Linear stability of an accelerated, current carrying wire array

The linear stability of an array of a large number of thin wires is considered. The wires form a cylindrical surface, accelerated toward the axis under the action of a current. Stability equations are derived and a complete classification of the modes is presented. In agreement with Felber and Rostoker [Phys. Fluids 24, 1049 (1981)], it is shown that there exist two types of modes: medial modes, with deformation in the rz plane, and lateral modes, with only azimuthal deformation. For a given axial wave number, k, the most unstable medial mode has all the wires moving in phase similar to an axisymmetric mode for a continuous shell, whereas the most unstable lateral perturbation has opposite displacements of neighboring wires. Lateral modes are of particular interest because they may remain unstable for parameters where medial modes are stable. Numerical analysis of the dispersion relation for a broad range of modes is presented. Some limiting cases are discussed. It is shown that k(1/2) scaling holds until surprisingly high wave numbers, even exceeding the inverse interwire distance. In the long-wavelength limit, the wires behave as a continuous shell with strong anisotropy of the electrical conductivity, i.e., high along the wires and vanishing across the wires. The results differ considerably from the modes of a thin, perfectly conducting shell. In particular, a new "zonal flow" mode is identified. [S1070-664X(99)01708-5].