Static Resonant Magnetic Perturbations Research Articles

Acceleration of plasma toroidal rotation driven by non-axisymmetric magnetic perturbation fields in the EAST tokamak

Plasma toroidal rotation acceleration in the co-current direction introduced by the n = 1 (toroidal mode number) static resonant magnetic perturbation (RMP) has been observed in the EAST tokamak. It strongly depends on the RMP coil configuration, which is manifested by its dependence on δϕUL (phase difference between upper and lower coils) and RMP current. Modeling results from NTVTOK based on the linear plasma response modeled by MARS-F shows that the Neoclassical Toroidal Viscosity (NTV) torque is in the co-current direction because of the dominant contribution from electrons with the condition that the electron normalized collisionality is much lower than that of ions in this experiment. The modeled dependence of core integrated NTV torque modulated by the magnitude of core magnetic perturbation on δϕUL is consistent with the experimental observations. Threshold condition related to normalized collisionality to achieve the transition from rotation braking to acceleration is obtained in the NTV modeling and agrees well with experimental observations. It is shown in the modeling that the discharges with rotation acceleration are located at the regime that electron contribution to NTV is dominant and the torque is in co-current direction, while others with rotation braking are located at the regime that ion contribution to NTV torque is dominant and the torque is in countercurrent direction. Though the modeling results are in qualitative agreement with the experimental results, there is quantity difference between the modeled NTV torque based on linear plasma response and the experimental values. Possible reason is that the 3D fields are underestimated by linear modeling, particularly in the case of RMP field penetration, as demonstrated by the RMP current threshold for the rotation acceleration observed in the experiments.

Prevention of mode coupling by external applied resonant magnetic perturbation on the J-TEXT tokamak

Toroidal coupling between m/n = 2/1 and m/n = 3/1 modes frequently occurs in the J-TEXT, where m (n) is the poloidal (toroidal) mode number. These coupled modes destabilize each other, leading to confinement degradation and even triggering a major disruption. This paper presents two control strategies for preventing the mode coupling through the application of a proper static resonant magnetic perturbation (RMP) field. Experimental results demonstrate that moderate 2/1 RMP can suppress the small, rotating 2/1 mode thus prevent coupling between the 2/1 and 3/1 modes. The 3/1 static RMP can excite a large 3/1 locked island while leave the small 2/1 mode rotating at 8 kHz. Enlarging the frequency difference between 2/1 and 3/1 modes makes mode coupling more difficult. Both strategies can break the frequency coupling condition between the 2/1 and 3/1 modes, and hence avoid coupling and mutual destabilizing.

A brief review of the development and optimization of the three-dimensional magnetic configuration system in the J-TEXT tokamak

The three-dimensional (3D) magnetic configuration system in the J-TEXT tokamak has featured in many experimental studies. The system mainly consists of three subsystems: the static resonant magnetic perturbation (SRMP) system, the dynamic resonant magnetic perturbation (DRMP) system and the helical coil system. The SRMP coil system consist of two kinds of coils, i.e. three six-loop coils and two five-loop coils. It can suppress tearing modes with a moderate strength, and may also cause mode locking with larger amplitude. The DRMP coil system consists of 12 single-turn saddle coils (DRMP1) and 12 double-turn saddle coils (DRMP2). Its magnetic field can be rotated at a few kHz, leading to either acceleration or deceleration of the tearing mode velocity and the plasma rotation. The helical coil system consists of two closed coils, and is currently under construction to provide external rotational transform in J-TEXT. The 3D magnetic configuration system can suppress tearing modes, preventing and avoiding the occurrence of major disruption.

Advances in physics and applications of 3D magnetic perturbations on the J-TEXT tokamak

In the last two years, three major technical improvements have been made on J-TEXT in supporting of the expanded operation regions and diagnostic capabilities. (1) The successful commission of the 105 GHz/500 kW/1 s electron cyclotron resonance heating (ECRH) system increasing the core electron temperature from 0.9 keV up to around 1.5 keV. (2) The poloidal divertor configuration with an X-point in the high-field side has been achieved. In particular, the 400 kW electron cyclotron wave has also been successfully injected into the diverted plasma. (3) A 256-channel electron cyclotron emission imaging diagnostic system and two sets of four-channel Doppler backscattering diagnostics have been successfully developed on J-TEXT, allowing detailed measurement of the electron temperature and density fluctuations for turbulence and MHD research. The locked mode (LM), especially the 2/1 LM, is one of the biggest threats to the plasma operation. Both the thresholds of 2/1 and 3/1 LM are observed to vary non-monotonically on electron density. The electrode biasing was applied successfully to unlock the LM from either a rotating or static resonant magnetic perturbation (RMP) field. In the presence of 2/1 LM, three kinds of standing wave (SW) structures have been observed to share a similar connection to the island structure, i.e. the nodes of the SWs locate around the O- or X-points of the 2/1 island. The control and mitigation of disruption is essential to the safe operation of ITER, and it has been systematically studied by applying a RMP field, massive gas injection (MGI) and shattered pellet injection on J-TEXT. When the RMP-induced 2/1 LM is larger than a critical width, the MGI shutdown process can be significantly influenced. If the phase difference between the O-point of LM and the MGI valve is +90° (or −90°), the penetration depth and the assimilation of impurities can be enhanced (or suppressed) during the pre-thermal quench (TQ) phase and result in a faster (or slower) TQ. A secondary MGI can also suppress the runaway electron (RE) generation, if the additional high-Z impurity gas arrives at the plasma edge before TQ. When the secondary MGI has been applied after the formation of the RE current plateau, the RE current can be dissipated, and the dissipation rate increases with the injected impurity quantity but saturates with a maximum of 28 MA s−1. The non-local transport is experimentally observed in the ion transport channel. The electron thermal diffusivity significantly increases with the ECRH power. Theoretical work shows that significant intrinsic current can be driven by electromagnetic turbulence, and the robust formation mechanism of the E × B staircase is identified from the Hasegawa–Wakatani system.

Drift orbit islands of energetic particles due to 3D fields in ITER

In this paper, we report a comparative study of the orbit islands formed by the guiding center drift motion of test energetic particles (EPs), including both high-energy deuterium ions and fusion-born α-particles, with respect to the magnetic islands formed by tracing the field lines, for an ITER plasma representing the 15 MA baseline scenario. The particle drift orbit is modified by the presence of static resonant magnetic perturbations (RMPs) of different toroidal mode numbers n (n = 1 and 3 in this study), forming orbit islands in the Poincaré plane by passing EPs. The key findings are as follows. (i) With an n = 1 RMP field, the size of the orbit islands combined with the total RMP field, including the plasma response, is about three times smaller than that obtained by assuming the corresponding vacuum field. (ii) The orbit island size is not sensitive to the EP energy, and is comparable to those of the magnetic islands. (iii) Passing EPs with outward radial orbital drift form orbit islands that shift inward with respect to the corresponding magnetic islands, and vice versa. This radial shift, ΔΨ, measured in the normalized equilibrium poloidal flux, is quantified as ΔΨ ≃ 0.03X for the ITER baseline plasma and assuming n = 1 RMPs, with , where M is the particle mass, M p is the proton mass, E is the particle energy, and Z is the particle charge number. (iv) Trapped EPs do not form drift orbit islands, even in the presence of the 3D fields produced by the 90 kAt ELM control coil current in ITER, and thus possess good confinement properties. Nevertheless, the deformation of the trapped particle drift orbits in the Poincaré plane shows that the canonical toroidal angular momentum of EPs is no longer conserved in the presence of the RMP fields.

Modeling q95 windows for the suppression of edge localized modes by resonant magnetic perturbations in the DIII-D tokamak

A toroidal asymptotic matching model of the response of a tokamak plasma to a static resonant magnetic perturbation (RMP) is used to simulate the n = 3 RMP-induced edge-localized-mode-suppression windows in q95 that are evident when the plasma current is slowly ramped in DIII-D discharge #145380. All quantities employed in the simulation are derived from experimental measurements, apart from the neutral particle data. Three cases are considered. In the first case, the natural frequencies of tearing modes resonant in the plasma are determined by the ion flows at the corresponding resonant surfaces, which is the prediction of nonlinear tearing mode theory. In the second case, the natural frequencies are determined by the local E×B velocities at the resonant surfaces. In the third case, the natural frequencies are determined by the electron flows at the resonant surfaces, which is the prediction of linear tearing mode theory. The second case gives the best agreement between the simulations and the experimental observations. The first and third cases only lead to partial agreement between the simulations and the observations. In the first case, the lack of complete agreement may be a consequence of using an inaccurate assumption for the neutral particle distribution in the pedestal. In the third case, the lack of complete agreement is probably due to the fact that the response of a tokamak plasma to an RMP is not accurately described by linear tearing mode theory.

Numerical simulation of neoclassical tearing modes induced by resonant magnetic perturbations in tokamak plasmas

A model of neoclassical tearing mode (NTM) induced by resonant magnetic perturbation (RMP) in the presence of the bootstrap current in tokamak plasmas is established based on the full magnetohydrodynamic equations. The model is solved numerically by using a finite difference method and the numerical results are obtained. It is found that, the NTM can be induced by the given stable equilibrium, added the perturbed bootstrap current in ohm equation, and the applied RMP. Moreover, with the increasing amplitude of the static RMP, locked mode occurs, which is determined by the plasma flow and fraction of bootstrap current. The mode locking threshold increases with the increasing of plasma rotation frequency and decreasing of fraction of bootstrap current. Furthermore, the dynamic RMP is investigated, results show that the mode locking threshold is lower compared to the static RMP applied, which provides a better way of adjusting the NTM to the frequency of dynamic RMP and slightly suppressing the neoclassical magnetic island.

An improved theory of the response of DIII-D H-mode discharges to static resonant magnetic perturbations and its implications for the suppression of edge localized modes

The plasma response to an externally generated, static, n = 2, resonant magnetic perturbation (RMP) in the pedestal region of DIII-D H-mode discharge #158115 is investigated using a toroidal generalization of the asymptotic matching model presented by Fitzpatrick [Phys. Plasmas 27, 042506 (2020)]. Just as in a recent paper [Q. M. Hu et al., Phys. Plasmas 26, 120702 (2019)], it is hypothesized that the density pump-out phenomenon is due to locked magnetic island chains induced at the bottom of the pedestal, whereas the suppression of edge localized modes is associated with a locked magnetic island chain induced at the top of the pedestal. Neutral penetration inside the last closed magnetic flux-surface is found to have a significant influence on locked magnetic island chain formation at the bottom of the pedestal. It is found that locked island formation at the top of the pedestal is only possible when q95 lies in certain narrow windows. Finally, it is inferred that, in order to successfully induce a locked island chain at the top of the pedestal, an external RMP field-coil system must generate a magnetic field that is simultaneously strongly amplified by the plasma (via the ideal kink response) and has a large resonant component at a rational surface that lies close to the top of the pedestal.

Theory of edge localized mode suppression by static resonant magnetic perturbations in the DIII-D tokamak

According to a recent paper [Hu et al., Phys. Plasmas 26, 120702 (2019)], mode penetration at the top of the pedestal is a necessary and sufficient condition for the suppression of edge localized modes (ELMs) by a resonant magnetic perturbation (RMPs) in an H-mode tokamak discharge. This paper employs asymptotic matching theory to model a particular DIII-D discharge in which ELMs were suppressed by an externally generated, static, n = 2, RMP whose amplitude was modulated at a frequency of 1 Hz. It is demonstrated that the response of the plasma to the applied RMP, in the immediate vicinities of the rational (i.e., resonant) surfaces, is governed by nonlinear, rather than by linear, physics. This is the case because the magnetic island widths associated with driven reconnection exceed the linear layer widths, even in cases where driven reconnection is strongly suppressed by plasma rotation. The natural frequency at a given rational surface (i.e., the helical frequency at which the locally resonant component of the RMP would need to propagate in order to maximize driven reconnection) is found to be offset from the local E×B frame in the ion diamagnetic direction. The size of the offset is mostly determined by neoclassical poloidal rotation. Finally, the predictions of a fully nonlinear plasma response model are found to be broadly consistent with the DIII-D experimental data.

Control of neoclassical tearing mode by synergetic effects of resonant magnetic perturbation and electron cyclotron current drive in reversed magnetic shear tokamak plasmas

Synergetic effects of resonant magnetic perturbation (RMP) and electron cyclotron current drive (ECCD) on stabilizing neoclassical tearing mode (NTM) in reversed magnetic shear (RMS) tokamak plasmas are numerically investigated based on a set of reduced MHD equations. For the moderate separation, it is found that the explosive burst induced by the fast reconnection of double tearing mode (DTM) in the RMS configuration can be completely suppressed by externally applied RMPs. Zonal flows with strong shear induced by a rotating RMP play an important role in this suppression process. Moreover, turning on ECCD in advance is essential to mitigate the NTM. For the large separation without the explosive burst, two strategies, i.e. a continuous ECCD with static RMP and a modulated ECCD with rotating RMP, are separately investigated. It is shown that when the NTM is decelerated by a relatively slow rotating RMP, the modulated ECCD can have a better stabilizing effect. In addition, the ECCD deposition widths in both radial and helical angle directions, as well as the ECCD on-duty time, are analyzed in detail. The best effectiveness of ECCD is obtained and the relevant physical mechanisms are discussed.

Rotation braking with n = 1 nonaxisymmetric magnetic perturbation in the EAST tokamak

The toroidal plasma rotation braking effect during the application of n = 1 static resonant magnetic perturbation is studied by momentum transport analysis in the EAST tokamak. The braking torque shows a global profile and two peaks located near the plasma core and the edge, respectively. The effect of momentum diffusion contributes significantly to the calculated torque. Simulation results with the obtained torque and momentum diffusion coefficients well reproduce the observed plasma rotation evolution. Neoclassical toroidal viscosity (NTV) torque is modeled for comparison with the experimental torque. The total integrated NTV torque is around −0.12 Nm, which is comparable to the observed braking torque (around −0.33 Nm). In the plasma edge, there is a peak in the NTV torque profile, which agrees well in amplitude with the obvious peak in the observed torque density profile. An additional peak in the NTV torque profile due to the ion bounce resonance is also located in the core region. However, the magnitude of this peak is much smaller than the observed one near the plasma core.

Suppressing magnetic island growth by resonant magnetic perturbation

The effect of externally applied resonant magnetic perturbations (RMPs) on the growth of magnetic islands is investigated based on two-fluid equations. It is found that if the local bi-normal electron fluid velocity at the resonant surface is sufficiently large, static RMPs of the same helicity and of moderate amplitude can suppress the growth of magnetic islands in high-temperature plasmas. These islands will otherwise grow, driven by an unfavorable plasma current density profile and bootstrap current perturbation. These results indicate that the error field can stabilize island growth, if the error field amplitude is not too large and the local bi-normal electron fluid velocity is not too low. They also indicate that applied rotating RMPs with an appropriate frequency can be utilized to suppress island growth in high-temperature plasmas, even for a low bi-normal electron fluid velocity. A significant change in the local equilibrium plasma current density gradient by small amplitude RMPs is found for realistic plasma parameters, which are important for the island stability and are expected to be more important for fusion reactors with low plasma resistivity.

Response of plasma rotation to resonant magnetic perturbations in J-TEXT tokamak

The response of plasma toroidal rotation to the external resonant magnetic perturbations (RMP) has been investigated in Joint Texas Experimental Tokamak (J-TEXT) ohmic heating plasmas. For the J-TEXT’s plasmas without the application of RMP, the core toroidal rotation is in the counter-current direction while the edge rotation is near zero or slightly in the co-current direction. Both static RMP experiments and rotating RMP experiments have been applied to investigate the plasma toroidal rotation. The core toroidal rotation decreases to lower level with static RMP. At the same time, the edge rotation can spin to more than 20 km s−1 in co-current direction. On the other hand, the core plasma rotation can be slowed down or be accelerated with the rotating RMP. When the rotating RMP frequency is higher than mode frequency, the plasma rotation can be accelerated to the rotating RMP frequency. The plasma confinement is improved with high frequency rotating RMP. The plasma rotation is decelerated to the rotating RMP frequency when the rotating RMP frequency is lower than the mode frequency. The plasma confinement also degrades with low frequency rotating RMP.

Simulation of runaway electrons, transport affected by J-TEXT resonant magnetic perturbation

The topology of a magnetic field and transport properties of runaway electrons can be changed by a resonant magnetic perturbation field. The J-TEXT magnetic topology can be effectively altered via static resonant magnetic perturbation (SRMP) and dynamic resonant magnetic perturbation (DRMP). This paper studies the effect of resonant magnetic perturbation (RMP) on the confinement of runaway electrons via simulating their drift orbits in the magnetic perturbation field and calculating the orbit losses for different runaway initial energies and different runaway electrons, initial locations. The model adopted is based on Hamiltonian guiding center equations for runaway electrons, and the J-TEXT magnetic turbulences and RMP are taken into account. The simulation indicates that the loss rate of runaway electrons is sensitive to the radial position of electrons. The loss of energetic runaway beam is dominated by the shrinkage of the confinement region. Outside the shrinkage region of the runaway electrons are lost rapidly. Inside the shrinkage region the runaway beam is confined very well and is less sensitive to the magnetic perturbation. The experimental result on the response of runaway transport to the application RMP indicates that the loss of runaway electrons is dominated by the shrinkage of the confinement region, other than the external magnetic perturbation.

Research on the effect of resonant magnetic perturbations on disruption limit in J-TEXT tokamak

The effect of resonant magnetic perturbations (RMPs) on high density limit and low-q limit discharges is studied in J-TEXT tokamak. It is found that a moderate amplitude of applied RMPs increases the density limit and delays the disruption, and the disruption precursor is suppressed with a slight reduction in toroidal plasma rotation. A too large amplitude of RMPs, however, leads to a lower density limit and an earlier disruption. For the optimal RMPs amplitude, the disruption is delayed by about 150 ms. For low-q discharges, the applied static RMP can either lower the limit of the edge safety factor qa from 2.15 to nearly 2.0 or sustain stable plasma discharge with qa = 2.1, and the disruptive precursor is also suppressed.

Utilizing resonant magnetic perturbations to enhance neoclassical tearing mode stabilization by rf current

A new method to stabilize the rotating neoclassical tearing mode (NTM) by using both the rf current drive and the static resonant magnetic perturbation (RMP) is investigated. When a non-uniform mode rotation is induced by the RMP, the stabilization of NTM by the rf current is found to be enhanced if the RMP phase has a half period difference from that of the rf wave deposition along the helical angle. The required rf current for mode stabilization is reduced by about one third if an appropriate RMP amplitude is applied.

Magnetic island and plasma rotation under external resonant magnetic perturbation in the T-10 tokamak

Experimental comparison of the m = 2, n = 1 mode and plasma rotation velocities at q = 2 magnetic surface in a wide range of the mode amplitudes is presented. Phase velocity of the mode rotation is measured with a set of poloidal magnetic field sensors located at the inner side of the vacuum vessel wall. Plasma rotation velocity at the q = 2 magnetic surface in the direction of the mode phase velocity is measured with the heavy ion beam probe diagnostics. In the presence of a static Resonant Magnetic Perturbation (RMP), the rotation is irregular that appears as cyclical variations of the mode and plasma instantaneous velocities. The period of these variations is equal to the period of the mode oscillations. In the case of high mode amplitude, the rotation irregularity of the mode is consistent with the rotation irregularity of the resonant plasma layer. On the contrary, the observed rise of the mode rotation irregularity in the case of low mode amplitude occurs without an increase of the rotation irregularity of the resonant plasma layer. The experimental results are simulated and analyzed with the TEAR code based on the two-fluid MHD approximation. Calculated irregularities of the mode and plasma rotation depend on the mode amplitude similar to the experimental data. For large islands, the rotation irregularity is attributed to oscillations of the electromagnetic torque applied to the resonant plasma layer. For small islands, the deviation of the mode rotation velocity from the plasma velocity occurs due to the effect of finite plasma resistivity.

Observation of beta-induced Alfvén Eigenmode in J-TEXT tokamak

High-frequency oscillations have been frequently observed under the conditions of tearing modes and runaway electrons in J-TEXT Ohmic plasmas. It is found the frequencies of these oscillations range from 20 to 45 kHz, being consistent with the beta-induced Alfvén Eigenmodes (BAEs) with the same order of the low-frequency gap induced by finite beta effects and the coupling of the shear Alfvén wave with the compressional response of the plasma. The exciting conditions for BAEs are investigated, which indicate that runaway electrons, as well as magnetic perturbations contributed by magnetic islands, are indispensable in the excitation of BAEs. In addition, externally applied static resonant magnetic perturbations (RMPs) are used to excite BAEs successfully for the first time in J-TEXT, as indicated by high frequency oscillations (~30 kHz). Further studies show that BAEs can be excited only when the coil current of RMP is stronger than 4 kA, and the strength of BAEs becomes stronger with stronger RMP. To assess the verification of the BAEs, the frequencies of observed modes are compared to the calculated frequencies of the BAE frequency gap in the Alfvén continuum, namely the continuum accumulation point (CAP), and they are found to be close.

Non-linear magnetohydrodynamic modeling of plasma response to resonant magnetic perturbations

The interaction of static Resonant Magnetic Perturbations (RMPs) with the plasma flows is modeled in toroidal geometry, using the non-linear resistive MHD code JOREK, which includes the X-point and the scrape-off-layer. Two-fluid diamagnetic effects, the neoclassical poloidal friction and a source of toroidal rotation are introduced in the model to describe realistic plasma flows. RMP penetration is studied taking self-consistently into account the effects of these flows and the radial electric field evolution. JET-like, MAST, and ITER parameters are used in modeling. For JET-like parameters, three regimes of plasma response are found depending on the plasma resistivity and the diamagnetic rotation: at high resistivity and slow rotation, the islands generated by the RMPs at the edge resonant surfaces rotate in the ion diamagnetic direction and their size oscillates. At faster rotation, the generated islands are static and are more screened by the plasma. An intermediate regime with static islands which slightly oscillate is found at lower resistivity. In ITER simulations, the RMPs generate static islands, which forms an ergodic layer at the very edge (ψ≥0.96) characterized by lobe structures near the X-point and results in a small strike point splitting on the divertor targets. In MAST Double Null Divertor geometry, lobes are also found near the X-point and the 3D-deformation of the density and temperature profiles is observed.

Dependence of plasma responses to an externally applied perturbation field on MHD oscillation frequency on the J-TEXT tokamak

The plasma response to externally applied perturbation fields is investigated on the J-TEXT tokamak using a set of static resonant magnetic perturbation (SRMP) coils. Several different experimental results are obtained including partial or complete suppression of the existing m/n = 2/1 tearing mode, mode locking or non-uniform magnetohydrodynamic (MHD) oscillations. These results depend sensitively on the tearing mode frequency and the amplitude of the perturbation field. It is found that mode locking is most likely to happen at a lower rotation frequency (< ∼5 kHz) and the threshold for mode locking has a linear relation with MHD frequency. However, complete suppression of the tearing mode happens in a region where the MHD frequencies are higher (∼6 kHz). The experimental observations are explained by numerical simulations based on reduced MHD equations. The error field contributes to an offset between the mode-locking thresholds for the two opposite spatial phases of the SRMP, through which the intrinsic error field of J-TEXT can be estimated.