Numerical simulation of laminar plasma dynamos in a cylindrical von K\'arm\'an flow

TL;DR

This study uses numerical simulations to investigate laminar plasma dynamos in a cylindrical von Kármán flow, revealing conditions for self-sustaining magnetic fields and effects of plasma parameters on dynamo behavior.

Contribution

It demonstrates the occurrence of laminar dynamo action in plasma flows and analyzes the influence of compressibility and Hall effects on dynamo thresholds and saturation.

Findings

Dynamo action occurs when magnetic Reynolds number exceeds a critical value.

Compressibility increases the critical magnetic Reynolds number for dynamo onset.

Hall effects alter the amplitude of the saturated magnetic field.

Abstract

The results of a numerical study of the magnetic dynamo effect in cylindrical von K\'arm\'an plasma flow are presented with parameters relevant to the Madison Plasma Couette Experiment. This experiment is designed to investigate a broad class of phenomena in flowing plasmas. In a plasma, the magnetic Prandtl number Pm can be of order unity (i.e., the fluid Reynolds number Re is comparable to the magnetic Reynolds number Rm). This is in contrast to liquid metal experiments, where Pm is small (so, Re>>Rm) and the flows are always turbulent. We explore dynamo action through simulations using the extended magnetohydrodynamic NIMROD code for an isothermal and compressible plasma model.We also study two-fluid effects in simulations by including the Hall term in Ohm's law. We find that the counter-rotating von K\'arm\'an flow results in sustained dynamo action and the self-generation of magnetic field when the magnetic Reynolds number exceeds a critical value. For the plasma parameters of the experiment, this field saturates at an amplitude corresponding to a new stable equilibrium (a laminar dynamo). We show that compressibility in the plasma results in an increase of the critical magnetic Reynolds number, while inclusion of the Hall term in Ohm's law changes the amplitude of the saturated dynamo field but not the critical value for the onset of dynamo action.