Magnetically Driven Rayleigh-Taylor Instability

A liner is a cylinder, a few centimeters in diameter and length, with a thin metal shell. If a large current is applied in axial direction, Lorentz forces drive the shell inwards. The imploding liner is subject to Rayleigh-Taylor instability.

To describe the acceleration of this fluid, incompressible Euler equations and Maxwell's electromagnetic equations are used, supplemented by Ohm's law. Nondimensionalization shows that the displacement current term is small. The governing equations are the usual incompressible fluid equations coupled to diffusion equations for the magnetic flux vector. We consider evolution in a single Fourier mode and hence the problem is 1-dimensional.

Numerical computation will be done with Crank-Nicholson method to solve the momentum and magnetic diffusion equations and to use an ODE boundary-value problem solver to calculate the fluid pressure.

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