G. Pereverzev

TORBEAM, a beam tracing code for electron-cyclotron waves in tokamak plasmas

The beam tracing technique is used to describe the propagation and absorption of Gaussian wave beams with frequencies in the electron-cyclotron frequency range in a fusion plasma. Like in the standard ray tracing method, Maxwells equations are reduced to a set of first-order ordinary differential equation. The technique employed here, however, allows for diffraction effects, neglected by the geometrical-optics procedure. The beam is specified in terms of the trajectory of the beam axis, the evolution of both the curvature of the wave front and the width of the field profile, as well as the absorption of the wave energy by the plasma. A Fortran code is presented, which solves the beam tracing equations in a tokamak geometry for arbitrary launching conditions and for both analytic and experimentally prescribed magnetic equilibria. Examples of wave propagation, power deposition and current profiles are computed and compared with ray tracing results.

Beam tracing in inhomogeneous anisotropic plasmas

An asymptotic method for solving the wave equation in the short-wavelength limit is presented. This method, called beam tracing, takes into account the wave properties, i.e., diffraction and interference. It reduces the full wave equation to a set of ordinary differential equations. In this respect, it differs from all other asymptotic techniques describing diffraction which end up with much more complicated partial differential equations. The resulting system of beam tracing equations is expressed in terms of the same Hamiltonian function as in geometric optics (ray tracing) and, similar to the ray tracing, allows powerful numerical solving algorithms. Thus the beam tracing combines the simplicity of ray tracing with a description of the wave phenomena, which are not included in the ray tracing. The beam tracing technique provides an efficient tool for calculation of wave fields in all problems where the short-wave approximation is applicable such as rf heating, current drive and plasma diagnostics with ...

Influence of the heating profile on impurity transport in ASDEX Upgrade

The transport of silicon has been investigated for various heating scenarios in ASDEX Upgrade H-mode discharges. Inside of r≈a/4, the diffusion coefficient D is either mainly neoclassical or anomalous depending on the heating method. For all investigated scenarios with NBI-heating and off-axis ECRH or off-axis ICRH, the diffusion coefficient is approximately neoclassical, and the effective heat diffusion coefficient χeff is below the neoclassical ion heat diffusion χi,neo in the plasma core. When central ECRH is added, χeff is above χi,neo, and D strongly increases by a factor of 3–10, i.e. becomes predominantly anomalous. For central ICRH, D is above the neoclassical level by a factor of 2. For radii outside of r≈a/4, D is always anomalous and increases towards the plasma edge. For ra/4, we find a clear scaling of D in terms of χeff, where D is about equal or above χeff. A strong inward drift parameter v/D is only observed in the core and only for cases, when the diffusion coefficient is neoclassical. With central wave heating, the drift parameter decreases to small values.

Gyrokinetic simulations of impurity, He ash and α particle transport and consequences on ITER transport modelling

The transport of light and heavy impurities, as well as of energetic a particles, produced by the background electrostatic plasma turbulence is investigated by means of linear and nonlinear simulations with three gyrokinetic codes, GS2, GYRO and the recently developed GKW. The basic transport mechanisms of impurities and energetic alpha particles are elucidated, in combination with a simple analytical derivation. The relevance of these theoretical results in the transport modelling of the ITER standard scenario is assessed by means of ASTRA simulations, in which the transport of minority species like alpha particles and He ash is described by means of formulae which fit the gyrokinetic results.

Performance projections for the lithium tokamak experiment (LTX)

Use of a large-area liquid lithium limiter in the CDX-U tokamak produced the largest relative increase (an enhancement factor of 5-10) in Ohmic tokamak confinement ever observed. The confinement results from CDX-U do not agree with existing scaling laws, and cannot easily be projected to the new lithium tokamak experiment (LTX). Numerical simulations of CDX-U low recycling discharges have now been performed with the ASTRA-ESC code with a special reference transport model suitable for a diffusion-based confinement regime, incorporating boundary conditions for nonrecycling walls, with fuelling via edge gas puffing. This model has been successful at reproducing the experimental values of the energy confinement (4-6 ms), loop voltage (<0.5 V), and density for a typical CDX-U lithium discharge. The same transport model has also been used to project the performance of the LTX, in Ohmic operation, or with modest neutral beam injection (NBI). NBI in LTX, with a low recycling wall of liquid lithium, is predicted to result in core electron and ion temperatures of 1-2 keV, and energy confinement times in excess of 50 ms. Finally, the unique design features of LTX are summarized.

Paraxial Gaussian wave beam propagation in an anisotropic inhomogeneous plasma

The beam tracing technique describes electromagnetic wave beam propagation in the short wavelength limit, including diffraction effects, not described by the usual geometric optics. It involves a set of ordinary differential equations: a central or reference ray is determined and around this the beam profile and the shape of the phase front are calculated. Here, these equations are obtained for a Gaussian wave beam. Analytic solutions in an inhomogeneous magnetized plasma are given for perpendicular propagation in a slab geometry. The beam is found to show a strong deformation of its cross section due to the anisotropy of the medium. The rotation of the cross section and that of the curvature of the phase front are discussed.

On lithium walls and the performance of magnetic fusion devices

It is shown that lithium walls resulting in zero-recycling regimes at the edge of magnetic fusion device can cause dramatic improvements of core plasma performance. The plasma temperature at the wall in these regimes is much larger than in conventional tokamaks. It reduces the core temperature gradient and, thus, related anomalous transport, allowing an increase in the achievable beta to the level ∼20%, due to wall stabilization and second stability core. Fusion relevant plasma temperature over entire core and high beta results in a strong enhancement of fusion power density. Modeling of the International Thermonuclear Experimental Reactor performance in zero-recycling regimes shows so significant improvement that fusion power increases with no apparent limits due to elimination of the strong core temperature gradient and associated turbulent transport and due to expansion of the burning zone to the entire cross section.

Electron heat transport in ASDEX Upgrade: experiment and modelling

The electron heat transport is investigated in ASDEX Upgrade using electron cyclotron heating (ECH) combining steady-state and power modulation schemes. Experiments in which the electron heat flux has been varied in the confinement region while the edge was kept constant were performed. They demonstrate that ∇ Te and ∇ Te/Te can be varied by a factor of 3 and 2, respectively. They allow a detailed determination of the transport characteristics by comparing steady-state and modulation data with modelling. The analyses clearly show the existence of a threshold (∇ Te/Te)crit above which transport increases. Both steady-state and modulation experiments agree with such a transport model. The experiments have been carried out at low density in the L-mode to ensure low electron–ion coupling and good conditions for studying electron heat transport. The experiments were carried out at two different values of plasma current and show that transport increases at low current, as well-known from global scaling laws for confinement time. In the pure off-axis cases the region inside the ECH deposition is just at the (∇ Te/Te)crit threshold, which allows it to be measured directly from the profile of ∇ Te/Te deduced from the experimental Te profile. Using this technique, it appears that the turbulence threshold agrees with that expected from the trapped electron mode driven turbulence. It has the correct absolute value and seems to have the correct radial dependence that is determined by the trapped electron fraction and by the density gradient. It almost does not vary with other plasma parameters. In contrast, the threshold calculated for electron temperature gradient modes is higher than the experimental values of ∇ Te/Te and this turbulence is therefore not expected to be excited under these experimental conditions.

Particle and impurity transport in the Axial Symmetric Divertor Experiment Upgrade and the Joint European Torus, experimental observations and theoretical understanding

Experimental observations on core particle and impurity transport from the Axial Symmetric Divertor Experiment Upgrade [O. Gruber, H.-S. Bosch, S. Gunter , Nucl Fusion 39, 1321 (1999)] and the Joint European Torus [J. Pamela, E. R. Solano, and JET EFDA Contributors, Nucl. Fusion 43, 1540 (2003)] tokamaks are reviewed and compared. Robust general experimental behaviors observed in both the devices and related parametric dependences are identified. The experimental observations are compared with the most recent theoretical results in the field of core particle transport

A generic data structure for integrated modelling of tokamak physics and subsystems

The European Integrated Tokamak Modelling Task Force (ITM-TF) is developing a new type of fully modular and flexible integrated tokamak simulator, which will allow a large variety of simulation types. This ambitious goal requires new concepts of data structure and workflow organisation, which are described for the first time in this paper. The backbone of the system is a physics- and workflow-oriented data structure which allows for the deployment of a fully modular and flexible workflow organisation. The data structure is designed to be generic for any tokamak device and can be used to address physics simulation results, experimental data (including description of subsystem hardware) and engineering issues.