A first-order perturbation expansion of the MHD equations is used to describe the onset of the interchange instability due to the high accelerations in railgun plasma-arc armatures. Powell considered the problem of perturbing an initial isothermal equilibrium with appropriate distributed current and density profiles, treating the perturbation equations with infinite conductivity. We model the arc the same way, but we include the effects of finite conductivity σ. A fourth-order mode equation is derived and solved numerically. We find continuous spectra of unstable modes for a nonzero plasma acceleration g, whose growth rates are mostly greater than , depending on the values of k and σ. The resistivity always raises growth rates higher than Powell's, especially for large k and large resistivity. The resulting growth rates in typical railgun situations are large enough to permit full development of the instability.
ASJC Scopus subject areas
- Nuclear and High Energy Physics
- Condensed Matter Physics