Kinetic Particle Simulation Study of Parallel Heat Transport in Scrape-off Layer Plasmas over a Wide Range of Collisionalities

Abstract

Fluid models are not generally applicable to fusion edge plasmas without external provision of kinetic factors: closure parameters and boundary conditions inside the sheath region. We explain the PARASOL-1D simulation, a particle-in-cell code with a binary collision Monte-Carlo model, and use it to determine four kinetic factors commonly needed in fluid codes. These are the electron and ion heat flux limiting factors, α e and α i , the ion adiabatic index, γ A , and the electron and ion temperature anisotropy, T || /T ⊥ . We survey these factors over a wide range of collisionalities and find that, as predicted, the conductive heat flux is accurately described by the Spitzer-Härm expression in the collisional limit and asymptotes to a constant value in the collisionless limit. However, unique behavior occurs in the weakly collisional regime when the ratio of the mean free path to connection length is 0.1 < λ mfp /L || < 10, when the SOL is between the conduction-and sheath-limited regimes. We find that α e can peak, becoming larger than the collisionless limit, γ A is less than unity, and only the ions are anisotropic. The effects of electron energy radiation and Langevin heating are explored. Finally, the strong deviations of the energy distribution function from Maxwellian in the weakly collisional and collisionless regimes are explained.

Study of mirror effect on scrape‐off layer‐divertor plasma based on a generalized fluid model incorporating ion temperature anisotropy

“…For the ion‐conductive heat fluxes, q i, ∥ = q i, ⊥ = 0 is assumed for simplicity in this study. The electron‐conductive heat flux, on the other hand, is estimated by a harmonic average of the Spitzer–Härm heat conduction and the free‐streaming heat flux like q e = (1/ + 1/ α e ) −1 , where the heat flux‐limiting factor of electron is set to be α e = 0.2 …”

“…Equation is equivalent to the Braginskii model . For δp i , the following viscous flux approximation is usually used: where the parallel ion viscosity η i is usually estimated in order to take kinetic effects into account as follows: …”

“…The electron-conductive heat flux, on the other hand, is estimated by a harmonic average of the Spitzer-Härm heat conduction q SH e = − SH e ( T e ∕ s) and the free-streaming heat flux q FS e = e √ T e ∕m e like q e = (1/q SH e + 1/ e q FS e ) −1 , where the heat flux-limiting factor of electron is set to be e = 0.2. [17] Here, we regard the third terms in the left sides of Equations 2-4 as the mirror effect terms. If we introduce nT i and…”

“…where the parallel ion viscosity i is usually estimated in order to take kinetic effects into account as follows: [17] (…”

“…Equation 17 demonstrates that the parallel gradient of M (dM/ds) depends inversely on the parallel gradient of B (dB/ds) up to whether the flow is subsonic or supersonic. In diverging field cases (dB/ds < 0), dM/ds becomes positive because the flow is supersonic.…”