Diffusion of plasma in two dimensions is studied in the guiding center model. It is shown that in this model diffusion always exhibits the anomalous 1/B variation with magnetic field. The velocity correlation function and the diffusion coefficient are calculated in detail using functional probabilities. In addition to the 1/B field dependence, the diffusion coefficient is unusual in that it depends weakly on the size of the system. These theoretical results are compared with those from computer experiments and their significance for real plasma is discussed.

Theoretical and numerical methods now give a complete solution to the problem of finite-β plasma equilibrium in mirror magnetic wells and toroidal devices. The equilibria can be made consistent on all of the progressively longer time scales of the guiding-center fluid model, including the particle magnetic drifts and the Coulomb scattering equilibrium of a neutral injected plasma. The theory of equilibrium in the guiding-center fluid model of a finite-β plasma with an arbitrary, anisotropic pressure tensor can be formulated as a classical magnetostatic system: ∇⋅B = 0, ∇×H = 0, B = H + 4πM(B). The plasma magnetization is found explicitly in terms of three physically distinct components related to the laws of conservation of magnetic moment, of longitudinal invariant, and of the sign of the velocity along B of particles that do not undergo mirror reflection. A condition is derived upon the field geometry whereby a large class of special equilibria can be found in which all particles on a given line drift on the same surface, the omnigenous surface. Such systems allow a specially simple connection between particle and fluid models in the guiding-center fluid theory. The usefulness of the theory is exemplified by application to the problem of a finite-β plasma in a magnetic well. Finally, a brief treatment of stability in terms of the energy principle is given. The omnigenous equilibria have particularly simple stability criteria.

A systematic account is given of the derivation of the dispersion relation for helicon waves in a uniform cylindrical plasma bounded by a vacuum. By retaining finite resistivity in the equations, boundary conditions present no difficulties, since the wave magnetic field is continuous through the plasma-vacuum interface. Two unexpected results are found. First, the wave attenuation remains finite in the limit of vanishing resistivity. This is due to the energy dissipated at the interface by the surface currents required to match the plasma wave field to the vacuum wave field. Zero wave attenuation for zero resistivity is recovered if electron inertia is included. Secondly, it is found that waves with azimuthal numbers m of opposite sign propagate differently, but the sense of polarization at the axis of the cylinder is independent of the sign of m.The argument of the dispersion function is complex and numerical results were obtained using a computer. The method of programming is described, and results are given applicable to propagation in metals at low temperatures, or in a typical gas discharge plasma for the m = 0 and m = ± 1 modes.An example of the amplitude of the wave fields as a function of radius is given for the axisymmetric mode, and of amplitude and phase for the m = ± 1 modes.

Downloaded 22 Oct 2012 to 136.159.235.223. Redistribution subject to AIP license or copyright; see http://jmp.aip.org/about/rights_and_permissions WIGHTMAN FUNCTIONS 2029Hausdorff topological space which is locally homeomorphic to an open subset of em. One pictures 2) as lying above its projection ~ into em. The projection f of a point P of 2) furnishes coordinates for that point. It is possible that several points of 2) project into the same point f of~. If the projection map is a global homeomorphism, then 2) is a schlicht domain (single sheeted). If 2)1' 2)2 are two domains over em and 2)1 can be mapped continuously into a subset of 2)2 so that corresponding points have the same coordinates, we say 2)1 lies inside (liegt im innern) 2)2 and write 2)1 < 2)2' Although 2)1 < 2)2, it is possible that 2)1 is more ramified (has more sheets) than 2)2' For schlicht domains 2)1 < 2)2 means the same as 2)1 c 2)2' Suppose ~ is a domain over em, such that ~ < 2)" for each of a set {2),,} of domains over em. Then, if P is a point of~, the projection preserving continuous map in the definition of < gives an image point PIX