Jukka Heikkinen

Formation and detection of internal transport barriers in low-current tokamaks

In low-current tokamaks, in the absence of radial electric fields (Er), the widths of the drift orbits are large and the direct orbit losses can extend deep into the plasma. Furthermore, in such a plasma even a modest Er can produce rotation with a poloidal Mach number (Mp) that exceeds unity. Using the Monte Carlo code ASCOT, which follows charged particle orbits in the five-dimensional phase space, the formation of an internal transport barrier (ITB) in such a tokamak is investigated. Carrying out the simulations for the geometry corresponding to the FT-2 tokamak, it is shown that if, under these conditions, a steep density gradient is created in the plasma, the plasma responds by generating a strong (much stronger than needed to compensate the diamagnetic drift) Er in the region of the strong gradient. The generation appears to be a pure neoclassical effect, but a global solution over the entire plasma cross section is required to fully identify it. As a result, an ITB-like situation with a strongly sheared E×B flow is obtained inside the plasma. In these circumstances Mp>1, and thus the orbits of the majority of ions become strongly squeezed. The neutral fluxes observed by neutral particle analysers are also simulated to find out if the neutral spectra can be utilized to estimate the Er values across the plasma cross section in the FT-2 tokamak.

Power transfer and current generation of fast ions with large‐kθ waves in tokamak plasmas

The direction and magnitude of power and momentum exchange between fast ions and electrostatic waves in slab and toroidal systems are obtained from global Monte Carlo simulations that include the quasilinear wave‐induced ion diffusion both in velocity space and through a radially localized (lower hybrid) wave structure with propagation in one preferential poloidal direction in tokamaks. The model considers a full linearized collision model, finite fast ion orbits, and losses in toroidal geometry, and can properly treat the boundary effects on the particle–wave interaction in the configuration space. For an isotropic steady ion source, reduction of wave Landau damping but no wave amplification by wave localization is found for a Gaussian wave intensity distribution in radius, irrespective of the steepness of the radial gradient of the fast ion source rate. Enhanced wave‐driven fast ion current, with magnitude, direction, and profile determined by the boundary conditions, net power transfer, and fast ion ra...

ITB formation in terms of ωE×B flow shear and magnetic shear s on JET

A linear empirical threshold condition ωE×B/γITG>0.68s-0.095 has been found for the onset of the ion internal transport barriers in the JET optimised shear database. Here, s is the magnetic shear, ωE×B the flow shearing rate and γITG is an approximate of the linear growth rate of the ion temperature gradient instability. The present empirical threshold condition for the ITB formation will provide a first clear indication of the strong correlation of s and ωE×B at the ITB transition. The empirical analysis consists of ITB discharges from a wide plasma parameter range; the toroidal magnetic field varies between 1.8-4.0 T, the auxiliary heating power between 10-30 MW and the diamagnetic energy between 3-12 MJ. The predictive simulations of several ITB discharges with the empirical ITB threshold condition reproduce the experiments with time averaged prediction errors of the order of 10-25% in Ti and Te profiles and 10-15% in ne profiles as well as the toroidal flow velocity with errors of the order of 10-20%. The simulated times of the onset of the ITB compared to the experimental ones are typically within 0.4 s and the simulated ITB widths within 0.1 in r/a throughout the whole simulations.

Expanding the operating space of ICRF on JET with a view to ITER

This paper reports on ITER-relevant ion cyclotron resonance frequency (ICRF) physics investigated on JET in 2003 and early 2004. Minority heating of helium three in hydrogen plasmas-(He-3)H-was systematically explored by varying the 3 He concentration and the toroidal phasing of the antenna arrays. The best heating performance (a maximum electron temperature of 6.2 keV with 5 MW of ICRF power) was obtained with a preferential wave launch in the direction of the plasma current. A clear experimental demonstration was made of the sharp and reproducible transition to the mode conversion heating regime when the 3 He concentration increased above similar to 2%. In the latter regime the best heating performance (a maximum electron temperature of 8 keV with 5 MW of ICRF power) was achieved with dipole array phasing, i.e. a symmetric antenna power spectrum. Minority heating of deuterium in hydrogen plasmas-(D)H-was also investigated but was found inaccessible because this scenario is too sensitive to impurity ions with Z/A = 1/2 such as C6+, small amounts of which directly lead into the mode conversion regime. Minority heating of up to 3% of tritium in deuterium plasmas was systematically investigated during the JET trace tritium experimental campaign (TTE). This required operating JET at its highest possible magnetic field (3.9 to 4 T) and the ICRF system at its lowest frequency (23 MHz). The interest of this scenario for ICRF heating at these low concentrations and its efficiency at boosting the suprathermal neutron yield were confirmed, and the measured neutron and gammay ray spectra permit interesting comparisons with advanced ICRF code simulations. Investigations of finite Larmor radius effects on the RF-induced high-energy tails during second harmonic (omega = 2 omega(c)) heating of a hydrogen minority in D plasmas clearly demonstrated a strong decrease in the RF diffusion coefficient at proton energies similar to 1 MeV in agreement with theoretical expectations. Fast wave heating and current drive experiments in deuterium plasmas showed effective direct electron heating with dipole phasing of the antennas, but only small changes of the central plasma current density were observed with the directive phasings, in particular at low single pass damping. New investigations of the heating efficiency of ICRF antennas confirmed its strong dependence on the parallel wavenumber spectrum. Advances in topics of a more technological nature are also summarized: ELM studies using fast RF measurements, the successful experimental demonstration of a new ELM-tolerant antenna matching scheme and technical enhancements planned on the JET ICRF system for 2006, they being equally strongly driven by the preparation for ITER.

Anomalous transport and multi-scale drift turbulence dynamics in tokamak ohmic discharge as measured by high resolution diagnostics and modeled by full-f gyrokinetic code

Quantitative reproduction of selected micro-, meso- and macro-scale transport phenomena as measured in the FT-2 tokamak is reached by Elmfire global full-f nonlinear gyrokinetic particle-in-cell simulation predictions. A detailed agreement with mean equilibrium flows, oscillating fine-scale zonal flows and turbulence radial correlation length observed by a set of sophisticated microwave backscattering techniques, as well as a good fit of the thermal diffusivity data in the central and gradient region of discharge are demonstrated. Both the shift and the broadening of the power spectrum of synthetic and experimental Doppler reflectometry diagnostics have been found to overlap perfectly at various radial positions, indicating similar rotation and spreading of the selected density fluctuations. At the same time similar radial electric field dynamics, spatial structure and outward geodesic acoustic mode (GAM) propagation have been observed by comparisons of the probability distribution function, the dominant frequency, the coherence and the cross-phase of the simulated and experimentally measured radial electric field fluctuations, identifying the turbulent driven GAM as a key contributor to the observed strong temporal variation of the radial electric field affected by impurity ions.

Observation of turbulence exponential wave number spectra at ion sub-Larmor scales in FT-2 tokamak

Implementation of the correlative enhanced scattering technique in the FT-2 tokamak has resulted in measurements of both frequency and wave number spectra of a small-scale microturbulence. It is found that during the dynamic current ramp-up discharge the turbulence possesses a wide wave number spectrum which could be described by universal exponential dependence in the range of 3–4 orders of amplitude characterized by two parameters—the turbulence level and scale length. Both parameters are found to decrease substantially when the shear of the poloidal plasma rotation estimated from Doppler frequency shift of the enhanced scattering signal increases at plasma periphery. Simultaneously transition to an improved confinement resulting in the suppression of anomalous electron transport and decrease in the electron energy confinement time is observed in the experiment.

Guiding-center simulations of nonlocal and negative inertia effects on rotation in a tokamak

The magnitude of the radial electric field (Er), resulting from nonambipolar fluxes of neoclassical origin, is evaluated using Monte Carlo guiding-center simulations for a low-current plasma corresponding to the FT-2 tokamak {Fisichiskii Tokamak-2, Ioffe Institute, St. Petersburg [S. I. Lashkul, V. N. Budnikov, E. O. Vekshina et al., Plasma Phys. Rep. 27, 1001 (2001)]}. The Er-values are found to significantly exceed those given by the standard neoclassical theory, based on thin-orbit assumption, when the plasma current is sufficiently low and the pressure gradient is sufficiently high. Strong Er-structures are found to form in the same low plasma-current range where enhanced confinement is reported in the FT-2 tokamak. In the simulations, the physics behind the strong increase in the field values is intimately related to the poloidal Mach-number, together with the wide ion orbits.

Bifurcation of the radial electric field in the presence of edge polarization in tokamaks

In guiding-center simulations of a tokamak plasma edge, bifurcations of both the radial electric field and the electrode current are observed for a threshold value of the electrode bias voltage, in qualitative agreement with experiments. The simulations are neoclassical and Monte Carlo based, also containing the perpendicular viscosity effect. Above the voltage threshold, an inward moving, solitary radial electric field structure is generated with a concomitant drop in the electrode current. The position, width, and height of the soliton depend on the magnitude and radial variation of the conductivity (and, thus, on local plasma parameters), finite orbit effects, and also on the perpendicular viscosity and neutral density. The obtained Er structures are narrower and higher than the ones measured in the edge polarization experiments in the Julich tokamak TEXTOR-94 [S. Jachmich et al., Plasma Phys. Controlled Fusion 40, 1105 (1998)].

Gyrokinetic equations and full f solution method based on Dirac’s constrained Hamiltonian and inverse Kruskal iteration

Gyrokinetic equations of motion, Poisson equation, and energy and momentum conservation laws are derived based on the reduced-phase-space Lagrangian and inverse Kruskal iteration introduced by Pfirsch and Correa-Restrepo [J. Plasma Phys. 70, 719 (2004)]. This formalism, together with the choice of the adiabatic invariant J=⟨p⋅∂x/∂ϕ⟩ as one of the averaging coordinates in phase space, provides an alternative to the standard gyrokinetics. Within second order in gyrokinetic parameter, the new equations do not show explicit ponderomotivelike or polarizationlike terms. Pullback of particle information with an iterated gyrophase and field dependent gyroradius function from the gyrocenter position defined by gyroaveraged coordinates allows direct numerical integration of the gyrokinetic equations in particle simulation of the field and particles with full distribution function. As an example, gyrokinetic systems with polarization drift either present or absent in the equations of motion are considered.

The effect of a radial electric field on ripple-trapped ions observed by neutral particle fluxes

The effect of a radial electric field on nonthermal ripple-trapped ions is investigated using toroidal Monte Carlo simulations for edge tokamak plasmas. The increase in the neutral particle flux from the ions trapped in local magnetic wells observed by the charge exchange (CX) detector at a low confinement to high confinement transition at ASDEX (Axially Symmetric Divertor Experiment). Upgrade tokamak [Proceedings of the 20th European Conference on Controlled Fusion and Plasma Physics, Lisbon (European Physical Society, Petit-Lancy, Switzerland, 1993), Vol. 17C, Part I, p. 267] is reproduced in the simulations by turning on a radial electric field near the plasma periphery. The poloidal and toroidal angles at which the CX detector signal is most sensitive to the radial electric field are determined. A fast response time of the signal in the range of 50–100 μs to the appearance of the electric field can be found in the simulations with a relatively large half-width of the negative electric field region.