Collisional Edge Plasma Research Articles

Recent progress in the design of the K-DEMO divertor

Abstract The preliminary conceptual design of the Korean fusion demonstration reactor (K-DEMO) with a major radius of 6.8 m and the fusion power of 2200 MW has been studied since 2012. The overall configuration of the K-DEMO divetor system based on the ITER-like water-cooled tungsten technology is a double-null type symmetric divertor subdivided into 32 toroidal modules for the vertical maintenance. A detached divertor scenario with impurity seeding was considered as the primary approach for the power exhaust to reduce the peak heat flux lower than the engineering limit of 10 MW/m2. The power exhaust performance at the scrap off layer was estimated by using UEDGE-2D code, a two-dimensional fluid transport code for collisional edge plasma and neutral species like N, Ne, and Ar. Particle and heat flux on inboard and outboard divertor targets were calculated for the detached cased depending on parameters such as the impurity seeding rate, pumping rate, and the pedestal density. On the other hand, a magnetic solution like X-divertor, snowflake divertor, and super X-divertor to expand the plasma wet area was considered for K-DEMO since the detached divertor increasing a radiation fraction by impurity seeding might be able to be unstable. However, the extremely high current of poloidal coils was required more than the engineering limit, 20 MA, to form magnetic field lines for the alternative divertors. Based on the physical calculation of the edge plasma, engineering analyses were carried out to find out the thermal and structural reliability. The thermo-hydraulic analysis confirmed thermal stability, whether all comprising materials are operating within their allowable temperature windows when the case of the peak heat flux is set to 10 MW/m2 on the outboard divertor target. The response surface optimization method derived two optimal design candidates employing two kinds of heat sink materials, respectively: the reduced activation ferritic martensitic (RAFM) steel and CuCrZr alloy. The drawbacks and merits of the two materials were definite. The optimal design with applying RAFM steel was vulnerable to withstand thermal and mechanical loads since low thermal conductivity caused too thin thickness of the heat sink. On the other hand, the CuCrZr alloy has critical drawbacks in terms of activation and radioactive waste despite its high thermal conductivity. Meanwhile, preliminary electromagnetic (EM) analysis was carried out to estimate the EM loads caused by the abnormal behaviors of plasma since EM loads are one of the most critical external loads for designing a DEMO divertor.

Bifurcation behaviour of rotation velocities in collisional edge plasma with steep gradients

Rotations in both poloidal and toroidal directions of a tokamak edge plasma have important interactions with various other plasma phenomena including plasma stability and transport. Solutions for rotation velocities were studied, using differential equations comprising the ambipolarity constraint and the parallel momentum balance equations of the revisited neoclassical theory, with the corrected contribution also from the gyro-viscosity tensor. Temperature and density profiles with realistic pedestal forms were considered given and controlled parametrically. The similarity of this equation system to reaction–diffusion equations was utilized in the numerical simulation and the study of critical points on the bifurcation diagrams. It was found that the steepness of the density and temperature gradients has important effects on the rotation stability and on its bifurcative behaviour.

An intrinsic source of radial electric field and edge flows in tokamaks

We propose a new mechanism for radial electric fields and edge flows in tokamaks that will also serve as an intrinsic momentum source in systems without an up–down symmetry. An essential feature of toroidal plasmas is that charge-dependent ∇B and curvature drifts would lead to a vertical polarization of the discharge if it were not for the Pfirsch–Schlüter currents that neutralize the resulting charge separation. However, in the presence of collisions, there is a residual vertical electric field that drives an E × B flow in the direction of increasing major radius, regardless of the orientation of the fields and currents. This flow is excluded from the hot core and is localized to the more collisional edge plasma. It has many features in common with the edge flows observed in tokamaks such as C-Mod. In an up–down symmetric geometry it carries no net toroidal angular momentum; however, its viscous interaction with asymmetric boundaries leads to a net momentum input to the plasma. Both this momentum input, and the residual vertical electric field, the source of these flows, may play an important role in the ∇B direction-dependence of the power threshold for the L–H transition.

Effect of poloidal density variation of neutral atoms on the tokamak edge.

Neutral atoms in the tokamak edge affect the electric field and plasma flow through charge exchange. Here, it is shown that these effects depend sensitively on the poloidal location of the atoms. It is found that the radial electric field and toroidal flow velocity in a collisional edge plasma are largest if the atoms are concentrated on the inboard side. This feature may explain MAST and COMPASS-D observations indicating easier H-mode access for inboard gas puffing. The results suggest an external means of controlling the toroidal flow and radial electric field and their shear, and have motivated further MAST measurements appearing to support the predictions.

Experimental study on highly collisional edge plasmas in W7-AS island divertor configurations

Abstract Edge plasma scenarios in island divertor configurations (‘natural’ magnetic islands intersected by targets) are studied by comparing data from moderate to high density NBI discharges with 3D code (EMC3/EIRENE) results. The data strongly indicate that high recycling with significant particle flux enhancement was achieved in this geometry. But, plasma pressure losses towards the targets are relatively strong, and high recycling sets in only at n e > 10 20 m −3 . The respective density enhancement in front of the targets is moderate (up to a factor of about three relative to the upstream density). These scenarios are also in basic agreement with B2/EIRENE code predictions. At n e > 1.5 × 10 20 m −3 detachment seems to develop. Improvements are expected from additional coils controlling the field line pitch inside the islands, and from optimized targets which will better focus recycling neutrals into the islands. Both are in preparation.

Experimental study on highly collisional edge plasmas in W7-AS island divertor configurations

Edge plasma scenarios in island divertor configurations (‘natural’ magnetic islands intersected by targets) are studied by comparing data from moderate to high density NBI discharges with 3D code (EMC3/EIRENE) results. The data strongly indicate that high recycling with significant particle flux enhancement was achieved in this geometry. But, plasma pressure losses towards the targets are relatively strong, and high recycling sets in only at n e > 10 20 m −3 . The respective density enhancement in front of the targets is moderate (up to a factor of about three relative to the upstream density). These scenarios are also in basic agreement with B2/EIRENE code predictions. At n e > 1.5 × 10 20 m −3 detachment seems to develop. Improvements are expected from additional coils controlling the field line pitch inside the islands, and from optimized targets which will better focus recycling neutrals into the islands. Both are in preparation.

Tokamak Edge Transport Theory

AbstractKinetic equations commonly used to study the plasma core of a tokamak do not allow a balance between parallel ion streaming and radial diffusion and are, therefore, inappropriate in the plasma edge. Standard core tokamak transport orderings allow large divergence‐free flows in flux surfaces, but only weak radial flows. Alternate orderings are required in the edge region where radial diffusion must balance large parallel ion flows to divertor target plates or limiters. Similarly, core transport formulae cannot be extended to the edge region without qualitative alteration. Here we address the necessary changes by considering a large parallel flow ordering appropriate for the scrape‐off layer of a tokamak. By deriving and solving a novel kinetic equation, we construct distinctive transport laws for an impure, collisional edge plasma. We find in particular a surprising form for parallel transport in the scrape‐off layer, in which the parallel flow of particles (and heat) are driven by a combination of the conventional gradients, as well as viscosity terms and new terms involving products of radial derivatives of the parallel mean velocity with density and temperature gradients. The new terms are not relatively small, and could affect understanding of limiter and divertor operation.

Fokker‐Planck Simulation of Electron Transport in SOL Plasmas with ALLA Code

AbstractThe recently developed Fokker‐Planck code ALLA [1] permits us to simulate the temporal evolution collisional edge plasmas in 1D in space, IV in velocity space. It was used to simulate the SOL parallel electron flow in Alcator C‐Mod (PFC MIT) and TdeV (CCFM) tokamaks. Plasma parameters are taken as „best guesses”︁ from available detachment experimental data [2,3]. We show that the actual electron distribution function is asymmetric in the direction parallel to the magnetic field and its tail starts to departure from the Maxwellian at energies around 2T. This feature can substantially affect probe measurements and modify reaction rates and plasma transport properties.

Massively Parallel Fokker‐Planck Code ALLAp

AbstractThe recently developed for workstations Fokker‐Planck code ALLA simulates the temporal evolution of 1V, 2V and 1D2V collisional edge plasmas [1]. In this work we present the results of code parallelization on the CRI T3D massively parallel platform (ALLAp version). Simultaneously we benchmark the 1D2V parallel vesion against an analytic self‐similar solution of the collisional kinetic equation[2]. This test is not trivial as it demands a very strong spatial temperature and density variation within the simulation domain.

Resistivity gradient driven versus drift wave turbulence

Drift wave and rippling mode turbulences are investigated numerically in a 2-D slab, using the full fluid electron dynamical system from which both spring. Non-adiabatic electron dynamics capable of free energy access from temperature and density gradients are localized in the vicinity of the resonant surface, either by resistive dissipation/thermal conduction or by 'rippling', i.e. coupling of temperature and electrostatic potential fluctuations by the equilibrium current. Which type of turbulence prevails, self-organized drift wave or instability driven rippling mode, is determined solely by the competition between these two localization mechanisms. Because the localization is through linear terms, the regime boundary between the two types of turbulence is precisely where the linear theory of Hassam and Drake (Phys. Fluids 26 (1983) 133) says it is. And since even the most collisional edge plasmas in tokamaks such as ASDEX or TFTR are firmly ensconced within the drift wave regime, it is concluded that 'resistivity gradient driven turbulence' has no relevance to present or future tokamak experiments. Non-linearly self-sustaining collisional drift wave turbulence, on the other hand, remains viable

A quiver-kinetic formulation of radio-frequency heating and confinement in collisional edge plasmas

The near fields in the collisional edge plasma of a radio-frequency-heated tokamak can cause one or more charged species to oscillate in the applied field with a quiver (or jitter) speed comparable to its thermal speed. By assuming the quiver motion dominates over drifts and gyromotion a completely new kinetic description of the flows in an edge plasma is formulated that retains Coulomb collisions and the relevant atomic processes. Moment equations are employed to obtain a description in which only a lowest-order quiver-kinetic equation need be solved to evaluate the slow time particle fluxes and current induced by the applied fields. The electron heating by collisional randomization of their quiver motion (inverse bremsstrahlung) is balanced by impact excitation losses since equilibration with the ions is too weak. A model plasma of electrons, neutrals, and a single cold ion species is considered to illustrate the utility of the quiver-kinetic formulation. The model predicts local electrostatic potential changes and a local E×B convective flux that is of the same magnitude and scaling as would be predicted by Bohm diffusion.

Formation of a spatially ordered structure in a finite- beta edge plasma.

A three-dimensional inhomogeneous magnetohydrodynamic equation is investigated numerically. It is found that a spatially ordered structure is formed at a saturated energy level by the excitation of the convective cell modes due to the three-dimensional nonlinear mode coupling. It is shown that the saturated energy level and radial plasma flux are proportional to the magnitude of the background density gradient. The experimental observation of a self-organized coherent structure in a finite-..beta.. collisional edge plasma is expected.