  A new plasma state has been investigated [C.~Akcay, J.~Finn, R.~Nebel and
D.~Barnes, Phys.~Plasmas $\textbf{24}$, 052503 (2017)], with a uniform applied
axial magnetic field in a periodic cylinder of length $L=2\pi R$, driven by
helical electrodes. The drive is single helicity, depending on
$m\theta+kz=m\theta-n\zeta$, where $\zeta=z/R$ 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 $(m,n)=(2,1)$.
