Experimental scaling of fluctuations and confinement with Lundquist number in the reversed-field pinch

Abstract

The scaling of the magnetic and velocity fluctuations with Lundquist number (S) is examined experimentally over a range of values from 7×104 to 106 in a reversed-field pinch (RFP) plasma. Magnetic fluctuations do not scale uniquely with the Lundquist number. At high (relative) density, fluctuations scale as b̃∝S−0.18, in agreement with recent numerical results. Fluctuations are almost independent of S at low (relative) density, b̃∝S−0.07. The range of measured exponents is narrow and is in clear disagreement with theories predicting b̃∝S−1/2. At high relative density, the scaling of the energy confinement time follows expectations for transport in a stochastic magnetic field. A confinement scaling law (nτE∝β4/5⋅T−7/10⋅a−3/5⋅Iφ2) is derived, assuming the persistent dominance of stochastic magnetic diffusion in the RFP and employing the measured scaling of magnetic fluctuations. The peak velocity fluctuations during a sawtooth cycle scale marginally stronger than magnetic fluctuations but weaker than a simple Ohm’s law prediction. The sawtooth period is determined by a resistive-Alfvénic hybrid time (Tsaw∝τRτA) rather than a purely resistive time.