Kinematic Dynamo — Magnetic Field Amplification

Parameters

Peak |B|: —
Growth rate: —

Physics

The kinematic dynamo problem asks: can a conducting fluid flow amplify a seed magnetic field against Ohmic dissipation?

The magnetic induction equation ∂B/∂t = ∇×(u×B) + η∇²B governs this. When the magnetic Reynolds number Rm = UL/η exceeds a critical threshold, stretching and folding of field lines overcomes diffusion — the dynamo grows.

Helical flows (like the ABC flow) satisfy the anti-dynamo theorem avoidance conditions and are efficient dynamo drivers.