Scaling laws for high-density plasmas

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Abstract
The classical ``similarity laws'' for electrical discharges in gases are rederived and shown to apply only to cases where the charge density is low enough so that the only important collisions are with gas molecules and there is no appreciable gas heating. If the charge density is high enough to be well above the transition from free to ambipolar diffusion, then the distribution functions of all the particles, and particularly the charge density, can be scaled by dividing by the neutral gas density N0 at some point in the discharge. The usual similarity laws scale the charge density by dividing by the square of the neutral gas density. These new high‐density plasma scaling laws are shown to apply to the experimental results of the current limit at which striations will appear in argon discharges as reported by two investigators. Here the pressure‐current product was plotted as a function of the pressure‐radius product and found to form one curve over a 4:1 range of tube radii. We believe that these high‐density scaling laws apply to a large group of plasma phenomena. Limitations of the new scaling laws are pointed out in connection with the spontaneous emission of excited states, three‐body collision, magnetic fields produced by the currents in a discharge, the rf shielding effect in a discharge of sufficiently high conductivity, and gravitational effects.

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