Sawtooth Period Research Articles

Velocity-space distribution function of fast ions in a sawtoothing plasma

This study explores the influence of sawtooth oscillations on the velocity space distribution of fast ions in tokamak plasma discharges. The relevant Fokker–Planck equation for fast ions is solved analytically. Two distinct effects arising from the temperature drop associated with a sawtooth crash and their impact on the distribution function of fast ions are considered. The first effect involves the modulation of the fusion alpha particle source on the timescale of the sawtooth period, linked to the drop in fusion yield resulting from the sawtooth temperature relaxations. The second effect is tied to the increase of the slowing-down time during the sawtooth ramp, causing particles born later in the sawtooth cycle to experience reduced slowing down compared to those born right after the crash, creating an accumulation-like mechanism at higher energies. In regimes where the sawtooth period is shorter than the fast ion slowing-down time, the combined influence of these effects gives rise to fast ion distribution functions that transiently exhibit positive slopes in velocity space.

Core electron temperature turbulence and transport during sawtooth oscillations in the DIII-D tokamak

Sawteeth are one of the concerning instabilities in ITER and future burning plasma experiments. Sawtooth dynamics and its interaction with broadband plasma turbulence has been a challenge for predictive simulations of core transport in future fusion devices. This study provides new observations of core turbulence behavior during sawtooth oscillations in DIII-D hydrogen L-mode neutral beam injection heated plasmas in an inner wall limited configuration. A strong correlation of electron temperature and density turbulence levels with the sawtooth oscillation phase has been observed at locations inside the T e inversion radius and/or safety factor q = 1 magnetic surface. The T e turbulence amplitude in the core during the sawtooth ramp exhibits a critical T e gradient behavior inside but not near the T e inversion radius/q = 1 magnetic surface. The most unstable mode calculated from the trapped gyro-landau fluid turbulence simulations reveal a change from low-k ion-type to low-k electron-type modes from pre- to post- sawtooth crash time periods.

Effect of anisotropic fast ions on internal kink stability in DIII-D negative and positive triangularity plasmas

Recent DIII-D experiments show that sawtooth stability is strongly affected by anisotropic fast ions from neutral beam injection (NBI) in both negative and positive triangularity plasmas. Fast ions from co-current NBI are stabilizing for the sawtooth stability, resulting in longer sawtooth periods. On the other hand, fast ions from counter-current NBI are destabilizing, leading to small and frequent sawteeth. The relative change of sawtooth period and amplitude is more than a factor of two. These observations appear to hold in both plasma shapes. Non-perturbative toroidal modeling, utilizing the magnetohydrodynamic-kinetic hybrid stability code MARS-K (Liu et al 2008 Phys. Plasmas 15 112503), reveals an asymmetric dependence of the stability of the n = 1 (n is the toroidal mode number) internal kink mode on the injection direction of NBI, being qualitatively consistent with the experimentally observed sawtooth behavior. The MARS-K modeling results suggest that anisotropic fast ions affect the mode growth rate and frequency through both adiabatic and non-adiabatic contributions. The asymmetry of the internal kink mode instability relative to the NBI direction is mainly due to the non-adiabatic contribution of passing fast ions, which stabilize (destabilize) the internal kink with the co-(counter-) current NBI as compared to the fluid counterpart. However, finite orbit width (FOW) correction to passing particles partially cancels the asymmetry. Trapped particles are always stabilizing due to precessional drift resonance. Modeling also shows that fast ions affect the internal kink in a similar manner in both negative and positive triangularity plasmas, although being slightly more unstable in the negative triangularity configuration already in the fluid limit. The similarity is mainly attributed to the fact that the mode is localized in the plasma core region, with very similar eigenmode structures in both negative and positive configurations. Furthermore, MARS-K modeling indicates that other factors, such as the plasma rotation and the drift kinetic effects of thermal plasmas, weakly modify the mode stability as compared to the drift kinetic resonance effects and FOW correction of fast ions.

Thermal ions heat transport induced by reversed shear Alfvén eigenmode on the HL-2A tokamak

Experimental investigations of thermal ions heat transport induced by reversed shear Alfvén eigenmodes (RSAEs) have been carried out on the HL-2A tokamak. It is found that the RSAEs are driven unstable by passing particles during the second half of sawtooth periods, and can not only degrade the bremsstrahlung radiations, but also cause obvious reduction of the ion temperature in the core plasma. Interestingly, the RSAEs excited by energetic ions can resonant with the thermal ions, and then lead to a heat transport process. Statistical results suggest there is a quadratic dependence between thermal ion heat flux perturbation and mode amplitude, which indicates a diffusive mechanism of plasma transport and is well explained by the theoretical interpretations derived from quasi-linear transport theory.

Mitigation of sawtooth crash as a manifestation of MHD mode coupling prior to disruption of KSTAR plasma

Self-generated n = 1 magnetic perturbation from coupled tearing modes results in mitigation of sawtooth crash, i.e. reduction of sawtooth period and crash amplitude by a factor of several 10 or 100 s (to a few ms and a few or 10 s eV, respectively), which is commonly observed prior to plasma disruption in the KSTAR tokamak. Quasi-3D visualization of the mitigation process shows strong correlations between the sawtooth dynamics and the tearing modes: (1) rapid destabilization of internal m/n = 1/1 mode in the core region followed by incomplete relaxation in the presence of the m/n = 2/1 and 3/1 tearing modes, where the spatial orientation of the relaxation channel is aligned with the displacement direction of core flux surfaces due to the tearing modes, and (2) more reduction of the sawtooth period and amplitude for higher amplitude tearing modes. Application of external n = 1 magnetic perturbation further reduces the sawtooth period and amplitude. The sawtooth mitigation is suggested as an additional disruption warning alarm.

Sawtooth oscillation behavior with varying amounts of applied stellarator rotational transform

Tokamak-like sawtooth oscillations are observed in the Compact Toroidal Hybrid (CTH), a current-carrying stellarator. CTH has the unique ability to change the amount of the applied vacuum rotational transform from external stellarator coils relative to the rotational transform generated by the internal plasma current to investigate the effects of strong three-dimensional magnetic shaping on sawtooth behavior. The observed sawteeth in CTH, for plasmas with monotonically decreasing rotational transform profiles dominated by the plasma current, have characteristics of those observed on tokamaks including (1) a central emissivity rise and then a sudden crash with a well-defined inversion radius, (2) the presence of an m = 1 emissivity fluctuation, and (3) the normalized inversion surface radius scales with the total edge rotational transform. We explore the properties of an ensemble of discharges in CTH in which the fractional rotational transform, defined as the vacuum rotational transform divided by the total rotational transform, is systematically varied from 0.04 to 0.42 to observe changes in sawtooth oscillation dynamics. Over this range of the fractional rotational transform, the measured sawtooth period decreased by a factor of two. At a high fractional rotational transform, the sawtooth amplitude is observed to consist of only low-amplitude oscillations while the measured crash time of the sawtooth oscillation does not appear to have a strong dependence on the amount of the fractional transform applied. Experimental results indicate that the low-amplitude sawteeth are accompanied by a decrease in the sawtooth period and predominantly correlated with the mean elongation (due to the increasing fractional rotational transform) of the non-axisymmetric plasmas within CTH rather than other global equilibrium parameters.

Sawtooth activities in EAST neutral beam injection plasma

Neutral beam injection (NBI) system has been proved to affect sawtooth activities through both producing energetic particles and supplying torque applied to the plasma. The impact of NBI on sawtooth crashes has been studied in the EAST tokamak, which is equipped with co- and counter NBIs. Statistical analysis shows that both strong co- and counter-NBI yield stronger sawtooth activities than cases when heating power is weak. A minimum sawtooth period is observed at a counter-NBI power of 0.2 MW. This is linked to zero-plasma rotation and a non-rotating precursor mode of the sawtooth instability. This indicates that the sawtooth instability is stabilized by plasma rotation as previously suggested. The fast-ion content differs between co- and counter-NBI, so energetic particles might additionally contribute to the sawtooth activities.

Lévy flights on a comb and the plasma staircase.

We formulate the problem of confined Lévy flight on a comb. The comb represents a sawtoothlike potential field V(x), with the asymmetric teeth favoring net transport in a preferred direction. The shape effect is modeled as a power-law dependence V(x)∝|Δx|^{n} within the sawtooth period, followed by an abrupt drop-off to zero, after which the initial power-law dependence is reset. It is found that the Lévy flights will be confined in the sense of generalized central limit theorem if (i) the spacing between the teeth is sufficiently broad, and (ii) n>4-μ, where μ is the fractal dimension of the flights. In particular, for the Cauchy flights (μ=1), n>3. The study is motivated by recent observations of localization-delocalization of transport avalanches in banded flows in the Tore Supra tokamak and is intended to devise a theory basis to explain the observed phenomenology.

Evolution of the central safety factor during stabilized sawtooth instabilities at KSTAR

A motional Stark effect (MSE) diagnostic has recently been installed in the KSTAR tokamak. A difficulty faced at KSTAR and common to other MSE diagnostics is calibration of the system for absolute measurements. In this report we present our novel calibration routine and discuss first results, evaluating the evolution of the the central safety factor during sawtooth instabilities. The calibration scheme ensures that the bandpass filters typically used in MSE systems are aligned correctly and identifies and removes systematic offsets present in the measurement. This is verified by comparing the reconstructed safety factor profile against various discharges where the locations of rational q surfaces have been obtained from MHD markers. The calibration is applied to analyse the evolution of q0 in a shot where the sawteeth are stabilized by neutral beam injection. Within the analysed sawtooth periods q0 drops below unity during the quiescent phase and relaxes close to or slightly above unity at the sawtooth crash. This finding is in line with the classical Kadomtsev model of full magnetic reconnection and earlier findings at JET.

Ordering block copolymers with structured electrodes.

We study the kinetics of alignment and registration of block copolymers in an inhomogeneous electric field by computer simulations of a soft, coarse-grained model. The two blocks of the symmetric diblock copolymers are characterized by different dielectric constants. First, we demonstrate that a combination of graphoepitaxy and a homogeneous electric field extends the maximal distance between the topographical guiding patterns that result in defect-free ordering compared to graphoepitaxy alone. In a second study, the electric field in the thin block copolymer film is fabricated by spatially structured electrodes on an isolating substrate arranged in a one-dimensional periodic array; no additional topographical guiding patterns are applied. The dielectrophoretic effect induces long-range orientational order of the lamellae and, additionally, registers the lamellar structure with the electrodes due to the field inhomogeneities at the edges of the structured electrodes. Thus, orientational and translational order is established by the inhomogeneous electric field. The simulations identify a process protocol of time-dependent electric potentials that suppresses defect formation by initially forming a sandwich-like structure and subsequently reorienting these lying into standing lamellae that are registered with the structure of the electrodes. This process-directed self-assembly results in large defect-free arrays of aligned and registered lamellae using electrodes with a saw-tooth period of 4 lamellar periodicities, L0, and a spacing of 10L0.

Pacing control of sawtooth and ELM oscillations in tokamaks

In tokamak plasmas, the sawtooth oscillation (ST) and the edge-localized-mode (ELM) are characterized by a phase of a slow evolution of the plasma conditions, followed by a crash-like instability that resets the plasma conditions when certain criteria of the plasma conditions are satisfied. Typically, the crashes induce losses of heat and energetic particles and may also trigger secondary instabilities. As the amplitude of the crash-like perturbation scales with the period between two crashes, period control of these oscillations is important for operations of large fusion facilities such as ITER and DEMO. In several present-day experimental facilities, a pacing control algorithm has been successfully applied for controlling the sawtooth period and the ELM period. However, a formal analysis has been lacking so far, which therefore forms the objective of the present paper. For this purpose, a reset model for the sawtooth period is introduced and, after a proper transformation a nonlinear discrete-time system is obtained, which is used for the formal analysis of pacing control. By representing the model in a Lur’e (or Lurie) form, we can derive conditions under which global asymptotic stability of the closed-loop (pacing) period control system is guaranteed. Moreover, we will show that the controller exhibits inherent robustness for model uncertainties. We envision that the analytical results in the area of pacing control of the sawtooth are also applicable to pacing period control of the ELM oscillation period. The presented reset model also explains why in recent experiments the sawtooth period locks with a periodically modulated power.

Simulations of sawtoothing in a current carrying stellarator

Numerical MHD simulations are used to gain insight into how sawteeth are affected by three-dimensional shaping from the Compact Toroidal Hybrid (CTH) stellarator field. CTH is a small stellarator-tokamak hybrid and sawteeth are sometimes seen on soft x-ray signals when operating with tokamak like profiles. We use NIMROD to compute numerical solutions having repeated sawtooth relaxations for a sequence of configurations with increasing helical stellarator field strength. The experimentally observed trend of the sawtooth period decreasing as the helical field strength is increased is recovered in the simulations. Careful attention to numerical convergence was required to obtain the results, and these considerations may be relevant to simulations of other phenomena in devices with non-axisymmetric plasmas such as perturbed tokamaks, RFPs, and stellarators.

Interaction of external n = 1 magnetic fields with the sawtooth instability in low-q RFX-mod and DIII-D tokamaks

External n = 1 magnetic fields are applied in RFX-mod and DIII-D low safety factor Tokamak plasmas to investigate their interaction with the internal MHD dynamics and in particular with the sawtooth instability. In these experiments the applied magnetic fields cause a reduction of both the sawtooth amplitude and period, leading to an overall stabilizing effect on the oscillations. In RFX-mod sawteeth eventually disappear and are replaced by a stationary m = 1, n = 1 helical equilibrium without an increase in disruptivity. However toroidal rotation is significantly reduced in these plasmas, thus it is likely that the sawtooth mitigation in these experiments is due to the combination of the helically deformed core and the reduced rotation. The former effect is qualitatively well reproduced by nonlinear MHD simulations performed with the PIXIE3D code. The results obtained in these RFX-mod experiments motivated similar ones in DIII-D L-mode diverted Tokamak plasmas at low q95. These experiments succeeded in reproducing the sawtooth mitigation with the approach developed in RFX-mod. In DIII-D this effect is correlated with a clear increase of the n = 1 plasma response, that indicates an enhancement of the coupling to the marginally stable n = 1 external kink, as simulations with the linear MHD code IPEC suggest. A significant rotation braking in the plasma core is also observed in DIII-D. Numerical calculations of the neoclassical toroidal viscosity (NTV) carried out with PENT identify this torque as a possible contributor for this effect.

Control of sawtooth via ECRH on EAST tokamak

Localized electron heating produced by electron cyclotron resonant heating (ECRH) system has been proven to be powerful tools for controlling sawtooth instabilities, because such system allows to directly modify the local plasma parameters that determine the evolution of sawtooth periods. In this paper, we present the experimental results carried out on experimental advanced superconducting tokamak (EAST) with regard to sawtooth period control via ECRH. The electron cyclotron heating system on EAST was capable of inject electron cyclotron wave toward certain locations inside or outside q = 1 magnetic surface on the poloidal cross section, which renders us able to investigate the evolution of sawtooth period against the ECRH deposition position. It is found that when ECRH deposition position is inside the q = 1 surface, the sawtooth oscillation is destabilized (characterized by reduced sawtooth period). So far, inside the q = 1 surface, there are not enough EAST experiment data that can reveal more detailed information about the relation between ECRH deposition position and sawtooth period. When ECRH deposition is outside the q = 1 surface, the sawtooth oscillation is stabilized (characterized by prolonged sawtooth period), and the sawtooth periods gradually decrease as ECRH deposition position sweeps away from q = 1 surface. The sawtooth periods reach maximum when ECRH deposition position falls around q = 1 surface. The magnetic shear at q = 1 surface is calculated to offer insights for the temporal evolution of sawtooth. The result has been found consistent with the Porcelli model.

Simple predictive electron transport models applied to sawtoothing plasmas

In this work, we introduce two simple transport models to evaluate the time evolution of electron temperature and density profiles during sawtooth cycles (i.e. over a sawtooth period time-scale). Since the aim of these simulations is to estimate reliable profiles within a short calculation time, two simplified ad-hoc models have been developed. The goal for these models is to rely on a few easy-to-check free parameters, such as the confinement time scaling factor and the profiles’ averaged scale-lengths. Due to the simplicity and short calculation time of the models, it is expected that these models can also be applied to real-time transport simulations. We show that it works well for Ohmic and EC heated L- and H-mode plasmas. The differences between these models are discussed and we show that their predictive capabilities are similar. Thus only one model is used to reproduce with simulations the results of sawtooth control experiments on the TCV tokamak. For the sawtooth pacing, the calculated time delays between the EC power off and sawtooth crash time agree well with the experimental results. The map of possible locking range is also well reproduced by the simulation.

Stabilization of sawteeth with third harmonic deuterium ICRF-accelerated beam in JET plasmas

Sawtooth stabilisation by fast ions is investigated in deuterium (D) and D-helium 3 (He3) plasmas of JET heated by deuterium Neutral Beam Injection combined in synergy with Ion Cyclotron Resonance Heating (ICRH) applied on-axis at 3rd beam cyclotron harmonic. A very significant increase in the sawtooth period is observed, caused by the ICRH-acceleration of the beam ions born at 100 keV to the MeV energy range. Four representative sawteeth from four different discharges are compared with Porcelli's model. In two discharges, the sawtooth crash appears to be triggered by core-localized Toroidal Alfvén Eigenmodes inside the q = 1 surface (also called “tornado” modes) which expel the fast ions from within the q = 1 surface, over time scales comparable with the sawtooth period. Two other discharges did not exhibit fast ion-driven instabilities in the plasma core, and no degradation of fast ion confinement was found in both modelling and direct measurements of fast ion profile with the neutron camera. The developed sawtooth scenario without fast ion-driven instabilities in the plasma core is of high interest for the burning plasmas. Possible causes of the sawtooth crashes on JET are discussed.

The merits of ion cyclotron resonance heating schemes for sawtooth control in tokamak plasmas

JET experiments have compared the efficacy of low- and high-field side ion cyclotron resonance heating (ICRH) as an actuator to deliberately minimise the sawtooth period. It is found that low-field side ICRH with low minority concentration is optimal for sawtooth control for two main reasons. Firstly, low-field side heating means that any toroidal phasing of the ICRH ($-90^{\circ }$,$+90^{\circ }$or dipole) has a destabilising effect on the sawteeth, meaning that dipole phasing can be employed, since this is preferable due to less plasma wall interaction from Resonant Frequency (RF) sheaths. Secondly, the resonance position of the low-field side ICRH does not have to be very accurately placed to achieve sawtooth control, relaxing the requirement for real-time control of the RF frequency. These empirical observations have been confirmed by hybrid kinetic–magnetohydrodynamic modelling, and suggest that the ICRH antenna design for ITER is well positioned to provide a control actuator capable of having a significant effect on the sawtooth behaviour.

Demonstration of sawtooth period control with EC waves in KSTAR plasma

The sawtooth period control in tokamak is important issue in recent years because the sawtooth crash can trigger TM/NTM instabilities and drive plasmas unstable. The control of sawtooth period by the modification of local current profile near the q =1 surface using ECCD has been demonstrated in a number of tokamaks [1, 2] including KSTAR. As a result, developing techniques to control the sawtooth period as a way of controlling the onset of NTM has been an important area of research in recent years [3]. In 2012 KSTAR plasma campaign, the sawtooth period control is carried out by the different deposition position of EC waves across the q =1 surface. The sawtooth period is shortened by on-axis co-ECCD (destabilization), and the stabilization of the sawtooth is also observed by off-axis co-ECCD at outside q =1 surface. In 2013 KSTAR plasma campaign, the sawtooth locking experiment with periodic forcing of 170 GHz EC wave is carried out to control the sawtooth period. The optimal target position which lengthens the sawtooth period is investigated by performing a scan of EC beam deposition position nearby q =1 surface at the toroidal magnetic field of 2.9 T and plasma current of 0.7 MA. The sawtooth locking by the modulated EC beam is successfully demonstrated as in [3-5] with the scan of modulation-frequency and duty-ratio at the low beta ( β N ~0.5) plasma. In this paper, the sawteeth behavior by the location of EC beam and the preliminary result of the sawtooth locking experiments in KSTAR will be presented.

Simulation on Sawtooth Period Control in Tokamak Plasma

Simulation on Sawtooth Period Control in Tokamak Plasma

Control of sawtooth periods by pulsed ECH/ECCD in the FTU tokamak

It is well known that fusion plasma operations can be limited in standard scenarios at high β by resistive instabilities, called neoclassical tearing modes (NTMs), which degrade the plasma confinement leading to a loss of plasma energy, and in some cases to disruption. The avoidance of their onset is a very important issue that has been largely investigated in many tokamaks. In particular, it has been shown that these modes, shaped as magnetic islands, can be triggered by finite seed perturbations associated with long sawtooth crashes. The control of the sawtooth periods is then a key step in the physics of plasma confinement in fusion devices: the shortening of these periods can reduce any triggered large seed island below the NTMs' growth threshold allowing maximum β values and high plasma performances to be achieved. A powerful tool for sawtooth control is the use of high localized electron cyclotron heating (ECH) and current drive (ECCD), capable of modifying the plasma current density and effecting the sawtooth period. Modulated ECH and ECCD have been used as triggers of sawtooth crashes to test conditions for an a priori constant sawtooth period. In the FTU high magnetic field compact tokamak (R0 = 0.93 m, a = 0.3 m, B0 = 4–8 T) similar experiments have been performed with an ECRH system of four gyrotrons operating at 140 GHz and delivering 0.5 MW each. Repetitive pulses of EC power from 1 to 2 gyrotrons up to 0.8 MW for 500 ms have been used to investigate the sensitivity of sawtooth periods during long and short EC switching on and off phases in view of a real time EC control system soon to be working in FTU. A new type of locking of the sawtooth periods to the EC modulation has been observed for deposition inside the q = 1 radius for EC on phase smaller than the ohmic period. In this paper, sawtooth period shortening and locking by ECH and co-ECCD inside the q = 1 radius is investigated and reproduced by numeric simulations.