Generalization of the Child-Langmuir law to the alternate extraction of positive and negative ions

Using a combined analytical and simulation approach, we investigate positive and negative ion extraction between two electrodes from an ion-ion plasma source. With a square voltage waveform applied to the electrodes, we obtain approximate analytical solutions for the time-averaged extracted current densities, which are given simply by: J(p)(ac) = [alpha - fL root M-p/q(p)V(0)]J(p)(dc), and J(n)(ac) = [(1 - alpha) - fL root M-v/q(n)V(0)]J(n)(dc), where J(ac) is the time-averaged current density, alpha is the square waveform duty cycle, f is the frequency, L is the electrode gap length, M is the ion mass, q is the ion charge, V-0 is the applied voltage amplitude, J(dc) is the dc extracted current density, and the subscripts p and n refer to positive and negative ions, respectively. In particular, if J(dc) is the dc space-charge limited current density, then these equations describe the square waveform generalization of the Child-Langmuir law. (C) 2014 AIP Publishing LLC.