Systems, methods and apparatus for regulating ion energies in a plasma chamber and chucking a substrate to a substrate support are disclosed. An exemplary method includes placing a substrate in a plasma chamber, forming a plasma in the plasma chamber, controllably switching power to the substrate so as to apply a periodic voltage function (or a modified periodic voltage function) to the substrate, and modulating, over multiple cycles of the periodic voltage function, the periodic voltage function responsive to a defined distribution of energies of ions at the surface of the substrate so as to effectuate the defined distribution of ion energies on a time-averaged basis.