Non-resonant Magnetic Perturbations Research Articles

Effect of magnetic perturbations on turbulence-flow dynamics at the L-H transition on DIII-D

Detailed 2D turbulence measurements from the DIII-D tokamak provide an explanation for how resonant magnetic perturbations (RMPs) raise the L-H power threshold PLH [P. Gohil et al., Nucl. Fusion 51, 103020 (2011)] in ITER-relevant, low rotation, ITER-similar-shape plasmas with favorable ion ∇B direction. RMPs simultaneously raise the turbulence decorrelation rate ΔωD and reduce the flow shear rate ωshear in the stationary L-mode state preceding the L-H transition, thereby disrupting the turbulence shear suppression mechanism. RMPs also reduce the Reynolds stress drive for poloidal flow, contributing to the reduction of ωshear. On the ∼100 μs timescale of the L-H transition, RMPs reduce Reynolds-stress-driven energy transfer from turbulence to flows by an order of magnitude, challenging the energy depletion theory for the L-H trigger mechanism. In contrast, non-resonant magnetic perturbations, which do not significantly affect PLH, do not affect ΔωD and only slightly reduce ωshear and Reynolds-stress-driven energy transfer.

Helically self-organized pinches: dynamical regimes and magnetic chaos healing

This paper deals with helical self-organization in current-carrying toroidal pinches for the magnetic confinement of fusion plasmas. We perform our study in the framework of 3D nonlinear visco-resistive magnetofluid modelling, where a large set of simulations is now available. A global picture is derived about how visco-resistive transport coefficients and magnetic boundary conditions rule the self-organized helical states for the reversed-field pinch configuration. Decreasing visco-resistive dissipation causes a transition from steady ohmic helical equilibria to intermittent states (sawtoothing activity), while selected helical magnetic perturbations applied at the boundary favor steady global quasi-helical solutions. The sawtoothing frequency decreases together with visco-resistive dissipation, while sawtoothing amplitude decreases when applying non-resonant magnetic perturbations. Simulations of the tokamak configuration allow us to draw a tight parallelism with reversed-field pinches: a similar role of dissipation and magnetic boundary conditions on the dynamics of the internal kink mode is found, with decreasing sawtoothing frequency and amplitude by decreasing dissipation and by applying suitable helical boundary conditions. Magnetic chaos healing is the topological feature of the transition from intermittent to quasi-quiescent helical states in reversed-field pinches. Bundles of Lagrangian coherent structures (LCS) in the weakly stochastic region surrounding the helical core constitute the skeleton of chaos healing, and behave as barriers to the transport of magnetic field lines. In this work, they are detected during the whole temporal evolution and it is proved that they can withstand the nonlinear dynamics even during sawtoothing activity. Furthermore, we show that LCS are connected to regions with strong gradients of the connection length of magnetic field lines to the edge. This provides a further indication of their possible role in the formation of electron temperature barriers. As a final result it is shown that a reasonable value of plasma rotation can further enhance the intensity of the dominant helical mode.

Effects of the applied magnetic fields with various toroidal phase differences on the neoclassical toroidal viscosity in JT-60SA

The integrated framework consisting of TOPICS, VMEC and FORTEC-3D, has been applied to provide an estimate of the neoclassical toroidal viscosity (NTV) produced by the applied magnetic perturbations (MPs). Six picture-frame error field correction coils in each row in JT-60SA realize the various patterns of the applied magnetic field spectrum. The NTV is investigated for various toroidal phase differences. As long as the same coil current is applied, the n = 3 MPs generate the same NTV, regardless of even or odd parity, or energizing the middle coils or not. The n = 1 MPs give rise to larger NTV than the n = 3 ones. The NTV invoked by the n = 1 resonant MPs is virtually equivalent to that by the n = 1 nonresonant MPs with five-fold coil current.

H-mode achievement and edge features in RFX-mod tokamak operation

The RFX-mod experiment is a fusion device designed to operate as a reversed field pinch (RFP), with a major radius m and a minor radius m. Its high versatility recently allowed operating it also as an ohmic tokamak, allowing comparative studies between the two configurations in the same device. The device is equipped with a state of the art MHD mode feedback control system providing a magnetic boundary effective control, by applying resonant or non-resonant magnetic perturbations (MP), both in RFP and in tokamak configurations. In the fusion community the application of MPs is widely studied as a promising tool to limit the impact of plasma filaments and ELMs (edge localized modes) on plasma facing components. An important new research line is the exploitation of the RFX-mod active control system for ELM mitigation studies. As a first step in this direction, this paper presents the most recent achievements in term of RFX-mod tokamak explored scenarios, which allowed the first investigation of the ohmic and edge biasing induced H-mode. The production of D-shaped tokamak discharges and the design and deployment of an insertable polarized electrode were accomplished. Reproducible H-mode phases were obtained with insertable electrode negative biasing in single null discharges, representing an unexplored scenario with this technique. Important modifications of the edge plasma density and flow properties are observed. During the achieved H-mode ELM-like electromagnetic composite filamentary structures are observed. They are characterized by clear vorticity and parallel current density patterns.

M3D-C1 simulations of the plasma response to RMPs in NSTX-U single-null and snowflake divertor configurations

In this work, single- and two-fluid resistive magnetohydrodynamic calculations of the plasma response to magnetic perturbations in single-null (SN) and snowflake (SF) divertor configurations are compared with those based on the vacuum approach. The calculations are performed using the code M3D-C1 and are based on simulated NSTX-U plasmas. Significantly different plasma responses were found from these calculations, with the difference between the single- and two-fluid plasma responses being caused mainly by the different screening mechanism intrinsic to each of these models. Although different plasma responses were obtained from these different plasma models, no significant difference between the SN and SF plasma responses were found. However, due to their different equilibrium properties, magnetic perturbations cause the SF configuration to develop additional and longer magnetic lobes in the null-point region than the SN, regardless of the plasma model used. The intersection of these longer and additional lobes with the divertor plates are expected to cause more striations in the particle and heat flux target profiles. In addition, the results indicate that the size of the magnetic lobes, in both single-null and snowflake configurations, are more sensitive to resonant magnetic perturbations than to non-resonant magnetic perturbations.

Evaluation of toroidal torque by non-resonant magnetic perturbations in tokamaks for resonant transport regimes using a Hamiltonian approach

Toroidal torque generated by neoclassical viscosity caused by external non-resonant, non-axisymmetric perturbations has a significant influence on toroidal plasma rotation in tokamaks. In this article, a derivation for the expressions of toroidal torque and radial transport in resonant regimes is provided within quasilinear theory in canonical action-angle variables. The proposed approach treats all low-collisional quasilinear resonant neoclassical toroidal viscosity regimes including superbanana-plateau and drift-orbit resonances in a unified way and allows for magnetic drift in all regimes. It is valid for perturbations on toroidally symmetric flux surfaces of the unperturbed equilibrium without specific assumptions on geometry or aspect ratio. The resulting expressions are shown to match the existing analytical results in the large aspect ratio limit. Numerical results from the newly developed code NEO-RT are compared to calculations by the quasilinear version of the code NEO-2 at low collisionalities. The importance of the magnetic shear term in the magnetic drift frequency and a significant effect of the magnetic drift on drift-orbit resonances are demonstrated.

Modification of plasma rotation with resonant magnetic perturbations in the STOR-M tokamak

The toroidal plasma flow velocity of impurity ions has been significantly modified in the Saskatchewan Torus-Modified (STOR-M) tokamak by means of resonant magnetic perturbations (RMP). It has been found that the toroidal flow velocities of OV and CVI impurity ions change towards the co-current direction after the application of a current through a set of (l = 2, n = 1) RMP field coils. It has been observed that the reduction of the toroidal flow velocity is closely correlated to the reduction of the magnetohydrodynamic (MHD) fluctuation frequency measured by Mirnov coils. Modulation of the flow velocity has been achieved by switching the RMP current pulses. Non-resonant magnetic perturbations have also induced a much smaller change in the toroidal plasma flow. A theoretical model has been adopted to assess the contributions of different drift mechanisms to magnetic islands rotation in STOR-M.

Braking due to non-resonant magnetic perturbations and comparison with neoclassical toroidal viscosity torque in EXTRAP T2R

The non-resonant magnetic perturbation (MP) braking is studied in the EXTRAP T2R reversed-field pinch (RFP) and the experimental braking torque is compared with the torque expected by the neoclassical toroidal viscosity (NTV) theory. The EXTRAP T2R active coils can apply magnetic perturbations with a single harmonic, either resonant or non-resonant. The non-resonant MP produces velocity braking with an experimental torque that affects a large part of the core region. The experimental torque is clearly related to the plasma displacement, consistent with a quadratic dependence as expected by the NTV theory. The work show a good qualitative agreement between the experimental torque in a RFP machine and NTV torque concerning both the torque density radial profile and the dependence on the non-resonant MP harmonic.

Evaluation of the toroidal torque driven by external non-resonant non-axisymmetric magnetic field perturbations in a tokamak

The toroidal torque driven by external non-resonant magnetic perturbations (neoclassical toroidal viscosity) is an important momentum source affecting the toroidal plasma rotation in tokamaks. The well-known force-flux relation directly links this torque to the non-ambipolar neoclassical particle fluxes arising due to the violation of the toroidal symmetry of the magnetic field. Here, a quasilinear approach for the numerical computation of these fluxes is described, which reduces the dimension of a standard neoclassical transport problem by one without model simplifications of the linearized drift kinetic equation. The only limiting condition is that the non-axisymmetric perturbation field is small enough such that the effect of the perturbation field on particle motion within the flux surface is negligible. Therefore, in addition to most of the transport regimes described by the banana (bounce averaged) kinetic equation also such regimes as, e.g., ripple-plateau and resonant diffusion regimes are naturally included in this approach. Based on this approach, a quasilinear version of the code NEO-2 [W. Kernbichler et al., Plasma Fusion Res. 3, S1061 (2008).] has been developed and benchmarked against a few analytical and numerical models. Results from NEO-2 stay in good agreement with results from these models in their pertinent range of validity.

Fast-ion redistribution and loss due to edge perturbations in the ASDEX Upgrade, DIII-D and KSTAR tokamaks

The impact of edge localized modes (ELMs) and externally applied resonant and non-resonant magnetic perturbations (MPs) on fast-ion confinement/transport have been investigated in the ASDEX Upgrade (AUG), DIII-D and KSTAR tokamaks. Two phases with respect to the ELM cycle can be clearly distinguished in ELM-induced fast-ion losses. Inter-ELM losses are characterized by a coherent modulation of the plasma density around the separatrix while intra-ELM losses appear as well-defined bursts. In high collisionality plasmas with mitigated ELMs, externally applied MPs have little effect on kinetic profiles, including fast-ions, while a strong impact on kinetic profiles is observed in low-collisionality, low q95 plasmas with resonant and non-resonant MPs. In low-collisionality H-mode plasmas, the large fast-ion filaments observed during ELMs are replaced by a loss of fast-ions with a broad-band frequency and an amplitude of up to an order of magnitude higher than the neutral beam injection prompt loss signal without MPs. A clear synergy in the overall fast-ion transport is observed between MPs and neoclassical tearing modes. Measured fast-ion losses are typically on banana orbits that explore the entire pedestal/scrape-off layer. The fast-ion response to externally applied MPs presented here may be of general interest for the community to better understand the MP field penetration and overall plasma response.

High resolution detection and excitation of resonant magnetic perturbations in a wall-stabilized tokamak

We report high-resolution detection of the 3D plasma magnetic response of wall-stabilized tokamak discharges in the High Beta Tokamak-Extended Pulse [T. H. Ivers et al., Phys. Plasmas 3, 1926 (1996)] device. A new adjustable conducting wall has been installed on HBT-EP made up of 20 independent, movable, wall segments instrumented with three distinct sets of 40 modular coils that can be independently driven to generate a wide variety of magnetic perturbations. High-resolution detection of the plasma response is made with 216 poloidal and radial magnetic sensors that have been located and calibrated with high-accuracy. Static and dynamic plasma responses to resonant and non-resonant magnetic perturbations are observed through measurement of the step-response following a rapid change in the toroidal phase of the applied perturbations. Biorthogonal decomposition of the full set of magnetic sensors clearly defines the structures of naturally occurring external kinks as being composed of independent m/n = 3/1 and 6/2 modes. Resonant magnetic perturbations were applied to discharges with pre-existing, saturated m/n = 3/1 external kink mode activity. This m/n = 3/1 kink mode was observed to lock to the applied perturbation field. During this kink mode locked period, the plasma resonant response is characterized by a linear, a saturated, and a disruptive plasma regime dependent on the magnitude of the applied field and value of the edge safety factor and plasma rotation.

Effects of 3D magnetic perturbations on toroidal plasmas

Small three-dimensional (3D) magnetic field perturbations have many interesting and possibly useful effects on tokamak and quasi-symmetric stellarator plasmas. Plasma transport equations that include these effects, most notably on diamagnetic-level toroidal plasma flows, have recently been developed. The 3D field perturbations and their plasma effects can be classified according to their toroidal mode number n: low n (say 1–5) resonant (with field line pitch, q = m/n) and non-resonant fields, medium n (∼20, due to toroidal field ripple) and high n (due to microturbulence). Low n non-resonant fields induce a neoclassical toroidal viscosity (NTV) that damps toroidal rotation throughout the plasma towards an offset rotation in the counter-current direction. Recent tokamak experiments have generally confirmed and exploited these predictions by applying external low n non-resonant magnetic perturbations. Medium n toroidal field ripple produces similar effects plus possible ripple-trapping NTV effects and ion direct losses in the edge. A low n (e.g. n = 1) resonant field is mostly shielded by the toroidally rotating plasma at and inside the resonant (rational) surface. If it is large enough it can stop plasma rotation at the rational surface, facilitate magnetic reconnection there and lead to a growing stationary magnetic island (locked mode), which often causes a plasma disruption. Externally applied 3D magnetic perturbations usually have many components. In the plasma their lowest n (e.g. n = 1) externally resonant components can be amplified by kink-type plasma responses, particularly at high β. Low n plasma instabilities (e.g. resistive wall modes, neoclassical tearing modes) cause additional 3D magnetic perturbations in tokamak plasmas. Tearing modes in their nonlinear (Rutherford) regime bifurcate the topology and form magnetic islands. Finally, multiple resonant magnetic perturbations (RMPs) can, if not shielded by plasma rotation effects, cause local magnetic stochasticity and increase plasma transport in the edge of H-mode plasmas. These various effects of 3D fields can be used to modify directly the plasma toroidal rotation (and possibly transport via multiple RMPs for controlling edge localized modes) and indirectly anomalous plasma transport. The present understanding and modelling of these various 3D magnetic field perturbation effects including for test blanket modules in ITER are summarized. Finally, implications of the present understanding and key open issues for developing a predictive capability of them for ITER are discussed.

First Observation of Edge Localized Modes Mitigation with Resonant and Nonresonant Magnetic Perturbations in ASDEX Upgrade

First experiments with nonaxisymmetric magnetic perturbations, toroidal mode number n=2, produced by newly installed in-vessel saddle coils in the ASDEX Upgrade tokamak show significant reduction of plasma energy loss and peak divertor power load associated with type-I edge localized modes (ELMs) in high-confinement mode plasmas. ELM mitigation is observed above an edge density threshold and is obtained both with magnetic perturbations that are resonant and not resonant with the edge safety factor profile. Compared with unperturbed type-I ELMy reference plasmas, plasmas with mitigated ELMs show similar confinement, similar plasma density, and lower tungsten impurity concentration.

Momentum-Transport Studies in HighE×BShear Plasmas in the National Spherical Torus Experiment

Experiments have been conducted at the National Sperical Torus Experiment (NSTX) to study both steady state and perturbative momentum transport. These studies are unique in their parameter space under investigation, where the low aspect ratio of NSTX results in rapid plasma rotation with ExB shearing rates high enough to suppress low-k turbulence. In some cases, the ratio of momentum to energy confinement time is found to exceed five. Momentum pinch velocities of order 10-40 m/s are inferred from the measured angular momentum flux evolution after nonresonant magnetic perturbations are applied to brake the plasma.

A Description of a D-3He Fusion Reactor Based on a Dipole Magnetic Field

This paper discusses an ideal magnetic container for a D-{sup 3}He fusion reactor which must ensure both the stability of the confined plasma and the ability to control the confinement of fusion products. A dipole magnetic field may be suitable for D-{sup 3}He fusion since it is predicted to be able to confine high-beta plasmas while allowing extraction of the high-energy charged fusion products for direct conversion as well as removal of fusion ash using resonant and/or nonresonant magnetic perturbations. New calculations of fusion product control and plasma stability with isotropic pitch-angle distributions are described. In addition, the parameters of a new, higher field dipole reactor design are discussed.