Effect Of Resonant Magnetic Perturbations Research Articles

Effects of resonant magnetic perturbations on turbulence and flows in the edge of HL-2A plasmas

The influence of resonant magnetic perturbations (RMPs) on the dynamics of turbulence and flows at the edge of the HL-2A tokamak is analyzed utilizing transfer entropy technique. The results have shown that the RMP damps the poloidal flows as well as the E × B shearing rate, whereas enhances the toroidal flows and leads to a broadened particle spectrum with increased small scale turbulence transport. The causality analysis indicates that the regulation impact of poloidal flow on turbulent fluctuations and particle flux is weakened, while that of the toroidal rotation on the latter is strengthened by the RMP field. The impact of the changes in poloidal flow dominates over that of the modified toroidal flow on turbulent transport in the edge. The magnetic perturbation and the flows generally show predator–prey oscillations, where the causal effect between the former and the toroidal flow transits to a synchronization relation in the presence of RMP. In addition, the RMP field will weaken the causal effect on poloidal Reynolds stress while strengthening the parallel-radial component simultaneously. The present findings provide a possible explanation on the effects of external fields on the edge transport, which is suggested to be dominated by the complex interactions among external perturbations, flows, and ambient microturbulence.

Effect of resonant magnetic perturbation on edge–core turbulence spreading in a tokamak plasma

Turbulence spreading from the edge to the core region of a tokamak with a resonant magnetic perturbation (RMP) is investigated using an electromagnetic Landau-fluid model in a toroidal geometry. As a RMP field with an appropriate amplitude is applied, long-wavelength fluctuations around the resonance surface can be excited due to forced magnetic reconnection. Strong shear flow at the magnetic island separatrix is observed, which can break the radially elongated vortex structures of the turbulent fluctuation. Inward turbulence spreading can be blocked by this shear flow, and the saturation level of turbulence intensity in the core region declines.

Neoclassical transport of impurities in tokamaks with non-axisymmetric perturbations

The effect of resonant magnetic perturbations (RMPs) on neoclassical transport of impurities is calculated in DIII-D and NSTX. The neoclassical fluxes are evaluated using the NEO code with nonlinear one-fluid nonaxisymmetric equilibrium calculated using M3D-C1. Neoclassical fluxes of impurities show significant changes with RMPs if the impurity resides in low-collisionality regime, but are weakly affected by RMPs in the Pfirsch–Schlüter (P–S) regime. Charge number (Z) of the impurity affects the collisionality of impurity species, which then determines the effect of 3D fields on neoclassical impurity transport. This suggests that RMPs can be possibly used for exhaust of low-Z impurities in these facilities, but have little effect for impurities with charge number greater than 10 or so. Additionally, it is shown that it is the change in the convective fluxes which is a main contributor in modifying the neoclassical impurity fluxes in the presence of RMPs.

Effect of resonant magnetic perturbations including toroidal sidebands on magnetic footprints and fast ion losses in HL-2M

Externally applied resonant magnetic perturbations (RMPs), generated by magnetic coils located outside the plasma (referred to as RMP coils), provide an effective way to control the edge localized mode (ELM) in tokamak devices. Due to the discrete nature of the toroidal distribution of these window-frame coils, toroidal sidebands always exist together with the fundamental harmonics designed for ELM control. In this work, the MARS-F code (Liu et al 2000 Phys. Plasmas 7 3681) is applied to investigate the detailed features of the RMP spectra considering both the dominant harmonic (n = 2) and the associated sideband (n = 6), and the impact of the combined fields on magnetic footprints as well as on the fast ion losses for a reference double-null scenario in the HL-2M device. It is found that the sum of the n = 2 and n = 6 RMP fields splits the footprint and widens the footprint area, as compared to the single-n (n = 2) harmonic case. The resistive plasma response breaks the up–down symmetry of the footprint pattern on the outer divertor plates, which is otherwise symmetric assuming vacuum RMP fields. Considering fast ion losses, a threshold value exists for the initially launched radial position of test particles, as well as for the RMP coil current, before the loss occurs. When the threshold criterion is satisfied, the combined n = 2 and n = 6 RMP fields enhance the fast ion loss rate by , as compared to that of the n = 2 component alone. These results illustrate the important role of the sideband of RMP fields on the magnetic footprints and fast ion losses in tokamak plasmas.

The effect of the plasma response on peeling–ballooning modes during edge localized modes mitigated by resonant magnetic perturbations

The effects of resonant magnetic perturbation (RMP) fields on peeling–ballooning (P–B) modes are studied with the experimental equilibria of EAST based on the four-field model in BOUT++ code. As the two basic types of plasma responses, the magnetic and the transport response to RMP are considered in our simulation to reveal the roles of the plasma response during edge localized mode mitigation. On the one hand, the results show that RMP can reduce the linear growth rates of the P–B modes and the pedestal energy loss in the nonlinear process by directly coupling with the P–B modes. The magnetic response can weaken the impacts of RMPs on the P–B modes by partially screening the applied RMP fields more precisely the resonant components. On the other hand, RMP can further reduce the linear growth rates of the P–B modes and the pedestal energy loss by changing the equilibrium pressure profiles through the transport response. More detailed analysis suggests that, compared with other resonant components of RMPs, the components whose corresponding rational surfaces are located at the top of the pedestal can lead to stronger reductions in the linear growth rates of the P–B modes, and can reduce pedestal energy loss more significantly by enhancing multi-mode coupling in the nonlinear process. Finally, the multi-mode coupling increases with the strength of the resonant components, so one can change the RMP poloidal spectrum by adjusting the phase difference between the upper and low RMP coils from to , and hence obtain the optimal coil phase difference that leads to the strongest reductions in the linear growth rates of the P–B modes and the pedestal energy loss through maximizing the strength of resonant components, especially the resonant components whose corresponding rational surfaces are located at the top of the pedestal.

Computational study of runaway electrons in MST tokamak discharges with applied resonant magnetic perturbation

A numerical study of magnetohydrodynamics (MHD) and tracer-particle evolution investigates the effects of resonant magnetic perturbations (RMPs) on the confinement of runaway electrons (REs) in tokamak discharges conducted in the Madison Symmetric Torus. In computational results of applying RMPs having a broad toroidal spectrum but a single poloidal harmonic, m = 1 RMP does not suppress REs, whereas m = 3 RMP achieves significant deconfinement but not the complete suppression obtained in the experiment [Munaretto et al., Nuclear Fusion 60, 046024 (2020)]. MHD simulations with the NIMROD code produce sawtooth oscillations, and the associated magnetic reconnection can affect the trajectory of REs starting in the core region. Simulations with m = 3 RMP produce chaotic magnetic topology over the outer region, but the m = 1 RMP produces negligible changes in field topology, relative to applying no RMP. Using snapshots of the MHD simulation fields, full-orbit relativistic electron test particle computations with KORC show ≈50% loss from the m = 3 RMP compared to the 10%–15% loss from the m = 1 RMP. Test particle computations of the m = 3 RMP in the time-evolving MHD simulation fields show correlation between MHD activity and late-time particle losses, but total electron confinement is similar to computations using magnetic-field snapshots.

Effects of resonant magnetic perturbations on neutral beam heating in a tokamak

The effects of resonant magnetic perturbations (RMPs) on tangential neutral beam heating in the EAST tokamak are studied numerically. RMPs with linear resistive magnetohydrodynamics response are used in the modeling. A variety of representing configurations of RMP coil currents are examined, and their effects on the neutral beam injection (NBI) heating efficiency are compared, in order to find a parameter window where deleterious effects of RMPs on NBI heating efficiency are minimized. It is found that the internal redistribution of fast ions by RMPs induces local accumulation of fast ions, resulting in higher local fast ion pressure than the case without RMPs. It is also found that the toroidal phasing of the RMP with respect to the fast ion source has slight effects on the steady-state radial profile of fast ions. The dependence of fast ion loss fraction on the RMP up-down phase difference shows a similar behavior as the dependence of the radial width of chaotic magnetic field on the phase difference. A statistical method of identifying resonances between RMPs and lost fast ions is proposed, and the results indicate that some resonances between RMPs and lost passing particles may be of non-integer fractional order, rather than the usual integer order.

Effects of resonant magnetic perturbations on radial electric fields in DIII-D tokamak

Gyrokinetic simulations of DIII-D tokamak equilibrium find that resonant magnetic perturbation (RMP) drives a neoclassical non-ambipolar electron particle flux, which causes a rapid change of equilibrium radial electric fields consistent with experimental observations during the suppression of the edge localized mode (ELM). The simulation results provide a support for the conjecture that RMP-induced changes of radial electric fields lead to the enhanced turbulent transport at the pedestal top during the ELM suppression (Taimourzadeh et al 2019 Nucl. Fusion 59 046005). Furthermore, gyrokinetic simulations of collisionless damping of zonal flows show that resonant responses to the RMP decrease the residual level of the zonal flows and damp the geodesic acoustic mode.

Nonlinear feedback algorithm for tearing-mode magnetic control in tokamak

Results of calculations and analysis of the tearing-mode evolution under the effect of resonant magnetic perturbation produced by a nonlinear feedback system in rotating tokamak plasma are presented. The TEAR-code used for calculations is based on the visco-resistive magnetohydrodynamic approximation that gives coupled diffusion-type equations for the magnetic flux perturbation and for the plasma rotation velocities in toroidal and poloidal directions. The code is supplemented by a computational unit simulating the nonlinear algorithm of the feedback system. The feedback gain and phase shift are automatically regulated in real time. The gain depends on the tearing-mode amplitude. At high feedback input signals, the gain does not exceed some finite value to reduce technical requirements for the feedback actuator and to mitigate the phase instability. In the process of the tearing-mode suppression, the gain gradually increases to provide the mode control under reduction of feedback input signal and rise of the intrinsic tearing-mode stability index. Besides that, the real-time control of the feedback phase shift is provided to additionally mitigate the phase instability. According to simulation, the used nonlinear characteristics of the feedback algorithm improve the efficiency of the tearing-mode suppression.

Experimental and simulation study of impurity transport response to RMPs in RF-heated H-mode plasmas at EAST

Spatial profiles of impurity emission measurements in the extreme ultraviolet (EUV) spectroscopic range in radiofrequency (RF)-heated discharges are combined with one-dimensional and three-dimensional transport simulations to study the effects of resonant magnetic perturbations (RMPs) on core impurity accumulation at EAST. The amount of impurity line emission mitigation by RMPs appears to be correlated with the ion Z for lithium, carbon, iron and tungsten monitored, i.e. stronger suppression of accumulation for heavier ions. The targeted effect on the most detrimental high-Z impurities suggests a possible advantage using RMPs for impurity control. Profiles of transport coefficients are calculated with the STRAHL one-dimensional impurity transport code, keeping $\nu /D$ fixed and using the measured spatial profiles of $\textrm{F}{\textrm{e}^{20 + }}$ , $\textrm{F}{\textrm{e}^{21 + }}$ and $\textrm{F}{\textrm{e}^{22 + }}$ to disentangle the transport coefficients. The iron diffusion coefficient ${D_{\textrm{Fe}}}$ increases from $1.0- 2.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ to $1.5- 3.0\;{\textrm{m}^2}\;{\textrm{s}^{ - 1}}$ from the core region to the edge region $(\rho \gt 0.5)$ after the onset of RMPs. Meanwhile, an inward pinch of iron convective velocity ${\nu _{\textrm{Fe}}}$ decreases in magnitude in the inner core region and increases significantly in the outer confined region, simultaneously contributing to preserving centrally peaked $\textrm{Fe}$ profiles and exhausting the impurities. The ${D_{\textrm{Fe}}}$ and ${\nu _{\textrm{Fe}}}$ variations lead to reduced impurity contents in the plasma. The three-dimensional edge impurity transport code EMC3-EIRENE was also applied for a case of RMP-mitigated high-Z accumulation at EAST and compared to that of low-Z carbon. The exhaust of ${\textrm{C}^{6 + }}$ toward the scrape-off layer accompanying an overall suppression of heavier ${\textrm{W}^{30 + }}$ is observed when using RMPs.

Effect of resonant magnetic perturbations on local plasma current density gradients and neoclassical tearing modes

The effect of externally applied resonant magnetic perturbations (RMPs) on the local equilibrium plasma current density profile is studied numerically based on two-fluid equations in simplified cylindrical geometry. It is found that a moderate RMP below its penetration threshold, via non-linear mode coupling, induces a parallel electric field around its rational surface that can significantly change the local flux-surface-averaged current density gradient. At a given RMP amplitude, the modification of the current density profile increases with increasing electron temperature, and it significantly depends on the bi-normal electron fluid velocity at the resonant surface. The effect of this modification on the magnetic island growth is demonstrated by the example of small m/n = 2/1 islands (m/n being the poloidal/toroidal mode numbers), driven by an unfavorable plasma current density profile and bootstrap current perturbation. The 2/1 mode growth is stabilized by moderate static 4/2 or 6/3 RMPs if the local electron fluid velocity is in the ion drift direction or sufficiently large in the electron drift direction. These results reveal that a weakly three-dimensional equilibrium, containing a moderate 4/2 RMP and the associated shielding current, can be more stable against the 2/1 mode, which often causes tokamak plasma major disruptions.

Turbulent transport of fast ions in tokamak plasmas in the presence of resonant magnetic perturbations

The effects of resonant magnetic perturbations on the turbulent transport of fast ions in tokamak devices are investigated using a theoretical transport model of test-particle type. The direct numerical simulation method is used to compute, via the transport model, the diffusion coefficients. The numerical results are in good agreement with other, analytically derived, estimations. It is found that finite Larmor radius effects algebraically decrease the transport, while the amplitude of magnetic perturbations has an opposite effect. In the presence of stochastic dynamics, the asymmetric toroidal magnetic field induces a small, radial, outward pinch. A synergistic mechanism of non-linear coupling between the effects of turbulence and those of magnetic perturbations enhances the radial diffusion. General scaling laws are proposed for the transport coefficients.

Effect of resonant magnetic perturbations with plasma response on particle orbit characters

The ion orbits considering the resonant magnetic perturbation (RMP) fields with plasma response are studied numerically using the full orbit code based on HL-2A tokamak parameters. The results show that RMP with plasma response can cause a more significant radial orbit expansion than the vacuum RMP field. Further study exhibits that the physical mechanism of the orbit expansion relates to the resonant field amplification (RFA) effect. The passing orbits expansion become quite large when ions pass through the region where the perturbed field is strongly amplified. Meanwhile, the trapped orbits expansion is determined by the average value of the perturbed field where corressponding orbit goes by. This indicates that the plasma response to RMP plays an important role in changing the characteristics of ion orbits, which can lead to a redistribution of fast ions and thus providing a possible mechanism for the degradation of plasma confinements in experiments.

Field amplification effect of resonant magnetic perturbation on ion orbits in tokamak plasma

<sec> The fast ion transport associated with resonant magnetic perturbation (RMP) contains rich physical spanning single particle motion of fast particle and plasmas response physics with RMP and their interaction. Full numerical simulation considering such physical ingredients should be performed in a long run for clarifying the underlying physical features of the fast ion confinement with RMP. Thus, the appropriate application of RMP is not only to avoid the detrimental effects but also to serve as an actuator to exert targeted control over the energetic particle profile. To achieve this goal, a comprehensive knowledge of the effects of RMP including plasma response on fast ions is necessary. </sec> <sec> In this work, the plasma response to RMP in HL-2A device is simulated by the MARS-F code under different parameters including finite resistivity, toroidal rotation frequency and toroidal mode number, and the three-dimensional (3D) magnetic field topology considering RMP is obtained. Then, Boris algorithm is used to track the ion orbit under these 3D fields, and the physical mechanism of ion orbit characteristics changed by the perturbed field is explored in detail. It is found that with the increase of finite resistivity, the average value of perturbed magnetic field decreases, and the orbit radial expansion turns smaller. The variation of toroidal rotation frequency can change the distribution of perturbed magnetic field, resulting in different orbit radial expansions for different kinds of orbits. What is more, if the toroidal mode number increases, the amplitude of perturbed magnetic field after response decreases obviously, thus resulting in little effect on orbit radial expansion. In a word, the plasma responded RMP field enhances the orbit radial expansion, and the maximum orbital radial expansion increases with the augment of average value of perturbed magnetic field on the orbit. Meanwhile, the amplitude of orbit expansion increases significantly when the ions pass through the region where the perturbed magnetic field is strongly amplified. This effect can explain the increase of ion prompt loss and enhancement of plasma radial transport in edge localized mode mitigation experiments by RMP. </sec>

The factors determining the evolution of edge-localized modes in plasmas driven by lower hybrid currents

Modulated lower-hybrid waves (LHWs) are injected into the Experimental Advanced Superconducting Tokamak to determine the physical principles responsible for the suppression or mitigation of edge-localized modes (ELMs). There are two cases of modulated-ELM evolution (stable and unstable cases), because of two different modulated pedestal densities. They can be attributed to additional magnetic perturbations induced by the LHWs, similarly to the effect of resonant magnetic perturbations. As regards the case of unstable modulated ELM evolution, the plasma stored energy increases as the LHWs turn on. In contrast, the central line-averaged electron density decreases, which is different from the case of ELM suppression or from the stably modulated case. The effect of LHWs or density ‘pump-out’ effect can pass across the top of the pedestal region and enter the interior of the density pedestal, causing a decrease in the electron density gradient and its value at the top of the pedestal. Simultaneously, the pressure gradient and edge bootstrap current density increase. For ELM suppression (or for the stable) case, LHWs can couple only with the plasma outside the top region of pedestal, because of the higher top value of density pedestal. Thus, LHWs can pump out the electron density significantly only in the pedestal foot region, producing a larger gradient of electron density pedestal. Statistical analysis of the data indicates that there is a threshold value of the central line-averaged electron density for each of the two modulated ELM cases. Furthermore, the ELM amplitude is modulated by LHWs with a time delay of hundreds of microseconds, which may be further evidence that LHWs have a significant impact on the evolution of ELMs and pedestal structures. All these results imply that there is a significant correlation between the ELM behavior and the electron density profiles modulated by LHWs.

The effect of resonant magnetic perturbation with different poloidal mode numbers on peeling–ballooning modes

The effect of resonant magnetic perturbation (RMP) with different poloidal mode numbers on peeling–ballooning (P–B) modes is simulated with the BOUT++ code. In order to investigate the physical mechanism of edge-localized mode mitigated by RMP, a series of RMPs with different poloidal mode numbers are applied into the four-field P–B mode simulation module separately. The results indicate that RMP has a better reducing effect on the energy loss from the pedestal when the resonant position is near the bottom and top of pedestal rather than near the middle. The RMP could influence P–B modes through the following effects: on the one hand, the E × B shearing rate is significantly stronger when the RMP (resonant surface locates at the top of the pedestal) is added, which can suppress the radial propagation of the negative pressure perturbation and reduce energy loss from the pedestal. On the other hand, the coupling of toroidal modes in the nonlinear phase is enhanced when RMPs are added, which motivated the growth of multiple toroidal modes, and the turbulence fluctuation level is weaker with the RMP when the resonant surface is located at the bottom of the pedestal.

Effects of resonant magnetic perturbations on the loss of energetic ions in tokamak pedestal

Resonant magnetic perturbations (RMPs) are extensively applied to mitigate or suppress the edge localized mode in tokamak plasmas, but will break the axisymmetric magnetic field configuration and increase the loss of energetic ions. The mechanism of RMPs induced energetic ion loss has been extensively studied, and is mainly attributed to resonant effects. In this paper, in the perturbed non-axisymmetric tokamak pedestal, we analytically derive the equations of guiding center motion for energetic ions including the bounce/transit averaged radial drift velocity and the toroidal precession frequency modified by strong radial electric field. The loss time of energetic ions is numerically solved and its parametric dependence is analyzed in detail. We find that passing energetic ions cannot escape from the plasma, while deeply trapped energetic ions can escape from the plasma. The strong radial electric field plays an important role in modifying the toroidal precession frequency and resulting in the drift loss of trapped energetic ions. The loss time of trapped energetic ions is much smaller than the corresponding slowdown time in DIII-D pedestal. This indicates that the loss of trapped energetic ions in the perturbed non-axisymmetric pedestal is important, especially for the trapped energetic ions generated by perpendicular neutral beam injection.

Impact of resonant magnetic perturbations on zonal flows and microturbulence

Results from a joint experimental and computational effort studying the effect of resonant magnetic perturbations (RMPs) on microturbulence levels and their connection to zonal flows in the DIII-D tokamak L-mode are presented. Beam emission spectroscopy measurements show a direct increase in density fluctuations at microturbulent scales with increasing RMP amplitude, suggesting that magnetic activity introduced by the RMP affects the regulation of microturbulence on DIII-D. This is analogous to how MHD-scale magnetic fluctuations arising from tearing modes have been observed in simulations to increase microturbulence levels in the reversed-field pinch (RFP). In the RFP, this is attributed to magnetic fluctuations eroding turbulence-limiting zonal flows; this work examines if a similar mechanism is present for DIII-D microturbulence. Gyrokinetic simulations find that the application of an RMP corresponds directly to a decrease in zonal flow levels, producing a similar increase of turbulent fluctuation levels over a range of RMP amplitudes as observed in the experiment.

The unstable ELM evolution modulated by lower hybrid waves on EAST

Modulated lower hybrid waves, are injected into the Experimental Advanced Superconducting Tokamak (EAST), to investigate the modulated evolutions of pedestal structure and unstable edge-localized modes (ELMs). The spectrum patterns of show that the ELM amplitude only slightly decreases while the ELM frequency becomes almost 3–5 times larger as the lower hybrid radio frequency (LHRF) jumps into the lower power level. Pedestal structure analysis indicates that higher LHRF power injection can increase the plasma stored energy and core plasma parameters, accompanying with the pedestal shift and gradient increase. Ion saturation contour current plots suggest that LHRF power can deposit in the plasma edge region to profoundly change the three-dimensional (3D) magnetic topology, similarly to the effect of resonant magnetic perturbations (RMPs), by inducing the helical current filaments (HCFs) following along the magnetic field lines in the scrape-off layer (SOL), which may cause the density pump-out effect by increasing the radial plasma transport. The modulated higher temperature and lower density of pedestal top-values can reduce the pedestal collisionality, which will strongly increase the bootstrap current density and gradually shift the Peeling-Ballooning mode (PBM) boundary. ELITE code stability analysis indicates that LHRF injection can lead to the relatively unstable ELMs with a higher pedestal gradient, simultaneously accompanying with the normalized pressure gradient and edge bootstrap current density increase. All of these results imply that there is a significant correlation between the ELM behavior and pedestal structure modulation because of LHRF dissipation at the plasma edge for the unstable ELM modulated case.

Numerical simulations of NBI fast ion loss with RMPs on the EAST tokamak

Fast ion losses in the presence of resonant magnetic perturbations (RMPs) on the EAST tokamak have been simulated by using the Monte Carlo orbit-following code GYCAVA (Xu et al 2019 Comput. Phys. Comm. 244 40). Fast ions produced by the co-current tangential neutral beam injection (NBI) were considered. The initial distribution of NBI fast ions was numerically computed by the TGCO code and the n = 1 vacuum and response RMP fields were numerically computed by the MHD code MARS-F (Liu et al 2000 Phys. Plasmas 7 3681). It is found that fast ion losses increase almost linearly with the RMP coil current. Poincaré plots show that fast ion losses in the presence of RMPs on EAST are mainly due to the orbit stochasticity induced by RMPs. The collision effect, including the slowing down and the pitch angle scattering, on fast ion losses have also been numerically studied. The synergy effect of RMPs and collision-induced pitch angle scattering can enhance the particle loss of fast ions. The collision effect, including the effective ion charge number effect, on the power loss of fast ions is weak. Fast ion losses increase with the effective ion charge number increasing, which is related to the pitch angle scattering effect. The plasma response to RMPs can enhance or reduce fast ion losses. The plasma response effect on fast ion losses depends on the RMP coil phasing, that is, the phase difference between the upper and lower coils. The heat loads on the outer wall clearly follow the n = 1 periodicity of the RMP coil configuration. Positions of maximum heat loads are closely related to the coil phasing of RMPs. These mean that the magnetic topology of RMPs is responsible for the toroidal distribution of heat loads.