Search

We develop a novel Monte Carlo strategy for the simulation of the Boltzmann-BGK model with both low-collisional and high-collisional regimes present. The presented solution to maintain accuracy in low-collisional regimes and remove exploding simulation costs in high-collisional regimes uses hybridized particles that exhibit both kinetic behaviour and diffusive behaviour depending on the local collisionality. In this work, we develop such a method that maintains the correct mean, variance, and correlation of the positional increments over multiple time steps of fixed step size for all values of the collisionality, under the condition of spatial homogeneity during the time step. In the low-collisional regime, the method reverts to the standard velocity-jump process. In the high-collisional regime, the method collapses to a standard random walk process. We analyze the error of the presented scheme in the low-collisional regime for which we obtain the order of convergence in the time step size. We furthermore provide an analysis in the high-collisional regime that demonstrates the asymptotic-preserving property.

International audience; The non-local expression proposed by Luciani-Mora-Virmont is implemented in a one dimensional fluid model for the scrape-off layer. Analytical solutions for heat equation are discussed as well as the impact of sheath boundary conditions on the continuity of the temperature profile. The non-local heat flux is compared to the Spitzer-Härm heat flux for different collisionality. KEYWORDS heat conduction, non-local transport, plasma physics 1 INTRODUCTION At the entrance of the scrape-off layer, the plasma collisionality í µí¼ˆ ⋆ defined as the ratio between the field line length and collision mean free path is found to be of order unity. Despite this low collisionality, the tokamak edge plasma modelling relies mostly on the fluid approach and collisional closures that are theoretically only valid at high collisionality. Departure between Braginskii fluid description and kinetic modelling has been highlighted, particularly an underestimation of temperature gradient by the fluid approach. [1] Several kinetic corrections have been proposed to improve the plasma description at intermediate collisionality. [2-5] In this contribution, we investigate kinetic corrections to the local Spitzer-Härm (Braginskii) closure for the heat flux; more precisely, we focus on applying the non-local expression for the heat flux proposed by Luciani-Mora-Virmont [6] to scrape-off layer physics. In particular, we adapt boundary conditions and implement the non-local expression into a 1D hydrodynamic model for the scrape-off layer.

Achieving high pedestal pressures in H(high)-mode plasmas confined in tokamaks is critical for obtaining fusion burning plasmas in ITER. Recent characterizations of quasi-equilibrium plasma parameter profiles in low collisionality H-mode pedestals in the DIII-D tokamak are briefly summarized. Critical plasma transport properties (large radial electron heat flow, density pinch) that establish the transport barrier structure of the pedestal profiles are identified. The paleoclassical transport model, which naturally includes a density pinch, is shown to provide the minimum electron heat and density transport in the pedestal. Microinstabilities can provide additional plasma transport within and especially at the top of pedestals. Macroscopic peeling-ballooning (P-B) instabilities cause periodic edge localized modes (ELMs) that limit the temporal and spatial growth of the pedestal initially and between ELMs. Externally imposed 3D resonant magnetic perturbations (RMPs) in the pedestal have been used to stabilize P-B modes and suppress ELMs. A magnetic flutter model of plasma transport induced by the 3D RMPs has been developed for low collisionality DIII-D pedestals. Comparisons of it with data on ELM suppression by RMPs indicate it can provide a “diffusivity hill” at the pedestal top that can impede pedestal growth and thereby stabilize P-B modes and suppress ELMs. Finally, transport equations for plasma density, electron and ion pressures and, most importantly, the plasma toroidal rotation frequency (and hence, via radial force balance, the radial electric field) in the presence of plasma transport due to collisional, paleoclassical, microturbulence-induced and 3D field effects are presented. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In SOL-divertor plasmas, a condition on the plasma flow velocity, called the Bohm criterion, is required for the formation of a stable sheath in front of a divertor plate. While, for a single-ion species, the usual analytical procedure gives the criterion as a unique solution for the incident ion flow velocity, for two-ion-species plasmas the procedure results in a relation between the ion flow velocities. We carried out full particle simulations with a one-dimensional particle code PARASOL, and clarified in detail the dependence of the condition for two-ion-species plasmas on collisionality and ions mass (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The retarding field analyzer (RFA) is one of the only widely accepted diagnostics for measuring the ion tem-perature Ti in the tokamak scrape-off layer. An overview of the outstanding RFA performance over ten years of operation in Tore Supra tokamak is given and the validation of Ti measurements is addressed. The RFA measurements in Tore Supra are found to be well reproducible. The ion-to-electron temperature ratio is higher than one at low-to-moderate ion-electron collisionality regime and converges to unity at high collisionality regime (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The drift kinetic equation solver NEO-2 [1] which is based on the field line integration technique has been applied to compute the generalized Spitzer function in a tokamak with finite plasma collisionality. The resulting generalized Spitzer function has specific features which are pertinent to the finite plasma collisionality. They are absent in asymptotic (collisionless or highly collisional) regimes or in results drawn from interpolation between asymptotic limits. These features have the potential to improve the overall ECCD efficiency if one optimizes the microwave beam launch scenarii accordingly (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Stochastic boundaries in fusion devices have been investigated in tokamaks, stellarators and reversed field pinch experiments for many years. However, since edge localized modes (ELMs) have been successfully eliminated in H-mode plasmas at the DIII-D tokamak [1,2] with small, edge resonant magnetic perturbations, they have become a widely investigated topic in tokamaks. In DIII-D stochastic boundaries are produced by coils external to the plasma. The magnetic field there consists of field lines with very different connection lengths, which produces a three dimensional, heterogenous structure of stochastic volume. The most obvious manifestation of the perturbed plasma edge is the strike line splitting observable in heat and particle fluxes, which changes with collisionality. The interaction of the magnetic perturbation and the magnetic equilibrium is of a resonant nature and the structure of the stochastic volume is a strong function of q(95). This is observed as a modulation of e.g. electron temperature as measured by ECE or Thomson scattering. In this work we summarize recent experimental findings on properties of the stochastic boundary in DIII-D. (C) 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Parallel electron heat flux in the SOL is determined via fully kinetic simulations using the one-dimensional particle-in-cell code PARASOL. The heat flux in fluid simulations is usually approximated in the collisional limit by the Spitzer-Harm heat flux qSH and in the collisionless limit by the one-way free-streaming heat flux qFS adjusted by the coefficient αe. Though αe is defined at the collisionless limit, in practice it is used generally and taken to be a constant ∼0.1. We survey the dependence of αe with respect to many plasma parameters: collisionality, source and sink relative position, source model, and sink radiation rate. Increasing radiation and the size of the radiation region generally increases αe. Without Langevin heating and electron radiation, αe is found tobe non-monotonic with collisionality. This effect is traced to the fact that in a collisionless plasma, the electron velocity distribution exhibits a high-energy tail, which implies that use of the one-way free-streaming heat flux is inaccurate. A new treatment for the free-streaming heat flux is proposed, wherein the symmetric bulk electron distribution is ignored, which makes αe ∼ 1 at all radiation rates for moderate and low collisionality. This method does not work for Langevin heating, which maintains a Maxwellian electron energy distribution (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

With the ITER tokamak magnetic confinement fusion is making the decisive step to realize a burning fusion plasma and prepare the basis for a demonstration power plant (DEMO). Despite the advantages of an intrinsically steady state magnetic field and better stability properties, the development of stellarators lags behind by about 1 1/2 device generations, because of the difficulties to realize the desired magnetic field configuration. The goal of the optimized stellarator Wendelstein 7-X is to overcome the principal deficiencies of the stellarator concept and demonstrate its reactor capability, combining sufficiently good thermal and fast ion confinement with reactor relevant s and collisionality under steady state conditions. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Several ASDEX-Upgrade Ohmic shots with different densities and temperatures corresponding to different collisionality regimes at the separatrix were simulated with transport code B2SOLPS5.0. The expression for the parallel viscosity was extended to be consistent with the neoclassical electric field in all collisionality regimes including plateau and banana regimes. It is demonstrated that for all shots in the core region deeper than the viscous layer (of the order of 1cm inside the separatrix) the relation between the radial electric field, parallel velocity, density and temperature gradients is close to the neoclassical one. This is consistent with the results of many simulations performed earlier for the collisional regimes. The contribution from the toroidal velocity, which is generated in the SOL and transported further to the core, to the radial electric field profile is found to be modest and comparable with density and temperature gradient contribution. The simulation results do not reproduce the dependence of the poloidal velocity of the turbulence on the collisionality measured in [1] deep inside the core. On the other hand, the shape of the radial electric field in the separatrix vicinity both inside and outside the separatrix is consistent with the measured poloidal rotation velocity of the turbulence. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In this paper we present results of numerical simulations of nitrogen seeded JET discharges. In particular, we have benchmarked the code against the type III ELMy JET pulses. In addition to recovering the main discharge parameters, the interplay between seeded nitrogen and intrinsic carbon is also reproduced. Predictions for the JET discharges with higher plasma current I-p = 3.5 MA and different input powers (14 80%) and simultaneously reduce both the plasma collisionality and Z(eff). Extrapolation to ITER shows compatibility of strongly radiative plasmas with the power amplification in excess of 10. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Enhanced heat flux to the divertor plates after an ELM crash in H-mode plasmas is a crucial issue for the tokamak reactor. Characteristic time of this heat flux is one of key factors of the influence on the plate. We investigate the transient behavior of SOL-divertor plasmas after an ELM crash with the use of a one-dimensional particle simulation code, PARASOL. Influence of the collisionality and the recycling rate on characteristic times of the fast-time-scale response and of the slow-time-scale response are examined. Fast-time-scale behaviors are affected by collisions, but slow-time-scale behaviors are insensitive to collisions. On the other hand, slow-time-scale behaviors are affected by recycling, but fast-time-scale behaviors are independent of recycling.

Tokamak edge plasma transport in a diverted geometry is studied employing Braginskii type two dimensional transport simulation and drift wave turbulence simulation. The two models are connected through local perpendicular transport coefficients. The basic idea behind is to replace fast time scale, repetitive turbulence vortex dynamics by a diffusion operator. To this end, parameterization of transport coefficients D and X is introduced. The transport is determined by the gradient drives inside the separatrix and non-adiabatic electron response induced by high collisionality in the low temperature open-magnetic-field-line regions.

The ambipolar radial electric field and ion heat flux in the presence of this field are studied using Monte Carlo guiding centre orbit following code ASCOT. These are studied as a function of temperature gradient in different collisionality regimes. Good agreement with the analytic theory is found for heat fluxes in plateau and banana regimes but in Pfirsch‐Schlüter regime sub‐neoclassical heat flux is found for steep temperature gradients. For radial electric field, deviations from analytic theory are significant.

The Spitzer-Harm parallel electron heat conductivity begins to fail even at surprisingly large values of collisionality because the energy squared dependence of the mean free path results in contributions from electrons not satisfying the short mean free path expansion. Self-similar solutions of model problems are employed to demonstrate that exponentially small, non-expandable modifications that cannot be retained in conventional treatments are the cause of the departure of heat transport from its Spitzer-Harm value.

It is shown that the ambipolarity constraint which results from neoclassical transport theory with gyroviscosity and inertia sets lower limits on the edge density and/or temperature and/or Z eff gradients. Toroidal momentum co, respectively counter,-injection reduces, respectively increases these lower bounds. Generally speaking, co, respectively counter,-injection increases, respectively reduces, the rotation velocities. The theory has so far been developed for the high collisionality regime only.

The Ergodic Divertor of TORE SUPRA induces a stochastic layer at the plasma edge by creating a resonant magnetic perturbation which destroys the magnetic surfaces. A radial electric field directed outwards is then established to confine the electrons along the open magnetic field lines. This electric field tends to deconfine ions. One may then expect that it strongly influences the neoclassical ion transport. We use a variational principle of minimum entropy production to study the transport of impurity ions in the stochastic layer. In low collisionality regime, a decontaminating outwards flux of impurity ions is found, contrasting with the neoclassical inwards flux which produces the deleterious accumulation of impurity ions in the nH profile.

Neutrals at the edge of tokamaks can influence confinement by altering the radial electric field and toroidal plasma flow velocity through charge exchange and ionization interactions when the high diffusivity of the neutrals results in neutral viscosity dominating over ion neoclassical and turbulent viscosities [1-5]. We find that the flow and electric field are very sensitive to the poloidal location of the neutrals and the ion collisionality [6,7]. These predictions are consistent with differences observed on MAST between measured toroidal flows for inboard and outboard gas puffing, and may also explain observations indicating that inboard puffing allows easier H mode access [8]. In particular, we find that the inward directed radial electric field and counter-current directed outboard toroidal flow velocity in a collisional or Pfirsch-Schluter edge plasma tend to be larger if the atoms are concentrated on the inboard side rather than on the outboard side [6,7] consistent with the MAST results and suggesting that the flow shear introduced by the limited penetration of the neutrals and the radial variation of the ion temperature gradient suppresses edge turbulence and plays a role in forming the edge transport barrier. The ion temperature gradient terms enter because ion heat flow modifies the neutral viscosity via charge exchange. The results are found to be relatively insensitive to neutral collisionality [4], which tends to cause up to order unity changes in amplitudes but not changes in direction. More importantly, the results are found to be sensitive to plasma collisionality [7] because of the important role played by ion temperature gradient terms as in standard neoclassical theory. In the case of banana regime ions and collisional neutrals [7], inboard puffing reduces the counter-current rotation, while the radial electric field always remains inward. Consequently, if there is a narrow collisional layer separating the separatrix from the pedestal as in Alcator C-Mod, then this effect will further shear the flow. However, for banana regime ions the largest outboard toroidal flow is obtained for outboard puffing and is in the counter-current direction suggesting that outboard puffing might be more effective in suppressing edge turbulence and generating an edge transport barrier in tokamaks which remain in the banana regime all the way to the separatrix (assuming no other source of flow shear). Finally, impurities affect the size of the flow and electric field; increasing the effect in the Pfirsch-Schluter regime and decreasing it when the ions are in the banana regime [7]. These results suggest that flexible neutral fueling is desirable since it may allow some external control over the tokamak edge and overall performance. In spite of any obvious source of momentum input, axisymmetric tokamak plasmas rotate toroidally. One mechanism causing the edge plasma to rotate can be summarized as follows. The magnetic field introduces a preferred direction. It breaks toroidal symmetry by requiring a Pfirsch-Schluter heat flux with a preferred toroidal direction in order to satisfy the energy balance equation. The heat flow is due to the combined poloidal and toroidal magnetic field there is no momentum input from magnetic fields. Because of charge exchange the neutral viscosity contains ion heat flow terms as well as the standard ion particle flow terms. These heat viscosity terms enable neutral atoms to transfer angular momentum between otherwise stationary flux surfaces. If the plasma did not interact with a wall there would be no net momentum transfer because of angular momentum. However, the plasma and neutrals do exchange momentum with the vessel wall, by ion losses and recycling, so