The equation ∇×B=αB is solved analytically in a toroidal coordinates system for the axisymmetric torus of arbitrary aspect ratio without the approximation of large aspect ratios.The solution is derived from the Helmholtz equation and is expressed in the series that contains the associated Legendre functions. A set of fundamental solutions is presented, each of which approaches asymptotically the solution for cylindrical geometry, whose azimuthal dependence is cos lψ, in the limit of large aspect ratios. The force-free magnetic field is given in the form of the infinite series of these solutions. By using the set of fundamental solutions, the contour of the magnetic surface, eigenvalues, and F-Θ curves of the circular cross section are calculated.

An anomalous discharge current flowing in the same direction as the charging current was observed in a low-density polyethylene film with evaporated silver electrodes at room temperature (25°C) after the application of a very high field above 2×108 V/m. The discharge transient current was computer-analyzed numerically by an explicit difference method. The anomalous current was attributed to the large amount of two types of injected space charge (electrons and holes) with ohmic electrodes, and not to one type of injected space charge (electrons or holes) with blocking electrodes.

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I n itia l C o n d itio n a n d C o o lin g T im e o f R e c o m b in in g H e liu m P la s m a fo r S t a ti o n a r y V U V L a s in g A c tio n