Limits of validity for orbital-motion-limited theory for a small floating collector

Abstract

The orbital-motion-limited (OML) theory has been widely used to calculate the ion response to a charged grain immersed in plasma. The theory assumes there are no potential barriers preventing plasma ions from reaching positiveenergy points in phase space. However, Allen et al. [J. Plasma Phys. 63, 299 (2000)] have recently shown that for any finite-size negatively charged dust grain in a Maxwellian plasma, there are always potential barriers sufficient to exclude some ions. We calculate the magnitude of the potential barriers, and determine which ions are subject to barriers. The OML theory is shown to become exact in the limit of small grain size, and to be very accurate in calculating ion current to the grain for typical conditions pertinent to dusty plasma. Thus OML theory is well justified in calculating the floating potential. However, we find that potential barriers can influence the shielding of the potential at r ≈ λ D under some conditions, especially large grams, high plasma density, and small T i /T e .

Orbital-motion-limited theory of dust charging and plasma response

“…The usefulness of OML charging theory traditionally lies with its surprisingly good agreement with OM on dust potential [16][17][18][19]26 . With the new OML formulation that is able to calculate dust charge and plasma reponse, it is an important next step to carry out a detailed comparison of the OML dust charge prediction with OM theory for a range of dust sizes.…”

“…22 that OML theory can not predict the dust charge, despite its success on dust potential as re-affirmed in Ref. 16,18 .…”

“…In the 1960s, Al'pert et al 14 and Laframboise 15 completed the current formulation. The OML theory is known to predict accurately the dust potential for a small 16,26 and not so small dust grain [17][18][19] , despite its simplifying assumption on collisionless ion orbit that misses the absorption radius effect away from a) Electronic mail: xtang@lanl.gov b) Electronic mail: delzanno@lanl.gov the dust surface 20,21 . Surprisingly, the existing formulation can not be used for predicting the plasma response, namely solving the plasma potential φ, as shown in Allen et al 22 .…”

Basic Processes in Complex (Dusty) Plasmas: Charging, Interactions, and Ion Drag Force

“…The transition from the DH form to the long-range asymptote (20) occurs at about the location where these two forms are equal [77], i.e. at…”

Particle Methods for Nonequilibrium Hypersonic and Plasma Flows

“…In particular, the particle charging and shielding is an unsolved problem in complex plasmas. The most used approach is the Orbital Motion Limited (OML) theory [16,17]. It claims that: (a) the particle surface potential is independent from the particle size and gas pressure; (b) the dust charge d Q is linearly dependent from the dust radius d r ; (c) the dust charge is independent from gas pressures P. The most accepted electric potential distribution around the particle is the Debye-Hückel (DH) form:…”