F. Engelmann

Importance of Electron Cyclotron Wave Energy Transport in ITER

The importance of electron cyclotron (EC) wave emission to the local electron power balance is analysed for various ITER operation regimes and, for comparison, for typical working conditions of FIRE, IGNITOR and the reactor-grade ITER concept as considered during the Engineering Design Phase (ITER-EDA). To cover the non-local effects in EC wave emission as well, the CYTRAN routine along with the ASTRA transport code is used. As a result, EC wave emission is shown to be a significant contributor to core electron cooling if the core electron temperature is about 35 keV or higher, as expected for ITER and tokamak reactor steady-state operation; in fact, it becomes the dominant core electron cooling mechanism at temperatures exceeding 40 keV, as such affecting the core plasma power balance in an important way.

Electron cyclotron radiative transfer in fusion plasmas

The radiative transfer in a system at local thermodynamic equilibrium is investigated on the basis of the solution of the (geometrical optics) transfer equation, accounting for the non-local nature of the radiative process due to both re-absorption of the emitted radiation and reflectivity of the walls of the system. The specific case of the electron cyclotron (EC) radiation in a cylindrical fusion plasma with specularly reflecting walls for which an analytical solution can be derived, is addressed and, in particular, the radial profile of the net power density radiated is evaluated by making use of an improved expression for the EC absorption coefficient. A detailed numerical analysis, carried out by varying both the wall reflection coefficient and the radial profile of the plasma temperature, reveals that a reversal of the net power density profile can occur on the plasma outboard for sufficiently high wall reflectivity. From a comparison with bremsstrahlung radiation profiles it is apparent that a local treatment of EC power emission is needed for sufficiently hot plasmas as expected, e.g. in the so-called advanced regimes of DT tokamak reactors. Furthermore, an exact approach is used to check the accuracy of approximate EC net power density profiles as calculated with the CYTRAN code showing that the latter provides a globally reasonable approximation. Evaluating the total EC radiated power from the exact local approach shows that its scaling with the reflection coefficient is very well described by a scaling following from a recently established global model for the EC radiation, which improves the well-known Trubnikov scaling. The results obtained are discussed in view of their possible relevance to affecting the plasma temperature profile.

Absorption of lower hybrid slow waves by fusion alpha particles

The absorption of lower hybrid slow (LHS) waves in a thermonuclear plasma is investigated by accounting for both (self-consistent) quasi-linear electron Landau damping and (linear) absorption by fusion alpha particles. The full cold plasma wave dispersion properties are taken into account. A cylindrical geometry is adopted and it is assumed that the poloidal component of the wave vector can be disregarded. Analytical expressions for both absorption coefficients are presented, with emphasis on the case where the parallel refractive index of the LHS wave is near the accessibility value. In this case, electromagnetic effects are important. Numerical results for the profile of the radial power deposition on both electrons and alpha particles as well as the driven current density are given and discussed for parameters typical of a NET-like plasma. In particular, the fraction of the power absorbed by the alpha particles is evaluated. Conditions which ensure the absence of wave absorption by alpha particles are discussed.

RAYTEC: a new code for electron cyclotron radiative transport modelling of fusion plasmas

As it was recognized that local electron cyclotron (EC) wave power losses can be a competitive contribution to the 1D electron power balance for reactor-grade tokamak plasmas in regimes as anticipated for steady-state operation, a systematic effort is ongoing to improve the modelling capability for the radial profile of EC wave emission. This effort aims at generating a hierarchy of codes that cover the non-local behaviour of EC wave transport for inhomogeneous plasmas and in the presence of reflecting walls with increasingly improved accuracy and also provide sufficient computational efficiency for being usable in 1D transport studies. The recently developed code RAYTEC, which explicitly addresses the geometrical effects present in toroidal plasmas with arbitrary cross-section, is described and used to investigate the impact of elongation of the plasma cross-section and of toroidicity on the angular dependence of the EC radiation field, on the profile of the net EC wave power density lost from the plasma and on the total EC power loss for ITER-like plasma conditions. Furthermore, a comparison is made with the results of simpler models in use to describe both local and total EC power losses as well as with ones obtained from analytical formulae that are introduced on the basis of Trubnikovs formula for EC power emission.

Benchmarking of codes for calculating local NET EC power losses in fusion plasmas

Abstract The codes SNECTR, CYTRAN, CYNEQ, and EXACTEC are compared in view of the calculation of the profile of the net electron cyclotron (EC) wave power density emitted for different electron temperature profiles and average temperatures of relevance for reactor-grade magnetoplasmas. The effects of either specularly or diffusely reflecting walls are assessed for a cylindrical plasma with circular cross-section, specular reflection, as assumed in EXACTEC, providing a lower bound to the net EC wave power losses in the hot plasma core (and therefore, as a rule, also to the total EC power loss) as well as to reabsorption in the edge plasma. The assumption of isotropy of the radiation intensity in the plasma that is adopted in both CYTRAN and CYNEQ (which cannot be justified a priori) is discussed and found to be adequate for strong diffuse reflection. However, it overestimates the net EC power loss in the plasma core for weakly as well as for specularly reflecting walls by up to 20%. The full transport code SNECTR (no longer in active use), for specular reflection, and the exact cylindrical code EXACTEC are in excellent agreement with each other while for strong diffuse reflection EXACTEC is found to underestimate the net EC power loss typically by 20%. EXACTEC, CYTRAN, and CYNEQ are confirmed to be well suited for use in systematic transport simulations of fusion plasmas.

Electron-cyclotron absorption in high-temperature plasmas: quasi-exact analytical evaluation and comparative numerical analysis

On the basis of the electromagnetic energy balance equation, a quasi-exact analytical evaluation of the electron-cyclotron (EC) absorption coefficient is performed for arbitrary propagation (with respect to the magnetic field) in a (Maxwellian) magneto-plasma for the temperature range of interest for fusion reactors (in which EC radiation losses tend to be important in the plasma power balance). The calculation makes use of Batemans expansion for the product of two Bessel functions, retaining the lowest-order contribution. The integration over electron momentum can then be carried out analytically, fully accounting for finite Larmor radius effects in this approximation. On the basis of the analytical expressions for the EC absorption coefficients of both the extraordinary and ordinary modes thus obtained, (i) for the case of perpendicular propagation simple formulae are derived for both modes and (ii) a numerical analysis of the angular distribution of EC absorption is carried out. An assessment of the accuracy of asymptotic expressions that have been given earlier is also performed, showing that these approximations can be usefully applied for calculating EC power losses from reactor-grade plasmas.

Electron cyclotron radiative transfer in the presence of polarization scrambling in wall reflections

An exact analytical solution of the equation of radiative transfer is obtained for a cylindrical system with specularly reflecting walls, accounting for the presence of polarization scrambling in the reflection process. The effects of polarization scrambling on the specific intensity of the radiation can be described via an effective wall reflection coefficient for the extraordinary (x) and ordinary (o) mode. For the special case of electron cyclotron radiation in a fusion plasma, a numerical analysis of the impact of polarization scrambling on both the specific intensity of the radiation and the radial profile of the net power radiated as well as on the total power loss is carried out for ITER-like parameters in steady-state operation.

Tokamak Global Confinement Data

Within the framework of the INTOR activities, a collection of experimental data from major tokamaks in the world was started, to provide the tokamak community with quantitative information on a choice of well documented discharges that can be used as a starting point for further analysis of the physics of tokamak plasmas. The response was excellent. It was therefore decided to publish these data in Nuclear Fusion as a Special Topic, after a check and updating by the contributors. Since the responsibility for the correctness of the data is with the persons who provided them, the data are published under their authorship. It is hoped that collecting and publishing representative tokamak data will become a continuing effort so that, after some time, there will be a data collection that is significantly wider than what can be found in published articles and reports and that can be easily accessed. The data will also be kept in a special database at the Max-Planck-Institut fur Plasmaphysik (IPP), Garching, using the ORACLE system; they can be made available upon request on a data carrier.

Controlled Fusion and Plasma Physics

This new book by Kenro Miyamoto provides an up-to-date overview of the status of fusion research and the important parts of the underlying plasma physics at a moment where, due to the start of ITER construction, an important step in fusion research has been made and many new research workers will enter the field. For them, and also for interested graduate students and physicists in other fields, the book provides a good introduction into fusion physics as, on the whole, the presentation of the material is quite appropriate for getting acquainted with the field on the basis of just general knowledge in physics. There is overlap with Miyamotos earlier book Plasma Physics for Nuclear Fusion (MIT Press, Cambridge, USA, 1989) but only in a few sections on subjects which have not evolved since. The presentation is subdivided into two parts of about equal length. The first part, following a concise survey of the physics basis of thermonuclear fusion and of plasmas in general, covers the various magnetic configurations studied for plasma confinement (tokamak; reversed field pinch; stellarator; mirror-type geometries) and introduces the specific properties of plasmas in these devices. Plasma confinement in tokamaks is treated in particular detail, in compliance with the importance of this field in fusion research. This includes a review of the ITER concept and of the rationale for the choice of ITERs parameters. In the second part, selected topics in fusion plasma physics (macroscopic instabilities; propagation of waves; kinetic effects such as energy transfer between waves and particles including microscopic instabilities as well as plasma heating and current drive; transport phenomena induced by turbulence) are presented systematically. While the emphasis is on displaying the essential physics, deeper theoretical analysis is also provided here. Every chapter is complemented by a few related problems, but only partial hints for their solution are given. A selection of references, mostly to articles covering original research, allows the interested reader to go deeper into the various subjects. There are a few quite relevant areas which are essentially not covered in the book (plasma diagnostics; fuelling). The discussion of particle and power exhaust is limited to tokamaks and is somewhat scarce. Other points which I did not find fully satisfactory are: the index is too selective and does not really allow easy access to any specific subject. Cross references between different sections treating related topics are not always given. There are quite a lot of typographical errors which as far as cross references are concerned may be disturbing. A list of the symbols used would be a helpful supplement, especially since some of them appear with different meanings. There are apparent imperfections in the structure of certain chapters. While the English is sometimes unusual, this generally does not affect the readability. Overall, the book can be warmly recommended to all interested in familiarizing themselves with the physics of magnetic fusion.