"Laboratory Plasma Dynamos, Astrophysical Dynamos, and Magnetic Helicity Evolution"
Eric G. Blackman and Hantao Ji

Summary:

Dynamos describe the amplification or sustenance of magnetic fields in electrically conducting media such as plasmas and liquid metals. The term "dynamo" means different things to the laboratory fusion plasma and astrophysical plasma communities, however. Laboratory plasmas are typically magnetically dominated, and laboratory dynamos describe how a magnetic configuration adjusts toward its relaxed state in the presence of an external electric field or injection of helicity driving the system away from its relaxed state. Small amplitude fluctuations arise from the injection through kink mode instabilities from large currents or tearing modes from large current gradients, leading to a turbulent EMF which drives the dynamo. These dynamos can be advantageous for plasma confinement because they can sustain a large magnetic field in an ordered configuration, but the sustenance requires instabilities, which produce unwanted energy dissipation.

Astrophysical plasmas typically involve large scale helical velocity fluctuations amplifying an initially weak magnetic field. The magnetic field is amplified and sustained on temporal and spacial scales that are significantly larger than the scale of the driving turbulence. The source of energy for this turbulence inside astrophysical rotators is usually convection or differential rotation. While laboratory dynamos always involve helicity, flow-driven dynamos can sometimes be non-helical, with a turbulent velocity amplifying the magnetic field through a random walk of stretching and shear. Some cases of magnetically-dominated dynamos do exist in astrophysics, in stellar coronae in particular.

Three unifying equations for helical dynamos are derived using Maxwell's equations, Ohm's law, and vector identities. These equations are then used to derive necessary conditions for dynamos to exist in a variety of circumstances: laboratory plasmas in the Reversed Field Pinch (RFP) configuration, time-dependent closed flow-driven helical dynamos,steady-state open flow-driven helical dynamos, and time-dependent open flow-driven helical dynamos. Things get messy. One important conclusion from the open flow-driven calculations is that these dynamos must be contain both large and small scale helicity, with their fluxes through the system boundary equal and opposite. This explains the bihelical structure of the solar corona. Furthermore, the evolution of magnetic helicity injected into the corona is conceptually analogous to laboratory systems with injected helicity such as Spheromaks.

In conclusion, laboratory plasma helical dynamos typically arise from a magnetically dominated initial state when an external toroidal electric field is applied, driving a current along the magnetic field lines and thereby injecting magnetic helicity of one sign into the system. For strong enough applied fields, instabilities occur, and the resulting fluctuations produce a turbulent EMF that drives the system back towards its relaxed state, which is the state in which magnetic helicity is at the largest scale possible. Astrophysical dynamos typically arise from an initial state with weak fields; velocity fluctuations produce the turbulent EMF that drives the dynamo. No magnetic helicity is injected, so the dynamo acts to seperate helicity of opposite signs spacially and spectrally. Coronae are the astrophysical phenomenon most directly analogous to magnetically-driven laboratory dynamos in configurations such as Spheromaks and RFPs.

Applications to my research:

One of the goals of the Swarthmore Spheromak Experiment (SSX) is to use laboratory experiments to enhance our understanding of stellar coronae and other astrophysical phenomena. This paper provides insight into how laboratory plasma physics and astrophysics are connected, in the context of dynamos that amplify or sustain magnetic fields in a plasma. Understanding what scientists in different fields mean when they talk about dynamos is vital for an interdisciplinary project such as mine.