Edge Localized Mode Crash Research Articles

Nonlinear coupling induced toroidal structure of edge localized modes

Edge localized modes (ELMs) are magnetohydrodynamic (MHD) instabilities that cause fast periodic relaxations of the strong edge pressure gradient in tokamak fusion plasmas. A novel diagnostic method allows the extraction of toroidal mode numbers, rotation velocities and spatial information during the ELM cycle including the crash. While mode number branches –6 and –10 are dominant just before the ELM crash, during the ELM crash –5 are observed in typical discharges with type-I ELMs in the tokamak experiment. These findings are compared to results from nonlinear MHD simulations. Although is linearly dominant, nonlinear coupling in which is particularly important leads to the dominance of –5 during the ELM crash, in excellent agreement with experimental observations. The simultaneous occurrence of these modes over a wide radial region leads to high stochasticity and thus increased transport.

Non-linear MHD modelling of edge localized modes dynamics in KSTAR

The explanation of the existence of the rotating MHD modes in the pedestal region before Type I edge localized mode (ELM) crash and in the inter-ELM periods (ELM precursors) observed in KSTAR is provided for the first time in the present paper. The dynamics of ELMs, observed using electron cyclotron emission imaging (ECEI) in KSTAR tokamak, is compared to the modelling results of the non-linear reduced resistive MHD code JOREK. The realistic KSTAR pulse parameters and geometry including X-point and scrape off layer (SOL) were used. The full ELM crash modelling was performed using JOREK code for single and multi-harmonic representation and in multi-cycles ELMy regimes including relevant flows. The most unstable toroidal modes numbers (n = 5–8), velocity (~5 km s−1 for n = 8 mode) and the direction of the mode rotation were reproduced in modelling. The two fluid diamagnetic effects and toroidal rotations included in the model were found to be the most important factors in explaining the experimentally observed rotation of the ballooning modes before the ELM crash and in the inter-ELM phase. In multi-harmonic multi-cycle simulations the spectrum of temperature fluctuations is similar to the experimental one in the inter-ELM phase, where several rotating modes with medium n numbers were detected in 5–30 kHz frequency range. The rotating modes can contain single or several harmonics which last from 0.2 ms to few ms in time, and can appear and disappear in the inter ELM period or persist until a new ELM crash.

Shrinking of core neoclassical tearing mode magnetic islands due to edge localized modes and the role of ion-scale turbulence in island recovery in DIII-D

Experimental signature of long-wavelength turbulence accelerating the recovery of Neoclassical Tearing Mode (NTM) magnetic islands after they have been transiently reduced in size due to interaction with Edge Localized Modes (ELMs) is reported for the first time. This work shows that perturbations associated with ELMs result in peaking of the electron temperature (Te) in the O-point region of saturated core m/n = 2/1 islands (m/n being the poloidal/toroidal mode numbers). In synchronization with this Te peak, the island width shrinks by as much as 30% suggesting a key role of the Te peak in NTM stability due to modified pressure gradient (∇p) and perturbed bootstrap current (δjBS) at the O-point. Next, this Te peak relaxes via anomalous transport (i.e., the diffusivity is 2 orders of magnitude larger than the neoclassical value) and the island recovers. Long-wavelength turbulent density fluctuations (ñ) are reduced at the O-point of flat islands but these fluctuations are increased when Te is peaked which offers an explanation for the observed anomalous transport that is responsible for the relaxation of the Te peak. Linear gyrokinetic simulations indicate that ñ inside the peaked island is dominantly driven by the Ion Temperature Gradient instability. These measurements suggest that ñ accelerates NTM recovery after an ELM crash via accelerating the relaxation of ∇p at the O-point. These observations are qualitatively replicated by coupled predator-prey equations and modified Rutherford equation. In this simple model, turbulence accelerates NTM recovery via relaxing ∇p and therefore restoring δjBS at the O-point. The key physics of the relationship between the Te peak and NTM stability has potentially far-reaching consequences, such as NTM control via pellet injection in high-β tokamak plasmas.

Investigation of the plasma shaping effects on the H-mode pedestal structure using coupled kinetic neoclassical/MHD stability simulations

The effects of plasma shaping on the H-mode pedestal structure are investigated. High fidelity kinetic simulations of the neoclassical pedestal dynamics are combined with the magnetohydrodynamic (MHD) stability conditions for triggering edge localized mode (ELM) instabilities that limit the pedestal width and height in H-mode plasmas. The neoclassical kinetic XGC0 code [Chang et al., Phys. Plasmas 11, 2649 (2004)] is used in carrying out a scan over plasma elongation and triangularity. As plasma profiles evolve, the MHD stability limits of these profiles are analyzed with the ideal MHD ELITE code [Snyder et al., Phys. Plasmas 9, 2037 (2002)]. Simulations with the XGC0 code, which includes coupled ion-electron dynamics, yield predictions for both ion and electron pedestal profiles. The differences in the predicted H-mode pedestal width and height for the DIII-D discharges with different elongation and triangularities are discussed. For the discharges with higher elongation, it is found that the gradients of the plasma profiles in the H-mode pedestal reach semi-steady states. In these simulations, the pedestal slowly continues to evolve to higher pedestal pressures and bootstrap currents until the peeling-ballooning stability conditions are satisfied. The discharges with lower elongation do not reach the semi-steady state, and ELM crashes are triggered at earlier times. The plasma elongation is found to have a stronger stabilizing effect than the plasma triangularity. For the discharges with lower elongation and lower triangularity, the ELM frequency is large, and the H-mode pedestal evolves rapidly. It is found that the temperature of neutrals in the scrape-off-layer (SOL) region can affect the dynamics of the H-mode pedestal buildup. However, the final pedestal profiles are nearly independent of the neutral temperature. The elongation and triangularity affect the pedestal widths of plasma density and electron temperature profiles differently. This provides a new mechanism of controlling the pedestal bootstrap current and the pedestal stability.

A model for generation of high wavenumber fluctuations by external magnetic field perturbations in edge pedestal plasmas

We study the impact of external magnetic perturbations on the stability of ballooning modes. A unique feature of our analysis is the two-step parametric process [Chaturvedi and Kaw, J. Geophys. Res. 81, 3257 (1976)], which enables us to calculate contributions from all the modes with high toroidal mode numbers. The analysis shows that the externally applied magnetic field perturbations can modify the linear dispersion characteristics of the ballooning mode. Specifically, the growth rate spectrum of the ballooning modes becomes broader in poloidal wavenumber (kθ) space, implying the generation of high-k fluctuations. The increase of high-k fluctuations (micro-turbulence) can lead to the mitigation of an edge localized mode crash by increasing turbulent transport in the pedestal. In addition to this, a new nonlinear instability is found even below the threshold of the ballooning mode instability when the amplitude of magnetic perturbation is sufficiently large (i.e., δB/B0≥1.0×10−4). A discussion is given of the implication of this new finding.

Scaling of the frequencies of the type one edge localized modes and their effect on the tungsten source in JET ITER-like wall

A database of 250 pulses taken randomly during the experimental campaigns of JET with the ITER-like wall (ILW) is used to study the frequency dependences of the type I edge localized modes (ELM). A scaling of the ELM frequency is presented as a function of the pedestal density drop dNped and a very simple model to interpret this scaling is discussed. In this model, the frequency of the ELMs is governed by the time needed by the neutral flux to refill the density of the pedestal. The filling rate is the result of a small imbalance between the neutral flux filling the pedestal and the outward flux that expels the particles to the SOL. The ELM frequency can be governed by such a mechanism if the recovery time of the temperature of the pedestal in JET occurs before or at the same time as the one of the density. This is observed to be the case. An effect of the fuelling is measured when the number of injected particles is less than 1 × 1022 particles s−1. In that case an increase of the inter-ELM time is observed which is related to the slower recovery of the density pedestal.Additionally, a scaling is found for the source of tungsten during the ELMs. The number of tungsten atoms eroded by the ELMs per second is proportional to dNped multiplied by the ELM frequency. This is possible only if the tungsten sputtering yield is independent of the energy of the impinging particle hitting the divertor. This result is in agreement with Guillemault et al (2015 Plasma Phys. Control. Fusion 57 085006) and is compatible with the D+ ions hitting the divertor having energies above 2 keV. Finally, by plotting the Wcontent/Wsource ratio during ELM crash, a global decreasing behaviour with the ELM frequency is found. However at frequencies below 40 Hz a scatter towards upper values is found. This scatter is found to correlate with the gas injection level. In a narrow ELM frequency band around 20 Hz, it is found that both the ratio Wcontent/Wsource and Wsource decrease with the gas injection.

Toroidal mode number determination of ELM associated phenomena on ASDEX Upgrade

In highly confined tokamak plasmas periodically appearing edge localized modes (ELMs) are accompanied by mode-like magnetohydrodynamic (MHD) activities with defined toroidal mode numbers.Here the method of determining toroidal mode numbers n on the ASDEX Upgrade tokamak with a toroidally spread magnetic pick-up coil array is reviewed and improved by taking into account intrinsic coil phases. ELM synchronization is used to characterize inter-ELM MHD activity and their development during the ELM cycle in terms of their mode numbers. The mode number development is correlated with the development of the pedestal parameters which shows that the inter-ELM modes cause transport across the pedestal. An estimation of the position of the modes is done via a comparison between the mode velocities and the plasma rotation profile at the edge.Results show that during the ELM cycle MHD modes appear at several positions in the strong gradient region with clearly defined toroidal structures in the range of n = 1–10. These structures of inter-ELM modes are preserved during the ELM crash where also a strong n = 0 phenomenon occurs.

Suppression of edge localized mode crashes by multi-spectral non-axisymmetric fields in KSTAR

Among various edge localized mode (ELM) crash control methods, only non-axisymmetric magnetic perturbations (NAMPs) yield complete suppression of ELM crashes beyond their mitigation, and thus attract more attention than others. No other devices except KSTAR, DIII-D, and recently EAST have successfully achieved complete suppression with NAMPs. The underlying physics mechanisms of these successful ELM crash suppressions in a non-axisymmetric field environment, however, still remain uncertain. In this work, we investigate the ELM crash suppression characteristics of the KSTAR ELMy H-mode discharges in a controlled multi-spectral field environment, created by both middle reference and top/bottom proxy in-vessel control coils. Interestingly, the attempts have produced a set of contradictory findings, one expected (ELM crash suppression enhancement with the addition of n = 1 to the n = 2 field at relatively low heating discharges) and another unexpected (ELM crash suppression degradation at relatively high heating discharges) from the earlier findings in DIII-D. This contradiction indicates the dependence of the ELM crash suppression characteristics on the heating level and the associated kink-like plasma responses. Preliminary linear resistive MHD plasma response simulation shows the unexpected suppression performance degradation to be likely caused by the dominance of kink-like plasma responses over the island gap-filling effects.

Impact of zonal flows on edge pedestal collapse

We perform a computational study of the role of zonal flows in edge pedestal collapse on the basis of a nonlinear three-field reduced magnetohydrodynamic (MHD) model. A dramatic change of dynamics takes place when ideal ballooning modes are completely stabilized. Analyses show that a new instability is developed due to a strong excitation of zonal vorticity, resulting in a series of secondary crashes. The presence of subsidiary bursts after a main crash increases the effective crash time and energy loss. These simulation results resemble the behavior of compound edge localized modes (ELMs). Analyses in this paper indicate that a complete understanding of ELM crash dynamics requires the self-consistent inclusion of nonlinear zonal flows-MHD interaction and transport physics.

Nonlinear Interaction of Edge-Localized Modes and Turbulent Eddies in Toroidal Plasma under n=1 Magnetic Perturbation.

The effect of static n=1 resonant magnetic perturbation (RMP) on the spatial structure and temporal dynamics of edge-localized modes (ELMs) and edge turbulence in tokamak plasma has been investigated. Two-dimensional images measured by a millimeter-wave camera on the KSTAR tokamak revealed that the coherent filamentary modes (i.e., ELMs) are still present in the edge region when the usual large scale collapse of the edge confinement, i.e., the ELM crash, is completely suppressed by n=1 RMP. Cross-correlation analyses on the 2D images show that (1)the RMP enhances turbulent fluctuations in the edge toward the ELM-crash-suppression phase, (2)the induced turbulence has a clear dispersion relation for wide ranges of wave number and frequency, and (3)the turbulence involves a net radially outward energy transport. Nonlinear interactions of the turbulent eddies with the coexisting ELMs are clearly observed by bispectral analysis, which implies that the exchange of energy between them may be the key to the prevention of large scale crashes.

Erratum: “Influence of equilibrium shear flow in the parallel magnetic direction on edge localized mode crash” [Phys. Plasmas 23, 042302 (2016)

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Dynamic spectra of radio frequency bursts associated with edge-localized modes

Electromagnetic emissions in the radio frequency (RF) range are detected in the high-confinement-mode (H-mode) plasma using a fast RF spectrometer on the KSTAR tokamak. The emissions at the crash events of edge-localized modes (ELMs) are found to occur as strong RF bursts with dynamic features in intensity and spectrum. The RF burst spectra (obtained with frequency resolution better than 10 MHz) exhibit diverse spectral features and evolve in multiple steps before the onset and through the ELM crash: (1) a narrow-band spectral line around 200 MHz persistent for extended duration in the pre-ELM crash times, (2) harmonic spectral lines with spacing comparable to deuterium or hydrogen ion cyclotron frequency at the pedestal, (3) rapid onset (faster than ~1 μs) of intense RF burst with wide-band continuum in frequency which coincides with the onset of ELM crash, and (4) a few additional intense RF bursts with chirping-down narrow-band spectrum during the crash. These observations indicate plasma waves are excited in the pedestal region and strongly correlated with the ELM dynamics such as the onset of the explosive crash. Thus the investigation of RF burst occurrence and their dynamic spectral features potentially offers the possibility of exploring H-mode physics in great detail.

Excitation of edge plasma instabilities and their role in pedestal saturation in the HL-2A tokamak

In HL-2A, the characteristics of the edge plasma instabilities and their effects on the dynamical evolution of the pedestal in H-mode plasmas have been investigated. In the edge pedestal region with steep pressure gradient, a quasi-coherent mode (QCM) has been observed in density fluctuations with a frequency range of 50–100 kHz. It appears during the edge localized mode (ELM)-free period after the L–H transition and prior to the first ELM. A threshold in the pedestal density gradient has been identified for the excitation of this mode. The QCM can also be observed during inter-ELM periods. It is excited early in the inter-ELM period, and disappears when the ELM onset starts. The radial wave-number of the mode is estimated with two radially separated reflectometers. It shows that the mode is radially propagating inward. The poloidal wave number estimated with the Langmuir probes is kθ ~ 0.43 cm−1. The mode propagates poloidally in the electron diamagnetic direction in the plasma frame. The toroidal mode number, deduced from Mirnov signals, is n ~ 7. The corresponding poloidal mode number is m ~ 21 according to the local safety factor value. The analysis for the dynamical evolution of the pedestal during the ELM cycle clearly shows that the mode is excited before the ELM onset. During and after the ELM crash, the mode disappears. It suggests that the QCM is driven by the pedestal density gradient, and the mode in return regulates the pedestal density evolution.

Edge localized mode rotation and the nonlinear dynamics of filaments

Edge Localized Modes (ELMs) rotating precursors were reported few milliseconds before an ELM crash in several tokamak experiments. Also, the reversal of the filaments rotation at the ELM crash is commonly observed. In this article, we present a mathematical model that reproduces the rotation of the ELM precursors as well as the reversal of the filaments rotation at the ELM crash. Linear ballooning theory is used to establish a formula estimating the rotation velocity of ELM precursors. The linear study together with nonlinear magnetohydrodynamic simulations give an explanation to the rotations observed experimentally. Unstable ballooning modes, localized at the pedestal, grow and rotate in the electron diamagnetic direction in the laboratory reference frame. Approaching the ELM crash, this rotation decreases corresponding to the moment when the magnetic reconnection occurs. During the highly nonlinear ELM crash, the ELM filaments are cut from the main plasma due to the strong sheared mean flow that is nonlinearly generated via the Maxwell stress tensor.

Influence of equilibrium shear flow in the parallel magnetic direction on edge localized mode crash

The influence of the parallel shear flow on the evolution of peeling-ballooning (P-B) modes is studied with the BOUT++ four-field code in this paper. The parallel shear flow has different effects in linear simulation and nonlinear simulation. In the linear simulations, the growth rate of edge localized mode (ELM) can be increased by Kelvin-Helmholtz term, which can be caused by the parallel shear flow. In the nonlinear simulations, the results accord with the linear simulations in the linear phase. However, the ELM size is reduced by the parallel shear flow in the beginning of the turbulence phase, which is recognized as the P-B filaments' structure. Then during the turbulence phase, the ELM size is decreased by the shear flow.

Characterisation of the deuterium recycling at the W divertor target plates in JET during steady-state plasma conditions and ELMs

Experiments in the JET tokamak equipped with the ITER-like wall (ILW) revealed that the inner and outer target plate at the location of the strike points represent after one year of operation intact tungsten (W) surfaces without any beryllium (Be) surface coverage. The dynamics of near-surface retention, implantation, desorption and recycling of deuterium (D) in the divertor of plasma discharges are determined by W target plates. As the W plasma-facing components (PFCs) are not actively cooled, the surface temperature (Tsurface) is increasing with plasma exposure, varying the balance between these processes in addition to the impinging deuteron fluxes and energies. The dynamic behaviour on a slow time scale of seconds was quantified in a series of identical L-mode discharges (JET Pulse Number (JPN)) by intra-shot gas analysis providing the reduction of deuterium retention in W PFCs by 1/3 at a base temperature (Tbase) range at the outer target plate between 65 °C and 150 °C equivalent to a Tsurface span of 150 °C and 420 °C. The associated recycling and molecular D desorption during the discharge varies only at lowest temperatures moderately, whereas desorption between discharges rises significantly with increasing Tbase. The retention measurements represent the sum of inner and outer divertor interaction at comparable Tsurface. The dynamic behaviour on a fast time scale of ms was studied in a series of identical H-mode discharges (JPN ) and coherent edge-localized mode (ELM) averaging. High energetic ELMs of about 3 keV are impacting on the W PFCs with fluxes of which is about four times higher than inter-ELM ion fluxes with an impact energy of about Eim = 200 eV. This intra-ELM ion flux is associated with a high heat flux of about 60 MW m−2 to the outer target plate which causes Tsurface rise by Δ T = 100 K per ELM covering finally the range between 160 °C and 1400 °C during the flat-top phase. ELM-induced desorption from saturated near-surface implantation regions as well as deep ELM-induced deuterium implantation areas under varying baseline temperature takes place. Subsequent refuelling by intra-ELM deuteron fluxes occurs and a complex interplay between deuterium fuelling and desorption can be observed in the temporal ELM footprint of the surface temperature (IR thermography), the impinging deuteron flux (Langmuir probes), and the Balmer radiation (emission spectroscopy) as representative for the deuterium recycling flux. In contrast to JET-C, a pronounced second peak, ≃ 8 ms delayed with respect to the initial ELM crash, in the Dα radiation and the ion flux has been observed. The peak can be related to desorption of implanted energetic intra-ELM D+ diffusing to the W surface, and performing local recycling.

Mode coupling and aspect ratio effects on low and high-n plasma instabilities

In magnetically confined toroidal plasmas such as tokamaks, magnetohydrodynamic (MHD) instabilities experience strong toroidal and nonlinear mode coupling effects. Resistive MHD simulations with the M3D code show the importance of mode coupling and compressible MHD effects, which contribute to stronger mode coupling. For the m/n = 1/1 internal kink mode and sawtooth crash and for the edge localized mode (ELM) at higher n, MHD reproduces many features of the experimental observations, including the fast sawtooth crash and the moderate n ∼ 10 toroidal harmonics of the ELM. A general property of the perpendicular momentum equation in toroidal fusion plasmas is that the unbalanced radial forces remain relatively small, so that the terms that are lowest order in small inverse aspect ratio mostly cancel. The higher order terms then have significant effects, even at small r/Ro and small amplitude. Effects are strongest for the lowest toroidal harmonics n ≃ 1 and the most strongly driven ones with highest amplitude. Unlike the n = 1 internal kink mode, the small amplitude ELM ballooning/peeling-type mode, and thus ELM MHD marginal stability, may be reasonably described by the lowest order in aspect ratio, for moderate and large n ≳ 10. The ELM crash, however, depends on higher order.

Observations of the effect of lower hybrid waves on ELM behaviour in EAST

Dedicated experiments focusing on the influence of lower hybrid waves (LHWs) on edge-localized modes (ELMs) were first performed during the 2012 experimental campaign of EAST, via modulating the input power of LHWs in the high-confinement-mode (H-mode) plasma mainly sustained by ion cyclotron resonant heating. Natural ELMs are effectively mitigated (ELM frequency increases, while its intensity decreases dramatically) as the LHW is applied, observed over a fairly wide range of plasma current or edge safety factor. By scanning the modulation frequency (fm) of LHW injected power in a target plasma dominated by the so-called small ELMs, we conclude that large ELMs with markedly larger amplitudes and lower frequencies are reproduced at low modulation frequencies (fm < 100 Hz). Analysis of the evolution of edge extreme ultraviolet radiation signals further indicates that plasma fluctuations at the pedestal region indistinctively respond to rapid modulation (fm ⩾ 100 Hz) of LHW injected power. This is proposed as the mechanism responsible for the observed fm dependence of the mitigation effect induced by LHWs on large ELMs. In addition, a critical threshold of LHW input power PLHW is estimated as , beyond which the impact of applied LHWs on ELM behaviours can be achieved. Finally, Langmuir probe measurements suggest that, rather than the concentration of free energy into a narrowband quasi-coherent precursor commonly observed growing until the ELM crash, the continuous development of broadband turbulence during the ELM-absent phase with the application of LHWs might contribute to the avoidance of ELM crashes. These results present new insights into existing experiments, and also provide some foundations and references for the next-step research about exploring in more depth and improving this new attractive method to effectively control the ELM-induced very large transient heat and particle flux.

Impact of the pedestal plasma density on dynamics of edge localized mode crashes and energy loss scaling

The latest BOUT++ studies show an emerging understanding of dynamics of edge localized mode (ELM) crashes and the consistent collisionality scaling of ELM energy losses with the world multi-tokamak database. A series of BOUT++ simulations are conducted to investigate the scaling characteristics of the ELM energy losses vs collisionality via a density scan. Linear results demonstrate that as the pedestal collisionality decreases, the growth rate of the peeling-ballooning modes decreases for high n but increases for low n (1 &amp;lt; n &amp;lt; 5), therefore the width of the growth rate spectrum γ(n) becomes narrower and the peak growth shifts to lower n. Nonlinear BOUT++ simulations show a two-stage process of ELM crash evolution of (i) initial bursts of pressure blob and void creation and (ii) inward void propagation. The inward void propagation stirs the top of pedestal plasma and yields an increasing ELM size with decreasing collisionality after a series of micro-bursts. The pedestal plasma density plays a major role in determining the ELM energy loss through its effect on the edge bootstrap current and ion diamagnetic stabilization. The critical trend emerges as a transition (1) linearly from ballooning-dominated states at high collisionality to peeling-dominated states at low collisionality with decreasing density and (2) nonlinearly from turbulence spreading dynamics at high collisionality into avalanche-like dynamics at low collisionality.

Pedestal and edge localized mode characteristics with different first wall materials and nitrogen seeding in ASDEX Upgrade

A comparison of ASDEX Upgrade (AUG) discharges performed with carbon and the full tungsten wall shows that the pedestal performance at low triangularity is not altered without gas puffing. The pedestal electron pressure is the same for both wall materials as is the confinement. With the tungsten wall the natural density is higher even without an additional gas puff. In typical operation with gas puffing the density is again higher in tungsten. This results in a higher collisionality with the tungsten wall. Pedestal pressure and plasma confinement, however, are not degraded until very large amounts of deuterium are puffed.The edge localized mode (ELM) crash in typical AUG discharges is observed to be composed of two independent phases. This is observed for both the carbon and the tungsten wall. The 1st phase of the crash is unaffected by scans of the plasma parameters as long as the pedestal pressure remains constant. The duration of the 2nd phase is strongly anti-correlated with the separatrix density and can be suppressed by the application of nitrogen seeding for divertor cooling. A consistent explanation for the two phases of the ELM crash does not seem possible when considering only the pre-ELM pedestal profiles. The scrape off layer (SOL) plasma provides the necessary free parameter for a consistent explanation, indicating the importance of the SOL in understanding the ELM crash evolution.