Sawtooth Collapse Research Articles

Numerical study of runaway current impact on sawtooth oscillations in tokamaks

Abstract This study investigates the influence of runaway current in runaway plasmas on the dynamics of sawtooth oscillations and resultant loss of runaway electrons (RE) using the 3D magnetohydrodynamic (MHD) code M3D-C$^{1}$ (Jardin {\it et al} 2012 {\it J. Comput. Sci. Discovery} {\bf 6} 014002). Using an HL-2A-like equilibrium, we confirm that in the linear phase, the impact of REs on resistive internal kink instabilities is consistent with previous research.
In the nonlinear phase, as the runaway current fully replaces the plasmas current, we observe a significant suppression of sawtooth oscillations, with the first sawtooth cycle occurring earlier compared to the case without runaway current. Following the first sawtooth collapse, plasma current density, runaway current density, and safety factor ($q$) flatten within the $q=1$ surface, albeit displaying fine structures. Subsequently, the growing high torodial ($n$) and poloidal ($m$) mode number modes disrupt the magnetic surfaces, leading to the loss of REs outside the $q=1$ surface, while minimally affecting the majority of REs well-confined within it. Thus, in the current model, the physical processes associated with the presence of sawtooth oscillations do not effectively dissipate runaway current, as REs are assumed to be collisionless. In addition, the final profile of runaway current density exhibits increased steepening near the $q=1$ surface in contrast to the initial profile, displaying a distinctive corrugated inhomogeneity influenced by the growing fluctuation of the $n=0$ component. Finally, detailed convergence tests are conducted to validate the numerical simulations.

Observation of resonant tearing mode induced by energetic-ion redistribution due to sawtooth collapse in HL-2A NBI plasmas

Recent observations on the HL-2A tokamak give new experimental evidence of resonant tearing modes (r-TMs) caused by the redistribution of energetic ions (EIs) due to sawtooth collapses in neutral beam injection plasmas. The m/n=2/1 (m and n are the poloidal and toroidal mode numbers) r-TMs with frequencies chirping down rapidly are found after strong bursts of fishbone modes and closely followed strong sawtooth collapses. The frequencies of fishbone modes and r-TMs chirp down from 10 to 7 kHz and 5 to 2 kHz rapidly, higher and lower than the 4–6 kHz existing weak resistive TMs. The fishbone modes propagate in ion diamagnetic drift directions in poloidal. In contrast, r-TMs propagate in the electron diamagnetic drift direction, though r-TMs are excited by EIs. It is suggested that counter-passing EIs, which originated from redistribution of EIs due to fishbone modes and combined with sawtooth collapses, excite r-TMs. Simulation results from the M3D-K code reveal that the counter-passing EIs play an important role in the excitation of r-TMs. The results can help broaden understanding of the interaction mechanisms between energetic particles and TMs, and open up a new perspective on the excitation mechanism of r-TMs.

Absolute calibration method of electron cyclotron emission imaging system on EAST tokamak

<sec>Electron cyclotron emission imaging (ECEI) system can provide the poloidal two-dimensional (2D) relative electron temperature perturbation profile of the core plasma with high spatial and temporal resolution. After absolute calibration of ECEI system, 2D absolute electron temperature profile and its perturbation can be provided. It can provide experimental data support for studying the local heat transport and the evolution of magnetic surface of macro magneto-hydro-dynamics instability. However, due to a large number of measurement channels and the wide measuring area of ECEI diagnostic system, the absolute calibration method in which a blackbody radiation source is used as a standard source, still has technical difficulties.</sec><sec>This paper provides an absolute calibration method of ECEI diagnostic system on EAST tokamak, which can cover all the channels of ECEI system. Firstly, the sawtooth inversion surface can be determined by measuring the relative electron temperature change before and after the collapse of the sawtooth. The magnetic surface position and the shape (<inline-formula><tex-math id="M1">\begin{document}${S_{{\text{inv}}}}$\end{document}</tex-math><alternatives><graphic specific-use="online" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240497_M1.jpg"/><graphic specific-use="print" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="13-20240497_M1.png"/></alternatives></inline-formula>) of the ECEI measuring area are fitted based on the position and shape of the inversion surface. Then, the one-to-one mapping relationship between laboratory coordinates of each ECEI channel and magnetic surface is obtained. Secondly, according to the assumption that the electron temperature is the same on each magnetic surface in equilibrium, the electron temperature of each magnetic surface is fitted by the electron cyclotron emission (ECE) system result, while the ECE system is absolutely calibrated. The calibration coefficient <i>k</i>(<i>i</i>, <i>j</i>) of each ECEI channel is obtained by comparing with the signal amplitude and the electron temperature on the magnetic surface. The relative error of absolute electron temperature between ECEI and ECE is no more than 6% at the same location.</sec><sec>Based on the absolute electron temperature profile provided by ECEI, the motion of the magnetic axis during sawtooth instability can be tracked. It is found that the radial displacement of the magnetic axis occurs followed by the poloidal displacement during sawtooth collapse. This result indicates that after absolute calibration, the ECEI system can provide more abundant information about experimental research.</sec>

Hybrid-kinetic simulation of synergy between fishbone/sawtooth and tearing mode-induced energetic-ion transport in a tokamak plasma

The resonant interaction between tearing mode (TM) and energetic ions redistributed by fishbone/sawtooth collapse has been observed recently in HL-2A neutral beam injection-heated high-density plasmas, where m is the poloidal mode number and n is the toroidal mode number. This event essentially results from a synergistic effect with a multiple-mode nature. Understanding such experimental phenomena, especially when using high-power auxiliary heating, is crucial for achieving high-performance plasmas with high confinement and high β N in the prospective thermonuclear fusion reactors. In this work, based on the typical experimental phenomenon of synergy between fishbone/sawtooth and TM on HL-2A, a self-consistent nonlinear hybrid-kinetic simulation is conducted utilizing the experimental parameters and profiles before the occurrence of this synergy as the code M3D-K input. In particular, we focus chiefly on the phase-space transport, loss and redistribution of energetic ions induced by two cases, one with only TM and one with synergy between fishbone/sawtooth and TM. It is found that the synergy of the fishbone/sawtooth and TM on energetic-ion transport, loss and redistribution is important and can dramatically enhance the loss rate of energetic ions compared with the case with only TM. It is due to the fact that such synergy can open up an efficient energetic-ion loss channel which connects the plasma center and edge. The phase space transport and redistribution of energetic ions induced by the two different cases are also respectively analyzed and compared in detail. Because of the overestimation of amplitudes of fishbone/sawtooth and TM in the simulations, the obtained energetic-ion transport level is only limited in the context of the numerical framework. These findings indicate that the synergy triggering the sawtooth collapse may lead to an enhancement of the energetic-ion transport and can help us understand the underlying mechanisms of synergy-induced energetic-ion transport.

Observation of the poloidally asymmetrical density perturbation of sawtooth collapse on J-TEXT

The detailed density perturbations provided by the advanced polarimeter–interferometer system (Polaris) during sawtooth collapse on the Joint Texas Experimental Tokamak (J-TEXT) are reported in this article. During a sawtooth collapse and the crash of plasma pressure at the center, it is found that the increase in density in the region between the inversion radius and mixing radius is poloidally asymmetrical, while the increase in temperature is poloidally symmetrical. The poloidal location where the density increases is dependent on the phase of the precursory m/n = 1/1 kink mode. It is always out of phase with the hot core of the m/n = 1/1 mode. The behaviors of density perturbations during sawtooth collapse observed in J-TEXT are beyond the expectations of the standard model, and this can shed new light on the understanding of sawtooth collapse.

Observation of the electron thermal transport and temperature fluctuations for electron cyclotron resonance heated plasmas on J-TEXT

First dedicated experiments have been carried out on the J-TEXT tokamak for investigating the electron thermal transport and plasma fluctuations before and during electron cyclotron resonance heating (ECRH). The electron thermal diffusivities are calculated using the diffusive space-time evolution characteristic of the electron temperature perturbations produced by internal sawtooth collapse. It is found that the electron thermal diffusivity significantly increases as ECRH is turned on. The temperature fluctuations in the ECRH-assisted ohmic plasmas measured by the correlation electron cyclotron emission (CECE) diagnostic have a larger amplitude and broader bandwidth than that of pure ohmic plasmas. However, there is a slight change in the density fluctuations. The electron thermal diffusivities and the bandwidth of the electron temperature fluctuations decrease simultaneously as density increases in ohmic plasmas. However, the same trend is not found for ECRH-assisted ohmic plasmas with fixed ECRH power. The electron thermal diffusivities increase almost linearly with the ECRH power for the same discharge parameters, while the temperature fluctuations become broader at the same time. Linear stability analysis using the gyrokinetic electromagnetic numerical experiment code indicates that there is a turbulence transition from the mixed mode of ion temperature gradient mode and trapped electron mode (TEM) to the pure (broader) TEM when changing from pure ohmic to ECRH-assisted ohmic plasmas. It is consistent with the temperature fluctuations measured by CECE, which is sensitive to the long-wavelength modes. All these results suggest that the long-wavelength temperature fluctuations play an important role in electron thermal transport. In ECRH-assisted ohmic plasmas, electron thermal transport may become dominated by ETGs when TEMs are suppressed at high density.

Effect of m/n = 2/1 neoclassical tearing mode on sawtooth collapse in JT-60U

We have investigated the role of the m/n = 2/1 neoclassical tearing mode (NTM) for suppression of the sawtooth collapse in JT-60U from the viewpoint of the anomalous transport of the current diffusion, namely flux pumping. In the stabilization experiments of m/n = 2/1 NTMs by electron cyclotron current drive of JT-60U, it has been clarified that the sawtooth collapses occur during or after the stabilization of m/n = 2/1 NTMs. It is also confirmed that the minimum safety factor, q min, is nearly unity before and after the stabilization of an m/n = 2/1 NTM. While the flux pumping by ELM-NTM coupling was reported in DIII-D, the suppression of the sawtooth collapse is observed without ELMs in this study. On the other hand, it is observed that the sawtooth precursor appears during the stabilization of the m/n = 2/1 NTM accompanying the disappearance of the fluctuation of the n = 1 helical core (HC), which is induced by the m/n = 2/1 NTM. In addition, the modulation of the toroidal rotation velocity having the frequency of the n = 1 HC is observed in the core region. Because the helical flow with HCs is a possible source of the dynamo loop voltage in tokamaks, these observations suggest that the suppression of the sawtooth collapse in JT-60U is realized by the dynamo loop voltage due to the n = 1 HC induced by the m/n = 2/1 NTM. Our result indicates that n = 1 HCs induced by other MHD modes also may induce anomalous current transport in tokamaks.

Redistribution of fast ions during sawtooth reconnection

In a tokamak-based fusion power plant, possible scenarios may include regulated sawtooth oscillations to remove thermalized helium from the core of the plasma. During a sawtooth crash, the helium ash and other impurities trapped in the core are driven by the instability to an outer region. However, in a fusion plasma, high energy ions will represent a significant population. We thus study the behaviour of these energetic particles during a sawtooth. This paper presents the modelling of the redistribution of fast ions during a sawtooth reconnection event in a tokamak plasma. Along the lines of the model for the evolution of the flux surfaces during a sawtooth collapse described in Ya.I. Kolesnichenko and Yu.V. Yakovenko 1996 Nucl. Fusion 36 159, we have built a time-dependent electromagnetic model of a sawtooth reconnection. The trajectories of the ions are described by a complete gyro-orbit integration. The fast particles were evolved from specific initial parameters (given energy and uniform spread in pitch) or distributed initially according to a slowing-down distribution created by fusion reactions. Our modelling is used to understand the main equilibrium parameters driving the motions during the collapse and to determine the evolution of the distribution function of energetic ions when different geometries of reconnection are considered.

Design of the high-resolution soft X-ray imaging system on the Joint Texas Experimental Tokamak.

A new soft X-ray diagnostic system has been designed on the Joint Texas Experimental Tokamak (J-TEXT) aiming to observe and survey the magnetohydrodynamic (MHD) activities. The system consists of five cameras located at the same toroidal position. Each camera has 16 photodiode elements. Three imaging cameras view the internal plasma region (r/a < 0.7) with a spatial resolution about 2 cm. By tomographic method, heat transport outside from the 1/1 mode X-point during the sawtooth collapse is found. The other two cameras with a higher spatial resolution 1 cm are designed for monitoring local MHD activities respectively in plasma core and boundary.

Improved criterion for sawtooth trigger and modelling

We discuss the role of neoclassical resistivity and local magnetic shear in the triggering of the sawtooth in tokamaks. When collisional detrapping of electrons is considered the value of the safety factor on axis, q(0, t), evolves on a new time scale, , where τη = 4πa2/[c2η(0)] is the resistive diffusion time, ν* = νe/(ϵ3/2ωte) is the electron collision frequency normalized to the transit frequency and ϵ = a/R0 is the tokamak inverse aspect ratio. Such an evolution is characterized by the formation of a structure of size around the magnetic axis, which can drive rapid evolution of the magnetic shear and decrease in q(0, t). We investigate two possible trigger mechanisms for a sawtooth collapse corresponding to crossing the linear threshold for the m = 1, n = 1 instability and non-linear triggering of this mode by a core resonant mode near the magnetic axis. The sawtooth period in each case is determined by the time for the resistive evolution of the q-profile to reach the relevant stability threshold; in the latter case it can be strongly affected by ν*.

Nonlinear variational method for predicting fast collisionless magnetic reconnection

A mechanism for fast magnetic reconnection in collisionless plasma is studied for understanding sawtooth collapse in tokamak discharges using a two-fluid model for cold ions and electrons. Explosive growth of the tearing mode enabled by electron inertia is analytically estimated using an energy principle with a nonlinear displacement map. Decrease in the potential energy in the nonlinear regime (where the island width exceeds the electron skin depth) is found to be steeper than in the linear regime, resulting in accelerated reconnection. Release of potential energy by such a fluid displacement leads to unsteady and strong convective flow, which is not damped by the small dissipation effects in high-temperature tokamak plasmas. Direct numerical simulation in slab geometry substantiates the theoretical prediction of the nonlinear growth.

Dynamics of fast ions during sawtooth oscillations in the TEXTOR tokamak measured by collective Thomson scattering

Experimental investigations of sawteeth interaction with fast ions measured by collective Thomson scattering on TEXTOR are presented. Time-resolved measurements of localized 1D fast-ion distribution functions allow us to study fast-ion dynamics during several sawtooth cycles. Sawtooth oscillations interact strongly with the fast-ion population in a wide range of plasma parameters. Part of the ion phase space density oscillates out of phase with the sawtooth oscillation during hydrogen neutral beam injection (NBI). These oscillations most likely originate from fast hydrogen ions with energies close to the full injection energy. At lower energies passing fast ions in the plasma centre are strongly redistributed at the time of sawtooth collapse but no redistribution of trapped fast ions is observed. The redistribution of fast ions from deuterium NBI in the plasma centre is found to vary throughout velocity space. The reduction is most pronounced for passing ions. We find no evidence of inverted sawteeth outside the sawtooth inversion surface in the fast-ion distribution function.

Runaway electron dynamics during impurity gas puffing on HT-7 tokamak

Runaway electrons have been studied by injection/gas puffing of argon and neon gases during low-density, current ramp-down deuterium discharges in the HT-7 tokamak [X. Gao, Plasma Sci. Technol. 1, 25 (1999)]. The argon and neon gases have been injected/puffed separately during runaway Ohmic discharges, and the effects of these gases on runaway electron dynamics have been observed with different gas pulse widths and varied injection times. It has been found that the injection of a noble gas such as argon or neon can terminate the already generated runaway currents in the discharge before the runaway electrons hit the limiter or vessel structures. It has also been observed that runaway electrons cannot gain high energies in the presence of noble gas, and thereby are cooled down to their thermal velocities. During puffing of argon gas, a time delay has been observed before triggering the secondary emission of runaway electrons with a gas pulse width of 10–20 ms, whereas the same effect has also been observed with neon gas with a gas pulse width of 40–50 ms. For a 60–100 ms gas pulse width the runaway electrons have been partially suppressed, and earlier termination of the discharges was observed due to sawtooth collapse of heat energy in the center of the discharge, characterized by hard x-ray and γ ray emissions. The maximum energy of runaway electrons (12 MeV) inferred from gamma spectra is in agreement with the runaway limiting energy predicted by a test particle description of the runaway dynamics [J. R. Martín-Solís et al., Phys. Plasmas 5, 2370 (1998)].

Soft X-Ray Computer Tomography of Double $m = 2$ Mode During Off-Axis Sawtooth Oscillation With Five Detector Arrays on the WT-3 Tokamak

An off-axis sawtooth oscillation is excited by electron cyclotron heating in a lower hybrid current drive plasma in the WT-3 tokamak. The internal structure of the plasma is investigated using computer tomography with five detector arrays after the application of singular value decomposition to the soft X-ray detector signals. It is found that the precursor oscillation of the off-axis sawtooth collapse is the m=2 mode. On the other hand, the double m=2 mode structure is observed as a post cursor of the collapse.

Propagation velocity of changes to confinement

Transient and non-transient changes to confinement properties of a tokamak equilibrium arise from several different plasma phenomena: a heat pulse triggered by a sawtooth; a cold pulse triggered by impurity injection or a giant ELM; the L ↔ H transitions triggered at the edge can produce a fast response in temperature towards the centre; MHD instabilities like sawtooth collapse, ELM or ‘outer’ mode cause negative-positive changes to the local energy density. Such changes to the confinement properties propagate through the plasma on timescales which are much smaller than the confinement time itself. A model to describe this based on turbulent guiding centre drift motion is developed. The theory for the non-linear model focuses on the propagation of perturbations to the plasma temperature and density. The model predicts a fluctuation-turbulence spectrum which agrees with that observed in experimental fluctuation measurements, apart from the predicted long wavelength part, which is not measured experimentally. A turbulence theory for the guiding centre velocity correlation function is developed in five steps, three of which have often been used in work on turbulence. Step 1 is the random phase approximation. Step 2 is the Markovian approximation. Step 3 is the discrete to continuum approximation. Step 4 is the solution of a prototype non-linear equation for one single harmonic. Step 5 is the solution of a non-linear equation for the entire spectrum of fluctuations using statistical techniques. The solution can be studied in two regimes. The long term or steady state regime has commonly been used in many turbulence theories. On the other hand the short term or ballistic regime predicts that perturbations propagate by advective or wave-like transport relevant to transient changes. The propagation speed is the characteristic guiding centre fluid drift velocity scaled by the ratio between the energy in the fluctuations and the thermal energy. Its magnitude agrees with experimental observations. The validity of the approximations in each of the five steps is discussed, together with how appropriate these are to a tokamak equilibrium with shear.

Observation of instabilities during density limit experiments in the Hefei Tokamak-7

During a recent campaign at the Hefei Tokamak-7 (HT-7) [M. Asif et al., Phys. Plasmas 12, 082502 (2005)], experiments were performed with a moveable graphite limiter to investigate the influence of the horizontal plasma position on the density limit. It has been found that in HT-7 density limits differ by the radiative instability in the plasma boundary and various magnetohydrodynamic (MHD) instabilities, which precedes the disruption. Control of the impurity content, edge, and recycling properties prevents the growth of the multifaceted asymmetric radiation from the edge (MARFE) and makes it possible to exceed the Greenwald limit in HT-7. It has been observed that the m=2, MHD component dominates during almost the whole discharge duration, when the density limit is approached at values of the edge safety factor 3&amp;lt;q(a)&amp;lt;4. The observed sawtooth oscillation shows that oscillation with m=1 and n=1, where m and n are the poloidal and toroidal mode numbers, respectively, triggers m=2 and n=1 in sawtooth collapse, which finally causes disruption in the HT-7 tokamak.

Energetic Particle Physics Studies on Alcator C-Mod

Energetic particle physics is studied in Alcator C-Mod in reactor relevant regimes with high density and equilibrated electron and ion temperatures. Stable Alfvén eigenmodes are excited with low-power active magnetohydrodynamic antennas in the absence of a significant energetic particle tail to directly measure the damping rate of the modes. Stable toroidal Alfvén eigenmode (TAE) damping rates between 0.5% < γ/Ω < 4.5% have been observed in diverted and limited plasmas. Alfvén eigenmodes are destabilized with high-power hydrogen minority ion cyclotron radio frequency (ICRF) heating (PICRF < 6 MW) in lower-density plasmas in the current rise and in relatively high-density ([bar]ne < 2.5 × 1020 m-3) H-mode plasmas, which creates an energetic hydrogen ion tail with calculated energies up to 400 keV. Low toroidal mode number (n < 4) unstable modes are observed in the current rise with magnetic pickup coils at the wall and phase contrast imaging density fluctuation measurements in the core. Observations of energetic particle modes or TAEs that decrease in frequency and mode number with time up to a large sawtooth collapse indicate that fast particles play a role in stabilizing sawteeth. Alfvén eigenmodes can also be used as diagnostics to precisely constrain the q profile and provide a qualitative measure of the fast particle distribution time evolution.

Study of sawtooth oscillations in the HT-7 superconducting tokamak

Experiments have been carried out with a moveable graphite limiter on the HT-7 tokamak in order to investigate the influence of the horizontal plasma position on the density limit. The observed sawtooth oscillation at values of the edge safety factor 3.5 < q ( a ) < 4 , has been studied in this Letter, which shows that oscillation with m = 1 and n = 1 , where m and n are the poloidal and toroidal mode numbers, respectively, trigger m = 2 and n = 1 , in sawtooth collapse which finally cause disruption in the HT-7 tokamak. We propose that the mode may be destabilized by the current density gradient. The q = 1 surface is appears at about r = 0.5 a , than the q = 2 surface must be close to the q = 1 surface. Therefore, the sawtooth collapse can greatly change the current profile near the q = 2 surface and then trigger the m = 2 mode that finally causes the disruption.

Observation of the m = 1 mode during the ramp phase of the sawtooth oscillations in LHCD plasmas on the HT-7 tokamak

A new oscillation with m = 1 and n = 1, where m and n are the poloidal and toroidal mode numbers, respectively, has been observed with lower hybrid current drive (LHCD) on the HT-7 tokamak. This mode appears during the sawtooth ramp, saturates, damps and finally disappears before the subsequent sawtooth collapse and before the appearance of the precursor oscillations. The necessary condition for its observation is that the sawtooth period exceeds 6–7 ms and that the LHCD power exceeds the threshold value of about 90 kW. We propose that the mode may be destabilized by the current density gradient, the evolution of which is determined by the suprathermal electrons generated by the LHCD.

Active and fast particle driven Alfvén eigenmodes in Alcator C-Mod

Alfvén eigenmodes (AEs) are studied to assess their stability in high density reactor relevant regimes where Ti≈Te and as a diagnostic tool. Stable AEs are excited with active magnetohydrodynamics antennas in the range of the expected AE frequency. Toroidal Alfvén eigenmode (TAE) damping rates between 0.5%&amp;lt;γ∕ω&amp;lt;4.5% have been observed in diverted and limited Ohmic plasmas. Unstable AEs are excited with a fast ion tail driven by H minority ion cyclotron radio frequency (ICRF) heating with electron densities in the range of n¯e=0.5–2×1020m−3. Energetic particle modes or TAEs have been observed to decrease in frequency and mode number with time up to a large sawtooth collapse, indicating the role fast particles play in stabilizing sawteeth. In the current rise phase, unstable modes with frequencies that increase rapidly with time are observed with magnetic pick-up coils at the wall and phase contrast imaging density fluctuation measurements in the core. Modeling of these modes constrains the calculated safety factor profile to be very flat or with slightly reversed shear. AEs are found to be more stable for an inboard than for central or outboard ICRF resonances in qualitative agreement with modeling.