Theory of discrete dynamo activity in laboratory plasmas: RFP sawteeth

Reversed field pinch experiments (RFP) exhibit relaxation phenomena which sustain the magnetic configuration longer than electrical resistivity should allow. This effect is due to the NMD dynamo. An interesting feature of the dynamo is that the relaxations often occur in a discrete and nearly periodic sawtoothing fashion. Unlike the tokamak sawtooth where a single Fourier harmonic is believed to play a central role in the sawtooth dynamics, RFP sawteeth are characterized by a set of tearing instabilities which play the essential role in the MHD dynamo. A theoretical explanation of the discrete dynamo is presented which is based upon a description of the RFP dynamics as a low order dynamical system. The calculation accounts for the evolution of the equilibrium that is affected by applied electrical fields, diffusion processes and the MHD dynamo, as well as a dynamical description of the MHD dynamo which is determined from the behavior of the tearing instabilities and the properties of the equilibrium. The system can be reduced to two ordinary differential equations for the averaged current gradient, which measures the degree of plasma relaxation, and the dynamo amplitude. The dynamical system exhibit a predator-prey type periodic limit cycle, which is characterized by amore » slow current peaking phase followed by a rapid crash. The sawtooth amplitude and period are predicted to increase with Lundquist number and plasma current, features which are in qualitative agreement with experimental observations.« less