Perturbed Field Lines Research Articles

Heuristic predictions of RMP configurations for ELM suppression in ITER burning plasmas and their impact on divertor performance

A subspace of resonant magnetic perturbation (RMP) configurations for edge localized mode (ELM) suppression is predicted for H-mode burning plasmas at 15 MA current and 5.3 T magnetic field in ITER. Perturbations to the core plasma can be reduced by a factor of 2 for equivalent edge stability proxies, while the perturbed plasma boundary geometry remains mostly resilient. The striated domain of perturbed field lines connecting from the main plasma (normalized poloidal flux <1 ) to the divertor targets is found to be significantly larger than the expected heat load width in the absence of RMPs. This facilitates heat load spreading with peak values at an acceptable level below 10MWm−2 on the outer target already at moderate gas fueling and low Ne seeding for additional radiative dissipation of the 100MW of power into the scrape-off layer (SOL). On the inner target, however, re-attachment is predicted away from the equilibrium strike point due to increased upstream heat flux, higher downstream temperature and less efficient impurity radiation.

Detachment in Fusion Plasmas with Symmetry Breaking Magnetic Perturbation Fields.

Power exhaust from the bulk plasma is significantly altered by symmetry breaking magnetic perturbation fields, because these create direct connections (perturbed field lines) from the confined high temperature plasma to solid surfaces. The same amount of power is distributed among those new exhaust channels as for a symmetric magnetic configuration, which reduces the local upstream heat flux flowing down the perturbed field lines, thereby making access to detachment easier (i.e., at lower upstream density) for the divertor plasma near the location corresponding to the symmetric magnetic separatrix. However, the divertor plasma regions with connection to the bulk plasma are extended nonaxisymmetrically further outside, where significant heat loads occur, unlike in the symmetric configuration. The temperature remains high at those locations, which reduces the divertor plasma dissipation capacity, making the mitigation of heat loads more difficult to achieve.

HINT modeling of three-dimensional tokamaks with resonant magnetic perturbation

In order to consider the nonlinear three-dimensional (3D) equilibrium response of the resonant magnetic perturbation field, the nonlinear 3D equilibrium is discussed for the 3D perturbed tokamak. To model the magnetic topology, a nonlinear 3D equilibrium calculation code, which has been developed in stellarator research, is applied to the perturbed tokamak. That code does not assume the existence of perfectly nested flux surfaces. In the nonlinear 3D equilibrium calculation, the change of the magnetic topology is due to the nonlinear 3D equilibrium response, which is the lowest order plasma response appearing in the 3D steady state. The parallel current flow along perturbed field lines three-dimensionally drives the perturbed field to break the magnetic topology. This effect is significant along the separatrix and must be considered to interpret the experimental observations.

The pattern of parallel edge plasma flows due to pressure gradients, recycling, and resonant magnetic perturbations in DIII-D

High resolution plasma transport simulations with the EMC3-EIRENE code have been performed to address the parallel plasma flow structure in the boundary of a poloidal divertor configuration with non-axisymmetric perturbations at DIII-D. Simulation results show that a checkerboard pattern of flows with alternating direction is generated inside the separatrix. This pattern is aligned with the position of the main resonances (i.e., where the safety factor is equal to rational values q=m/n for a perturbation field with base mode number n): m pairs of alternating forward and backward flow channel exist for each resonance. The poloidal oscillations are aligned with the subharmonic Melnikov function, which indicates that the plasma flow is generated by parallel pressure gradients along perturbed field lines. An additional scrape-off layer-like domain is introduced by the perturbed separatrix which guides field lines from the interior to the divertor targets, resulting in an enhanced outward flow that is consistent with the experimentally observed particle pump-out effect. However, while the lobe structure of the perturbed separatrix is very well reflected in the temperature profile, the same lobes can appear to be smaller in the flow profile due to a competition between high upstream pressure and downstream particle sources driving flows in opposite directions.

Method for comparison of tokamak divertor strike point data with magnetic perturbation models

Resonant magnetic perturbations (RMPs) used to control type-I edge-localized modes produce a splitting of the peaks of heat flux profile on the divertor. The additional peaks can appear outside the areas connected to the plasma core by the perturbed field lines due to perpendicular transport. This effect has been studied so far using demanding three-dimensional transport simulations. We present a simple method to quantitatively estimate the heat flux profile that the RMP will produce on the divertor. The method needs only field line tracing to determine the so-called tangle distance function, and knowledge of the heat flux profile on the unperturbed heat flux profile. We find good agreement between this method and a transport simulation.

Set of wires to simulate tokamaks with poloidal divertor

AbstractSimple wire models have been proposed to simulate magnetic configurations in tokamaks. Here we consider electric currents in five parallel infinite wires to obtain double-null magnetic surfaces with specific choices of magnetic axis positions, triangularity, and elongation. As an example, we choose the position and the electric current of each wire to obtain magnetic surfaces similar to those expected in the tokamak international thermonuclear experimental reactor. Moreover, we also integrate the perturbed field line differential equation to simulate chaotic layers near the hyperbolic points and deposition patterns at the divertor plate observed in tokamaks. To simulate that, we add to the model a perturbing error field, due to asymmetries in the tokamak coils, and introduce a random collisional term to the field line mapping to reproduce escape pattern alterations due to particle collisions.

Towards understanding ELM mitigation: the effect of axisymmetric lobe structures near the X-point on ELM stability

The application of resonant magnetic perturbations (RMPs) with toroidal mode number n = 4 or n = 6 is observed to result in a significant increase in ELM frequency, despite a reduction in the edge pressure gradient. A picture for how type-I ELMs are mitigated, or destabilized, when magnetic perturbations are applied is proposed. Despite the magnetic perturbation incurring a drop in the pedestal pressure gradient, the critical pressure for an ELM to be triggered is dropped even further. Various mechanisms which could cause this degradation of the stability boundary are outlined. The stability of the edge of MAST H-mode plasmas has been tested when lobe structures are present in the separatrix after application of RMPs. The axisymmetric stability analysis presented here shows that when the plasma boundary is simulated with a model for the observed lobe structures included, the ballooning stability is degraded. This degradation in ballooning stability originates from the perturbed field lines dwelling in the region of unfavourable curvature due to the presence of lobe structures rather than the change in the plasma boundary shape.

Simulation of microtearing turbulence in national spherical torus experiment

Thermal energy confinement times in National Spherical Torus Experiment (NSTX) dimensionless parameter scans increase with decreasing collisionality. While ion thermal transport is neoclassical, the source of anomalous electron thermal transport in these discharges remains unclear, leading to considerable uncertainty when extrapolating to future spherical tokamak (ST) devices at much lower collisionality. Linear gyrokinetic simulations find microtearing modes to be unstable in high collisionality discharges. First non-linear gyrokinetic simulations of microtearing turbulence in NSTX show they can yield experimental levels of transport. Magnetic flutter is responsible for almost all the transport (∼98%), perturbed field line trajectories are globally stochastic, and a test particle stochastic transport model agrees to within 25% of the simulated transport. Most significantly, microtearing transport is predicted to increase with electron collisionality, consistent with the observed NSTX confinement scaling. While this suggests microtearing modes may be the source of electron thermal transport, the predictions are also very sensitive to electron temperature gradient, indicating the scaling of the instability threshold is important. In addition, microtearing turbulence is susceptible to suppression via sheared E × B flows as experimental values of E × B shear (comparable to the linear growth rates) dramatically reduce the transport below experimental values. Refinements in numerical resolution and physics model assumptions are expected to minimize the apparent discrepancy. In cases where the predicted transport is strong, calculations suggest that a proposed polarimetry diagnostic may be sensitive to the magnetic perturbations associated with the unique structure of microtearing turbulence.

Turbulence simulations of barrier relaxations and transport in the presence of magnetic islands at the tokamak edge

The control of transport barrier relaxation oscillations by resonant magnetic perturbations (RMPs) is investigated with three-dimensional turbulence simulations of the tokamak edge. It is shown that single harmonics RMPs (single magnetic island chains) stabilize barrier relaxations. In contrast to the control by multiple harmonics RMPs, these perturbations always lead to a degradation of the energy confinement. The convective energy flux associated with the non-axisymmetric plasma equilibrium in the presence of magnetic islands is found to play a key role in the erosion of the transport barrier that leads to the stabilization of the relaxations. This convective flux is studied numerically and analytically. In particular, it is shown that in the presence of a mean shear flow (generating the transport barrier), this convective flux is more important than the radial flux associated with the parallel diffusion along perturbed field lines.

The influence of three-dimensional stochastic magnetic boundaries on plasma edge transport and the resulting plasma wall interaction

The three-dimensional (3D) features of plasma edge profiles and wall interaction patterns induced by edge resonant magnetic perturbation fields (RMP) are discussed comparing TEXTOR and DIII-D. We show that the scrape-off layer (SOL) profiles and decay lengths depend the edge safety factor, the RMP base mode as well as on the plasma rotation during RMP application indicating modification of SOL transport by the 3D perturbation fields. This is compatible with channelling of particle and heat efflux along open perturbed field lines in the very edge of the plasma boundary into a completely re-arranged, helically striated 3D divertor footprint. The distribution of the measured divertor heat and particle fluxes at DIII-D match the vacuum modelled magnetic footprint topology in L-mode while in H-mode the striation width exceeds the modelled footprint width by 15–30%. This 3D structure of the measured heat and particle fluxes results in a new situation for the material erosion properties and initial quantification of the net-erosion within the 3D footprint shows in L-mode a 50% decrease of the chemical erosion yield and evidence for a comparably small 15-20% increase in physical sputtering. Extrapolation of these findings to ITER by vacuum modelling of the magnetic footprint for the actual ELM control coils shows a similar vacuum magnetic footprint topology as found at DIII-D during RMP ELM suppression. However, the open field lines escape the CFC covered ITER divertor area potentially transferring net-erosion characteristics from the CFC domain onto the Tungsten including so far unconsidered heat and particle loads on this sensitive material.

Aspects of three dimensional transport for ELM control experiments in ITER-similar shape plasmas at low collisionality in DIII-D

A study of three-dimensional (3D) perturbed magnetic field structures and transport for edge localized mode control experiments with resonant magnetic perturbations at DIII-D is presented. We focus on ITER-Similar Shape plasmas at ITER relevant electron pedestal collisionalities . This study is performed in comparison with results from TEXTOR-Dynamic Ergodic Divertor circular limiter plasmas. For both experiments the magnetic field structure is analyzed in the vacuum paradigm—superimposing the external RMP field on the unperturbed equilibrium. For TEXTOR L-mode plasmas this description holds for normalized poloidal flux ΨN > 0.7 without tearing modes driven by the RMP field. For DIII-D H-mode plasmas the validity of this approach still needs to be established. In this paper a method is discussed to diagnose the degree of edge stochastization based on a comparison between modeled magnetic footprints on the divertor targets and experimental data. Clear evidence is presented for the existence of a generic separatrix perturbation causing striation of target particle fluxes. However, heat fluxes into these striations are small. This observation can be explained by accounting for the different heat and particle source locations and the 3D trajectories of the open, perturbed field lines toward the divertor target. Analysis of the transport characteristics filling the perturbed separatrix lobes based on initial EMC3/EIRENE modeling suggests the existence of open field lines connecting the stochastic edge to the target pattern. However, the width and inward most extent of the actual stochastic layer cannot yet be quantified.

Particle transfer in edge transport barrier with stochastic magnetic field

Charged particle losses at the plasma edge affected by resonant magnetic perturbations (RMP) are considered by taking into account the electron and ion flows both parallel and perpendicular to perturbed field lines. Calculations are done for H-mode plasmas of low collisionality, i.e., under conditions where significant pump out of particles has been observed in experiments on the DIII-D tokamak [J. Luxon, Nucl. Fusion 42, 614 (2002)] with RMP from the I-coils. It is demonstrated that the perpendicular ion flux, arising by magnetic field stochastization due to the deviation of poloidal rotation from the neoclassical one, is of more importance than the parallel ion flow. With both loss contributions included, computations provide a pump out level in agreement with observations if the screening of RMP by the plasma rotation is taken into account. The impact of possible enhancement in the perpendicular electron transport due to fluctuations observed with RMP in the edge transport barrier is assessed.

Modelling of pedestal transport during ELM suppression by external magnetic field perturbations

Particle and energy transport in the edge transport barrier is analysed in the presence of magnetic field perturbations from external resonant coils successfully used recently for the mitigation of type I edge localized modes (ELMs). The modification of transport due to charged particle and heat flows along perturbed field lines in a small region near the separatrix, spanning from 2% to 4% of the total poloidal flux, where complete stochastization is provided by the overlap of the main magnetic islands, is taken into account. The observed reduction of the density in plasmas of low collisionality is explained by the generation of charged particle flows along perturbed field lines, the increase in the electron and ion temperatures in the barrier—by the reduction of the perpendicular neoclassical transport with decreasing density and non-locality of parallel heat transport. On the basis of the heat flux limit concept in a deeply collisionless regime, the parallel thermal conductivities are taken to be 17 times smaller for electrons and 7 times smaller for ions than from a standard free-streaming estimate. The model elaborated before is developed further by taking into account the radial variation of the inclination angle of stochastic field lines and convective energy losses including the acceleration of ions by the pressure gradient and ambipolar electric field. It is demonstrated that convection of parallel kinetic energy of ions gives greater losses than parallel thermal conduction in the outer 50% of the stochastic layer and its inclusion improves the agreement with experimental results. This modelling is performed by assuming in agreement with observations that the influx of recycling neutrals through the separatrix is not reduced with I-coils compared with its level between ELMs before the mitigation stage. By trying to match experimental profiles with this influx decrease, some enhanced thermal losses of another nature than that considered here are needed in order to mitigate the drop in the perpendicular thermal conductivities for the assumed density scaling. The impact of the neutral particle influx increase by gas puffing applied in order to restore the plasma density is investigated.

Mechanisms of Edge-Localized-Mode Mitigation by External-Magnetic-Field Perturbations

Particle and energy transport in the tokamak edge transport barrier is analyzed in the presence of magnetic field perturbations from external resonant coils. In recent experiments such coils have been verified as an effective tool for mitigation of the edge-localized modes of type I. The observed reduction of the density in plasmas of low collisionality is explained by the generation of charged particle flows along perturbed field lines. The increase of the electron and ion temperatures in the barrier is interpreted by the reduction of perpendicular neoclassical transport with decreasing density and nonlocality of parallel heat transport. The found modification of the pressure gradient implies the stabilization of ballooning-peeling MHD modes responsible for type I ELMs.

Ergodic magnetic limiter for the TCABR

In this work it is considered the effect of an ergodic magnetic limiter on the plasma confined in the TCABR tokamak. The poloidal distribution of the limiter currents is determined taking into account the toroidal geometry of this tokamak. The plasma equilibrium field is analytically obtained by solving the Grad-Schlüter-Shafranov equation in polar toroidal coordinates. The perturbing limiter field is obtained as a vacuum field by solving the Laplace equation. Supposing the limiter action as a sequence of delta-function pulses, a symplectic map is derived by using a Hamiltonian formulation for the perturbed field line. Examples are given to illustrate the influence of this design on the topology of the perturbed field line structure.

Widening the magnetic footprints in a poloidal divertor tokamak: a proposal

A dynamic ergodization for the control of heat deposition on divertor plates in a poloidal divertor tokamak is proposed. A weak ergodization of magnetic field lines near the magnetic separatrix by external rotating magnetic field perturbations is considered. The analysis of perturbed field lines is carried out using the computationally efficient method of the shifted separatrix mapping. The structure of the stochastic layer of open field lines near the X point and of the magnetic footprints on the divertor plates is studied for different harmonics of the magnetic perturbations. The perturbation field generates both an ergodic widening of the divertor footprints and a laminar deformation, which is averaged out by the proposed rotation of the perturbation field. Some technical implications of the application of such a perturbation field for the Next Step Device are discussed.

Diffusive processes in a stochastic magnetic field.

The statistical representation of a fluctuating (stochastic) magnetic field configuration is studied in detail. The Eulerian correlation functions of the magnetic field are determined, taking into account all geometrical constraints: these objects form a nondiagonal matrix. The Lagrangian correlations, within the reasonable Corrsin approximation, are reduced to a single scalar function, determined by an integral equation. The mean square perpendicular deviation of a geometrical point moving along a perturbed field line is determined by a nonlinear second-order differential equation. The separation of neighboring field lines in a stochastic magnetic field is studied. We find exponentiation lengths of both signs describing, in particular, a decay (on the average) of any initial anisotropy. The vanishing sum of these exponentiation lengths ensures the existence of an invariant which was overlooked in previous works. Next, the separation of a particle's trajectory from the magnetic field line to which it was initially attached is studied by a similar method. Here too an initial phase of exponential separation appears. Assuming the existence of a final diffusive phase, anomalous diffusion coefficients are found for both weakly and strongly collisional limits. The latter is identical to the well known Rechester-Rosenbluth coefficient, which is obtained here by a more quantitative (though not entirely deductive) treatment than in earlier works.

Impurity penetration through the stochastic layer near the separatrix in tokamaks

It is shown that a stochastic layer produced by ripple perturbations near the separatrix in tokamaks, leads to anomalous plasma flow out of the bulk plasma along perturbed field lines, which brings out impurities. This suggests that the stochastic layer may play a cleaning role. There is an opposite process of anomalous impurity diffusion into the plasma. The balance of these two processes defines the impurity concentration in the bulk plasma.

Onset of chaotic field line trajectories in tokamaks

The onset of chaotic field line trajectories on tokamak plasmas perturbed by external resonant helical currents has been investigated. The spatial distribution of field lines is obtained integrating numerically the differential equations for the perturbed field lines and investigating the Poincare maps characteristic of these fields. Several algorithms have been computed to identify the transition to large-scale stochasticity for this quasi-integrable dynamical system, which, for a given m.h.d. equilibrium, is determined by the enhancement of the coupling between the helical perturbation and the toroidicity, as the helical current increases.

First-order displacement of a magnetic field line in an Elmo bumpy torus.

A perturbation procedure is employed to derive a formula for the field-line displacement in a magnetic configuration consisting of a dominant (unperturbed) field with closed field lines and a small additional (perturbation) field that causes the perturbed field lines to fail to close on themselves. An expression for the spatial displacement of the perturbed field line per circuit, obtained in a first-order perturbation approximation in the Clebsch representation, is given in terms of an action integral representing a longitudinal adiabatic invariant. Numerical results are also presented to compare the first-order approximation with the exact relation.