We study the Rayleigh-Taylor instability in finite-conductivity accelerated plasma arcs of the type found in electromagnetic rail launchers. For a plasma of length l, acceleration a, and thermal speed vT we consider the case where vT2/al1, which is valid when 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 large wave number K but with KR2/l. The analytical results show good agreement with previous numerical calculations.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics