Outer Flux Surface Research Articles

Plasma edge simulations including realistic wall geometry with SOLPS-ITER

Abstract In plasma edge simulations using the SOLPS-ITER code, the simulated Scrape-Off Layer plasma domain has historically been restricted to magnetic flux surfaces contacting divertor targets at both ends. We present here a newly developed numerical solver for the B2.5 plasma solver in SOLPS-ITER, allowing the numerical grid to be extended to the true vessel boundaries. The new, unstructured Finite Volume scheme can deal with arbitrary grids and magnetic topologies in the 2D poloidal plane. It includes a correct numerical treatment of possibly misaligned faces and cells w.r.t. the magnetic field to cope with, for example, strong divertor target shaping. The solver combines the benefits of an accurate numerical separation of fast parallel and slow radial transport, with a realistic description of the wall geometry, and the possibility of local grid refinement to capture sharp features in the Scrape-Off Layer flows. Generalized sheath boundary conditions are presented that can be imposed at all vessel boundaries, removing an important modeling uncertainty related to the specification of ad hoc decay length boundary conditions at the outer flux surfaces. The resulting model is applied to an AUG single-null case, a standard benchmark case for SOLPS-ITER. We analyze in particular the impact of the extended plasma model on upstream and divertor plasma conditions, and the improved predictions of heat and particle loads to the main chamber wall. The extended solver also allows for a much improved qualitative agreement between fluid and kinetic neutral simulations, because the fluid neutral solution, which is obtained on the plasma grid, now also extends to the true main chamber and divertor vessel boundaries.

Adjoint approach to calculating shape gradients for three-dimensional magnetic confinement equilibria

The shape gradient quantifies the change in some figure of merit resulting from differential perturbations to a shape. Shape gradients can be applied to gradient-based optimization, sensitivity analysis and tolerance calculation. An efficient method for computing the shape gradient for toroidal three-dimensional magnetohydrodynamic (MHD) equilibria is presented. The method is based on the self-adjoint property of the equations for driven perturbations of MHD equilibria and is similar to the Onsager symmetry of transport coefficients. Two versions of the shape gradient are considered. One describes the change in a figure of merit due to an arbitrary displacement of the outer flux surface; the other describes the change in the figure of merit due to the displacement of a coil. The method is implemented for several example figures of merit and compared with direct calculation of the shape gradient. In these examples the adjoint method reduces the number of equilibrium computations by factors of$O(N)$, where$N$is the number of parameters used to describe the outer flux surface or coil shapes.

Optimisation of confinement in a fusion reactor using a nonlinear turbulence model

The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using first-principles nonlinear simulations which accurately capture the turbulent cascade and large-scale zonal flows. The simulations utilise a novel approach, with gyrofluid treatment of the small-scale drift waves and gyrokinetic treatment of the large-scale zonal flows. A simple near-circular equilibrium with standard parameters is chosen as the initial condition. The figure of merit, fusion power per unit volume, is calculated, and then two control parameters, the elongation and triangularity of the outer flux surface, are varied, with the algorithm seeking to optimise the chosen figure of merit. A twofold increase in the plasma power per unit volume is achieved by moving to higher elongation and strongly negative triangularity.

Interactions of toroidally coupled tearing modes in the KSTAR tokamak

The evolutions of toroidally coupled radially-distant and radially-adjacent tearing modes are visualized in 2D in detail on the Korea superconducting tokamak for advanced research. The coupled tearing modes are in-phase on the out-board mid-plane and become destabilized or compete with each other depending on their spatial separation. When two coupled tearing modes are far apart, both are increasingly destabilized. On the other hand, when they become close to each other, one becomes stabilized while the other becomes destabilized. In such cases, an additional tearing mode is often formed on outer rational flux surface and the three tearing modes compete. The competitions suggest that spatial overlap (merging) of coupled magnetic islands is difficult.

Modeling of rapid shutdown in the DIII-D tokamak by core deposition of high-Z material

MHD modeling of encapsulated payload pellet injection (shell pellet injection) for disruption mitigation is carried out under the assumption of idealized delivery of the radiating payload to the core, neglecting the physics of shell ablation. The shell-pellet method is designed to produce an inside-out thermal quench in which core thermal heat is radiated while outer flux surfaces remain intact, protecting the divertor from large conducted heat loads. In the simulation, good outer surfaces remain until the thermal quench is nearly complete, and a high radiated energy fraction is achieved. When the outermost surfaces are destroyed, runaway electron test orbits indicate that the rate of runaway electron loss is very fast compared with prior massive gas injection simulations, which is attributed to the very different current profile evolution that occurs with central cooling.

Comparison of measured impurity poloidal rotation in DIII-D with neoclassical predictions under low toroidal field conditions

Predictive understanding of plasma transport is a long-term goal of fusion research. This requires testing models of plasma rotation including poloidal rotation. The present experiment was motivated by recent poloidal rotation measurements on spherical tokamaks (NSTX and MAST) which showed that the poloidal rotation of C+6 is much closer to the neoclassical prediction than reported results in larger aspect ratio machines such as TFTR, DIII-D, JT-60U and JET working at significantly higher toroidal field and ion temperature. We investigated whether the difference in aspect ratio (1.44 on NSTX versus 2.7 on DIII-D) could explain this. We measured C+6 poloidal rotation in DIII-D under conditions which matched, as best possible, those in the NSTX experiment; we matched plasma current (0.65 MA), on-axis toroidal field (0.55 T), minor radius (0.6 m), and outer flux surface shape as well as the density and temperature profiles. DIII-D results from this work also show reasonable agreement with neoclassical theory. Accordingly, the different aspect ratio does not explain the previously mentioned difference in poloidal rotation results.

A simulation study of large power handling in the divertor for a Demo reactor

Power exhaust for a 3 GW class fusion reactor with an ITER-sized plasma was investigated by enhancing the radiation loss from seeding impurity. The impurity transport and plasma detachment were simulated under the Demo divertor condition using an integrated divertor code SONIC, in which the impurity Monte-Carlo code, IMPMC, can handle most kinetic effects on the impurity ions in the original formula. The simulation results of impurity species from low Z (neon) to high Z (krypton) and divertor length with a plasma exhausted power of 500 MW and radiation loss of 460 MW, and a fixed core–edge boundary of 7 × 1019 m−3 were investigated at the first stage for the Demo divertor operation scenario and the geometry design. Results for the different seeding impurities showed that the total heat load, including the plasma transport and radiation , was reduced from 15–16 MW m−2 (Ne and Ar) to 11 MW m−2 for the higher Z (Kr), and extended over a wide area accompanied by increasing impurity recycling. The geometry effect of the long-leg divertor showed that full detachment was obtained, and the peak qtarget value was decreased to 12 MW m−2, where neutral heat load became comparable to and due to smaller flux expansion. Fuel dilution was reduced but was still at a high level. These results showed that a divertor design with a long leg with higher Z seeding such as Ar and Kr is not fulfilled, but will be appropriate to obtain the divertor scenario for the Demo divertor. Finally, influences of χ and D⊥ enhancement were seen significantly in the divertor, i.e. the radiation and density profiles became wider, leading to full detachment. Both qtarget near the separatrix and Te at the outer flux surfaces were decreased to a level for the conventional technology design. On the other hand, the problem of fuel dilution became worse. Extrapolation of the plasma transport coefficients to ITER and Demo, where density and temperature will be higher than ITER and edge-localized modes are mitigated, is a key issue for the divertor design.

Parallel resistivity and ohmic heating of laboratory dipole plasmas

The parallel resistivity is calculated in the long-mean-free-path regime for the dipole plasma geometry; this is shown to be a neoclassical transport problem in the limit of a small number of circulating electrons. In this regime, the resistivity is substantially higher than the Spitzer resistivity due to the magnetic trapping of a majority of the electrons. This suggests that heating the outer flux surfaces of the plasma with low-frequency parallel electric fields can be substantially more efficient than might be naively estimated. Such a skin-current heating scheme is analyzed by deriving an equation for diffusion of skin currents into the plasma, from which quantities such as the resistive skin-depth, lumped-circuit impedance, and power deposited in the plasma can be estimated. Numerical estimates indicate that this may be a simple and efficient way to couple power into experiments in this geometry.

MAGNETIC RELAXATION IN THE SOLAR CORONA

This is a mathematical study of the long-lived hydromagnetic structures produced in the tenuous solar corona by the turbulent, resistive relaxation of a magnetic field under the condition of extremely high electrical conductivity. The relaxation theory of Taylor, originally developed for a laboratory device, is extended to treat the open atmosphere where the relaxing field must interact with its surrounding fields. A boundary-value problem is posed for a two-dimensional model that idealizes the corona as the half Cartesian plane filled with a potential field (1) that is anchored to a rigid, perfectly conducting base and (2) that embeds a force-free magnetic field in the form of a flux-rope oriented horizontally and perpendicular to the Cartesian plane. The flux-rope has a free boundary, which is an unknown in the construction of a solution for this atmosphere. Pairs of magnetostatic solutions are constructed to represent the initial and final states of a flux-rope relaxation that conserve both the total magnetic helicity and total axial magnetic flux, using a numerical iterative method specially developed for this study. The collection of numerical solutions found provides an insight into the interplay among several hydromagnetic properties in the formation of long-lived coronal structures. In particular, the study shows (1) that the outward spread of reconnection between a relaxing flux-rope and its external field may be arrested at some outer magnetic flux surface within which a constant-α force-free field emerges as the minimum-energy state and (2) that this outward spread is complicated by an inward, partial collapse of the relaxing flux-rope produced by a loss of internal magnetic pressure.

Electron temperature gradient driven transport in a MAST H-mode plasma

Gyrokinetic simulation of a MAST-like equilibrium is used to establish the turbulent transport resulting from the electron temperature gradient driven mode for core and edge parameters. The thermal diffusion coefficients calculated in these simulations are found to be experimentally significant for core parameters but underestimate the observed transport on outer flux-surfaces.

Rapid electron internal transport barrier formation during magnetic shear reversal in fully non-inductive TCV discharges

The rapid formation of an electron internal transport barrier (eITB) is observed during a slow evolution (≃200 ms) from a centrally peaked to a hollow current density profile, while all external actuators remain constant. The time constant for the barrier formation appears to be shorter than the electron energy confinement time. The improved confinement associated with the barrier formation occurs first in a localized region off-axis. Then the effects propagate to inner and outer flux surfaces on a confinement time scale. The temporal and spatial localizations of the barrier formation suggest a threshold in the magnetic shear profile that triggers the onset of the eITB. The threshold-like behaviour can be attributed to the sudden appearance of a minimum q (or zero-shear) flux surface in the safety factor profile. Based on modelling of the current profile evolution using the ASTRA transport code, the appearance of the zero-shear flux surface is correlated with the temporal and spatial formation of the barrier.

Toward a global magnetospheric equilibrium model

In this paper we take a first step toward the development of a realistic global magnetospheric model in which the magnetic forces are equilibrated by plasma pressure forces. Such a model describes a “quasi‐static” equilibrium, a condition valid at most times in the Earth's magnetosphere. The work reported here involves the coupling in two dimensions of a numerical inner/middle magnetosphere model in flux coordinates, which solves the Grad‐Shafranov equation in “inverse” form, with an asymptotic magnetotail model farther away from Earth. We discuss the obtained configurations (including the resulting magnetic fields and electric currents) under different observation‐based inputs (parameters include plasma and total pressures, as well as the magnetic flux boundary). In particular, we focus on the boundary value problem, in which we take realistic shapes for the outer magnetic flux surface (close to the magnetopause) and plasma pressure distributions as model inputs and obtain the total pressure variation in the tail as a by‐product of the model.

Three‐dimensional magnetotail equilibria with prescribed boundary shapes

Three‐dimensional magnetotail equilibrium configurations are presented that are derived from a prescribed outer flux surface, equivalent to a closed magnetopause. The explicit solutions neglect the effects of field‐aligned currents, closely associated with a bending of field lines in the x, y plane, but include tail flaring in y and z. Most of the solutions are derived for an axisymmetric boundary, approximately consistent with force balance between the unperturbed solar wind and the magnetosphere at a closed magnetopause (Newtonian approximation). This force balance is used to relate the downtail variation of the tail radius to that of the total interior magnetotail pressure, equivalent to the lobe magnetic pressure. However, these properties are not sufficient to determine the tail configuration. We demonstrate this by deriving solutions with identical boundaries and identical variation of the total pressure along the tail but different amounts of field line flaring in the x, y plane. Under these conditions, stronger field line flaring is associated with a reduction of the magnetotail plasma pressure near midnight and an increase of the plasma sheet thickness from midnight toward the tail flanks. A reduction of the tail boundary flaring leads to an increase of the plasma sheet thickness near the Earth but does not significantly affect the cross‐tail variation. Nonuniform boundary flaring with a flattening of the tail, corresponding to a more significant increase of the tail radius in y, can reduce the plasma sheet thickening from midnight to the tail flanks or even reverse it to a thinning. The explicit solutions illustrate the effects on the tail structure of both the instantaneous force balance between the magnetosphere and the solar wind and the history of this interaction, which affects the plasma and magnetic flux distribution inside the magnetotail.

Parallel and radial transport of ELM plasma in the SOL and divertor of JT-60U

Parallel and radial transport of ELMs in the Scrape-Off-Layer and divertor were investigated in JT-60U. The time lag from the start of magnetic fluctuations to the peak of the ion saturation current (js) at low-field-side (LFS) divertor was consistent with convective transport of the ELM plasma along field lines. However, the time lag to the start of the js enhancement was shorter than the convection time between the LFS midplane and divertor. In addition, js started to increase both at high-field-side and LFS divertors simultaneously, which is not explained by the convection model. Large multi-peaks appeared in the time traces of js at the midplane and near the X-point. The radial distribution of the first peak show that the ELM particle flux is transported to outer SOL flux surfaces up to 15cm from the separatrix. The radial expansion speed at the midplane was in the range of 1–2.5km/s.

Plasma flow measurement in high- and low-field-side SOL and influence on the divertor plasma in JT-60U

Three reciprocating Mach probes were installed at the high-field-side (HFS) baffle, low-field-side (LFS) midplane and just below the X-point in JT-60U tokamak in order to investigate the SOL flow pattern. Profiles of particle fluxes produced by parallel SOL flow and E r × B-drift flow were evaluated from Mach number, electron temperature, density and floating potential. The drift particle flux was dominant near the separatrix, while it became smaller than the parallel particle flux at the outer flux surfaces. Total particle fluxes towards HFS and LFS divertors were investigated at various plasma densities. The drift flux was comparable to the parallel flux at relatively low densities, while the parallel flux became dominant at high densities. Drift flux in the private flux region was also evaluated, and it contributed to produce in–out asymmetries in the divertor ion flux and particle recycling under attached divertor condition.

On Island Formation in a Locally Perturbed Tokamak Equilibrium

AbstractTo control the plasma transport at the edge of a tokamak the outer flux surfaces can be artificially destroyed by applying a resonant helical magnetic field, as it is demonstrated at Pulsator [1],[2], [3], Tore Supra [4],[5] and proposed for TEXTOR‐94 [6] in the concept of “ergodic divertors”.As a measure of the efficiency of the perturbation field e.g. the level of the field line diffusion coefficient DFL the width Δi of the magnetic islands and the related Chirikov parameter are of importance [7],[8],[9],[10].For the planned Dynamic Ergodic Divertor (DED) at TEXTOR‐94 where the perturbation coils are located at the high field side the standard expression for Δi using the Fourier components of the magnetic field perturbation [7] leads to results significantly different from field line tracing calculations [11].The standard expression is commonly used in terms of the perturbation magnetic field δB [5],[7],[8],[9],[12],[13]. But when replacing the Fourier components of the perturbation vector potential by those of the magnetic field finite aspect ratio effects have been neglected so far. For present tokamaks with ϵ = r/R ≃ 0.3 this can lead to an error in the field line diffusion of one to two orders of magnitude.In this paper it is shown that taking into account the finite aspect ratio at this point leads to correct results compared to the highly precise field line tracing calculations by the Gourdon code. The island width then is recognized to depend significantly on the poloidal position of the perturbation field. This is in contrast to the standard expression. Also the role of the choice of the magnetic coordinate system is considered.

J * optimization of small aspect ratio stellarator/tokamak hybrid devices

A new class of low aspect ratio toroidal hybrid stellarators is found using a more general plasma confinement optimization criterion than quasisymmetrization. The plasma current profile and shape of the outer magnetic flux surface are used as control variables to achieve near constancy of the longitudinal invariant J* on internal flux surfaces (quasiomnigeneity), in addition to a number of other desirable physics target properties. A range of compact (small aspect ratio A), low plasma current devices have been found with significantly improved confinement, both for thermal as well as energetic (collisionless) particle components. With reasonable increases in magnetic field and geometric size, such devices can also be scaled to confine 3.5 MeV alpha particle orbits.

Effects of Rotation on Ideal Ballooning Modes

AbstractThe stability of ideal ballooning modes in presence of a rigid toroidal rotation is revisited. Centrifugal forces induce poloidal asymmetry in the equilibrium pressure and affect the shape of the flux surfaces. Taking this two effects into account shows that the rigid rotation has a stabilising role on the the inner flux surfaces (for which r < Lp, where Lp is the pressure scale length). On the other hand, rotation is shown to have a destabilising role on the outer flux surfaces (for which r > Lp). However, the instability at the outer plasma is found to be terminated by a new stable zone which may be conjectured to be a “third” region of stability.

Magnetospheric equilibrium with anisotropic pressure

Self‐consistent magnetospheric equilibria with anisotropic pressure are obtained by employing an iterative metric method for solving the inverse equilibrium equation in an optimal flux coordinate system. A method of determining plasma parallel and perpendicular pressures from either analytic particle distributions or particle distributions measured along a satellite's path is presented. The numerical results of axisymmetric magnetospheric equilibria including the effects of finite beta, pressure anisotropy, and boundary conditions are presented for a bi‐Maxwellian particle distribution. For the isotropic pressure cases the finite beta effect produces an outward expansion of the constant magnetic flux surfaces in relation to the dipole field lines, and along the magnetic field the toroidal ring current is maximum at the magnetic equator. The effect of pressure anisotropy is found to further expand the flux surfaces outward. Along the magnetic field lines the westward ring current can be peak away from the equator owing to an eastward current contribution resulting from pressure anisotropy. As pressure anisotropy increases, the peak westward current can become more singular. The outer boundary flux surface has a significant effect on the magnetospheric equilibrium. For the outer flux boundary resembling the dayside compressed flux surface due to solar wind pressure, the deformation of the magnetic field can be quite different from that for the outer flux boundary resembling the taillike flux surface.

Three-dimensional magnetohydrodynamic studies of the reversed-field pinch

Three-dimensional computational studies of nonlinear resistive megnetohydrodynamic (MHD) instabilities in the reversed-field pinch are presented. It is found that multihelicity mode coupling effects alter the evolution of m=1 modes from that obtained in single helicity. Strong mode coupling to m=0 and m=2 is observed. Magnetic island overlap results in stochastic field lines. At low values of the pinch parameter this is confined to the central region of the pinch; for larger values the stochasticity may extend to the wall. Healing of outer flux surfaces is observed as modes peak and relax. Decay of positive toroidal flux is retarded. Impact on confinement is discussed, and connection is made with experimental observations.