The Efficiency of Magnetic Field Amplification at Shocks by Turbulence

Understand

Turbulent dynamo field amplification has often been invoked to explain the strong field strengths in thin rims in supernova shocks ($\sim 100 \, \mu$G) and in radio relics in galaxy clusters ($\sim \mu$G).

• We present high resolution MHD simulations of the interaction between pre-shock turbulence, clumping and shocks, to quantify the conditions under which turbulent dynamo amplification can be significant.
• We demonstrate numerically converged field amplification which scales with Alfv\'en Mach number, $B/B_0 \propto {\mathcal M}_{\rm A}$, up to ${\mathcal M}_{\rm A} \sim 150$.
• This implies that the post-shock field strength is relatively independent of the seed field.