T. G. Northrop

Charged Particle Diffusion by Violation of the Third Adiabatic Invariant

An equation which describes statistically the motion of charged particles in response to fluctuating electric and magnetic fields is derived. The particles are assumed to be moving in a mirror‐type magnetic geometry. In addition to a static magnetic field there are small superposed fields fluctuating randomly on such a time scale that the first and second adiabatic invariants, M and J, are conserved, but the third or flux invariant φ is violated. By using second adiabatic theory a two dimensional diffusion equation is obtained valid on a much longer time scale than that of the fluctuations. Elements of the diffusion tensor are time—space correlations of fluctuation‐induced perturbations in the guiding center drifts. These drift perturbations are systematically derived and shown to reduce simply in various special cases.

Extensions of guiding center motion to higher order

In a static magnetic field, some well‐known guiding center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, Pφ, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second‐order motion is included, Pφ is no longer a constant. The above extensions of guiding center theory help to resolve the different tokamak orbits obtained either by using the guiding center equations of motion or by using conservation of Pφ.

A self-consistent model for the particles and fields upstream of an outgassing comet: 1. Gyrotropic and isotropic ion distributions

The magnetic field and solar wind flow parameters in the vicinity of a weakly outgassing comet are determined using a self-consistent model which treats the cometary ions kinetically. Two different assumptions are made concerning the cometary ion distribution function; the pickup cometary ions form either a velocity space gyrotropic ring distribution or a velocity space Isotropic shell distribution in the solar wind frame of reference. The individual currents due to the solar wind and cometary ions, which determine the magnetic field, are calculated in each case. Using theoretically determined parameters which reflect the conditions expected at comet Kopff (a typical short-period comet and one possible target for the future CRAF/Cassini mission) for various heliocentric distances, we are able to determine how the global field and flow characteristics are influenced by the nature of the cometary ion distribution function.

A self‐consistent model for the particles and fields upstream of an outgassing comet: 2. A time‐dependent description

In a previous paper [Flammer et al., 1991], we determined the global variation of the magnetic field and solar wind flow parameters in the unshocked region upstream of an outgassing comet using a kinetic treatment for the cometary ions. Two different assumptions were made concerning the cometary ion distribution function: the pickup cometary ions formed either a velocity space gyrotropic ring distribution or a velocity space isotropic shell distribution in the solar wind frame of reference. In the present paper we consider the general case wherein the newly picked up ions are elastically pitch angle scattered from the initial ring distribution to a shell with some characteristic time scale τ. Using theoretically determined parameters which reflect the conditions expected at comet Kopff (a typical short-period comet and a possible target for the CRAF/Cassini mission) for various heliocentric distances, we determine how the pitch angle scattering rate affects the global morphology.

MAGNETIC FIELD GEOMETRY AND THE ADIABATIC INVARIANTS OF PARTICLE MOTION.

The first correction term to the lowest‐order magnetic moment of a charged particle is written in terms of the curl of the magnetic field and the eight coefficients specifying the torsions, shears, and curvatures of the field lines. Certain of the coefficients are absent; thus in a vacuum field the lowest‐order magnetic moment will not be affected by them. The influence of field geometry on the first correction to the second invariant is also investigated. A surface on which the lowest‐order term of the invariant is constant is composed of field lines, as is well known. In portions of a surface, where the field lines have large components of curvature tangent to the surface, the first‐order correction term is large, and the guiding center deviates from the surface more than where the radii of field line curvature are normal to the surface. This fact explains some phenomena observed in recent numerical integrations of guiding‐center trajectories in Ioffe‐type mirror geometries.