Geometric scalings for the electrostatically driven helical plasma state

A new plasma state has been investigated [Akcay et al., Phys. Plasmas 24, 052503 (2017)], with a uniform applied axial magnetic field in a periodic cylinder of length L = 2 π R, driven by helical electrodes. The drive is single helicity, depending on m θ + k z = m θ − n ζ, where ζ = z / R and k = − n / R. For strong ( m , n ) = ( 1 , 1 ) drive, the state was found to have a strong axial mean current density, with a mean-field safety factor q 0 ( r ) just above the pitch of the electrodes m / n = 1 in the interior. This state has possible applications to DC electrical transformers and tailoring of the current profile in tokamaks. We study two geometric issues of interest for these applications: (i) scaling of properties with the plasma length or aspect ratio and (ii) behavior for different helicities, specifically ( m , n ) = ( 1 , n ) for n > 1 and ( m , n ) = ( 2 , 1 ).