S.Yu. Medvedev

Edge kink/ballooning mode stability in tokamaks with separatrix

Stability limits against external kink modes driven by large current density and pressure gradient values in the pedestal region are investigated for tokamak plasmas with separatrix. Stability diagrams for modes with different toroidal wave numbers under variations of pressure gradient and current density in the pedestal region are presented for several equilibrium configurations related to TCV. A scaling for the toroidal wave number of the most unstable mode is proposed. The influence of the plasma cross-section geometry on the stability limits is discussed.

Requirements for pellet injection in ITER scenarios with enhanced particle confinement

The requirements for pellet injection parameters for plasma fuelling are assessed for ITER scenarios with enhanced particle confinement. The assessment is based on the integrated transport simulations including models of pedestal transport, reduction of helium transport and boundary conditions compatible with SOL/divertor simulations. The requirements for pellet injection for the inductive H-mode scenario (HH98y,2 = 1) are reconsidered taking account of a possible reduction of the particle loss obtained in some experiments at low collisionalities. The assessment of fuelling requirements is carried out for the hybrid and steady state (SS) scenarios with enhanced confinement with HH98y,2 > 1. A robustness of plasma performance to the variation of particle transport is demonstrated. A new type of SS scenario is considered with neutral beam current drive and electron cyclotron current drive instead of lower hybrid current drive (LHCD) to extend the range of stable operation and to avoid the reduction of the edge LHCD efficiency caused by pellet injection.

Modeling of the Feedback Stabilization of the Resistive Wall Modes in a Tokamak

The problem of feedback stabilization of the resistive wall modes (RWMs) in a tokamak is discussed. An equilibrium configuration with the parameters accepted for the stationary ITER scenario 4A is considered as the main scenario. The effect of the vacuum chambers shape on the plasma stability is studied. Ideal MHD stability is analyzed numerically by using the KINX code. It is shown that, in a tokamak with the parameters of the designed T-15M tokamak, RWMs can be stabilized by a conventional stabilizing system made of framelike coils. However, the maximum possible gain in β in such a tokamak is found to be smaller than that in ITER. It is shown that, in this case, a reduction in the plasma—wall gap width by 10 cm allows one to substantially increase the β limit, provided that RWMs are stabilized by active feedback.

Accessibility and properties of ELMy H-mode and ITB plasmas in TCV

This paper presents experimental results on the accessibility and the properties of plasmas with improved confinement in TCV. First, the H-mode threshold power is measured in Ohmic plasmas. Above an Ohmic threshold density, the threshold power increases with the density. A lower threshold density is found when additional electron cyclotron heating (ECH) is applied. At these low densities, the threshold power increases dramatically with decreasing density. Only a small fraction of the wide operational domain leading to the Ohmic H-mode is found to lead to a stationary regime with edge localized modes (ELMs). The ELMs have an irregular frequency, but in TCV they can be triggered by an external magnetic perturbation that induces a rapid vertical movement of the plasma. With this perturbation, the ELM frequency can be increased. The ELM triggering mechanism is provided by the vertical movement of the plasma away from the X-point of a single null configuration. This movement induces a positive current at the plasma edge, and we deduce that the ELMs are being controlled by this modification of the plasma edge current.Electron internal transport barriers (eITBs) are produced deep in the plasma during the stationary phase of TCV discharges. Different scenarios of ECH or electron cyclotron current drive (ECCD) at different radial locations have been used to obtain eITBs with and without inductively driven current. The eITBs are characterized by steep electron temperature gradients, high confinement improvement and a large fraction of bootstrap current. In plasmas with fully non-inductively driven current the size and the strength of the eITB are controlled by the location of the power deposition and by the co- or counter-direction of the central ECCD. Finally, a small inductive perturbation of an otherwise non-inductively driven plasma current profile progressively shrinks the eITB, confirming the link between current profiles and eITBs.

Methods for numerical simulation of ideal MHD stability of axisymmetric plasmas

Abstract The development of variational methods to compute ideal MHD stability of axisymmetric plasmas is reviewed. Attention is focussed on degeneracy in the MHD ideal stability problem. Difference schemes for spectral elliptic degenerate problems are investigated. New simple and effective numerical methods for MHD stability calculations are proposed.

Dynamical coupling between magnetic equilibrium and transport in tokamak scenario modelling, with application to current ramps

The modelling of tokamak scenarios requires the simultaneous solution of both the time evolution of the plasma kinetic profiles and of the magnetic equilibrium. Their dynamical coupling involves additional complications, which are not present when the two physical problems are solved separately. Difficulties arise in maintaining consistency in the time evolution among quantities which appear in both the transport and the Grad–Shafranov equations, specifically the poloidal and toroidal magnetic fluxes as a function of each other and of the geometry. The required consistency can be obtained by means of iteration cycles, which are performed outside the equilibrium code and which can have different convergence properties depending on the chosen numerical scheme. When these external iterations are performed, the stability of the coupled system becomes a concern. In contrast, if these iterations are not performed, the coupled system is numerically stable, but can become physically inconsistent. By employing a novel scheme (Fable E et al 2012 Nucl. Fusion submitted), which ensures stability and physical consistency among the same quantities that appear in both the transport and magnetic equilibrium equations, a newly developed version of the ASTRA transport code (Pereverzev G V et al 1991 IPP Report 5/42), which is coupled to the SPIDER equilibrium code (Ivanov A A et al 2005 32nd EPS Conf. on Plasma Physics (Tarragona, 27 June–1 July) vol 29C (ECA) P-5.063), in both prescribed- and free-boundary modes is presented here for the first time. The ASTRA–SPIDER coupled system is then applied to the specific study of the modelling of controlled current ramp-up in ASDEX Upgrade discharges.

The negative triangularity tokamak: stability limits and prospects as a fusion energy system

The paper discusses edge stability, beta limits and power handling issues for negative triangularity tokamaks. The edge magnetohydrodynamic stability is the most crucial item for power handling. For the case of negative triangularity the edge stability picture is quite different from that for conventional positive triangularity tokamaks: the second stability access is closed for localized Mercier/ballooning modes due to the absence of a magnetic well, and nearly internal kink modes set the pedestal height limit to be weakly sensitive to diamagnetic stabilization just above the margin of the localized mode Mercier criterion violation. While a negative triangularity tokamak is thought to have a low beta limit with its magnetic hill property, it is found that plasmas with reactor-relevant values of normalized beta beta(N) > 3 can be stable to global kink modes without wall stabilization with appropriate core pressure profile optimization against localized mode stability, and also with increased magnetic shear in the outer half-radius. The beta limit is set by the n = 1 mode for the resulting flat pressure profile. The wall stabilization is very inefficient due to strong coupling between external and internal modes. The n > 1 modes are increasingly internal when approaching the localized mode limit, and set a lower beta in the case of the peaked pressure profile leading to a Mercier unstable core. With the theoretical predictions supported by experiments, a negative triangularity tokamak would become a prospective fusion energy system with other advantages including a larger separatrix wetted area, more flexible divertor configuration design, wider trapped particle-free scrape-off layer, lower background magnetic field for internal poloidal field coils, and larger pumping conductance from the divertor room.

Comparing magnetic triggering of ELMs in TCV and ASDEX Upgrade

Frequency locking of edge localized modes (ELMs) to the vertical plasma movements induced by magnetic perturbations first demonstrated in TCV was successfully repeated in ASDEX Upgrade. However, the ELMs were triggered in ASDEX Upgrade when the plasma was moving down towards the X-point with a consequent decrease in the plasma current density in the edge region, in contrast to the previous observation on TCV in which ELMs were triggered when the edge current was increased by an upward plasma movement. This opposite behaviour observed in the magnetic triggering of ELMs has been investigated by using a free-boundary tokamak simulator, DINA-CH. The passive stabilization loops (PSLs) located inside the vacuum vessel of ASDEX Upgrade produce similar external linking flux changes to those generated by the G-coil sets in TCV for opposite vertical plasma movements. Therefore, both plasmas experience similar local flux surface expansions near the upper G-coil set and PSL when the ELMs are triggered. In ASDEX Upgrade, however, the localized expansion of the plasma flux surfaces near the upper PSL is observed with the global shrinkage of the plasma column accompanied by the downward plasma movement.

Low frequency heating and flow driven by the dynamic ergodic divertor in tokamaks

The profile and dissipation of the field excited by dynamic ergodic divertor (DED) coils in tokamak plasmas are calculated, and an estimate is made of the poloidal/toroidal velocities driven by this field. The coils are idealized as an inboard sheet current composed of a toroidal sequence of helical line current segments expanded in Fourier series with poloidal/toroidal mode numbers M/N, and mode amplitudes depending on feeding. Numerical calculations with cylindrical and toroidal codes show maxima of field dissipation due to Alfv´ en wave mode conversion effect taking place at the rational magnetic surfaces where q = M/N. The effects of toroidicity and ion collisions in the dielectric tensor in the upper DED frequency range described (f = 5–10 kHz) are found to be very important in absorption calculations. At the q = 3 resonant magnetic surface typical for DED coil design, it is estimated that ponderomotive forces produced by 20 kW of dissipation can drive local toroidal and poloidal flows of respective orders 8 km s −1 and 10 km s −1 in the TEXTOR tokamak.

Integrated modelling of DEMO-FNS current ramp-up scenario and steady-state regime

An approach to the integrated modelling of plasma regimes in the projected neutron source DEMO-FNS based on different codes is developed. The consistency check of the steady-state regime is carried out, namely, the possibility of the plasma current ramp-up, acceptance of growth rates of MHD modes in the steady-state regime, heat loads to the wall and divertor plates and neutron yield value. The following codes are employed for the integrated modelling. ASTRA transport code for calculation of plasma parameters in the steady-state regime, NUBEAM Monte Carlo code for NBI incorporated into the ASTRA code, DINA free boundary equilibrium and evolution code, SPIDER free boundary equilibrium and equilibrium reconstruction code, KINX ideal MHD stability code, TOKSTAB rigid shift vertical stability code, edge and divertor plasma B2SOLPS5.2 code and Semi-analytic Hybrid Model (SHM) code for self-consistent description of the core, edge and divertor plasmas based on the experimental scaling laws. The consistent steady-state regime for the DEMO-FNS plasma and the plasma current ramp-up scenario are developed using the integrated modelling approach. Passive copper coils are suggested to reduce the plasma vertical instability growth rate to below ∼30 s −1 .The outer divertor operation in the ‘high-recycling’ regime is numerically demonstrated with a maximal heat flux density of 7–9 MW m −2 that is technically acceptable.