Generalization of the Child-Langmuir law to the alternate extraction of positive and negative ions
- Laboratoire de Physique des Plasmas, CNRS, Sorbonne Universités, UPMC Univ Paris 06, Univ Paris-Sud, Ecole Polytechnique, 91128 Palaiseau (France)
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{sub p}{sup ac}=[α−fL√((M{sub p})/(q{sub p}V{sub 0}) )]J{sub p}{sup dc}, and J{sub n}{sup ac}=[(1−α)−fL√((M{sub n})/(q{sub n}V{sub 0}) )]J{sub n}{sup dc}, where J{sup ac} 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, V{sub 0} is the applied voltage amplitude, J{sup dc} is the dc extracted current density, and the subscripts p and n refer to positive and negative ions, respectively. In particular, if J{sup dc} is the dc space-charge limited current density, then these equations describe the square waveform generalization of the Child-Langmuir law.
- OSTI ID:
- 22407951
- Journal Information:
- Physics of Plasmas, Vol. 21, Issue 12; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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