Oscillating-field current drive (OFCD) is a steady-state magnetic helicity injection method to drive net toroidal current in a plasma by applying oscillating poloidal and toroidal loop voltages. OFCD is added to standard toroidal induction to produce about 10% of the total current in the Madison symmetric torus. The dependence of the added current on the phase between the two applied voltages is measured. Maximum current does not occur at the phase of the maximum helicity injection rate.

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... of OFCD on magnetic fluctuations and dissipated power are shown. Various types of current sustainment for toroidal laboratory plasmas are forms of magnetic helicity injection. Helicity K R A Bd is the total linkage of flux of the magnetic field B r A in the plasma volume . Helicity constrains relaxed states due to its approximate time invariance [1] [2] [3] [4] , and relates to the toroidal plasma current through the poloidal flux, which links toroidal flux in general. The time derivative in a torus can be written dK=dt 2V t t ÿ 2 R J Bd, which suggests magnetic helicity injection as current drive. The first term on the right represents inductive helicity injection with a toroidal loop voltage V t and toroidal flux t , as in the standard (or "steady") toroidal induction used for the reversed field pinch (RFP) [5] . Helicity injection is applied to balance the helicity dissipation, due to the resistive electric field J, represented by the last term. Oscillating-field current drive (OFCD) [6 -8] is a type of steady-state, inductive helicity injection (sometimes called F ÿ pumping or ac helicity injection). In OFCD, sinusoidal toroidal and poloidal loop voltages t sin!t ÿ and p sin!t are applied. The poloidal voltage leads to an oscillating toroidal flux with amplitude p =!, and so the cycle-averaged inductive helicity injection rate is t p sin=!. Since an ac voltage has zero cycle average, OFCD sustainment is steady state (unlike toroidal induction), which would make it well suited to compact RFP reactor designs with high mass-power density [9] . Also it is expected to have Ohmic current-drive efficiency, driving the bulk electron distribution [10] . 3D MHD calculations [11, 12] indicate OFCD is capable of sustaining all the current in an RFP. The sinusoidal loop voltages induce symmetric oscillations in the plasma pinch velocity and magnetic field. The resulting electromotive field drives edge current with a radial gradient leading to MHD tearing instability. The helical, tearing fluctuations in flow and field, u and b, cause magnetic relaxation through an electromotive field hu bi (or "dynamo") which acts to flatten the current profile, transporting current from the edge to the core. Two chief issues for OFCD are the dynamics of the current penetration by magnetic relaxation and the effect of the relaxation on plasma energy confinement. While the presence of the fluctuations implies possibly detrimental effects on confinement [13, 14] , recent calculations [12] show their amplitudes are not much different than for toroidal induction. In this Letter we report that OFCD has been used to produce about 10% of the total plasma current in the Madison symmetric torus (MST) [15] RFP (see Fig. 1 ). The dependence of the current on the relative OFCD phase is measured, and notably the maximum current does not occur at the phase of maximum helicity injection. Magnetic fluctuation amplitudes are also found to depend on the phase, and the maximum current occurs with the minimum amplitudes. Compared to toroidal induction alone, the time-average poloidal mode m 0 fluctuation amplitudes are smaller at the maximum OFCD current, as is the total dissipated power, implying in this case that the OFCD need not degrade confinement, and could actually be improving it. We also observe that the relaxation process is entrained to the applied oscillations. The OFCD currentdrive efficiency is about 0:1 A=W, about the same as that for the toroidal induction. Previously, OFCD was used to drive about 5% of the current in the ZT-40M RFP [16] . However, the detailed phase dependence and effect on MHD tearing activity were not investigated in that case. 0 10 20 30 40 50 60 70 t (ms) 0 100 200 300 plasma I (kA) Antidrive Drive Off OFCD Start FIG. 1. Time dependences of the plasma current for three different pulses. The dashed curve is for the OFCD drive case, the dotted curve is for the OFCD antidrive case, and the solid curve is for the case with OFCD turned off.