[en] In this paper the calculated ECRH power deposition profiles p_ECRH(ρ) are compared with the experimentally derived ones in ASDEX Upgrade. ECRH power deposition is calculated by the beamtracing code and with its help the p_ECRH(ρ) behaviour at different ECRH scenarios is investigated. Experimentally, power deposition can be obtained from electron temperature differences dT_e after switching on/off ECRH or from the perturbed electron temperature T-tilde _e when modulated ECRH is applied. The complete experimental recovery of the p_ECRH(ρ) requires the determination of its maximum, centre ρ₀ and width w₀. The centre of the deposition ρ₀ is determined experimentally from the temperature response, from dT_e after switching on/off ECRH or alternatively from T-tilde _e in modulated ECRH experiments. The measured width is broadened quickly by perpendicular heat transport, which makes the experimental determination of w₀ very difficult. A scheme in which off-axis cw ECRH is applied in order to reduce the transport in the core plasma, where the modulated ECRH is deposited, is used in the determination of w₀. We estimate the ECRH deposition width w₀ in an indirect way, in which T-tilde _e(ρ) profiles determined experimentally from FFT are compared to those calculated with the transport code ASTRA. Finally, the total absorbed ECRH power is obtained experimentally by using a self-consistent power balance scheme

[en] The beam tracing approximate description of the propagation and absorption of wave beams is studied and compared to the corresponding exact solution of the wave equation for two simplified models relevant to electron cyclotron resonance heating and reflectometry diagnostics.

[en] 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. (paper)

[en] The numerical codes ASTRA and B2SOLPS5.2 are coupled to perform an integrated modeling of particle and energy transport and to obtain continuous self-consistent profiles of the main plasma parameters from the magnetic axis up to target plates. The unique distinguishing feature of the new coupling scheme is the presence of a region of overlap of the 1D and 2D computational domains, where the 1D solution coincides with the 2D one at the equatorial midplane. In the 2D transport equation system, all relevant drift flows and currents are taken into account, which allows us to calculate the poloidal variation of the density, temperatures and electrostatic potential, and obtain neoclassical radial fluxes in a self-consistent manner. Such an approach allows us to model tokamaks for which neoclassical effects give a significant contribution to the ion heat transport, and in particular, spherical tokamaks. (paper)

[en] A crucial point of the theoretical study of lower-hybrid (LH) current drive in a tokamak plasma is the spectral gap problem, i.e., the fact that the parallel (to the magnetic field) refractive index spectrum generated at the plasma edge does not appear to be wide enough for the interaction of the wave with a large number of electrons. This is in contrast with experimental observations. Diffraction is one of the mechanisms that can lead to the observed wave spectrum broadening and solve the spectral gap problem. For this reason, a new beam tracing code, LHBEAM, has been developed in order to study the diffraction effects on the propagation and the absorption of LH waves in tokamak plasma. In this work, the parallel spectral width is addressed on the basis of the beam tracing approximate solution. A preliminary implementation of the results is done in LHBEAM which has been also compared with the ray tracing code C3PO for the assessment of the trajectory of the central ray and of the evolution of the parallel refractive index on this ray.

[en] Tokamak scenario development requires an understanding of the properties that determine the kinetic profiles in non-steady plasma phases and of the self-consistent evolution of the magnetic equilibrium. Current ramps are of particular interest since many transport-relevant parameters explore a large range of values and their impact on transport mechanisms has to be assessed. To this purpose, a novel full-discharge modelling tool has been developed, which couples the transport code ASTRA (Pereverzev et al 1991 IPP Report 5/42) and the free boundary equilibrium code SPIDER (Ivanov et al 2005 32nd EPS Conf. on Plasma Physics vol 29C (ECA) P-5.063 and http://epsppd.epfl.ch/Tarragona/pdf/P5_063.pdf), utilizing a specifically designed coupling scheme. The current ramp-up phase can be accurately and reliably simulated using this scheme, where a plasma shape, position and current controller is applied, which mimics the one of ASDEX Upgrade. Transport of energy is provided by theory-based models (e.g. TGLF (Staebler et al 2007 Phys. Plasmas 14 055909)). A recipe based on edge-relevant parameters (Scott 2000 Phys. Plasmas 7 1845) is proposed to resolve the low current phase of the current ramps, where the impact of the safety factor on micro-instabilities could make quasi-linear approaches questionable in the plasma outer region. Current ramp scenarios, selected from ASDEX Upgrade discharges, are then simulated to validate both the coupling with the free-boundary evolution and the prediction of profiles. Analysis of the underlying transport mechanisms is presented, to clarify the possible physics origin of the observed L-mode empirical energy confinement scaling. The role of toroidal micro-instabilities (ITG, TEM) and of non-linear effects is discussed. (paper)

[en] In this paper transient phenomena related to the electron heat transport when electron cyclotron resonance heating (ECRH) power is switched on or off are investigated by predictive and interpretative transport analysis. In the latter two numerical approaches-one based on the transport code ASTRA and the other by COBRA code-are compared. The transport simulations were done in the ASTRA code based on a critical ∇T_e/T_e model. The results for the evolution of the electron temperature in steady state and transient phases are compared with the experiment. The changes of the heat diffusivity with the ECRH power are compared with the results of the transport calculations from the interpretative analysis. The critical ∇T_e/T_e model reproduces well both the heat diffusivity and the electron temperature evolution in the region outside the ECRH deposition, and the results show good agreement with the experimental data there. The model cannot recover the electron temperature changes inside the ECRH deposition region with accuracy due to the simple assumption made in transport below the threshold

[en] Characteristics of toroidal plasma rotation have been experimentally investigated using charge exchange recombination spectroscopy in the ASDEX Upgrade tokamak. Ion cyclotron resonance frequency (ICRF) heating is found to cause a reduction of the toroidal rotation velocity, V_φ, driven by neutral beam injection (NBI) in the co- and counter-current directions. The reduction of plasma rotation is attributed to an increasing momentum diffusivity connected with the confinement degradation by the additional ICRF power flux, and not to an ICRF induced toroidal force related to radial non-ambipolar transport of resonant particles. Toroidal momentum transport is found to be anomalous in various plasma regimes including standard and improved H-modes and ion-internal transport barrier (ITB) plasmas. In the inner half of those plasmas, except for high density H-modes with on-axis NBI only, the momentum diffusivity, χ_φ, is found to be similar to the ion and electron heat diffusivities, χ_i and χ_e. In the outer half region, χ_φ becomes smaller than χ_i, while χ_φ is still comparable with χ_e except for ITB plasmas. It is found that the normalized gradient length of the toroidal rotation velocity, R/L_Vφ is smaller than that of the ion temperature, R/L_Ti, in H-modes and ITB plasmas. The magnitude of R/L_Vφ in an ITB region exceeds that in H-modes, as seen for the T_i profile. In H-modes, the T_i profile is stiff ( R/L_Ti ∼ 5), while the V_φ profile is not stiff, with R/L_Vφ ranging from 0 to 7. The V_φ profile tends to become flat at high densities with on-axis NBI only. Additional ICRF heating can lead to a small decrease in both R/L_Ti and R/L_Vφ, while it sometimes causes a flattening of the V_φ profile in the inner region. It is shown that the neoclassical correction of V_φ does not affect strongly the results obtained with the measured V_φ

[en] The current ramp-up phase of ITER demonstration discharges, performed at JET, is analysed and the capability of the empirical L-mode Bohm-gyroBohm and Coppi-Tang transport models as well as the theory-based GLF23 model to predict the temperature evolution in these discharges is examined. The analysed database includes ohmic (OH) plasmas with various current ramp rates and plasma densities and the L-mode plasmas with the ion cyclotron radio frequency (ICRF) and neutral beam injection (NBI) heating performed at various ICRF resonance positions and NBI heating powers. The emphasis of this analysis is a data consistency test, which is particularly important here because some parameters, useful for the transport model validation, are not measured in OH and ICRF heated plasmas (e.g. ion temperature, effective charge). The sensitivity of the predictive accuracy of the transport models to the unmeasured data is estimated. It is found that the Bohm-gyroBohm model satisfactorily predicts the temperature evolution in discharges with central heating (the rms deviation between the simulated and measured temperature is within 15%), but underestimates the thermal electron transport in the OH and off-axis ICRF heated discharges. The Coppi-Tang model strongly underestimates the thermal transport in all discharges considered. A re-normalization of these empirical models for improving their predictive capability is proposed. The GLF23 model, strongly dependent on the ion temperature gradient and tested only for NBI heated discharges with measured ion temperatures, predicts accurately the temperature in the low power NBI heated discharge (rms < 10%) while the discrepancy with the data increases at high power. Based on the analysis of the JET discharges, the modelling of the current ramp-up phase for the H-mode ITER scenario is performed with particular emphasis on the sensitivity of the sawtooth-free duration of this phase to transport model.