Plasma, Fourth State of Matter, and Magnetic Fields and Electric Fields
There is not necessarily a preexisting magnetic or electric field in a plasma, since the charges can be randomly distributed. Think of plasma as similar to a metallic state conductor -- a sea of mobile electrons (and, of course, ions in plasma, so perhaps it better approximates a semiconductor, with electrons and holes). A plasma in thermal equilibrium, not exposed to an external electromagnetic field, should be uncharged. 

That said, unbalances occur for a number of reasons. For example, electrons are thousands of times less massive and therefore more mobile than ions, so charge separation occurs, leading to a plasma potential.. Lasers can generate a charged plasma, accelerating particles with the wakefield effect.