When you have a (rotating) bar, the allowed orbits tend to intersect with each other. This has not effect on the stars, since they're so small relative to the s

When you have a (rotating) bar, the allowed orbits tend to intersect with each other. This has not effect on the stars, since they're so small relative to the space involved that they never collide; but gas clouds are quite large, and they will intersect with each other. The resulting collisions cause them to lose some of their (orbital) energy and sink onto smaller orbits. If I remember correctly, a second effect is that the collisions tend to cause the gas to concentrate/pile up near the leading edge of the bar, which causes an offset between the mass of the stars (making up the bar) and bulk of the gas; the stars end up pulling on the gas in the direction opposite to the orbital motion, and so the gas loses energy and angular momentum, shifting onto smaller orbits. It really has nothing to do with magnetic fields: you readily get this effect in hydrodynamical simulations without any magnetism, and most of the gas in the bar region isn't in the form of plasma anyway (it's primarily a mixture of neutral atomic hydrogen and molecular hydrogen).