Linear stability of an accelerated, current carrying wire array

The linear stability of an array of a large number of thin wires is conside red. The wires form a cylindrical surface, accelerated toward the axis unde r the action of a current. Stability equations are derived and a complete c lassification of the modes is presented. In agreement with Felber and Rosto ker [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 mo st unstable medial mode has all the wires moving in phase similar to an axi symmetric mode for a continuous shell, whereas the most unstable lateral pe rturbation has opposite displacements of neighboring wires. Lateral modes a re of particular interest because they may remain unstable for parameters w here 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 number s, even exceeding the inverse interwire distance. In the long-wavelength li mit, the wires behave as a continuous shell with strong anisotropy of the e lectrical 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. [S 1070-664X(99)01708-5].