Static Magnetic Perturbations Research Articles

Active control of Alfvén eigenmodes by external magnetic perturbations with different spatial spectra

Alfvén eigenmodes have been suppressed and excited in tokamak plasmas by (just) modifying the poloidal spectra of externally applied static magnetic perturbations. This effect is observed experimentally when toroidal spectra of n = 2, n = 4 as well as a mixed spectrum of n = 2 and n = 4 is applied. Under the n = 2 magnetic perturbations, the modes are excited or suppressed by modifying the coil phasing between the upper and the lower set of coils. Regardless of the absolute rotation, an even parity for the n = 4 perturbation is observed to reduce the amplitude of the Alfvénic instabilities, while an odd parity amplifies it. To combine the stabilizing (and destabilizing) effect of n = 2 and n = 4, a mixed spectrum is applied, finding similar reduction (and amplification) trends. However, the impact on the mode amplitude is more subtle, due to the reduced coil current required for a mixed spectrum. The signal level on the fast-ion loss detector is sensitive to the applied poloidal spectrum, which is consistent with Hamiltonian full-orbit modelling of an edge resonant transport layer activated by the 3D perturbative fields. An internal redistribution of the fast-ion population is induced, modifying the phase-space gradients driving the Alfvénic instabilities, and ultimately determining their existence. The calculated edge resonant layers for both n = 2 and n = 4 toroidal spectra are consistent with the observed suppressed and excited phases. Moreover, hybrid kinetic-magnetohydrodynamic (MHD) simulations reveal that this edge resonant transport layer overlaps in phase-space with the population responsible for the fast-ion drive. The results presented here may help to control fast-ion driven Alfvénic instabilities in future burning plasmas with a significant fusion born alpha particle population.

Instability and turbulent relaxation in a stochastic magnetic field

An analysis of instability dynamics in a stochastic magnetic field is presented for the tractable case of the resistive interchange. Externally prescribed static magnetic perturbations convert the eigenmode problem to a stochastic differential equation, which is solved by the method of averaging. The dynamics are rendered multi-scale, due to the size disparity between the test mode and magnetic perturbations. Maintaining quasi-neutrality at all orders requires that small-scale convective cell turbulence be driven by disparate scale interaction. The cells in turn produce turbulent mixing of vorticity and pressure, which is calculated by fluctuation-dissipation type analyses, and are relevant to pump-out phenomena. The development of correlation between the ambient magnetic perturbations and the cells is demonstrated, showing that turbulence will ‘lock on’ to ambient stochasticity. Magnetic perturbations are shown to produce a magnetic braking effect on vorticity generation at large scale. Detailed testable predictions are presented. The relations of these findings to the results of available simulations and recent experiments are discussed.

Pitch angle scattering of fast particles by low frequency magnetic fluctuations

The adiabatic invariance of the magnetic moment during particle motion is of fundamental importance to the dynamics of magnetized plasma. The related rate of pitch angle scattering is investigated here for fast particles that thermally stream through static magnetic perturbations. For a uniform magnetic field with a localized perturbation, it is found that the curvature parameter κ2=min(Rc/ρL) does not predict the level of pitch angle scattering. Instead, based on numerical integration of particle orbits in prescribed magnetic fields, we derive predictions for the particle scattering rates, which can be characterized by the relative perturbation amplitude A≃δB/B, and the particle Larmor radius normalized by the field-aligned wavelength of the perturbations, ρL/λ||. Particles with ρL/λ||≃1 are subject to strong pitch angle scattering, while the level of scattering vanishes for both the limits of ρL/λ||≪1 and ρL/λ||≫1. The results are summarized in terms of a scattering operator, suitable for including the described scattering in basic kinetic models.

Nonlinear two-fluid modeling of plasma response to RMPs for the ELM control in the ITER baseline

Numerical modeling, combining the toroidal ideal MHD code GPEC and the nonlinear two-fluid MHD code TM1, was used for comprehensive studies of the plasma response to resonant magnetic perturbations (RMPs) with toroidal mode number n = 1–5 for controlling edge-localized modes (ELMs) in ITER for the standard operation scenario (15 MA Q = 10). Several issues related to RMP ELM control are investigated, including the optimization of the RMP coils configuration, the evaluation of the magnitude of density pump-out and the q 95 windows of ELM suppression. GPEC calculates the magnetic response, which consistently includes the very important edge kink/peeling response to static magnetic perturbations. GPEC two-dimensional scans of the relative coil current phasing among the three rows of internal coils, at fixed coil current amplitude, reveal the optimal phasing for the RMP coil configuration with n = 1–5, respectively. The poloidal half wavelength of resonant mode at the edge of plasma calculated by GPEC indicates that the midplane row coils have the best resonant coupling with the plasma for n = 2, while the upper and lower row coils have the best resonant coupling with the plasma for n = 3. Based on the plasma kinetic equilibrium and the GPEC calculations of the magnetic response, TM1 was used to simulate the conditions for RMP field penetration in the ITER pedestal. TM1 shows magnetic island formation at the foot of ITER pedestal with RMP coil current threshold ranging from 4 kAt to 8 kAt with n = 2 to 4. These magnetic islands at the pedestal-foot lead to density pump-out, the magnitude of which scales as and ranges from 5% to 20% at the pedestal-top when scanning the coil current from 4 to 60 kAt. The density pump-out is found to be weaker for higher n RMP. The nonlinear TM1 simulations also show field penetration at the pedestal-top, where the threshold of RMP coil current depends on the q 95. The alignment of the magnetic island and the location of the pedestal-top decreases the height and width of the pedestal to suppress ELMs. Simulations by two-dimensional scans of RMP coil current and q 95 reveal the accessible q 95 windows of ELM suppression for both n = 3 and 4 RMPs. The predicted q 95 windows of ELM suppression are very similar to the ones in currently operating tokamaks and the required RMP coil current for ELM suppression is less than 40–50 kAt, which is well within the designed capability for ITER. In addition, the simulations indicate that wide q 95 windows of ELM suppression may be accessible in ITER by operating with dominant n = 4 (or n = 5) RMPs.

Efficient estimation of drift orbit island width for passing ions in a shaped tokamak plasma with a static magnetic perturbation

Non-axisymmetric magnetic perturbations contribute to the transport of fast ions in tokamaks. While knowledge of the perturbed magnetic topology suffices for characterizing the displacement of thermal particles (few keV), the trajectories of fast particles (0.1–few keV) vary depending on their charge, mass, kinetic energy and velocity pitch. The computational effort needed to follow the drift orbits for a large number of phase space samples (as done in Monte Carlo simulations) is too high for scenario simulators, so it is necessary to develop computationally efficient reduced models. In this paper, we present a method that allows to estimate the locations, widths and overlaps of resonant drift orbit islands in the guiding center phase space of passing fast ions with small computational effort. The new method constitutes a significant improvement over the method presented in our previous work (Shinohara K. et al 2018 Nucl. Fusion 58 082026), both in performance and in accuracy. This is achieved by deriving an expression for the drift orbit island width from the perturbed guiding center velocity in the straight-orbit coordinates of the unperturbed drift surfaces and eliminating the need for computationally expensive Poincaré maps. When applied to resonant magnetic perturbation fields in a KSTAR tokamak plasma, our new estimates for the island widths are shown to agree with Poincaré maps from orbit-following simulations to within 15%. The island positions and the chaotic regions caused by island overlaps also agree well.

Observation of toroidal Alfvén eigenmode excited by energetic electrons induced by static magnetic perturbations in the EAST tokamak

A toroidal Alfvén eigenmode (TAE) excited by barely trapped energetic electrons during the application of a static magnetic perturbations (MPs) is observed for the first time in tokamak ohmic heating plasmas. This TAE appears when the current of a static n = 2 MPs exceeds a threshold value, at which a forced n = 2 magnetic reconnection happens. Here, n is the toroidal mode number. This TAE is located near the plasma edge, which agrees with the calculation of the TAE gap. It propagates in the ion diamagnetic direction and has a dominant toroidal mode number n = 2. The frequency of the TAE is consistent with the precessional frequency of the barely trapped energetic electrons with energy around 150 keV. An increase of the hard x-ray emission intensity in this energy range is observed just after the n = 2 magnetic reconnection. The energetic electrons may be accelerated by the magnetic islands formed after reconnection. The TAE is stabilized after a reduction in the contents of energetic electrons. This observation suggests that the application of static MPs may provide us with a novel method to actively control Alfvén eigenmodes in fusion plasmas.

Estimation of orbit island width from static magnetic island width, using safety factor and orbit pitch

In order to account for the effect of field perturbations on the transport of fast ions in integrated codes used for the simulation of operational scenarios, it is crucial to develop computationally efficient reduced transport models. Such modeling efforts may greatly benefit from a simple method that determines the width of the island-like structures, which are produced by resonant perturbations in the phase space of the fast ion guiding centers and are known to play a key role for fast ion transport enhancement. In this paper, we present a method for estimating the widths of such ‘orbit islands’ for passing particles in the presence of static magnetic perturbations. The method consists of mapping the boundaries of magnetic islands from magnetic flux space () into the canonical angular momentum space () of the fast ions. As a working example, we consider co-passing neutral beam (NB) ions subject to a resonant magnetic perturbation (RMP) in a KSTAR tokamak plasma. The estimated orbit island width deviates by less than 25% from the value obtained from Poincaré plots of the actual guiding center trajectories, even when the magnetic drifts are large (here, up to 50% of the minor radius). Our analysis also shows that most of the fast ion transport can be attributed to the effect of isolated islands, which means that stochastization of particle trajectories due to resonance overlaps does not play a major role in the case studied here. The island mapping method proposed here eliminates the need to compute and analyze Poincaré maps of particle trajectories, so that computation times can be reduced tremendously by several orders of magnitude. A further speed-up may be achieved by the development of a method for estimating the width of magnetic islands under realistic conditions.

Modeling non-stationary, non-axisymmetric heat patterns in DIII-D tokamak

Non-axisymmetric stationary magnetic perturbations lead to the formation of homoclinic tangles near the divertor magnetic saddle in tokamak discharges. These tangles intersect the divertor plates in static helical structures that delimit the regions reached by open magnetic field lines reaching the plasma column and leading the charged particles to the strike surfaces by parallel transport. In this article we introduce a non-axisymmetric rotating magnetic perturbation to model the time evolution of the three-dimensional magnetic field of a single-null DIII-D tokamak discharge developing a rotating tearing mode. The non-axiymmetric field is modeled using the magnetic signals to adjust the phases and currents of a set of internal filamentary currents that approximate the magnetic field in the plasma edge region. The stable and unstable manifolds of the asymmetric magnetic saddle are obtained through an adaptive calculation providing the cuts at a given poloidal plane and the strike surfaces. For the modeled shot, the experimental heat pattern and its time development are well described by the rotating unstable manifold, indicating the emergence of homoclinic lobes in a rotating frame due to the plasma instabilities.

The impact of static magnetic perturbations on edge localized modes

The physics of edge localized modes (ELMs) mitigated by static magnetic perturbations (SMPs) with a toroidal mode number n=0 is studied. Three-field reduced magnetohydrodynamics (MHD) equations are solved by BOUT++ code. In the simulation, an effective mitigation of ELM has been observed when SMPs are added. A new mechanism of ELM mitigation is proposed that n=0 SMPs can excite a wide toroidal mode spectrum through E×B shearing rate which diminishes turbulent transport in the nonlinear phase. The mechanism is confirmed by the simulation results and relevant physical analysis in this paper.

Fast-Ion Losses due to Externally Applied Static Magnetic Perturbations in the Large Helical Device

Fast-Ion Losses due to Externally Applied Static Magnetic Perturbations in the Large Helical Device

A drift-magnetohydrodynamical fluid model of helical magnetic island equilibria in the pedestals of H-mode tokamak plasmas

A drift-magnetohydrodynamical (MHD) fluid model is developed for an isolated, steady-state, helical magnetic island chain, embedded in the pedestal of a large aspect ratio, low-β, circular cross section, H-mode tokamak plasma, to which an externally generated, multiharmonic, static magnetic perturbation whose amplitude is sufficiently large to fully relax the pedestal toroidal ion flow is applied. The model is based on a set of single helicity, reduced, drift-MHD fluid equations which take into account neoclassical poloidal and toroidal flow damping, the perturbed bootstrap current, diamagnetic flows, anomalous cross-field diffusion, average magnetic-field line curvature, and coupling to drift-acoustic waves. These equations are solved analytically in a number of different ordering regimes by means of a systematic expansion in small quantities. For the case of a freely rotating island chain, the main aims of the calculation are to determine the chain’s phase velocity, and the sign and magnitude of the ion polarization term appearing in its Rutherford radial width evolution equation. For the case of a locked island chain, the main aims of the calculation are to determine the sign and magnitude of the polarization term.

Impact of stochastic magnetic fields on plasma rotation and radial electric fields in the plasma edge of the tokamak TEXTOR

In this contribution we report on spectroscopic measurements of plasma rotation and the radial electric field in the plasma boundary under the operation of the dynamic ergodic divertor in TEXTOR. Under the influence of the stochastic magnetic field we observe an increase of both poloidal and toroidal rotation of carbon nuclei into ion-diamagnetic drift/co-current direction. With static magnetic perturbation the electric field in the ergodic region increases by 10kV/m and becomes positive. Application of dynamic perturbation leads to a comparable change of the rotation, independent of the direction of the rotation of the DED field and only depending on the degree of ergodization. We introduce a model to explain the experimental findings by the onset of transverse currents in the ergodic region and a subsequent torque onto the plasma.

Reduction of Thermal Wall Load by Gas Puffing in Reversed-Field Pinch Device, TPE-RX

We report that the thermal wall load due to locked modes can be decreased by means of gas puffing in the reversed-field pinch (RFP) device, TPE-RX [Y. Yagi et al.: Fus. Eng. Design 45 (1999) 409]. Under standard RFP operation in TPE-RX, the phase- and wall-locked modes, i.e., spatially localized and stationary magnetic perturbations, respectively, appear after the current-rising phase. The locked modes cause a severe thermal wall load of the order of 100 MW/m2 on the first wall. It is estimated that the temperature on the plasma-facing wall at the mode-locking position sometimes exceeds the melting temperature of stainless steel. The thermal wall load increases with plasma current, Ip. We have succeeded in mitigating the high thermal wall load by gas puffing during discharges. It is shown that the maximum temperature increment of the vacuum vessel wall is halved when a gas-puffing rate of 200 Pa m3/s is applied at Ip=350 kA. The characteristics of the temperature increase of the vacuum vessel are presented, and they indicate the nature of the locked mode in RFP discharges in TPE-RX.

Magnetic field stochasticity in the presence of current sheets

The stochasticity of field lines around a current sheet induced by static magnetic perturbations is investigated. By means of Hamiltonian analysis, it is pointed out that the system exhibits two different chaotic regimes, depending on the wavelength of the perturbation: At short wavelengths (shorter than the length of the separatrix), resonant processes determine the onset of stochasticity and can be modeled by a simple mapping; at long wavelengths of the perturbation, stochasticity is mainly due to the breaking of adiabatic invariants.

Nonlinear tearing mode interactions and mode locking in reversed-field pinches

The nonlinear interaction of a set of tearing instabilities and plasma flow is studied in a cylindrical plasma. An analytic theory of mode locking is developed, which includes the effects of the localized electromagnetic torques, plasma inertia, and cross-field viscosity. The calculation is specialized for the case of mode locking on the Madison Symmetric Torus (MST) reversed-field pinch [R. N. Dexter et al., Fusion Technol. 19, 131 (1991)]. In MST plasmas, a set of m=1 tearing instabilities become phase locked and form a toroidally localized, rotating magnetic disturbance. An evolution equation for the phase velocity of this magnetic disturbance is derived that accounts for two types of electromagnetic torques. The external torques describe the interaction of the tearing modes with static magnetic perturbations located outside the plasma region. The interior torques describe the nonlinear interaction of three tearing modes that satisfy a wave number resonance condition. For conditions typical of MST, the internal torques dominate the external torques, which suggest the nonlinear interaction of tearing instabilities play a prominent role in the momentum degradation and mode locking.

Stationary magnetic pertubation diagnostic on TFTR (abstract)a)

Stationary magnetic perturbations (SMPs) in tokamaks may consist of (1) static magnetic field errors, (2) dynamic magnetic field errors, and (3) stationary MHD modes (or locked mode). The diagnostic aimed to detect the latter two classes of SMPs on the TFTR tokamak has two pairs of sensors, each consisting of a saddle loop for measuring predominantly radial field and auxiliary loops for measuring predominantly toroidal and vertical fields. Members of each pair are placed 180° apart toroidally. Predominantly n=1 SMPs are found in various discharges including ohmic discharges. Abrupt changes in SMP signals precede a ‘‘tail-end’’ disruption, suggesting a causality relationship. Variations in the SMP signals are also coincident with severe performance degradation of super shots and pellet injected discharges. An analysis of individual and paired signals appears to indicate that these SMPs are dynamic field errors as well as stationary MHD modes.

The structure and dynamics of electrostatic and magnetostatic drift holes

Localized, nonwavelike phase-space density fluctuations with self-trapping potentials, called drift holes, are studied for systems with density gradients. The three-dimensional structure of maximally probable, isolated electrostatic drift holes is determined and shown to satisfy a condition for self-trapping. The dynamics of such structures is examined. It is shown that under a broad set of conditions the potential amplitude, hole depth, and velocity-space width grow nonlinearly while maintaining the self-trapping structure. The nonlinear instability responsible for growth requires dissipative coupling between the trapped particles and the passing particles of the opposite species. Two saturation mechanisms for this instability are described and saturated amplitude estimates are given. It is shown that when the hole velocity is small compared to the speed of light, self-consistent coupling of stationary magnetic perturbations to the electrostatic potential is possible and produces structures called magnetostatic drift holes. The role of electrostatic and magnetostatic drift holes as a constituent of intermittent plasma turbulence is discussed.