X-point Configuration Research Articles

Structures in magnetohydrodynamic turbulence: Detection and scaling

We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stem from numerical simulations of decaying three-dimensional magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic field; the magnetic Prandtl number is taken equal to unity, and we use a periodic box with grids of up to 1536³ points and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X -point configuration embedded in three dimensions, the so-called Orszag-Tang vortex, or an Arn'old-Beltrami-Childress configuration with a fully helical velocity and magnetic field. In each case two snapshots are analyzed, separated by one turn-over time, starting just after the peak of dissipation. We show that the algorithm is able to select a large number of structures (in excess of 8000) for each snapshot and that the statistical properties of these clusters are remarkably similar for the two snapshots as well as for the two flows under study in terms of scaling laws for the cluster characteristics, with the structures in the vorticity and in the current behaving in the same way. We also study the effect of Reynolds number on cluster statistics, and we finally analyze the properties of these clusters in terms of their velocity-magnetic-field correlation. Self-organized criticality features have been identified in the dissipative range of scales. A different scaling arises in the inertial range, which cannot be identified for the moment with a known self-organized criticality class consistent with magnetohydrodynamics. We suggest that this range can be governed by turbulence dynamics as opposed to criticality and propose an interpretation of intermittency in terms of propagation of local instabilities.

A CORONAL MASS EJECTION AND HARD X-RAY EMISSIONS ASSOCIATED WITH THE KINK INSTABILITY

We present a morphological study of the 2004 August 18 solar eruption that occurred in the active region NOAA 10656 near the west limb using extreme-ultraviolet (EUV) data from the Transition Region and Coronal Explorer (TRACE), Halpha filtergram of Big Bear Solar Observatory, white light images of Mauna Loa Solar Observatory (MLSO), hard X-ray (HXR) data of the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), and microwave data of the Owens Valley Solar Array. In this event, we have an excellent set of observations for tracing the early evolution of the coronal mass ejection (CME) from a flux rope emergence to its propagation into space as a well-connected series of events thanks to the coronameter's field of view (FOV) down to 1.1 solar radius in an overlap with that of the TRACE. This data set reveals continuously evolving EUV, Halpha, and WL features that suggest the rise of a small, low-lying loop, its writhing motion, break of the kinked loop at its crossing point, and transformation of the ejecta to the CME. The HXR and microwave sources are found in varying locations with a complicated temporal dependence, which, we interpret, is due to two successive flares in the event.more » The first flare appears to be associated with the rise of the small loop, which then triggers the second flare. During the second flare a HXR coronal source is detected at the crossing point of the kinked loop, and more intriguingly, the kinked loop apparently breaks at the crossing point of the two legs, which indicates a magnetic reconnection at the X-point configuration. After the break of the kinked UV loop, a CME structure shows up in the MLSO FOV, and propagates away from the Sun. It is concluded that this CME occurred due to the kink instability.« less

Alfvén eigenmodes in magnetic X-point configurations with strong longitudinal fields

AbstractA perturbative three-dimensional analysis is presented of Alfvén waves in a magnetic X-point configuration with a strong longitudinal guide field. The waves are assumed to propagate in the direction of the X-line, and both the plasma beta and equilibrium plasma current are taken to be zero. This provides a simple model of Alfvén wave propagation in the divertor region of tokamak plasmas. It is shown that the presence of the X-point places constraints on the structure of the leading-order (shear Alfvén) eigenfunctions. These eigenfunctions, and fast wave corrections to them, are determined explicitly for two cases. In the first of these the stream function for the shear Alfvén flow is azimuthally symmetric in the X-point plane and singular at the X-line; in the second case the stream function is largely confined to two quadrants in the X-point plane and is non-singular. For the latter scenario it is shown that coupling of the shear and fast waves is strongly localized to the vicinity of the separatrix.

Snowflake divertor plasmas on TCV

Starting from a standard single null X-point configuration, a second order null divertor (snowflake (SF)) has been successfully created on the Tokamak à Configuration Variable (TCV) tokamak. The magnetic properties of this innovative configuration have been analysed and compared with a standard X-point configuration. For the SF divertor, the connection length and the flux expansion close to the separatrix exceed those of the standard X-point by more than a factor of 2. The magnetic shear in the plasma edge is also larger for the SF configuration.

Development of steady-state scenarios compatible with ITER-like wall conditions

A key issue for steady-state tokamak operation is to determine the edge conditions that are compatible both with good core confinement and with the power handling and plasma exhaust capabilities of the plasma facing components (PFCs) and divertor systems. A quantitative response to this open question will provide a robust scientific basis for reliable extrapolation of present regimes to an ITER compatible steady-state scenario. In this context, the JET programme addressing steady-state operation is focused on the development of non-inductive, high confinement plasmas with the constraints imposed by the PFCs. A new beryllium main chamber wall and tungsten divertor together with an upgrade of the heating/fuelling capability are currently in preparation at JET. Operation at higher power with this ITER-like wall will impose new constraints on non-inductive scenarios. Recent experiments have focused on the preparation for this new phase of JET operation. In this paper, progress in the development of advanced tokamak (AT) scenarios at JET is reviewed keeping this long-term objective in mind. The approach has consisted of addressing various critical issues separately during the 2006–2007 campaigns with a view to full scenario integration when the JET upgrades are complete. Regimes with internal transport barriers (ITBs) have been developed at q95 ∼ 5 and high triangularity, δ (relevant to the ITER steady-state demonstration) by applying more than 30 MW of additional heating power reaching βN ∼ 2 at Bo ∼ 3.1 T. Operating at higher δ has allowed the edge pedestal and core densities to be increased pushing the ion temperature closer to that of the electrons. Although not yet fully integrated into a performance enhancing ITB scenario, Neon seeding has been successfully explored to increase the radiated power fraction (up to 60%), providing significant reduction of target tile power fluxes (and hence temperatures) and mitigation of edge localized mode (ELM) activity. At reduced toroidal magnetic field strength, high βN regimes have been achieved and q-profile optimization investigated for use in steady-state scenarios. Values of βN above the ‘no-wall magnetohydrodynamic limit’ (βN ∼ 3.0) have been sustained for a resistive current diffusion time in high-δ configurations (at 1.2 MA/1.8 T). In this scenario, ELM activity has been mitigated by applying magnetic perturbations using error field correction coils to provide ergodization of the magnetic field at the plasma edge. In a highly shaped, quasi-double null X-point configuration, ITBs have been generated on the ion heat transport channel and combined with ‘grassy’ ELMs with ∼30 MW of applied heating power (at 1.2 MA/2.7 T, q95 ∼ 7). Advanced algorithms and system identification procedures have been developed with a view to developing simultaneously temperature and q-profile control in real-time. These techniques have so far been applied to the control of the q-profile evolution in JET AT scenarios.

Particle acceleration at a three-dimensional reconnection site in the solar corona

We study test panicle trajectories in the vicinity of a three-dimensional (3D) magnetic null point during spine reconnection. Particles are injected into the steady-state non-uniform magnetic and electric fields derived by Priest & Titov (1996), and the equations of motion numerically integrated. We use input parameters typical of the solar corona, for which reconnection has been suggested as the fundamental mechanism responsible for particle acceleration in flare events. We show that substantial acceleration is possible in the 3D spine reconnection configuration, in the strong electric field regime. The energy gain is strongly dependent on the location of injection into the simulation box, as was the case in 2D X-point configurations. In our 3D geometry, we first vary the location of injection within a plane through the spine, and derive an analytical value for the injection angle for which maximum energy gain is achieved. Secondly we vary the azimuthal location of particle injection and show that as one moves away from the plane with maximum electric field magnitude, higher final energies can be achieved, though this requires substantially longer times.

Electron Inertial Effects on Rapid Energy Redistribution at Magnetic X‐Points

The evolution of nonpotential perturbations to a current-free magnetic X-point configuration is studied, taking into account electron inertial effects as well as resistivity. Electron inertia is shown to have a negligible effect on the evolution of the system whenever the collisionless skin depth is less than the resistive scale length. Nonpotential magnetic field energy in this resistive MHD limit initially reaches equipartition with flow energy, in accordance with ideal MHD, and is then dissipated extremely rapidly on an Alfvenic timescale that is essentially independent of Lundquist number. In agreement with resistive MHD results obtained by previous authors, the magnetic field energy and kinetic energy are then observed to decay on a longer timescale and exhibit oscillatory behavior, reflecting the existence of discrete normal modes with finite real frequency. When the collisionless skin depth exceeds the resistive scale length, the system again evolves initially according to ideal MHD. At the end of this ideal phase, the field energy decays typically on an Alfvenic timescale, while the kinetic energy (which is equally partitioned between ions and electrons in this case) is dissipated on the electron collision timescale. The oscillatory decay in the energy observed in the resistive case is absent, but short-wavelength structures appear in the field and velocity profiles, suggesting the possibility of particle acceleration in oppositely directed current channels. The model provides a possible framework for interpreting observations of energy release and particle acceleration on timescales down to less than a second in the impulsive phase of solar flares.

Disruption heat loads on the JET MkIIGB divertor

Combined analysis of divertor thermocouple and IR camera measurements during JET disruptions can provide valuable information on the distribution of the energy loads, even if the stored energy of the JET plasmas is small compared to that foreseen for the next-generation tokamaks. Typically the energy collected at the divertor represents a small fraction of the pre-disruption plasma energy; this is consistent with the high level of radiation observed and with part of the magnetic energy being transferred to the plasma-coupled conductors. The data for this paper are taken from the whole set of disruptive plasmas of JET operation in the years 2000 and 2001. In most of the MkIIGB disruptions, the plasma displaces upwards (away from the divertor); therefore, only a small number of downward events are available for analysis. However, divertor heat loads seem to be more strongly correlated to the delay of the loss of the X-point with respect to the thermal quench than the direction of the plasma displacement.When the plasma thermal energy is lost with the plasma still in X-point configuration, the septum and the tiles wetted by the strike-points, often more than one tile per strike-point, experience a sharp increase in temperature, equivalent to up to 1 MJ m-2. When the thermal quench occurs at the same time as, or after, the loss of plasma vertical control, no significant divertor tile temperature \ obreak increase can be observed for both upwards and downwards events. Most of the disruptions purposely made to produce runaway electrons went towards the divertor and, although not systematically, lead to local (mostly at the septum) temperature increase equivalent to a load up to 2 MJ m-2, often toroidally asymmetric.

Turbulent transport studies in JET edge plasmas in X-point configurations

Reciprocating Langmuir probe measurements were obtained in dedicated JET experiments to investigate turbulent transport at the edge and SOL plasmas. The measured turbulent radial particle flux, radial velocity and diffusion coefficient were compared with results from the 2-D plasma edge code B2-EIRENE. Qualitatively, the experimental results and the modelling calculations show a similar behaviour, with the radial particle flux increasing from inside the separatrix to some point in the SOL and then decreasing again. However, there is a quantitative disagreement between code calculations and measurements in X-point plasmas. Two explanations have been proposed to reconcile these observations: first temperature fluctuations, with the appropriate phase could modify the derived particle turbulent flux. Second, code simulations including the effect of drifts at the plasma edge show that large convective cells appear in this region, leading to large parallel flows in the SOL, which have been measured. Such drifts could lead to a net inwards particle pinch which could compensate for the measured large turbulent out flux.

Helium exhaust in divertor–closure configuration with W-shaped divertor of JT-60U

The W-shaped divertor of JT-60U was modified from inner-leg pumping to both-leg pumping. After the modification, the pumping rate was remarkably improved with both-leg pumping in a divertor-closure configuration, which means both separatrixes close to the divertor slots. In steady state, efficient helium exhaust was realized in a divertor-closure configuration with both-leg pumping in ELMy H-mode plasmas. A global particle confinement time of τ He = 0.4 s and τ He /τ I = 3 was achieved in attached plasmas, well within the range generally considered necessary for successful operation of a future fusion reactor, such as ITER-FEAT. The helium exhaust efficiency in the divertor-closure configuration was extended by 45% as compared to the one with inner-leg pumping. In the high X-point configuration with both-leg pumping, the helium exhaust efficiency and the pumping rate of deuterium deteriorated because of the backflow through the outer slot.

Analytical solutions to the Grad–Shafranov equation for tokamak equilibrium with dissimilar source functions

Exact solutions to the Grad–Shafranov equation for ideal magnetohydrodynamic (MHD) tokamak equilibria with dissimilar functional dependences of the pressure and poloidal current source profiles are presented. The current density profile has three free parameters, which is sufficiently flexible to describe equilibria consistent with external magnetic measurements. Experimental x-point and limiter plasma configurations can be represented by a superposition of solutions with the same eigenvalue. Both normal and reversed shear current profiles are allowed. An efficient algorithm for least squares fitting of numerically obtained experimental equilibria to the exact solution functions is described and applied to the ASDEX Upgrade (axially symmetric divertor experiment) tokamak [Plasma Physics and Controlled Nuclear Fusion Research 1992 (International Atomic Energy Agency, Vienna, 1993), Vol. I, p. 127].

Dynamics of MHD perturbations in the presence of singular lines

Typical effects relevant to space and laboratory plasmas, induced by the presence of singular lines in a magnetic configuration, are presented. They refer to modifications of flute perturbations in the scrape–off layer of a divertor, the onset of stochasticity around the magnetic separatrix, and the trapping of fast MHD waves in the vicinity of singular lines. In particular, a WKB analysis performed for X-point and current sheet configurations points out the occurence of global modes characterized by regular and irregular trajectories.

Heating and acceleration at X-point reconnection

We have performed numerical simulations of the non-relativistic particle motion in the external static magnetic and electric fields of an X-point configuration. The properties of both the perpendicular and the parallel invariants have been examined and the size of the region where the adiabatic properties of the particle motion are violated is estimated. The change of the longitudinal invariant due to the crossing of the separatrices has also been evaluated. In the non-adiabatic region, particle trajectories have been found which exhibit chaotic behaviour: we have used symplectic integration and observed a positive value of the maximum Lyapunov exponent and a fractional value of the correlation dimension (≃ 2.5). The population dynamics of a thousand particles has also been investigated. The study of the velocity distributions indicate that particle acceleration is mainly perpendicular to the magnetic field, leading to the development of a large anisotropy in the distribution function.

Resistive modes at a magnetic X-point

The characteristic time of (incompressible) resistive modes in the neighbourhood of an X-point in the absence of external forcing is found to scale, when normalized on the Alfven time, as ( epsilon mod ln epsilon mod )-1 with epsilon the ratio between the Alfven and the resistive time. In X-point configurations with oblique separatrices, the mode time-scale becomes faster as the angle between the separatrices decreases. When this angle becomes of the order of mod ln epsilon mod -1, the ( epsilon mod ln epsilon mod )-1 scaling breaks down. Similar to the case of a resonant magnetic line configuration, resistive modes can be driven unstable by the inhomogeneity of the current density.

On current sheets in two-dimensional ideal magnetohydrodynamics caused by pressure perturbations

In this paper it is shown that in ideal magnetohydrodynamics (IMHD) a two-dimensional equilibrium with an X-shaped neutral point (X-point) configuration reacts to small and smooth perturbations of the plasma pressure by the development of sheets with singular current density while the X-point structure is replaced by a different kind of configuration containing either cusp-like or T-shaped singularities. This behavior is demonstrated by computing the time dependent response to a suitable initial perturbation using a relaxation method within ideal MHD. The two-dimensional configurations considered in this paper are motivated by models of space plasma systems like, e.g. the Earth’s magnetotail containing a distant X-point where perturbations caused by the solar wind may force the formation of current sheets and the subsequent occurrence of magnetic reconnection.

Characteristics of ohmic H-modes in COMPASS-D

The COMPASS-D tokamak has recently obtained H-mode plasmas in a single-null X-point configuration with no additional heating. Clear H-mode signatures have been observed including reduction in Dalpha light and the unmistakable appearance of ELMs and ELM-free periods. Recycling and gas puff can play crucial roles in achieving and terminating the H-modes. The emergence of distinct ELMs, from the apparently-random fluctuations, of the background Dalpha light, is usually one of progression, taking some 10s of ms rather than a sudden discontinuity. The relatively slow evolution allows for detail examination of important phenomena, such as improvements to confinement and fluid rotation. The H-mode quality improves with density, unless impurity accumulation becomes important. Improvements to the energy and particle confinement are observed and are accompanied by positive increases in the radial electric field at approximately=4 cm inside the last closed flux surface (LCFS). The ohmic powers in discharges with clearly defined H-modes have not been less, so far, than the power obtained from power threshold scalings from larger machines.

Magnetic Reconnection at Stressed X-Type Neutral Points

The reconnection and relaxation of two-dimensional stressed (non-potential) x-type neutral point magnetic fields are studied via solution of the nonlinear resistive 2-D MHD equations and by analytical solution of the linear eigenvalue problem. The linear dispersion relation was generalized for azimuthally nonsymmetric perturbations, and have found that for modes with azimuthal mode numbers m > 0, the relaxation can occur at a rate faster than that for n = m = 0, where n is the radial quantum'' number. One finds that for nearly azimuthally symmetric magnetic perturbations that are zero at the boundary; i.e. the frozen-in'' (sometimes called fine-tied'') boundary conditions, the fields relax incompressibly and nonlinearly to the unstressed x-type neutral point at a rate close to that predicted by linear theory. Also, fully compressible nonlinear MHD simulations have been performed, which show that the interaction between the plasma flow velocity and the magnetic field is the important physical effect, while the inclusion of thermodynamics does not affect the evolution considerably. A Lyapunov functional for the nonlinear incompressible 2-D resistive MHD equations is derived to show that the current-free x-point configuration is a global equilibrium to which general initial conditions relax.

Local expansion method for fast plasma boundary identification in JET

A local expansion technique for the reconstruction of the plasma boundary is presented. The method is particularly accurate in identifying the separatrix in X-point configurations. It is applied to JET discharges and the results are compared with those of a full equilibrium code and with other independent diagnostics. It is found that the majority of the H-mode discharges at JET have been achieved in marginal limiter configurations. The method is sufficiently reliable and fast for real time shape control

Latest results from JET

Plasma-wall interactions have been important in many aspects of JET's programme during the past year. A major achievement has been the first production of significant fusion power from the deuterium-tritium reaction. Techniques of tritium handling and recovery have been developed and tested. The tokamak has operated extensively in the X-point configuration and comparisons have been made between carbon and beryllium target materials. Experiments have been made to ameliorate the heat load on the divertor targets by strong gas puffing as well as by careful tile design and alignment. ELMs have been utilized to produce a quasi steady-state H-mode with duration of about 20 s.

B2-EIRENE simulation of ASDEX and ASDEX-Upgrade scrape-off layer plasmas

The 2D multifluid edge code B2 coupled with the 3D neutral gas Monte Carlo code EIRENE is being used for edge interpretation and model validation on the axisymmetric poloidal divertor experiments ASDEX and ASDEX-Upgrade. For this purpose B2 was significantly improved especially by a fully implicit treatment of the topological cuts appearing in X-point configurations, and a reasonably accurate handling of inclined target plates. A fast, automatic grid generator has been developed, which allows direct implementation of experimental MHD equilibria into B2-EIRENE. Typical ASDEX and ASDEX-Upgrade simulations are presented and discussed.