We obtain analytical results for the Rayleigh–Taylor instability in finite conductivity accelerated plasma arcs. Our results apply to the case vT2/al ≫ 1, where l is the plasma length, a is the acceleration, and VT is the thermal speed. This case is valid in electromagnetic rail launchers where the projectile mass is large compared to the plasma mass. The conductivity σ enters via a magnetic Reynolds number R = σμ(al3)1/2. The fourth order mode equation is solved analytically using an asymptotic WKB expansion in 1/R. We find the first order 1/R correction to the classical Rayleigh–Taylor dispersion relation for wavenumber K with 1 ≪ Kl ≪ R2.
ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Electrical and Electronic Engineering