Reconstruction of Tokamak Equilibria with Pedestal Profiles Using the SPIDER Code

Equilibrium reconstruction codes are the tools of crucial impotence for the interpretation of experimental data in modern tokamaks. In case of non-monotonic reversed shear or "skin" profiles at the edge, the standard reconstruction methods To avoid the restrictions of the previous generation of codes and to improve accuracy and efficiency of equilibrium reconstruction, a new adaptive grid plasma equilibrium reconstruction solver in the frame of the SPIDER [3] code has been developed. The automatic mapping of the magnetic surfaces provided by the adaptive grid code allows for a very accurate resolution of the pedestal region while using the adaptive flux grid in the plasma for efficient free-boundary equilibrium calculations. The changes in the mapping of magnetic surfaces due to the presence of pedestals are estimated for fixed and free boundary equilibrium reconstructions of ELMy TCV shots. Using the measured temperature and density profiles, the current density profile is reconstructed and the influence of the bootstrap current in the pedestal is investigated. The application of the new method to configurations with large fraction of noninductive current, e.g. the TCV shots with high bootstrap current fraction, is discussed. Equilibrium reconstruction taking into account non-inductive current density The adaptive grid plasma equilibrium reconstruction solver is a module of the SPIDER code and was presented in In the reconstruction method, both plasma boundary and current density profile are calculated with the use of basis functions for the profile representation and a regularization technique is applied during the fitting process. The toroidal plasma current density is represented as: where a k , b k are fitting coefficients (k = 0 ÷ m), ψ is the normalized poloidal flux with ψ = 0 on magnetic axis and ψ = 1 at the edge, R is the major radius. A Singular Value Decomposition (SVD) technique is used to obtain the fitting coefficients taking into account the specified measurement uncertainties. The error of the "fitting" is determined by the relation: α , the index α denotes flux loops, magnetic probes and PF coil currents, S calc is the calculated value, S exp is measured value, ε is the relative error of measurement/simulation. In the presence of non inductive current sources and with a prescribed pressure gradient the following current density representation is used

Reconstruction of Tokamak Equilibria with Pedestal Profiles Using the SPIDER Code

Equilibrium reconstruction codes are the tools of crucial impotence for the interpretation of experimental data in modern tokamaks. In case of non-monotonic reversed shear or "skin" profiles at the edge, the standard reconstruction methods To avoid the restrictions of the previous generation of codes and to improve accuracy and efficiency of equilibrium reconstruction, a new adaptive grid plasma equilibrium reconstruction solver in the frame of the SPIDER [3] code has been developed. The automatic mapping of the magnetic surfaces provided by the adaptive grid code allows for a very accurate resolution of the pedestal region while using the adaptive flux grid in the plasma for efficient free-boundary equilibrium calculations. The changes in the mapping of magnetic surfaces due to the presence of pedestals are estimated for fixed and free boundary equilibrium reconstructions of ELMy TCV shots. Using the measured temperature and density profiles, the current density profile is reconstructed and the influence of the bootstrap current in the pedestal is investigated. The application of the new method to configurations with large fraction of noninductive current, e.g. the TCV shots with high bootstrap current fraction, is discussed. Equilibrium reconstruction taking into account non-inductive current density The adaptive grid plasma equilibrium reconstruction solver is a module of the SPIDER code and was presented in In the reconstruction method, both plasma boundary and current density profile are calculated with the use of basis functions for the profile representation and a regularization technique is applied during the fitting process. The toroidal plasma current density is represented as: where a k , b k are fitting coefficients (k = 0 ÷ m), ψ is the normalized poloidal flux with ψ = 0 on magnetic axis and ψ = 1 at the edge, R is the major radius. A Singular Value Decomposition (SVD) technique is used to obtain the fitting coefficients taking into account the specified measurement uncertainties. The error of the "fitting" is determined by the relation: α , the index α denotes flux loops, magnetic probes and PF coil currents, S calc is the calculated value, S exp is measured value, ε is the relative error of measurement/simulation. In the presence of non inductive current sources and with a prescribed pressure gradient the following current density representation is used

Optimization of the snowflake diverted equilibria in the TCV tokamak

In support of the TCV experimental campaign aiming at studying H-mode plasmas with snowflake (SF) divertor, free boundary equilibrium and stability studies were performed with the SPIDER and KINX codes. Due to the high flexibility of plasma shaping capabilities of TCV, SF divertor conditions can be reached for various plasma geometries. However, at high plasma current some configurations require poloidal field (PF) coil currents close to the machine limit. This is particularly important when the equilibrium sensitivity to the edge pedestal profiles, which is higher than for standard X-point configurations, is taken into account. That is why the configuration optimization should also include the profile sensitivity study when planning the shot scenario

Edge Stability and Pedestal Profile Sensitivity of Snowflake Diverted Equilibria in the TCV Tokamak

A second order null divertor (snowflake) has been successfully created and controlled in the TCV Tokamak. The results of ideal MHD edge stability computations show an enhancement of the edge stability properties of the snowflake equilibria compared to standard X-point configurations...

Comparison of the calculations of the stability properties of a specific stellarator equilibrium with different MHD stability codes

A particular configuration of the LHD stellarator with an unusually flat pressure profile has been chosen to be a test case for comparison of the MHD stability property predictions of different three-dimensional and averaged codes for the purpose of code comparison and validation. In particular, two relatively localized instabilities, the fastest growing modes with toroidal mode number n = 2 and n = 3 were studied using several different codes, with the good agreement that has been found providing justification for the use of any of them for equilibria of the type considered

Experimental investigation and validation of neutral beam current drive for ITER through ITPA Joint Experiments

Joint experiments investigating the off-axis neutral beam current drive (NBCD) capability to be utilized for advanced operation scenario development in ITER were conducted in four tokamaks (ASDEX Upgrade (AUG), DIII-D, JT-60U and MAST) through the international tokamak physics activity (ITPA). The following results were obtained in the joint experiments, where the toroidal field, B t, covered 0.4-3.7 T, the plasma current, Ip, 0.5-1.2 MA, and the beam energy, Eb, 65-350 keV. A current profile broadened by off-axis NBCD was observed in MAST. In DIII-D and JT-60U, the NB driven current profile has been evaluated using motional Stark effect diagnostics and good agreement between the measured and calculated NB driven current profile was observed. In AUG (at low δ ∼ 0.2) and DIII-D, introduction of a fast-ion diffusion coefficient of Db ∼ 0.3-0.5 m2 s-1 in the calculation gave better agreement at high heating power (5 MW and 7.2 MW, respectively), suggesting anomalous transport of fast ions by turbulence. It was found through these ITPA joint experiments that NBCD related physics quantities reasonably agree with calculations (with Db = 0-0.5 m2 s-1) in all devices when there is no magnetohydrodynamic (MHD) activity except ELMs. Proximity of measured off-axis beam driven current to the corresponding calculation with Db = 0 has been discussed for ITER in terms of a theoretically predicted scaling of fast-ion diffusion that depends on Eb/Te for electrostatic turbulence or βt for electromagnetic turbulence. © 2011 IAEA, Vienna

MHD Stability and Energy Principle for Two-Dimensional Equilibria without Assumption of Nested Magnetic Surfaces

Abandoning the assumption of nested magnetic surfaces in tokamak plasma expands the field of research and opens up new approaches for both theoretical and experimental plasma physics. The computer code KINX for calculations of the ideal MHD stability was developed for studies of doublet plasmas with two magnetic axes and using block-structured grids in each subdomain with nested magnetic surfaces. Then, the MHD_NX code on unstructured grids was developed to calculate the stability of two-dimensional equilibria with an arbitrary topology of magnetic surfaces. The study of equilibrium and stability of equilibrium configurations with toroidal current density reversal and axisymmetric n = 0 islands, which are associated with internal transport barrier and low current density at the magnetic axis, as well as with the operation of tokamaks in the alternating current regime, leads to more general issues of MHD stability of two-dimensional solutions of the Grad-Shafranov equations with islands under other types of symmetrychain of islands in helical symmetry and cylindrically symmetric m = 0 islands in configurations with the longitudinal field reversal. New ideal MHD unstable modes have been discovered for various types of two-dimensional island configurations. The energy principle with MHD-compatible boundary conditions at open magnetic field lines is necessary for the self-consistent stability analysis of divertor configurations in tokamaks with a finite current density at the separatrix, taking into account the plasma outside the separatrix. Several codes have been developed for calculations of plasma equilibrium and stability, taking into account the influence of currents outside the separatrix, which are ready for integration with other codes for edge plasma modeling