collapse periodically with increasing alternating period of the walls, leaving mixing windows in between where nearly global chaos and hence, uniform mixing takes place.

Virial Theorem for Plasmas

ABS>A generalization of the Chandrasekhar-Fermi virial theorem is outlined to include plasmas. From this generalization it may be concluded that in the absence of confining gravitational fields, self-confinement of plasmas cannot be achieved. (B.O.G.)

Chaotic streamlines in convective cells

Abstract Streamlines in Rayleigh-Benard cells are investigated. The emergence of tori and a robust chaotic region surrounding these tori in the Arter flow are studied. One may construct a Hamiltonian of the flow, which oscillates on a fast time scale, and whose average is conserved along the invariant tori. The chaotic region arises due to the intersection of unstable manifolds emanating from stagnation points, with constant average Hamiltonian surfaces. The scaling of the size of the chaotic region with the nonintegrability parameter is defined by the location of the stagnation points.

Energy of plasma waves

A new definition of the sign of wave energy is given, which is valid where the old definition based on an expansion procedure breaks down. It is shown that a beam‐plasma wave does not produce explosive instabilities.