DS1's engine makes thrust by magnetically charging atoms and then repelling them from the spacecraft. This stream of atoms spewing out the back of the thruster pushes DS1 forward.
Solar power provides the energy.
They are heated and bombarded with electrons until they form a plasma, with electrons separated from the cores of the atoms, which become xenon ions. The positively charged xenon ions move towards the back of the chamber. Once they are between the positive and negative grids at the very back of the chamber, they are electrostatically accelerated away from the positive grid and towards the negative one. Since the push from the positive grid on the positive ions is much greater than the pull of the negative grid towards the positive ions, they shoot past the negative grid and out into space at a high speed. The expelled ions propel the ship forward.