Electrostatic shielding in plasmas and the physical meaning of the Debye length

Abstract

This paper examines the electrostatic shielding in plasmas, and resolves inconsistencies about what the Debye length really is. Two different interpretations of the Debye length are currently used: (1) The potential energy approximately equals the thermal energy, and (2) the ratio of the shielded to the unshielded potential drops to 1/e. We examine these two interpretations of the Debye length for equilibrium plasmas described by the Boltzmann distribution, and non-equilibrium plasmas (e.g. space plasmas) described by kappa distributions. We study three dimensionalities of the electrostatic potential: 1-D potential of linear symmetry for planar charge density, 2-D potential of cylindrical symmetry for linear charge density, and 3-D potential of spherical symmetry for a point charge. We resolve critical inconsistencies of the two interpretations, including: independence of the Debye length on the dimensionality; requirement for small charge perturbations that is equivalent to weakly coupled plasmas; correlations between ions and electrons; existence of temperature for nonequilibrium plasmas; and isotropic Debye shielding. We introduce a third Debye length interpretation that naturally emerges from the second statistical moment of the particle position distribution; this is analogous to the kinetic definition of temperature, which is the second statistical moment of the velocity distribution. Finally, we compare the three interpretations, identifying what information is required for theoretical/experimental plasma-physics research: Interpretation 1 applies only to kappa distributions; Interpretation 2 is not restricted to any specific form of the ion/electron distributions, but these forms have to be known; Interpretation 3 needs only the second statistical moment of the positional distribution.

Modeling anisotropic Maxwell–Jüttner distributions: derivation and properties

“…In the case of anisotropic temperature, the Maxwell distribution becomes anisotropic on the kinetic degrees of freedom, which contribute differently in the internal energy of the system (e.g., solar wind: Olsen and Leer, 1999;Feldman et al, 1975;Pilipp et al, 1987;Phillips and Gosling, 1990;Kasper et al, 2002;Matteini et al, 2007;Štverák et al, 2008 -magnetosphere: Pilipp andMorfil, 1976;Renuka and Viswanathan, 1978;Tsurutani et al, 1982;Sckopke et al, 1990;Gary, 1992;Bavassano Cattaneo et al, 2006;Nishino et al, 2007;Cai et al, 2008;Winglee and Harnett, 2016 also see the corresponding formulations in Krall and Trivelpiece, 1973;Livadiotis and McComas, 2014a;Livadiotis, 2015).…”

Debye screening under non-equilibrium plasma conditions

“…It is then even more astonishing that Livadiotis & McComas (2014) arrived at a completely different result when considering the same context and instead of the above relation obtained…”

“…This clarifies how, why, and in which form at all Kappa distributions originate. It becomes evident that according to the understanding of Livadiotis & McComas (2014), the electron temperature of the Kappa distribution function is not κ-dependent, but constant, while in the understanding of the other authors the change from thermal to suprathermal electron populations (i.e., lowering κ e -indices from higher to lower values) also is followed with a corresponding change, that is, an increase, of the electron temperatures. We examine this problem again from a slightly different aspect below.…”

“…Results presented for the Debye screening under nonequilibrium plasma conditions are highly disjunct, controversial, and substantially in conflict with each other (Hansen & Fajans 2015;Meyer-Vernet & Perche 1989;Bryant 1996;Treumann et al 2004;Livadiotis & McComas 2014;Fahr et al 2015). This is the case even though directly connected with highly nonthermal Kappa-type distribution functions f e = f κ e , Debye lengths should in principle be directly calculable.…”

Derivation of the entropic formula for the statistical mechanics of space plasmas

“…On the other hand, the preservation of local correlations among particles creates a conceptual separation of particles in correlation clusters. Debye spheres are correlation clusters that may include up to trillions of particles since space plasmas are weakly coupled (Bryant, 1996;Rubab and Murtaza, 2006;Gougam and Tribeche, 2011;Livadiotis and McComas, 2014). This structure can lead to the additivity of entropy: the entropy of a multi-particle state is the sum of the entropies of all the one-particle states involved.…”