Linear stability of an accelerated wire array
The linear stability of an array of a large number of thin wires is considered. The wires form a cylindrical surface which is accelerated towards the axis under the action of a current excited in the array by an external source. General equations governing stability of this system are derived and a complete classification of all the modes present in such a system is presented. In agreement with an earlier analysis by Felber and Rostoker, it is shown that there exist two types of modes: medial modes, in which the wires experience deformation in the rz plane, and lateral modes, in which only a purely azimuthal deformation is present. For a given axial wave number k, the maximum growth rate for medial perturbations corresponds to a mode in which all the wires move "in phase" (an analog of an axisymmetric mode for a continuous cylindrical shell), whereas for the lateral perturbations the maximum growth rate corresponds to the opposite displacements of the neighboring wires. Numerical analysis of a dispersion relation for a broad range of modes is presented: Some limiting cases are discussed. In particular, it is shown that a traditional k1/2 scaling holds until surprisingly high wave numbers, even exceeding the inverse inter- wire distance. In the limit of long-wavelength perturbations, a model of a continuous shell becomes valid; the presence of the wires manifests itself in this model by a strong anisotropy of electrical conductivity, high along the wires and vanishing across the wires. The resulting modes differ considerably from the modes of a thin perfectly conducting shell. In particular, a new mode of "zonal flows" is identified.
- Research Organization:
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE Office of Defense Programs (DP)
- DOE Contract Number:
- W-7405-Eng-48
- OSTI ID:
- 5776
- Report Number(s):
- UCRL-JC-132255; DP0210000; ON: DE00005776
- Resource Relation:
- Conference: American Physical Society 40th Annual Meeting of the Division of Plasma Physics, New Orleans, LA, November 16-20, 1998
- Country of Publication:
- United States
- Language:
- English
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