They cease to be elements when they lose all their electrons. Easy enugh for hydrogen. They are just undefined pieces of nuclear material fusing and fissioning freely and happily. There is no chemical reaction then, so no chemical elements. It's just plasma. Ions is an inbetween state where you can get the elements back again with ordinary electrical interactions. Right, plasma is a fourth state of matter, no elements.
Thus you have a bunch of charged particles going around. Electrons, protons, deuterons, a few tritons, alphas (helium nucleii), and heavier elements with maybe much of their electrons stripped off due to the high temperature. So when you get such charged particle currents (convection anyone?) you get magnetic fields.