Correct, nuclei and electrons spiral along the magnetic field lines, and by that, the magnetic field lines are used to exert pressure on the plasma. The magnetic field is applied from the outside, and the strength falls off with distance into the plasma. Inside the plasma, it's the collisions that maintain containment. Neutral atoms (from recombination) may leak out of the plasma.currents running through wires are neutral but the magnetic field still affects them.
im not sure how it works, but i suspect that the positive and negative charges will spiral along the magnetic field lines with opposite senses (CW CCW)