I would expect the ion beam to have an angular spread of at least a few degrees. However since the Rogowski coil (NB which is a coiled-coil so not technically a solenoid) will just be slowing down the ions in the direction along the beam, as it slows the beam will spread out further. Until all the parallel motion is extracted from the ions, or they collides with the edge.
The perpendicular ion velocity also increases due to the like charges repelling. So you want the coil long enough & with enough turns to extract enough energy, before the beam blows up significantly. However I suspect you want it short enough that you can let it expand and dissipate the perpendicular component of its energy once safely out the other side.
