Sawtooth Reconnection Research Articles

Effects of plasmoid formation on sawtooth process in a tokamak

For realistic values of the Lundquist number in tokamak plasmas, 1/1 magnetic islands lead to the formation of a secondary thin current sheet, which breaks up into a chain of small magnetic islands, called plasmoids. The role of plasmoid dynamics during the sawtooth reconnection process in fusion plasmas remains an unresolved issue. In this study, systematic simulations are performed to investigate the resistive internal kink mode using the full resistive magnetohydrodynamics equations implemented in the NIMROD code in a simplified tokamak geometry. For Lundquist number S≥1.6×107, the secondary current sheet is found to be unstable to plasmoids during the nonlinear resistive kink mode evolution with a critical aspect ratio of the current sheet of ∼70. The merging of small plasmoids leads to the formation of a monster plasmoid that can significantly affect the primary island evolution. This may provide an explanation for the partial reconnection observed in sawtooth experiments.

Full-orbit and drift calculations of fusion product losses due to explosive fishbones on JET

Fishbones are ubiquitous in high-performance JET plasmas and are typically considered to be unimportant for scenario design. However, during recent high-performance hybrid scenario experiments, sporadic and explosive fishbone oscillations with sawtooth reconnection were observed coinciding with reduced performance and a main chamber hotspot. Fast ion loss diagnostics showed fusion products ejected from the plasma by the fishbones. We present calculations of the perturbed motion of non-resonant fusion products in the presence of fishbones assuming a fixed linear mode structure and frequency. Using careful reconstruction of the equilibrium and measurements of the perturbation, we show that the measured fishbone spatial structure in these experiments can be well modelled as a linear MHD internal kink mode. Both drift and full-orbit calculations predict losses of fusion products at the same location of the observed hotspot, however the calculated energy content of those losses is negligible and cannot be contributing significantly. The fast ions responsible for the hotspot and the reason for their loss both remain unexplained.

Fast sawtooth reconnection at realistic Lundquist numbers

Magnetic reconnection, a ubiquitous phenomenon in astrophysics, space science and magnetic confinement research, frequently proceeds much faster than predicted by simple resistive MHD theory. Acceleration can result from the break-up of the thin Sweet–Parker current sheet into plasmoids, or from two-fluid effects decoupling mass and magnetic flux transport over the ion inertial length or the drift scale depending on the absence or presence of a strong magnetic guide field. We describe new results on the modelling of sawtooth reconnection in a simple tokamak geometry (circular cylindrical equilibrium) pushed to realistic Lundquist numbers for present day tokamaks. For the resistive MHD case, the onset criteria and the influence of plasmoids on the reconnection process agree well with earlier results found in the case of vanishing magnetic guide fields. While plasmoids are also observed in two-fluid calculations, they do not dominate the reconnection process for the range of plasma parameters considered in this study. In the two-fluid case they form as a transient phenomenon only. The reconnection times become weakly dependent on the S-value and for the most complete model—including two-fluid effects and equilibrium temperature and density gradients—agree well with those experimentally found on ASDEX Upgrade

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.

Formation of plasmoids during sawtooth crashes

The nonlinear growth of the internal kink mode is studied numerically using reduced magnetohydrodynamic equations in cylinder geometry. For low Lundquist numbers, S < 107, the already well-known results have been reproduced: a m/n = 1/1 magnetic island (m: poloidal, n: toroidal mode number) grows while the original core shrinks until full reconnection is achieved. For higher S values, however, the dynamics is found to be qualitatively different from the well-known Kadomtsev's model (Kadomtsev 1975 Sov. J. Plasma Phys. 1 389). The growth of the 1/1 island causes the development of a very thin current sheet which becomes tearing unstable. The current sheet is thus broken up and secondary islands (plasmoids) form. These plasmoids strongly speed up the reconnection and eventually coalesce into one secondary island. The formation of a large secondary island stops the fast reconnection process, leading even to a partial reversal of this process. The final state of sawtooth reconnection is thus no longer an axis-symmetric equilibrium as in the case of complete reconnection for low S values, but a helical equilibrium with two coexisting magnetic islands.

Particle Flow during Sawtooth Reconnection: Numerical Simulations of Experimental Observations

The core plasma density in ohmic, sawtoothing regime in Tore Supra and JET tokamaks measured by fast-sweeping reflectometry develops a central peak. This peak is surrounded by a density plateau, which extends up to the q = 1 reconnection surface. Such mexican hat like profiles differ from the smooth dome of the temperature profile. Detailed tomographic reconstructions of the density in the poloidal plane show the development of crescent and ring structures during the sawtooth cycle. 3D full MHD nonlinear simulations with the XTOR-2F code recover these structures and show that they can be explained by the MHD activity related to the sawtooth instability. They show also that the electron density evolution is dominated by the perpendicular MHD flows, while the temperature, obtained with ECE measurements is dominated by parallel diffusion.

Development of KSTAR ECE imaging system for measurement of temperature fluctuations and edge density fluctuations

The ECE imaging (ECEI) diagnostic tested on the TEXTOR tokamak revealed the sawtooth reconnection physics in unprecedented detail, including the first observation of high-field-side crash and collective heat transport [H. K. Park, N. C. Luhmann, Jr., A. J. H. Donné et al., Phys. Rev. Lett. 96, 195003 (2006)]. An improved ECEI system capable of visualizing both high- and low-field sides simultaneously with considerably better spatial coverage has been developed for the KSTAR tokamak in order to capture the full picture of core MHD dynamics. Direct 2D imaging of other MHD phenomena such as tearing modes, edge localized modes, and even Alfvén eigenmodes is expected to be feasible. Use of ECE images of the optically thin edge region to recover 2D electron density changes during L/H mode transitions is also envisioned, providing powerful information about the underlying physics. The influence of density fluctuations on optically thin ECE is discussed.

Diffusion in a stochastic magnetic field in ASDEX Upgrade

Heat diffusion coefficients in a stochastic magnetic field are determined in the case of frequently interrupted regime of neoclassical tearing modes and of incomplete sawtooth reconnection in the ASDEX Upgrade tokamak. Here the experimentally measured perturbations and profiles are used and the mapping technique is applied. With the derived diffusion coefficients the nonstationary diffusion equation is solved, making it possible to study time evolution of fast MHD phenomena in ASDEX Upgrade. The proposed phenomenological approach relies heavily on experimental information and requires very moderate computing resources.

Recent Developments in Electron Cyclotron Emission Research on Magnetically Confined Plasmas

Electron cyclotron emission (ECE) has been an important diagnostic for measuring the temporal evolution of the electron temperature profile in magnetically confined plasma devices for more than 25 years. Recent advances in ECE measurements, such as two-dimensional ECE imaging and ECE intensity correlation techniques, have provided detailed information on sawtooth reconnection, neoclassical tearing mode behavior, electron heat transport, fast electron dynamics, and fast particle-driven Alfvén eigenmodes. ECE spectral analysis is benefiting from improved ECE modeling and significant increases in computational power that allow fast, real-time, temperature measurements. Mode-converted electron Bernstein wave emission (EBE) diagnostics are being developed to study overdense (ɷpe ≫ ɷce) plasmas, a regime where conventional ECE diagnostics cannot be applied and one commonly encountered in high-β devices, such as the spherical torus and reversed-field pinch. While ECE diagnostic techniques are now well established on many existing magnetically confined plasmas, significant challenges lie ahead for applying ECE techniques to reactor-grade plasmas such as ITER, where Te(0) is expected to reach 20 to 40 keV. This paper reviews the recent advances in ECE, electron cyclotron absorption, and EBE diagnostics and discusses the challenges for ECE measurements on ITER.

Stochastic sawtooth reconnection in ASDEX Upgrade

In this paper we investigate non-complete sawtooth reconnection in the ASDEX Upgrade tokamak. Such reconnection phenomena are associated with internal m/n = 1/1 kink mode which does not vanish after the crash phase (as would be the case for complete reconnection). It is shown that this sawtooth cannot be fully described by pure m/n = 1/1 mode and that higher harmonics play an important role during the sawtooth crash phase. We employ the Hamiltonian formalism and reconstructed perturbations to model incomplete sawtooth reconnection. It is demonstrated that stochastization appears due to the excitation of low-order resonances which are present in the corresponding q-profiles inside the q = 1 surface which reflects the key role of the q0 value. Depending on this value two completely different situations are possible for one and the same mode perturbations: (i) the resonant surfaces are present in the q-profile leading to stochasticity and sawtooth crash (q0 ≈ 0.7 ± 0.1); (ii) the resonant surfaces are not present, which means no stochasticity in the system and no crash event (q0 ≈ 0.9 ± 0.05). Accordingly the central safety factor value is always less than unity in the case of a non-complete sawtooth reconnection. Our investigations show that the stochastic model agrees well with the experimental observations and can be proposed as a promising candidate for an explanation of the sawtooth reconnection.

Testing a model for triggering sawtooth oscillations in tokamaks

Simulations of JET and TFTR discharges with the BALDUR integrated modeling code are used to test a sawtooth model that consists of sawtooth triggering mechanisms [Porcelli et al., Plasma Phys. Contolled Fusion 38, 2163 (1996)] together with a modified version of the Kadomtsev sawtooth reconnection model [Kadomtsev, Sov. J. Plasma Phys. 1, 389 (1975)]. In simulations of 12 TFTR low confinement (L-mode) and 5 JET high confinement (H-mode) discharges, sawtooth triggering conditions are examined in order to determine which physical mechanisms are responsible for the crashes. It is found that most sawtooth crashes in the simulations are triggered by the m=1 resistive internal kink instability in plasmas that are in the semicollisional regime. However, in some discharges, some of the sawtooth crashes are triggered as a consequence of the driving force for the internal kink instability overcoming the fast ion stabilization. In rare instances, a sawtooth crash is triggered when the driving force for the internal kink instability overcomes the stabilization produced by the diamagnetic rotation of thermal ions. Generally, the median sawtooth period is found to increase as the magnetic reconnection fraction is increased. Optimal agreement with experimental data for the discharges considered is obtained with a magnetic reconnection fraction of approximately 37% although there is considerable scatter in the sawtooth periods observed in each discharge, both in the experimental data and in the simulations.

Theoretical study of the influence of sawtooth oscillations on fast ion transport and neutron emission in NBI experiments on JET

The effect of sawtooth crashes on fusion reactions and the concomitant neutron emission are investigated analytically and numerically. The sawtooth induced redistribution of the plasma is described by a generalization of the Kadomtsev sawtooth reconnection model. Simple expressions for the changes in local and global rates of reactions produced by fast ions are obtained, which predict quite different results for tokamaks with different relationships between the q=1 radius, the radial profile width of fast ions and the plasma radius. Special attention is paid to numerical simulations of the changes of neutron emission in JET NBI experiments. Experimental results and numerical calculations of the line integrated neutron flux to the JET neutron profile monitor, and of the change of global neutron emission, are compared in detail and found to be consistent