## Dissertations from ProQuest

#### Title

Interchange and filamentation instabilities in resistive MHD applied to electromagnetic rail-launch devices

1991

Article

#### Degree Name

Doctor of Philosophy (Ph.D.)

Physics

#### First Committee Member

Manuel Huerta, Committee Chair

#### Abstract

A first order perturbation expansion of the equations of resistive MHD is used to describe the interchange and filamentation instabilities in accelerated plasma arcs found in electromagnetic rail launchers. Due to the resistivity the time development operators are not selfadjoint and lead to fourth order mode equations. The modes are of the form $v(x,y,t)=v\sbsp{n}{k}(x)e\sp{iky}e\sp{-i\omega t}.$ In the filamentation case for each k there is a discrete family of modes where the members of the family differ by the number n of nodes. In the parameter ranges commonly found in electromagnetic launchers all the modes are stable. In the case of the interchange instability the mode equation has an internal singularity. For each k there is a continuous spectrum of unstable modes with normalizable eigenfunctions. A set of eigenfunctions were calculated that we expect correspond closely to the discrete spectrum of modes that exist in the case of infinite conductivity.

#### Keywords

Engineering, Mechanical; Physics, Electricity and Magnetism