Proceedings of the Physical Society · 1959 · 268 citations · 8 references
EngineeringPhysicsGlow DischargeFluid MechanicsPlasma TransportApplied PhysicsWall PotentialApplied Plasma PhysicBasic Plasma PhysicMagnetohydrodynamicsTransport PhenomenaPlasma PhysicsPlasma BoundaryStable Plasma-sheath BoundaryMultiphase FlowGas Discharge Plasma
Using the derived criterion, the authors analyze the collision‑free Tonks–Langmuir model to determine boundary conditions at the plasma sheath. The study analytically solves the low‑pressure plane‑symmetric plasma equation, yielding closed‑form expressions for ion mean velocity, mean square velocity, and wall potential, and establishes a general, energy‑distribution‑independent criterion for a stable plasma‑sheath boundary that refines Bohm’s original condition and agrees with experimental data.
It is shown that the low pressure plane symmetric plasma equation, using the collision-free model of Tonks and Langmuir, can be solved analytically. Simple expressions are obtained for the mean velocity and the mean square velocity of the ions, and for the wall potential with respect to the plasma. The conditions for the formation of a stable plasma-sheath boundary are briefly examined and a general criterion is obtained without considering any specific mechanism of ion transport. No assumptions are made regarding the energy distribution of the ions, and the result is therefore a refinement on Bohm's original criterion which was derived by assuming a monoenergetic ion flux. With the aid of the criterion developed in the present treatment conclusions are then drawn in the case of the collision-free model regarding conditions applying at the plasma boundary. The experimental results are found to be consistent with these theoretical conditions.
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A General Theory of the Plasma of an Arc
Lewi Tonks, Irving Langmuir · Physical Review · 1929 · 970 citations
Potential Distribution, First Order Correction, Engineering +10