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Tungsten (W), a promising candidate as divertor plasma facing material in magnetic fusion devices, is anticipated to promptly redeposit when sputtered or evaporated from surface due to its small ionization energy and long gyro radius. Using an artificial factor for the reaction cross sections, effects of ionization lengths to the re-deposition rate was studied by a newly developed particle-in-cell code. Treating numbers of particles in a super particle, electric charge, and mass as particle variables in the code, a special scheme for ionization and recombination was developed and used for the calculation. Simulations on W test particles with imaginary properties (neglecting the electric force) revealed the effects of ejection angles. Simulations with secondary electrons from surface showed that the sheath potential is weakened and the re-deposition rate becomes small. It was found that the multi-ionization as well as the ionization mean-free-path influences the re-deposition rate in both simulations. (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Particle-in-cell (PIC) simulations are the very powerful method to understand physics of edge plasmas in fusion devices. Poisson solver with a regular grid in a rectangular vessel is very fast, but it cannot simply be applicable to simulations in complicated divertor configuration. In this paper, a simple and fast Poisson solver with arbitrary boundary shape and condition for PIC simulation is proposed. Boundary points are essential for this Poisson solver, on which the charge density is appropriately given and the boundary condition is satisfied. For particle simulations in the open system, it is necessary to distinguish whether a traced particle moves freely or hits the wall boundary during a time step. A new method for PIC simulation to discriminate a particle position before the boundary or beyond the boundary is also presented. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Simulations with an integrated code TOPICS-IB showed that a small pellet can significantly reduce the ELM energy loss by penetrating deeply into the pedestal and triggering high-n ballooning modes localized near the pedestal top, with conditions; the injection from the low-field-side with a speed fast enough to approach the pedestal top when the pedestal pressure is about 95% of natural ELM onset. The effectiveness of the above suitable conditions of pellet injection for ELM pacing has been confirmed by JT-60U and then ITER simulations. The pellet particle content required for ELM pacing is larger for the pedestal plasma with higher density and farther from the stability boundary of ideal ballooning mode near the pedestal top. For an ITER standard scenario, the required pellet particle content is about a few % of pedestal particle content, which gives the physics background to the present design value. Simulations also showed that fueling pellets can be injected from the high-field-side just after ELM pacing pellets without disturbing the pacing. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The simulation study of nonlocal transport from edge to core in tokamak plasmas is performed using the 4-field reduced MHD model. A toroidally-elongated cylindrical particle source is applied in the plasma edge, after saturation of the resistive ballooning turbulence is attained. After a short time, the source is switched off and plasma response is investigated in detail. The nonlocal transport appears at the location far from the edge source. It is found that the particle source induces (0,0) and (±1, 0) modes of density fluctuations, where (m, n) indicates the set of poloidal mode number m and the toroidal mode number n. These modes interact with each other by the nonlinear and/or toroidal couplings. The symmetry of (±1, 0) modes breaks after switching-off the source and the formation of the spiral structure with poloidal rotation is observed, which yields a connection between core and edge regions. In this simulation, the convective cell mode such as (1,0) mode contributes the nonlocal transport. The simulation result indicates that two dimensional transport plays an essential role to produce the nonlocal transport. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The Monte-Carlo (MC) approach has a lot of flexibility in impurity transport modeling in the SOL and divertor region. However, in the divertor plasma simulation with the noble impurity seeding, characteristic time of the impurity transport especially in the sub-divertor chamber is long because the MC calculation of the impurity gas transport can be finished only by exhaust. The impurity MC calculation for such long exhaust processes is difficult in a series of the iterative calculation of a suite of integrated divertor codes SONIC. In order to overcome such a problem, a backflow model has been developed. Amount of the backflow flux from the sub-divertor chamber to the divertor region is evaluated in advance, and then simulating impurity flux is injected from the exhaust slot to the divertor region like a backflow. By this model, the MC calculation time is reduced significantly and iterative calculation of SONIC becomes possible within a reasonable calculation time. As a demonstration, the SONIC code with the backflow model has been applied to investigation of power handling in JT-60SA divertor. The SONIC simulation showed that low divertor heat load (< 10 MW/m2) with the low SOL density (< 1.5 × 1019m–3), which is required in the full non-inductive current drive scenario, was achieved by the Ar gas puffing of 0.86 Pa m3/s. (© 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)

We have developed a self-consistent integrated simulation model of core and scrape-off-layer (SOL)/divertor transport. This model enables the user to investigate operational scenarios with compatible high-confinement core plasmas and detached divertor plasmas. A 1.5D core code TOPICS-IB and a 2D divertor code SONIC are successfully coupled using a Multiple Program Multiple Data parallel computing system. This integrated code, which can include Monte-Carlo models for neutrals and impurities, provides efficient plasma/neutral simulations. The dynamic simulation for the L/H transition in JT-60SA is carried out by this integrated code using a current-diffusive ballooning mode (CDBM) transport model that includes the E×B shearing effect. The impact of SOL/divertor transport on the L/H transition is studied (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Power handling in the divertor is one of the most important issues for fusion tokamak reactor design. In this study, the effect of the divertor leg length on power handling in the SlimCS DEMO reactor is investigated for future divertor design. Simulation with the SONIC code suite shows enhancement of recycling in the outer divertor region due to effects of the long divertor leg and the deep V-shaped corner. As a result, the ion and electron temperature at the outer divertor significantly decreases. In addition, the peak of the Ar impurity radiation, which is located close to the outer divertor target in the standard divertor geometry, moves upstream. The former effect decreases the heat load to the outer divertor due to ion conduction and convection, while the latter reduces the heat load due to the impurity radiation. The peak of the total heat load on the outer divertor decreases by about 30 % (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

An accurate calculation of heat load on the divertor plates in a tokamak must take into account kinetic effects, present when the electron velocity distribution function (EVDF) in the plasma column departs from a thermal distribution. In this work PARASOL-1D, a particle-in-cell code with a Monte-Carlo binary collision model, is used to find and explain the electron heat flux-limiting factor αe and the heat transmission coefficient (HTC) γe in the complex SOL. We develop and test two simple models for these kinetic factors that take as input the temperature of the SOL and the temperature of the electrons striking the divertor plates. Both models assume a piecewise EVDF, with a symmetric bulk electron population and a high-energy tail of electrons moving only in the direction of the nearest diverter plate. The model EVDF are fit to the simulation-derived EVDF by allowing the variables for the densities and temperatures in the bulk and tail to vary independently. The block model, which assumes a bulk population of infinite parallel temperature in the bulk, is found to reproduce the kinetic factors for a wide range of conditions in the complex SOL much better than both the classical and Gaussian models (© 2012 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The accumulation process of high-Z impurity in toroidal rotating tokamak plasma is investigated. A new inward pinch of high-Z impurity due to the ionization/recombination processes is derived using an analytic model. This inward pinch is driven by the large deviation of a drift orbit from a magnetic surface and the resultant variation of the charge state along the drift orbit. The pinch velocity increases with increasing toroidal rotation speed in both the co-direction and the ctr-direction. The inward pinch expected by the analytic model is really observed in the numerical simulation using the IMPGYRO code (© 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)

The plasma flow in the scrape-off layer (SOL) plays an important role for the control of heat and particle including impurity in magnetic fusion reactors. SOL flow patterns have recently been studied by the particle simulations, and the effects of finite-orbit-size of ions are found to be essential for the flow-pattern formation [Takizuka et al., Nucl. Fusion 49, 075038 (2009)]. Based on these simulation results, a new model of the edge plasma flow is developed by introducing the “ion-orbit-induced flow” to the fluid equations. A tokamak plasma is divided into three regions; core region, transition layer and SOL region. The “ion-orbit-induced flow” is modeled by separating untrapped part and trapped part, and by taking account the collision effect and poloidal distribution. The “ion-orbit-induced flow” becomes large at the edge region (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The effect of the pressure profile on the energy loss caused by edge localized modes (ELMs) has been investigated by using an integrated simulation code TOPICS-IB based on a core transport code with a stability code for the peeling-ballooning modes and a transport model for scrape-off-layer and divertor plasmas. The steep pressure gradient inside the pedestal top is found to broaden the region of the ELM enhanced transport through the broadening of eigenfunctions and enhance the ELM energy loss. The ELM energy loss in the simulation becomes larger than 15 % of the pedestal energy, as is shown in the database of multi-machine experiments. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

In order to understand the particle pumping on JT-60U, we analyze the roles of atomic and molecular processes using SOLDOR/NEUT2D code. A case of short strike point distance shows that most of neutrals produced on the targets go toward the exhaust slot directly. Whereas, neutrals are scattered in the spherically at random for the long distance case by collision processes and a few of them go toward the slot. It is clarified that the incident neutrals to the slot at low ne/high Te divertor plasma condition are dominated by atoms. Those at high ne/low Te condition are dominated by molecules due to elastic collision. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of oblique magnetic field on release condition of a spherical dust particle from a plasma-facing vertical wall is studied analytically. The magnetic pre-sheath and the Debye sheath are coupled to obtain the plasma quantities and the electric field at the wall, which are necessary to analyze the release condition. It is clarified that for the deeper potential drop inside the Debye sheath than the floating one the critical radius for release increases as the magnetic field approaches parallel to the wall. The smaller dust than the critical one can be released from the wall. On the other hand in the case of the shallower potential drop the critical radius disappears at some angle of the oblique magnetic field. From this analysis we find that the size of the released dust particle can be controllable by adjusting the plasma parameters such as plasma density and temperature as well as biasing the wall potential. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Taken impurity radiation and momentum loss in the divertor region into consideration, the applicability of Core-SOL-Divertor(CSD) model to the divertor detachment is investigated. Three solutions for the low recycling state, the high recycling state and the detached state can be obtained from the CSD model. The dependence of the ratio of the decay length for the density (Δn) and temperature (ΔT) in the SOL region is also examined, and it is found that Δn/ΔT ∼ T0.5s scaled by the SOL temperature (Ts), which is based on the experimental data, has a good potential to reproduce B2-EIRENE results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A simulation study of the divertor for JT-60SA is discussed in both double-null (DN) and single-null (SN) configurations. In the DN case, the transition of peak heat load on the targets and divertor plasma states from CDN (connected double-null) to DDN (disconnected double-null) are shown in the simulation. The radiative cooling power in the divertor plasma is discussed in this study. The carbon impurity generated by the sputtering on the divertor target is included in the simulation. In the gas puffing cases of fueling gas (D2) and impurity gas (Ne), the reduction of heat load is confirmed consistently with increasing the radiative cooling loss power in the diverter plasma. The loss power and the distribution of radiative cooling in the divertor plasma are studied in this paper. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The dynamics of SOL-divertor plasmas after an ELM crash is studied with a one-dimensional particle simulation code, PARASOL. The ELM crash occurs off-centrally in the SOL region, and the ELM heat flux to the near divertor plate and that to the far divertor plate become asymmetric. The peak heat flux to the near plate is larger as compared to the far plate. The asymmetry in the peak heat flux increases with the connection-length ratio. The imbalance in the heat deposition, however, is small. The radial transport loss of ELM flux creates the asymmetry in the heat deposition, but the imbalance is still not large even for the large radial transport loss rate. The electron heat flux to the far plate brought by the SOL current is one of the causes of a small imbalance in the heat deposition. Another cause is the asymmetric SOL flow and its convective heat flux, whose stagnation point stays for a long period near the ELM crash location. (© 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.

The effect of the gravitational force on release conditions of a spherical dust particle from a plasma-facing wall is studied by one-dimensional analysis. For release of the dust, where the gravitational force is directed toward the wall, the strong enough electric field is required and these exists the threshold wall potential, which does not depend on the plasma quantities, but the shape of the dust particle. At the deeper wall potential than the threshold, we found the critical dust radius for release, where the dust smaller than the critical one is released by the repulsive electrostatic force. The gravitational force decreases the critical radius of the release. In the case of the gravitational force directed from the wall, the dust particle is released by the gravitational force even if the applied potential is shallower than the threshold one. From this analysis we found that the size of the released dust particle is controllable by adjusting the plasma parameters such as plasma density and temperature as well as biasing the wall potential.

Dynamics of dust particles in a divertor plasma is simulated using numerical solutions of dust momentum and charging equations in an electrostatic sheath and an ionizing presheath, where an electrostatic force and a drag force due to absorption of plasma ions are taken into account. Spatial distributions of plasma parameters in a divertor are obtained with particle simulations including ionization by electron-impact. We found that the critical dust radius exists. Dust particles with a larger radius than this critical one are incapable to come off a divertor plate because the ion drag force is stronger compared to the electrostatic force. Control of the plate potential can suppress the dust motion from the plate. The radii of heavy dust particles are classified with respect to equilibrium positions. Considering dust particles started at the plate with radii smaller than the critical one, two types of dust motion were found. Dust particles with the first type of motion come back to the plate before approaching their equilibrium positions. The second type of motion is presented by smaller dust particles which oscillate around their equilibrium positions.

A review of the present status of 2-D fluid codes for the simulation of the boundary plasma in tokamaks has been given in this paper. The major physics issues contained are: (1) plasma and impurity transport model, (2) neutral gas transport model, and (3) atomic/molecular data base. Example results of the simulation of gaseous divertor in ITER (EDA) are also shown to make the discussions clear.

Numerical simulation of the behavior of carbon impurity for the JT-60U divertor experiment has been carried out. Two approaches are examined for the impurity model: (1) a full charge state model and (2) a single average ion model. The full model simulates fairly well the power loss due to the impurities. The amount of power loss obtained by the single average ion model disagrees with that of the full model.