Kotov solps42 report

Numerical study of the ITER divertor plasma with the B2-EIRENE code package Vladislav Kotova , Detlev Reitera , Andrey S. Kukushkinb a Institut für Energieforschung 4 - Plasmaphysik, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany b ITER International Team, Cadarache, France Bericht des Forschungszentrums Jülich Jül-4257, November, 2007 with some corrections compared to the printed version 2 Abstract The problem of plasma-wall interaction and impurity control is one of the remaining criti- cal issues for development of an industrial energy source based on nuclear fusion of light isotopes. In this field sophisticated integrated numerical tools are widely used both for the analysis of current experiments and for predictions guiding future device design. The present work is dedicated to the numerical modelling of the edge plasma region in divertor configurations of large-scale tokamak fusion devices.

A well established software tool for this kind of modelling is the B2-EIRENE code. It was originally developed for a relatively hot (≥ 10 eV) “high recycling divertor”. It did not take into account a number of physical effects which can be potentially important for “detached conditions” (cold, - several eV, - high density, - ≈ 1021 m−3 , - plasma) typical for large tokamak devices. This is espe- cially critical for the modelling of the divertor plasma of ITER: an international project of an experimental tokamak fusion reactor to be built in Cadarache, France by 2016.

This present work is devoted to a major upgrade of the B2-EIRENE package, which is routinely used for ITER modelling, essentially with a significantly revised version of EIRENE: the Monte-Carlo neutral transport code. The main part of the thesis address three major groups of the new physical effects which have been added to the model in frame of this work: the neutral-neutral collisions, the up-to date hydrogen molecular reaction kinetics and the line radiation transport. The impact of the each stage of the upgrade on the self-consistent (between plasma, the neutral gas and the radiation field) solution for the reference ITER case is analysed. The strongest effect is found to be due to the revised molecular collision kinetics, in particular due to hitherto neglected elastic collisions of hydrogen molecules with ions.

The newly added non-linear effects (neutral-neutral collisions, radiation opacity) are found to be quite sig- nificant for ITER conditions (large size and density) as well, despite the fact that their experimental identification in the presently available smaller devices (including JET) is very difficult. An experimental validation of this particular package which is used for the ITER design has been carried out for a series of discharges at the Joint European Torus (JET) tokamak (UK, Culham). A relatively good (within a factor 2) agreement for the outer divertor has been found. At the same time, a significant discrepancy between the modelling and the experiment is seen in the inner divertor.

As in the case of ITER the model for molecular kinetics has a significant impact on the solution. The new version of the coupled code (SOLPS4.2) has been made available to the ITER International Team and is now extensively used there. It has already provided significant revisions of currently predicted divertor operational scenarios.2 Scrape-off-Layer and Divertor .3 Motivation and outline of the thesis .2 The EIRENE code .1 Monte-Carlo method for transport problems .2 Description of the code. 24 2 Neutral-neutral collisions 29 2.1 Parameters of self collisions .2 Parameters of cross-collisions .3 Effective collision rates .4 Calculating the collision rates .5 The effect of neutral-neutral collisions .2 Collision rate for Maxwellian background .3 Cross sections and collision rates .4 General relations for the transfer rates .5 Transfer rates for Maxwellian background .6 Transformation to background with shift .2 Hydrogen molecular chemistry .3 The effect of molecular kinetics .1 Comparison of the full B2-EIRENE runs .2 Analysis for the fixed plasma background.

68 5 6 CONTENTS 4 Radiation opacity 81 4.1 Transport of photons .2 Photo-induced ionization .3 The effect for the ITER divertor plasma. 90 5 Impact on the ITER modelling 97 6 First experimental validation for JET 101 6.1 The experimental and model set-up .2 Comparison with experiment .3 Comparison of different models. 112 7 Conclusions 117 A Technical notes 125 A.1 Software and hardware .2 Some technical information about EIRENE .3 Implementing BGK in the EIRENE code .4 Implementing the Track Length Estimator for transfer rates .5 Implementation of the photon transport coupled to CRM. 130 B Some details of the model for elastic collisions 133 B.1 Sampling the incident velocity.

134 C Notations for vector and tensor operations 135 D Hydrogen molecular chemistry in ITER: some examples 137 E Results of the JET modelling 141 E.1 Fusion research The topic of this work is numerical modelling of the divertor plasma of tokamak fusion devices. Therefore the terms “fusion”, “tokamak” and “divertor” should be explained first. The ultimate goal of the fusion energy research is creation of a new industrial-scale energy source based on the nuclear fusion of light elements. Due to repulsive Coulomb forces acting between charged nuclei a fusion reaction can only occur if the kinetic en- ergy of the reagents is high enough: tens of kilo-electron volts.

The reaction easiest to achieve is the DT reaction D+T→ 4 He+n+17. This reaction can be efficient already when the average kinetic energy (the temperature) of the reagents is around 10 keV [1], Chapter 1, [2]. For such high temperatures the matter forms a mixture of stripped ions and electrons known as a hot plasma. The principal problem of the fusion research is how to sustain the reaction which can produce industrially relevant amount of energy in a controllable way.

Individual fusion reactions have been routinely demonstrated on particle accelerators since 1930th but a net positive energy gain can not be achieved in this way. Achieving a positive energy release, that is, obtaining more energy from the fusion reactions than it was spent to create the hot plasma, is called the break-even. To reach the break-even the plasma parameters have to meet the so called Lawson criterion. It states that the nτ product must exceed roughly 1020 m−3 · s [2].

Here n is the plasma density and τ the time scale of the energy loss from the plasma. Presently a modified version of the Lawson criterion, the so called triple product, is used more frequently, see e. The Lawson criterion shows that there are basically two ways to achieve the break- even. One can try to create an extremely dense plasma during short time.

This principle is exploited in inertial confinement (inertial fusion) which is based on the compression of small pellets by intense laser radiation or ion and electron beams [3]. In such devices the plasma exists only for nano-seconds but its density can reach 1030 m−3 (higher than the solid-state density). The alternative is to confine a not so dense plasma for relatively long time, ensuring its good thermal insulation. This approach is realized in magnetic confinement devices.

A charged particle in magnetic field gyrates around the filed lines due to Lorentz force. The magnetic field of several Tesla allows to “suspend” the plasma, isolating it from the solid walls. The devices of this kind have plasma densities only up to 1020 m−3 but the energy confinement time is in the range of seconds. Different kinds of devices with magnetic confinement have been studied in the past and are studied now: tokamaks, stellarators, magnetic mirrors, reversed field pinches and others [3].

Tokamaks represent the main- stream of modern fusion research. They are the best stud- ied and the most extensively developed devices. The first projects of fusion reactors (the devices targeting at the in- dustrial level energy production) are based on this concept. However, a significant progress has been made recently for other types of devices as well, especially for stellarators [4].

The tokamak magnetic configuration was first proposed in the USSR by A. It became the Figure 1: The tokamak mag- leading type of devices in fusion research since 1967 when netic configuration (repro- the electron temperature exceeding 1 keV was first ob- duced from [3]). served in tokamak T-3 in Kurchatov Institute, Moscow [6]. A schematic of the tokamak geometry and magnetic field is shown in Figure 1.

A magnetic field inside a long coil (a solenoid) is parallel to its axis. In the absence of collisions the charged particles could escape from such a magnetic field only through the ends of the solenoid. To avoid these end losses, one can connect both ends of the solenoid making the geometry toroidal. This kind of magnetic field in a toka- mak, which is created by external coils is called the toroidal field Bφ.

The toroidal field is inherently non-uniform. In particular, it is higher at the inner side of the torus. In a non-uniform magnetic field different kinds of drift motion are possible e. gradient drift and curvature drift [7, 8].

The drifts can effectively transport particles across the magnetic 8 CONTENTS field even in the absence of collisions. This drift motion can be mitigated by inducing a plasma current in the toroidal direc- tion. This current creates a component of the magnetic field in the poloidal plane (poloidal field) Bθ , Figure 1. The poloidal plane is the plane containing the torus axis.

It can be shown that the presence of the poloidal magnetic field mitigates the drift motion [5], see e. In real devices the poloidal field is created not only by plasma current, but also by extra magnetic coils (poloidal field coils). They are used to enhance stability, to allow an active feedback control of the plasma equilibrium and to shape the magnetic field. The poloidal field is typically an order of magnitude lower than the toroidal one.

The toroidal and poloidal magnetic field together form helical magnetic field lines. Most of them do not return to the initial point after a finite number of turns around the torus, but instead fill a closed surface. One speaks therefore not about the field lines but about the nested magnetic surfaces (flux surfaces). In most of the modern tokamaks the plasma is elongated in vertical direction to make more effective use of the magnetic field (in this way the plasma is pushed towards the high field region).

The distance between the axis of the torus and the centre of gravity of the poloidal projection of the plasma volume is called the major radius R, Figure 1. The shortest distance between this centre of gravity and the boundary of the plasma volume is called the minor radius a. The toroidal current in tokamaks is induced by the alternating magnetic flux created by the vertical central solenoid: the so called inductive current drive. Therefore, the tokamak is an intrinsically pulsed machine, although the duration of the pulses can be very long (up to hundreds seconds) and a non-inductive current current drive is also possible.

The toroidal current can also heat the plasma (ohmic heating) but this heating becomes ineffective for temperatures higher than ≈1.5 keV because of the low plasma resistivity at high temperatures. To reach higher temperatures (10 keV and higher), the auxiliary heating is used. It can be either injection of fast neutral particles (Neutral Beam Injection, NBI) or the resonance electromagnetic waves (Electron Cyclotron and Ion Cyclotron Resonance Heating, ECRH and ICRH). The transport of the charged particles along the magnetic field (magnetic surfaces) can be described by a theory which considers only collisions between particles, - the classical theory [9, 10, 11].

However, the experimentally observed transport across the magnetic field is much stronger (at least an order of magnitude) than predicted by the classical the- ory or a more advanced theory which takes into account the non-uniformity of the mag- netic field (the neo-classical theory, see [1], Sections 4. The origins of this so-called anomalous transport are still being extensively studied.