Bohm Criterion of Plasma Sheaths away from Asymptotic Limits

Sheath theory has a central place in plasma physics as its original

formulation coincided with the recognition of plasma physics as a

sub-field in physics and it applies to any plasma bounded by a

material boundary. One of the most celebrated findings in sheath

theory is the so-called Bohm criterion that predicts a threshold, the

so-called Bohm speed, which would set a lower bound for the plasma

exit flow speed at the sheath entrance.

Traditionally, evaluation of Bohm speed from the Bohm criterion

invokes drastic simplification of plasma transport that ignores the

transport physics in the plasma-sheath transition problem. The

established Bohm criterion analysis are also performed in the asymptotic

limit of vanishing Debye length, and hence their applicability becomes

suspect in a realistic plasma.

Here, we drive an expression for the Bohm speed from a set of

anisotropic plasma transport equations. The thermal force,

temperature isotropization and heat flux enter into the evaluation

of the Bohm speed. Away from the asymptotic limit, it is shown

from the simulation results that there exists a plasma-sheath

transition region, where the quasi-neutrality is weakly perturbed,

rather than a single sheath entrance in the asymptotic limit,

so a Bohm speed is predicted for the entire transition region.

By comparison with kinetic simulation results, the Bohm speed model

in our work is shown to be accurate in the sheath transition

region over a broad range of collisionality.

Our analysis can be readily extended for more complicated plasmas,

such as a high-recycling divertor where a strong hydrogen

recirculation loop exists. The resulting Bohm speed is consistent with

the underlying plasma transport model, where atomic processes such as

ionization and ion-neutral friction are considered.