Stationary distribution functions for ohmic Tokamak-plasmas in the weak-collisional transport regime by MaxEnt principle

Abstract

In previous works, we derived stationary density distribution functions (DDF) where the local equilibrium is determined by imposing the maximum entropy (MaxEnt) principle, under the scale invariance restrictions, and the minimum entropy production theorem.In this paper we demonstrate that it is possible to reobtain these DDF solely from the MaxEnt principle subject to suitable scale invariant restrictions in all the variables. For the sake of concreteness, we analyze the example of ohmic, fully ionized, tokamakplasmas, in the weak-collisional transport regime. In this case we show that it is possible to reinterpret the stationary distribution function in terms of the Prigogine distribution function where the logarithm of the DDF is directly linked to the entropy production of the plasma. This leads to the suggestive idea that also the stationary neoclassical distribution functions, for magnetically confined plasmas in the collisional transport regimes, may be derived solely by the MaxEnt principle.

Maximal entropy distribution functions from generalized Rényi entropy

“…The main objective of the our work is to obtain a shortest derivation of the RDF for the charged particle distribution, studied in the previous works [20]- [23]. We mention that by using the classical MaxEnt principle in [23] we obtained new derivation of the RDF studied in [20]- [22].…”

“…The RDF for charged particle distribution, derived from Generalized Maximal Entropy principle 5.2.1 The RDF obtained from classical MaxEnt principle [20]- [23] The reference state studied in [20]- [23] has the form…”

“…where P φ , λ and w are the invariants appearing in the axial symmetric magnetic field variables [20]- [23] Θ is the scale parameter for energy, γ the shape parameter of the gamma distribution that appears in Eq. ( 69).…”

“…In contrast to the case of BS, RE, TE, in the case of GRE, even in the simplest case when the total phase space is a Cartesian product of two smaller spaces, the stationarity condition is expressed by a more complicated functional equation [16], whose solutions has complex algebraic decays. The maximal generalized entropy (GMax-Ent) PDF's, whose study is the object of this article, are interesting because in a series of our previous works [20]- [23] we proved that the reference distribution function (RDF) for charged particle distribution in tokamak can be obtained by maximization of the BSE, subject to scale invariant, algebraically the simplest, restrictions. In order to obtain a better approximation of the PDF of the charged particles in tokamak, in this work we enlarge the family of RDF obtained previously by MaxEnt principle with scale invariant restrictions, by considering RDF's obtained from the maximization of the Generalized Rényi entropy.…”

Data driven theory for knowledge discovery in the exact sciences with applications to thermonuclear fusion

“…Consequently, also any scaling expressions should present the same invariances. Assuming the validity of the assumptions previously cited, the choice of specific dimensionless variables is determined a priori from theoretical considerations and not derived from the data 24 , 25 .…”