Radial transport in bounded cylinders and physics of ``universal'' profiles

Even strong magnetic fields cannot confine electrons radially in a cylinder if the cylinder length is defined by endplates that are not far apart. The sheaths on the endplates will adjust themselves to allow the electron density $n$ to ``follow'' the radial electric field, even though the electrons are actually lost to the ends, not to the sidewall. This nanosecond mechanism allows electrons to follow the Boltzmann relation, even across the B-field. If the plasma is ionized near the wall, the ions will be driven inwards by the resulting E- field, which is scaled to $T_{e}$. Thus, the (weakly magnetized) ions will reach the center faster than at their thermal velocities. When equilibrium is reached, the field is reversed to push the ions outward to the sidewall, their closest escape path. Under these conditions, $n$ is always peaked on axis. A detailed treatment\footnote{D. Curreli and F.F. Chen, Phys. Plasmas \textbf{18}, 113501 (2011).} of this problem yields the surprising fact that the density and potential profiles in equilibrium are independent of neutral pressure and cylinder radius, varying only with $T_{e}$. A simple physical argument shows why this has to be true.