Sawtooth Period Research Articles

Fast seeding of NTMs by sawtooth crashes in TCV and their preemption using ECRH

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.

An overview of FTU results

Since the 2010 IAEA-FEC Conference, FTU has exploited improvements in cleaning procedures and in the density control system to complete a systematic exploration of access to high-density conditions in a wide range of plasma currents and magnetic fields. The line-averaged densities at the disruptive limit increased more than linearly with the toroidal field, while no dependence on plasma current was found; in fact, the maximum density of 4.3 × 1020 m−3 was reached at B = 8 T even at the minimum current of 0.5 MA, corresponding to twice the Greenwald limit. The lack of plasma current dependence was due to the increase in density peaking with the safety factor. Experiments with the 140 GHz electron cyclotron resonance heating (ECRH) system were focused on the sawtooth (ST) period control and on the commissioning of a new launcher with real-time steering capability that will act as the front-end actuator of a real-time system for ST period control and tearing mode stabilization. Various ECRH and electron cyclotron current-drive modulation schemes were used; with the fastest one, the ST period synchronized with an 8 ms modulation period. The observed period variations were simulated using the JETTO code with a critical shear model for the crash trigger. The new launcher was of the plug-in type, allowing quick insertion and connection to the transmission line. Both beam characteristics and steering speed were in line with design expectation. Experimental results on the connection between improved coupling of lower hybrid waves in high-density plasmas and reduced wave spectral broadening were interpreted by fully kinetic, non-linear model calculations. A dual-frequency, time-of-flight diagnostic for the measurement of density profiles was developed and successfully tested. Fishbone-like instabilities driven by energetic electrons were simulated by the hybrid MHD-gyrokinetic XHMGC code.

Overview of recent and current research on the TCV tokamak

Through a diverse research programme, the Tokamak à Configuration Variable (TCV) addresses physics issues and develops tools for ITER and for the longer term goals of nuclear fusion, relying especially on its extreme plasma shaping and electron cyclotron resonance heating (ECRH) launching flexibility and preparing for an ECRH and NBI power upgrade. Localized edge heating was unexpectedly found to decrease the period and relative energy loss of edge localized modes (ELMs). Successful ELM pacing has been demonstrated by following individual ELM detection with an ECRH power cut before turning the power back up to trigger the next ELM, the duration of the cut determining the ELM period. Negative triangularity was also seen to reduce the ELM energy release. H-mode studies have focused on the L–H threshold dependence on the main ion species and on the divertor leg length. Both L- and H-modes have been explored in the snowflake configuration with emphasis on edge measurements, revealing that the heat flux to the strike points on the secondary separatrix increases as the X-points approach each other, well before they coalesce. In L-mode, a systematic scan of the auxiliary power deposition profile, with no effect on confinement, has ruled it out as the cause of confinement degradation. An ECRH power absorption observer based on transmitted stray radiation was validated for eventual polarization control. A new profile control methodology was introduced, relying on real-time modelling to supplement diagnostic information; the RAPTOR current transport code in particular has been employed for joint control of the internal inductance and central temperature. An internal inductance controller using the ohmic transformer has also been demonstrated. Fundamental investigations of neoclassical tearing mode (NTM) seed island formation by sawtooth crashes and of NTM destabilization in the absence of a sawtooth trigger were carried out. Both stabilizing and destabilizing agents (electron cyclotron current drive on or inside the q = 1 surface, respectively) were used to pace sawtooth oscillations, permitting precise control of their period. Locking of the sawtooth period to a pre-defined ECRH modulation period was also demonstrated. Sawtooth control has permitted nearly failsafe NTM prevention when combined with backup NTM stabilization by ECRH.

Sawtooth behavior in reversed toroidal magnetic field plasma in the EAST tokamak

Experiments with different directions of toroidal magnetic fields were performed on the EAST tokamak. The sawtooth behavior has been investigated in both ohmical and LHCD–ICRF plasmas (lower hybrid current drive and ion-cyclotron radio frequency). It is found that the magnetic configuration only has a negligible effect on sawtooth behavior. Sawtooth periods changed dramatically in the LHCD–ICRF plasma where the direction of electron diamagnetic drift velocity was inversed. The rotation directions of sawtooth precursor reversed when the direction of the toroidal magnetic field was changed. We also found that the period of sawtooth depends on the stability, including linear growth and nonlinear evolution, of the sawtooth precursor. Finally, we propose that the longer sawtooth is due to the stabilized internal modes, which stabilize by energetic ions produced by ICRF.

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*.

Sawtooth control using electron cyclotron current drive in the presence of energetic particles in high performance ASDEX Upgrade plasmas

Sawtooth control using steerable electron cyclotron current drive (ECCD) has been demonstrated in ASDEX Upgrade plasmas with a significant population of energetic ions in the plasma core and long uncontrolled sawtooth periods. The sawtooth period is found to be minimized when the ECCD resonance is swept to just inside the q = 1 surface. By utilizing ECCD inside q = 1 for sawtooth control, it is possible to avoid the triggering of neoclassical tearing modes (NTMs), even at significantly higher pressure than anticipated in the ITER baseline scenario. Operation at 25% higher normalized pressure has been achieved when only modest ECCD power is used for sawtooth control compared to identical discharges without sawtooth control when NTMs are triggered by the sawteeth. Modelling suggests that the destabilization arising from the change in the local magnetic shear caused by the ECCD is able to compete with the stabilizing influence of the energetic particles inside the q = 1 surface.

Power requirements for electron cyclotron current drive and ion cyclotron resonance heating for sawtooth control in ITER

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 α 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.

Robust sawtooth period control based on adaptive online optimization

The systematic design of a robust adaptive control strategy for the sawtooth period using electron cyclotron current drive (ECCD) is presented. Recent developments in extremum seeking control (ESC) are employed to derive an optimized controller structure and offer practical tuning guidelines for its parameters. In this technique a cost function in terms of the desired sawtooth period is optimized online by changing the ECCD deposition location based on online estimations of the gradient of the cost function. The controller design does not require a detailed model of the sawtooth instability. Therefore, the proposed ESC is widely applicable to any sawtoothing plasma or plasma simulation and is inherently robust against uncertainties or plasma variations. Moreover, it can handle a broad class of disturbances. This is demonstrated by time-domain simulations, which show successful tracking of time-varying sawtooth period references throughout the whole operating space, even in the presence of variations in plasma parameters, disturbances and slow launcher mirror dynamics. Due to its simplicity and robustness the proposed ESC is a valuable sawtooth control candidate for any experimental tokamak plasma, and may even be applicable to other fusion-related control problems.

Sawtooth period control strategies and designs for improved performance

The sawtooth instability is associated with the triggering of neo-classical tearing modes, core fuelling, α-confinement and the exhaust of thermal helium. Sawtooth control is therefore important for optimal reactor performance in ELMy H-modes. Control schemes for the sawtooth period have been published in the literature, but the systematic design of high-performance controllers (yielding accurate and fast convergent responses) has not been addressed. In this work, three control strategies for high-performance sawtooth control are presented using electron cyclotron current drive (ECCD). Both degrees of freedom of the ECCD actuator will be explored and combined with advanced controller designs. First, the ECCD deposition location is used as a control variable, for which a gain-scheduled feedback controller and static feedforward control is derived. Second, the use of the driven current as a control variable is explored, and a simple controller is designed based on the identified dynamics. In the third approach both control variables are joined in an overall controller design, which enables the combination of high-performance control of the sawtooth period and control of the gyrotron power. Time-domain simulations with a combined Kadomtsev–Porcelli sawtooth model show that each strategy obtains a better closed-loop performance than standard linear feedback techniques on merely the deposition location.

Integrated real-time control of MHD instabilities using multi-beam ECRH/ECCD systems on TCV

Simultaneous real-time control of multiple MHD instabilities is experimentally demonstrated in the TCV tokamak. Multiple sources of EC heating and current drive, injected through real-time controlled launchers, are used to stabilize 3/2 and 2/1 neoclassical tearing modes (NTMs) rapidly after their appearance. Control of the sawtooth instability using a new sawtooth-pacing technique is demonstrated, providing precise control of the time of appearance of the sawtooth crash. Efficient NTM preemption can then be performed by applying pulsed power on the mode rational surface at the time of the seed-island generating sawtooth crash. These three elements are combined into one integrated control system which can simultaneously control the sawtooth period, preempt the formation of NTMs and suppress these if they appear.

Rapid Collapse of a Plasma Sawtooth Oscillation in the HT-7 Tokamak

The rapid collapse of a sawtooth oscillation which is characterized by the absence of any discernible precursor oscillation in the HT-7 tokamak has been observed in detail on a fast time scale. The contour plot of the raw data of soft-x-ray signals shows that sawtooth crash simultaneously on both the high field side and the low field side with symmetry. Only spatial structure of sawtooth exists in the whole sawtooth period. A larger heat outflow and profile of emission intensities flatten during sawtooth crash by means of soft x-ray tomography. The plausible interpretation is the stochastization of magnetic field lines lead to a transition from semicollisional to collisionless reconnection regimes during non-linear pre-crash phase in which the growth rate is rapidly increased and no any discernible precursor oscillation.

Sawtooth control using electron cyclotron current drive in ITER demonstration plasmas in DIII-D

Sawtooth control using electron cyclotron current drive (ECCD) has been demonstrated in ITER-like plasmas with a large fast ion fraction, wide q = 1 radius and long uncontrolled sawtooth period in DIII-D. The sawtooth period is minimized when the ECCD resonance is just inside the q = 1 surface. Sawtooth destabilization using driven current inside q = 1 avoids the triggering of performance-degrading neoclassical tearing modes (NTMs), even at much higher pressure than required in the ITER baseline scenario. Operation at βN = 3 without 3/2 or 2/1 NTMs has been achieved in ITER demonstration plasmas when sawtooth control is applied using only modest ECCD power. Numerical modelling qualitatively confirms that the achieved driven current changes the local magnetic shear sufficiently to compensate for the stabilizing influence of the energetic particles in the plasma core.

Demonstration of sawtooth period locking with power modulation in TCV plasmas

Corroborating evidence is presented that the sawtooth period can follow the modulation frequency of an externally applied high power electron cyclotron wave source. Precise, fast and robust open loop control of the sawtooth period with a continuously changing reference period has been achieved. This period locking is not associated with the crash, but with the phase evolution of the inter-crash dynamics. This opens new possibilities of open loop control for physics studies and maybe for reactor performance control.

Sawtooth Control Experiments on HT-7 and EAST Tokamak

Sawtooth control experiments were performed on HT-7 with a limiter configuration and on the Experimental Advanced Superconducting Tokamak (EAST) with a double null configuration. The sawtooth period can be modified by lower hybrid wave (LHW) and ion cyclotron resonance frequency (ICRF). Different sawtooth behavior was observed with the same plasma density, LHW power but different plasma currents on HT-7. There was a dwell time between LHW added and the sawtooth stabilization on HT-7 while the sawtooth stabilization immediately happened when LHW power was injected on EAST. The possible mechanism of the sawtooth control is discussed in this paper. All the experimental results have proved that power deposition of the radio frequency (RF) should be the key factor for sawtooth control.

Unified theory of the semi-collisional tearing mode and internal kink mode in a hot tokamak: implications for sawtooth modelling

In large hot tokamaks like JET, the width of the reconnecting layer for resistive modes is determined by semi-collisional electron dynamics and is much less than the ion Larmor radius. Firstly a dispersion relation valid in this regime is derived which provides a unified description of drift-tearing modes, kinetic Alfvén waves and the internal kink mode at low beta. Tearing mode stability is investigated analytically recovering the stabilizing ion orbit effect, obtained previously by Cowley et al (1986 Phys. Fluids 29 3230), which implies large values of the tearing mode stability parameter Δ′ are required for instability. Secondly, at high beta it is shown that the tearing mode interacts with the kinetic Alfvén wave and that there is an absolute stabilization for all Δ′ due to the shielding effects of the electron temperature gradients, extending the result of Drake et al (1983 Phys. Fluids 26 2509) to large ion orbits. The nature of the transition between these two limits at finite values of beta is then elucidated. The low beta formalism is also relevant to the m = n = 1 tearing mode and the dissipative internal kink mode, thus extending the work of Pegoraro et al (1989 Phys. Fluids B 1 364) to a more realistic electron model incorporating temperature perturbations, but then the smallness of the dissipative internal kink mode frequency is exploited to obtain a new dispersion relation valid at arbitrary beta. A diagram describing the stability of both the tearing mode and dissipative internal kink mode, in the space of Δ′ and beta, is obtained. The trajectory of the evolution of the current profile during a sawtooth period can be plotted in this diagram, providing a model for the triggering of a sawtooth crash.

A new mechanism for sawtooth period control

Experiments and simulations show that the sawtooth period can be influenced and precisely tuned by modulated ECCD power.

Numerical demonstration of injection locking of the sawtooth period by means of modulated EC current drive

In this paper the sawtooth period behaviour under periodic forcing by electron cyclotron waves is investigated. The deposition location is kept constant while the gyrotron power is modulated with a certain period and duty cycle. Extensive simulations on a representative dynamic sawtooth model show that when this modulation is properly chosen, the sawtooth period quickly synchronizes to the same period and remains locked at this value. It is shown that the range of modulation periods and duty cycles over which sawtooth period locking occurs, depends on the deposition location, but is particularly large for depositions near the q = 1 surface. The simulation results reveal a novel approach to control the sawtooth period in open loop, based on injection locking, which is a well-known technique to control limit cycles of non-linear dynamic oscillators. The locking and convergence results are therefore used in a simple open-loop locking controller design, with which accurate sawtooth period tracking to any desired value is indeed demonstrated. Injection locking appears to let the sawtooth period converge to the modulation period quickly, partly because it does not suffer from slow EC mirror launcher dynamics. Moreover, simulations show that the method has a relatively large robustness against general uncertainties and disturbances. Hence, injection locking is expected to outperform conventional sawtooth control methods using a variable deposition location and constant gyrotron power. Finally, the recent result with sawtooth pacing is shown to be a special case of the general locking effect.

Progress and scientific results in the TCV tokamak

The TCV tokamak has the dual mission of supporting ITER and exploring alternative paths to a fusion reactor. Its most unique tools are a 4.5 MW electron cyclotron resonance heating system with seven real-time controllable launchers and a plasma control system with 16 independent shaping coils. Recent upgrades in temperature, density and rotation diagnostics are being followed by new turbulence and suprathermal electron diagnostics, and a new digital real-time network has been commissioned. The shape control flexibility of TCV has enabled the generation and control of the first ‘snowflake’ divertor, characterized by a null point in which both the poloidal field and its gradient vanish. The predicted increases in flux expansion and edge magnetic shear have been verified experimentally, and stable EC-heated snowflake ELMy H-modes have been obtained and characterized. ECCD modulation techniques have been used to study the role of the current profile in energy transport, and simulations reproduce the results robustly. The relation between impurity and electron density gradients in L-mode is explained in terms of neoclassical and turbulent drives. Studies of torqueless plasma rotation have continued, highlighting the important role of MHD and sawtooth relaxations in determining the rotation profiles. A newly predicted mechanism for turbulent momentum transport associated with up–down plasma asymmetry has been verified in TCV. Sawtooth period control, neoclassical tearing mode control and soft x-ray emission profile control have been demonstrated in TCV using the new digital control hardware, as a step on the way to more complex applications.

Feedback control of the sawtooth period through real time control of the ion cyclotron resonance frequency

Modification of the sawtooth period through ion cyclotron resonance frequency (ICRF) heating and current drive has been demonstrated in a number of experiments. The effect has been seen to depend critically on the location of the ICRF absorption region with respect to the q = 1 flux surface. Consequently, for ICRF to be a viable tool for sawtooth control, one must be able to control the ICRF absorption location in real time so as to follow variations in the location of the q = 1 surface. To achieve this, the JET ICRF system has been modified to allow the JET real time central controller to control the frequency of the ICRF generators. An algorithm for real time determination of the sawtooth period has been developed and a closed loop controller, which modifies the frequency of the ICRF generators to bring the measured sawtooth period to the desired reference value, has been implemented. This paper shows the first experimental demonstration of closed loop sawtooth period control by real time variation of the ICRF wave frequency.

Systematic design of a sawtooth period feedback controller using a Kadomtsev–Porcelli sawtooth model

A systematic methodology for structured design of feedback controllers for the sawtooth period is presented, based on dedicated identification of the sawtooth dynamics. Therefore, a combined Kadomtsev–Porcelli model of a sawtoothing plasma actuated by an electron cyclotron current drive system has been set-up. This is used to derive the linearized input–output relations (transfer functions) from the varying deposition location of the electron cyclotron waves (ECW) to the sawtooth period. These transfer functions are derived around a large collection of operating points. Assessment of these control-relevant transfer functions shows that a sawtooth period controller requires an integral (I) action to guarantee closed-loop stability with zero steady-state error. Additional proportional-integral (PI) action can be applied to further increase the closed-loop performance. The parameters of both the I and PII controllers have been optimized in terms of stability, performance and robustness. Moreover, the effect of the mechanical ECW launcher on the closed-loop performance is studied for realistic cases. It is shown that the launcher dynamics seriously affects the achievable closed-loop performance in present-day experiments.