Plasma driven by helical electrodes*

We present a plasma state driven by helically symmetric electrodes $(m,n)$ in the presence of a uniform axial magnetic field in a periodic cylinder[1], with applications as an electrical transformer or for tailoring the current profile in a tokamak or RFP. For strong drive there is a $(m,n)$ state with mean-field current density and flat $q_0 \approx m/n=1$ in the interior. It has large helical flows, a bi-directional parallel current density $\lambda$, and an $O-$ line encircled by all of the field lines. We show a Cowling-like theorem $\langle\eta\lambda B^{2}\rangle=0$ and discuss the relationship with magnetic helicity. The transient stage is discussed. Integration of the current density streamlines is used to quantify primary-to-secondary leakage for the transformer application. Results varying $(m,n)$ the plasma length are presented. Sensitivity studies to (a) boundary conditions, (b) resistivity profile, and (c) electrode shape are presented. Results with finite $(m,n)$ radial magnetic field are introduced, showing high transformer efficiencies. 3D studies of finite length plasmas are presented. [1] C. Akcay, J. M. Finn, R. A. Nebel and D. C. Barnes, "Electrostatically driven helical plasma state", Phys. Plasmas 24, 052503 (2017).