From the orbit theory to a guiding center parametric equilibrium distribution function

Abstract

Abstract. This work proposes a parametric equilibrium distribution function F eq to be applied to the gyrokinetic studies of the Finite Orbit Width behavior of guiding centers representing several species encountered in axisymmetric tokamak plasma, as fusion products, thermal bulk and energetic particles from Ion Cyclotron Radiation Heating and Negative Neutral Beam Injections.After the analysis of the basic results of orbit theory obtained with a particularly convenient orbit coordinates set, it is shown how the proposed F eq satisfies the two conditions that make it an equilibrium distribution function: (i) it must depend only on the constants of motion and adiabatic invariants, and (ii) the guiding centers must remain confined for suitably long time.Furthermore, the F eq can be modeled, with a proper choice of its parameters, to reproduce the most common distribution functions. A local Maxwellian distribution function is obtained for the thermal plasma in the Zero Orbit Width approximation. For the fusion α particles, F eq can also reproduce the Slowing Down (SD) distribution function. More generally, for supra-thermal particles, when external heatings are present, such as (N)NBI and ICRH, the proposed model distribution function shows similarities with the anisotropic SD and the biMaxwellian distribution functions.F eq can be used to fit experimental profiles and it could provide a useful tool for experimental and numerical data analysis. Moreover, it could help to develop analytical computations for facilitating data interpretation in the light of theoretical models. This distribution function can be easily implemented in gyrokinetic codes, where it can be used to simulate plasma also in the presence of external heating sources.

Orbital spectrum analysis of non-axisymmetric perturbations of the guiding-center particle motion in axisymmetric equilibria

“…Moreover, the Actions, being both canonical momenta and constants of motion, provide an excellent framework for building an equilibrium distribution function, a task that until recently has been known to be problematic Ref. 33.…”

Bayesian derivation of plasma equilibrium distribution function for tokamak scenarios and the associated Landau collision operator

“…The following parametric distribution function has been proposed in Ref. [1] as equilibrium distribution function (EDF) for charged particles in fusion plasmas, representing, e.g., supra-thermal particle distribution produced by additional external heating sources in tokamak experiments:…”

“…Moreover, N , α w , T w , P φ0 , ∆ P φ , λ 0 and ∆ λ are control parameters. In [1], the orbit theory has been described through the constant of motions (COMs) P φ , w, λ, where the canonical momentum P φ , is treated as a spatial coordinate; the same choice is taken also here ‡. Together with (1), the regularized EDF,…”

“…has been proposed in [1] as general plasma EDF for describing populations of particles encountered in many tokamak scenarios. In (3), H(w b −w) is the Heaviside step function which takes into account the presence of a mono-chromatic source of birth energy w b .…”

“…Moreover, it can also represent nearly isotropic equilibria as for the case of Slowing-Down alpha particles and core thermal plasma populations. In [1] it has been proposed a heuristic derivation of f eq whilst, in the present work, a rigorous one is shown based on probabilistic principles and general hypothesis for deriving a class of EDFs which includes also the distribution function (1) and (2). The distribution function, f eq = f eq (P φ , w, λ), in (1) is an EDF because it depends solely on COMs.…”