Stochastic flux freezing and magnetic dynamo

Area of Science:

• Plasma Physics
• Magnetohydrodynamics
• Turbulence Theory

Background:

• Magnetic flux conservation is a key concept in plasma physics.
• High magnetic Reynolds numbers characterize many astrophysical and laboratory plasmas.
• Turbulent dynamics can significantly alter magnetic field behavior.

Purpose of the Study:

• To investigate the validity of magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers.
• To explore the role of Lagrangian particle dynamics and spontaneous stochasticity.
• To establish a theoretical framework for stochastic flux freezing.

Main Methods:

• Analysis of Lagrangian particle trajectories and Richardson diffusion.
• Application of a Lagrangian path-integral approach.
• Numerical simulations of resistive hydromagnetic equations and stochastic particle methods.

Main Results:

• Magnetic flux conservation holds in a statistical sense, not conventionally.
• Spontaneous stochasticity of particle trajectories breaks Laplacian determinism.
• Stochastic flux freezing is established, persisting at infinite magnetic Reynolds number.
• Numerical results show similarity between magnetic Prandtl number (Pr(m))=1 and 0 dynamos, highlighting stochasticity's role.

Conclusions:

• Spontaneous stochasticity is crucial for understanding magnetic flux conservation in turbulent plasmas.
• The findings have implications for kinematic dynamos, nonlinear magnetohydrodynamic turbulence, and magnetic reconnection.
• Flux conservation remains stochastic even at infinite magnetic Reynolds number.