Ion oscillations in a cold positive-ion electron-beam thermal electron plasma

The effective electron temperature Te¿ for ion oscillations in a uniform plasma traversed by an electron beam is Te(1+a)/(1¿a/2ß) where Te is the plasma-electron temperature, and ¿ and ß are the ratios of electron-beam and plasma-electron-number densities and energies, respectively; the speed ¿¿ of ion sound waves is (kTe¿/m+)¿. The drift speed of ions at the corresponding sheath¿plasma boundaries is also approximately a¿.