Parametrization of current–voltage characteristics and operation domains of cylindrical emissive probes in collisionless Maxwellian plasmas at rest

Abstract

Important progress has recently been made on the Orbital Motion Theory for cylindrical emissive probes immersed at rest in collisionless and Maxwellian plasmas. However, due to the computational cost of its numerical algorithm, only solutions for specific values of the physical parameters were found, thus preventing its direct application to the interpretation of experimental current-voltage characteristics (I p − V p curves). In this work, and thanks to an analytical analysis of a Jacobian matrix appearing in the algorithm, the computational cost was reduced by a factor in the order of N r , where N r is the number of grid points. This achievement, together with the implementation of parallel programming, allowed to construct a database with more than 18,000 I p − V p curves for a broad range of physical parameters, including the emission level, the probe radius-to-Debye length, and the ion-toelectron temperature ratios. The boundaries in parameter space of the operational regimes of emissive probes, covering both orbital motion limited (OML) and space charge limited (SCL) transitions were computed. A novel OML/non-OML transition for emissive probes operating at low bias was found. The numerical results were used to propose useful analytical laws for the SCL boundary happening at negative bias, the reduction of the emitted electron current due to SCL effects, and the floating potential of emissive probes. The applications of the results to the modeling of low work function tethers and three experimental methods for measuring the plasma potential, i.e. the separation point, the inflection point, and the floating potential techniques, were discussed. The formation of an inverse sheath for strong emission was investigated.

Kinetic analysis of the plasma sheath around an electron-emitting object with elliptic cross section

“…7, the emission of electrons delays the transition into the non-OML regime to higher b p . Such a result, which was previously found for cylinders [24,47], is a consequence of the reduction of the electric field in the proximity of Γ due to the higher density of electrons (see Fig. 3), yielding in turn a reduction of Γ-originated ions.…”

“…For a cylinder (e p = 0), the transition happens for radius around 1.5λ DE [47], but even larger radii do not produce a significant reduction of the ratio. The current ratio drops weakly with b p for low-bias conditions (φ p = −5 in our case), as well as for high bias ones [49].…”

“…Reference [24] contains the details of the numerical code, which has recently been used to create a broad database of current-voltage characteristics for emissive cylinders [47].…”

“…Theoretical results were obtained for non-emitting cylinders, thin tapes and infinite prisms with convex and concave cross-sections in the high bias limit [22,36], and spheroids in the Laplace limit [35]. For electron-emitting cylinders, the OML parameter domain has been found recently [47]. The VP solver allows to revisit previous results, typically based on asymptotic analysis and sensible approximations, and to explore deeper the role of the electron emission.…”

“…The numerical results show that the current emitted by ellipses at moderate bias can be approximated with good accuracy by that emitted by cylinders of radius equal to the semi-major axis, if appropriate dimensionless variables are used. A broad, recently-built database of solutions for electron-emitting cylinders [47] can thus be used for ellipses.…”