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In KSTAR experiments exhibiting sawtooth instability, the formation of multiple flux tubes (MFTs) has been frequently observed when electron cyclotron resonance heating or a current drive is applied near the inversion radius of the sawtooth. On the global scale, these MFTs evolve into a single flux tube mode or dual modes. The modes are observed as multiple Fourier harmonics in the spectrogram. A comprehensive correlation analysis of 2D imaging diagnostic data reveals a notable energy transfer within structures of varying sizes during the global mode transition. Broadband fluctuations are enhanced, and energy transfer between Fourier harmonics occurs in the presence of MFTs. Cross-power spectrum in the presence of multiple Fourier harmonics aligns with power law of inverse cascade. This suggests that energy inverse cascade process can contribute to formation of MFTs.

In this article, partial and full collapses of sawtooth activity are investigated with the high-resolution two-dimensional electron cyclotron emission (ECE) Imaging diagnostic in EAST. The partial collapse in normal sawtooth behavior is detected during the precursor phase of an L-mode plasma heated by ICRF. The electron heat diffusivity is determined with the time-to-peak analysis. The experimental results revealed that heat diffusivity suppresses at the time of the partial collapse. As a result, the partial collapse process interrupts and the small amount of heat releases outward. The hot core survives and is enclosed by the cold magnetic island. The inversion radii are estimated with the help of sawtooth and the only single inversion radius is found during the entire collapse process. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Visco-resistive magnetohydrodynamic simulations are used to investigate the role of resistivity and viscosity in the reversed field pinch sawtooth crash. Specifically, we examine the temporal behavior of the linearly stable (m, n) = (0, 1) mode. Both volume-averaged dissipation and dissipation levels in the region near the m = 0 resonance are found to influence characteristic time scales. Increasing resistivity causes the mode rise time, fall time, and total crash duration to decrease, while increasing viscosity has the opposite effect. Examination of energy flow during the sawtooth crash reveals that despite the linear stability of the (0, 1) mode, it receives most of its energy from the mean current profile during the crash rather than from nonlinear interactions with other modes. Resistivity and viscosity do not impact mode behavior directly through dissipative energy loss but rather through modification of the large scale current profile evolution and radial structure of the mode. Computational results are compared to experimental data from the Madison Symmetric Torus and found to largely agree when resistivity and viscosity are similar. [ABSTRACT FROM AUTHOR]

Control of the tearing mode by sawtooth activity has been achieved in the Joint European Torus tokamak experiments. It has been shown that the tearing mode can be stabilized by short-period sawtooth oscillation. Based on the experimental results, a model for the tearing mode stabilized by sawtooth activity has been proposed, which mainly focuses on the periodic variation of the current during sawtooth activity. Both the current oscillation and the induced electric field which is due to the rapid variation of the current play important roles in the tearing mode stabilization. [ABSTRACT FROM AUTHOR]

The profiles of the W transport coefficients have been experimentally calculated for a large database of identical ASDEX Upgrade H-mode discharges where only the radio-frequency (RF) power characteristics have been varied [Angioni et al., Nucl. Fusion 57, 056015 (2017)]. Central ion cyclotron resonance heating (ICRH) in the minority heating scheme has been compared with central and off-axis electron cyclotron resonance heating (ECRH), using both localized and broad heat deposition profiles. The transport coefficients have been calculated applying the gradient-flux relation to the evolution of the intrinsic W density in-between sawtooth cycles as measured using the soft X-ray diagnostic. For both ICRH and ECRH, the major player in reducing the central W density peaking is found to be the reduction of inward pinch and in the case of ECRH, the rise of an outward convection. The impurity convection increases, from negative to positive, almost linearly with RF-power, while no appreciable changes are observed in the diffusion coefficient, which remains roughly at neoclassical levels independent of RF power or background plasma conditions. The ratio vW/DW is consistent with the equilibrium ▿ nW=nW prior to the sawtooth crash, corroborating the separate estimates of diffusion and convection. These experimental findings are slightly different from previous results obtained analysing the evolution of impurity injections over many sawtooth cycles. Modelling performed using the drift-kinetic code NEO and the gyro-kinetic code GKW (assuming axisymmetry) overestimates the diffusion coefficient and underestimates the experimental positive convection. This is a further indication that magneto-hydrodynamic/neoclassical models accounting for 3D effects may be needed to characterize impurity transport in sawtoothing tokamak plasmas. [ABSTRACT FROM AUTHOR]

Electron cyclotron emission imaging (ECEI), as an advanced diagnostic, provides two-dimensional (2D) images of electron temperature fluctuation in the core plasma region. The ECEI system on Experimental Advanced Superconducting Tokamak (EAST) tokamak consists of 384 channels by 24 (vertical) × 16 (horizontal). The system nearly covers the wholesurface in cross-section of EAST. Here, we present a quantitative method to estimate the sawtooth collapse time. All of the electron temperature fluctuations inside thesurface are summed up, and the collapse time is estimated as the time lag between the maximum and minimum values of the total fluctuation during one sawtooth cycle. Using this method, statistical analysis of sawtooth behaviors is studied in the EAST Ohmic heating plasma. Relationships of heat flux, sawtooth period and collapse time are also presented. [ABSTRACT FROM PUBLISHER]

In this work, we consider magnetic reconnection in thin current sheets with both resistive and electron inertia effects. When the current sheet is produced by a primary instability of the internal kink type, the analysis of secondary instabilities indicates that reconnection proceeds on a time scale much shorter than the primary instability characteristic time. In the case of a sawtooth crash, non-collisional physics becomes important above a value of the Lundquist number, which scales like S ~ (R/de)12/5, in terms of the tokamak major radius R and of the electron skin depth de. This value is commonly achieved in present day devices. As collisionality is further reduced, the characteristic rate increases, approaching Alfvéenic values when the primary instability approaches the collisionless regime. [ABSTRACT FROM AUTHOR]

The paper commences with a review of ice-induced vibrations in full-scale structures in the field, in medium-scale tests, and particularly, in small-scale indentation tests. The mechanics of compressive ice failure is reviewed, with emphasis on the processes leading to the formation of a layer of microstructurally modified material under the indenter, as well as fracture. Previous tests in the present series using small-scale indentors are reviewed, and a recently conducted series of tests is introduced. This series involved confined ice specimens of cylindrical shape 154 mm in diameter moving at various constant displacement rates against a 20-mm diameter indentor attached to an elastic-compliant structure. The displacement rates (ice speeds) were chosen so as to induce “sawtooth” vibrations. Two beam structures, one stiff and the other flexible, were used. In general, the desired sawtooth pattern was achieved, particularly with the more flexible system, but also with the stiffer one at higher ice speeds. Some results involving “lock-in” were obtained with the stiffer setup. Measurements were made of the distribution of pressure at the ice–indentor interface using pressure-sensitive film, and thin sections were taken from the indented samples. The thin sections in all cases showed the presence of a microstructurally modified layer of ice adjacent to the indentor. Pressure distributions showed that regular vibrations were associated mainly with activity in the layer, whereas the larger spall fractures generally caused irregular load patterns with significant loss of contact area under the indentor. The regular failure can be analysed as a self-sustained oscillation, which is common among dissipative systems. The system in this case comprises the moving ice field and the compliant structure with which the ice interacts, resulting in autonomous vibrations of the sawtooth variety. Regularity was interrupted by the larger spalling fractures. [ABSTRACT FROM AUTHOR]

We study the de Gennes free energy for smectic A liquid crystals over S2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter ε, and investigate the behaviors of the minimizers when the field strength is of order O(ε-1). In this regime, we show via Γ-convergence that a chevron structure where the director connects two minimum states of the sphere is favored. We also analyze the Chen-Lubensky free energy, which includes the second order gradient of the smectic order parameter, and obtain the same general behavior as for the de Gennes case. Numerical simulations illustrating the chevron structures for both energies are included. [ABSTRACT FROM AUTHOR]

Sawtooth oscillations in tokamaks are defined by their effect on electron temperature: a rapid flattening of the core profile followed by an outward heat pulse and a slow core recovery caused by central heating. Recent high-resolution, multi-chord interferometer measurements on JTEXT extend these studies to particle transport. Sawteeth only partially flatten the core density profile, but enhanced particle diffusion on the time scale of the thermal crash occurs over much of the profile, relevant for impurities. Recovery between crashes implies an inward pinch velocity extending to the center. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The optimization of LHD discharges in inward-shifted configurations with 1/3 sawtooth like activity is an open issue. These relaxation events limit the LHD performance driving a periodic plasma deconfinement. The aim of this study is to analyze the 1/3 sawtooth like activity in plasmas with different stability properties to foreseen the best operation conditions and minimize its undesired effects. We summarize the results of several MHD simulations for plasmas with Lundquist numbers between 105 and 106 in the slow reconnection regime, studying the equilibria properties during the onset of a chain of 1/3 sawtooth like events. The research conclusions point out that the hard MHD limit can be reached in the inner plasma region after the onset of a strong 1/3 resonant sawtooth like event and trigger a plasma collapse. The collapse can be avoided if the system remains in the soft MHD limit, namely, in a regime with a pressure gradient and a magnetic turbulence below the critical values to drive the soft-hard MHD transition. In the soft MHD limit the system relaxations are the non resonant 1/3 sawtooth like events or a weak version of the 1/3 resonant sawtooth like events. A system relaxation in the soft MHD regime drives a minor plasma deconfinement that does not limit the LHD performance if the event periodicity is not very high. [ABSTRACT FROM AUTHOR]

The transport of impurities by a sawtooth crash is simulated with the XTOR-2F code. Impurities are modeled as passive scalars, evolving in the compressible MHD flow inferred from the main MHD plasma. For a peaked impurity density profile, the non-linear kink flow of the sawtooth crash redistributes the profile efficiently and most of the particles in the peak inside the q=1 surface are expelled. For an initially hollow impurity density profile, the crash leads to a significant penetration up to the magnetic axis. The results are compared with Kadomtsev's model. Despite essentially different mechanisms, the evolution of the particle content inside the q=1 surface for Kadomtsev's model and for the non-linear case are virtually identical for the peaked profile, while the model slightly overestimates penetration for the hollow case. [ABSTRACT FROM AUTHOR]

In this paper, we study experimentally the effect of the geometry parameters of a saw-tooth surface and a micropart on the motion of the micropart. The experiments are performed for a range of the saw-tooth pitch p, micropart length l, and exciting frequency f applied to the surface. By the use of particle tracking velocimetry method, we obtain the time-dependent velocity and then the ensemble-averaged velocity of the microparts. The results show that the velocity of the micropart increases up to a certain value of pf and then decreases with increasing pf. The widths of the profiles are similar for the same value of the relative scale l/ p but the peaks of the profiles are slightly larger and the profiles are shifted leftward for larger pitches of the saw-tooth surface. It implies that the motion of the micropart depends more on the characteristic surface velocity pf than on the relative scale l/ p and that a larger pitch of the sawtooth creates a larger asymmetric force on the micropart. © 2013 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

Many tokamaks have observed that sawteeth of sufficient duration may trigger neoclassical tearing modes (NTMs) that lead to plasma performance degradation. In this paper, TCV's ability to accurately control the period of individual sawteeth is exploited, using localized electron cyclotron resonance heating and current drive (ECRH and ECCD), to trigger NTMs under controlled conditions, providing an excellent environment for the study of the seeding of NTMs by sawtooth crashes. The TCV experiments show evidence of a fast formation of seed islands with poloidal/toroidal mode numbers m/n = 3/2 and 2/1 within a few tens of microseconds following the sawtooth crash. Crashes of sawteeth with a longer period duration are observed to generate larger seed islands but also increase the plasma stability to conventional tearing modes. While these two effects compete, the NTM stability is found to decrease with increasing sawtooth period. The seed island size can be reduced and, thereby, the NTM stability improved, by increasing the value of the safety factor q95. Alternatively, NTM stability can be increased by application of preemptive ECRH at the resonant surface of the NTM. Preemptive ECRH is found to enlarge the plasma operational domain by improving the conventional tearing stability and by reducing the coupling between the driving (m/n = 1/1 or 2/2) and the driven modes (m/n = 2/1 or 3/2), resulting in smaller sawtooth generated seed islands. The efficiency of preemptive ECRH increases when sufficient ECRH power is applied in a short time interval prior to the sawtooth crash. [ABSTRACT FROM AUTHOR]

13 MW of electron cyclotron current drive (ECCD) power deposited inside the q = 1 surface is likely to reduce the sawtooth period in ITER baseline scenario below the level empirically predicted to trigger neoclassical tearing modes (NTMs). However, since the ECCD control scheme is solely predicated upon changing the local magnetic shear, it is prudent to plan to use a complementary scheme which directly decreases the potential energy of the kink mode in order to reduce the sawtooth period. In the event that the natural sawtooth period is longer than expected, due to enhanced a particle stabilization for instance, this ancillary sawtooth control can be provided from > 10MW of ion cyclotron resonance heating (ICRH) power with a resonance just inside the q = 1 surface. Both ECCD and ICRH control schemes would benefit greatly from active feedback of the deposition with respect to the rational surface. If the q = 1 surface can be maintained closer to the magnetic axis, the efficacy of ECCD and ICRH schemes significantly increases, the negative effect on the fusion gain is reduced, and off-axis negative-ion neutral beam injection (NNBI) can also be considered for sawtooth control. Consequently, schemes to reduce the q = 1 radius are highly desirable, such as early heating to delay the current penetration and, of course, active sawtooth destabilization to mediate small frequent sawteeth and retain a small q = 1 radius. Finally, there remains a residual risk that the ECCD + ICRH control actuators cannot keep the sawtooth period below the threshold for triggering NTMs (since this is derived only from empirical scaling and the control modelling has numerous caveats). If this is the case, a secondary control scheme of sawtooth stabilization via ECCD + ICRH + NNBI, interspersed with deliberate triggering of a crash through auxiliary power reduction and simultaneous pre-emptive NTM control by off-axis ECCD has been considered, permitting long transient periods with high fusion gain. The power requirements for the necessary degree of sawtooth control using either destabilization or stabilization schemes are expected to be within the specification of anticipated ICRH and ECRH heating in ITER, provided the requisite power can be dedicated to sawtooth control. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We analyze experimentally chemical wave propagation in the disordered flow field of a porous medium. The reaction fronts travel at a constant velocity that drastically depends on the mean flow direction and rate. The fronts may propagate either downstream and upstream but, surprisingly, they remain static over a range of flow rate values. Resulting from the competition between the chemical reaction and the disordered flow field, these frozen fronts display a particular sawtooth shape. The frozen regime is likely to be associated with front pinning in low velocity zones, the number of which varies with the ratio of the mean flow and the chemical front velocities. [ABSTRACT FROM AUTHOR]

Sawteeth in tokamak plasmas correspond to periodic relaxations of the temperature and density in the central region of the plasma, caused by the internal kink mode. They play an important role in core confinement and impurity transport in the central region of a tokamak discharge, and they can trigger secondary instabilities. Being able to control their dynamics is therefore important. In this article, we explore by means of MHD simulations the control of sawteeth, relying on current or power deposition in the vicinity of the q  =  1 surface. To do so, simulations with the full-MHD code xtor-2f (Lütjens and Luciani 2010 J. Comput. Phys. 229 8130–43), which features power and current source terms mimicking the effects of ECCD and ECRH, are performed. Simulations show that a deposition of current inside the inversion radius leads to an increase of the sawtooth frequency whereas a deposition near or outside the inversion radius leads to a decrease of the sawtooth frequency, in agreement with theoretical and experimental predictions. For power depositions, the situation appears however to be more complex. The modification of the sawtooth shape in presence of additional heating or current drive is also investigated. The existence of a critical shear setting the condition of the sawtooth crash is found to apply, although the inter-crash dynamics is often too complex and MHD-dependent to be summarized as a periodic instantaneous redistribution of current and energy, as assumed in the analytical models. Finally, we briefly explore possible scenarios for the triggering of magnetic islands, and show how controlling the sawteeth can help to prevent the triggering of tearing instabilities. [ABSTRACT FROM AUTHOR]

We present a numerical investigation of electron cyclotron beams interacting with electron density fluctuations in the ITER 15 MA H-mode scenario. In particular, here we study how the beam from the equatorial launcher, which shall be utilized to influence the sawtooth instability, is affected by the fluctuations. Moreover, we present the theory and first estimates of the power that is scattered from the injected O-mode to a secondary X-mode in the presence of the fluctuations. It is shown that for ITER parameters the scattered power stays within acceptable limits and broadening of the equatorial beams is less than those from the upper launcher. [ABSTRACT FROM AUTHOR]