Resistive ballooning mode

Linear growth rate

The linear growth rate γ of the RBM instability is given as

where | ∇ p | ∼ p L p is the pressure gradient g e f f = c s | ∇ B B | ∼ 1 / R 0 is the effective gravity produced by a non-homogeneous magnetic field, R₀ is the major radius of the device, L_p is a characteristic length of the pressure gradient, and c_s is the plasma sound speed.

Similarity with the Rayleigh–Taylor instability

The RBM instability is similar to the Rayleigh–Taylor instability (RT), with Earth gravity g → replaced by the effective gravity g → e f f , except that for the RT instability, g → acts on the mass density ρ of the fluid, whereas for the RBM instability, g → e f f acts on the pressure p of the plasma.