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

2014 
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: Jpac=[α−fLMpqpV0]Jpdc, and Jnac=[(1−α)−fLMnqnV0]Jndc, where Jac is the time-averaged current density, α 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, V0 is the applied voltage amplitude, Jdc is the dc extracted current density, and the subscripts p and n refer to positive and negative ions, respectively. In particular, if Jdc is the dc space-charge limited current density, then these equations describe the square waveform generalization of the Child-Langmuir law.
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