Max Planck Institute for Plasma Physics

The major increase in discharge duration and plasma energy in a next-step DT fusion reactor will give rise to important plasma-material effects that will critically influence its operation, safety and performance. Erosion will increase to a scale of several cm from being barely measurable at a micron scale in today's tokamaks. Tritium co-deposited with carbon will strongly affect the operation of machines with carbon plasma-facing components. Controlling plasma wall interactions is critical to achieving high performance in present-day tokamaks and this is likely to continue to be the case in the approach to practical fusion reactors. Recognition of the important consequences of these phenomena has stimulated an internationally co-ordinated effort in the field of plasma-surface interactions supporting the engineering design activities of the international thermonuclear experimental reactor project (ITER) and significant progress has been made in better understanding these issues. This paper reviews the underlying physical processes and the existing experimental database of plasma-material interactions both in tokamaks and laboratory simulation facilities for conditions of direct relevance to next-step fusion reactors. Two main topical groups of interactions are considered: (i) erosion/re-deposition from plasma sputtering and disruptions, including dust and flake generation, (ii) tritium retention and removal. The use of modelling tools to interpret the experimental results and make projections for conditions expected in future devices is explained. Outstanding technical issues and specific recommendations on potential R and D avenues for their resolution are presented. (orig.)

Progress in the area of MHD stability and disruptions, since the publication of the 1999 ITER Physics Basis document (1999 Nucl. Fusion 39 2137-2664), is reviewed. Recent theoretical and experimental research has made important advances in both understanding and control of MHD stability in tokamak plasmas. Sawteeth are anticipated in the ITER baseline ELMy H-mode scenario, but the tools exist to avoid or control them through localized current drive or fast ion generation. Active control of other MHD instabilities will most likely be also required in ITER. Extrapolation from existing experiments indicates that stabilization of neoclassical tearing modes by highly localized feedback-controlled current drive should be possible in ITER. Resistive wall modes are a key issue for advanced scenarios, but again, existing experiments indicate that these modes can be stabilized by a combination of plasma rotation and direct feedback control with non-axisymmetric coils. Reduction of error fields is a requirement for avoiding non-rotating magnetic island formation and for maintaining plasma rotation to help stabilize resistive wall modes. Recent experiments have shown the feasibility of reducing error fields to an acceptable level by means of non-axisymmetric coils, possibly controlled by feedback. The MHD stability limits associated with advanced scenarios are becoming well understood theoretically, and can be extended by tailoring of the pressure and current density profiles as well as by other techniques mentioned here. There have been significant advances also in the control of disruptions, most notably by injection of massive quantities of gas, leading to reduced halo current fractions and a larger fraction of the total thermal and magnetic energy dissipated by radiation. These advances in disruption control are supported by the development of means to predict impending disruption, most notably using neural networks. In addition to these advances in means to control or ameliorate the consequences of MHD instabilities, there has been significant progress in improving physics understanding and modelling. This progress has been in areas including the mechanisms governing NTM growth and seeding, in understanding the damping controlling RWM stability and in modelling RWM feedback schemes. For disruptions there has been continued progress on the instability mechanisms that underlie various classes of disruption, on the detailed modelling of halo currents and forces and in refining predictions of quench rates and disruption power loads. Overall the studies reviewed in this chapter demonstrate that MHD instabilities can be controlled, avoided or ameliorated to the extent that they should not compromise ITER operation, though they will necessarily impose a range of constraints.

Collisionless electron-temperature-gradient-driven (ETG) turbulence in toroidal geometry is studied via nonlinear numerical simulations. To this aim, two massively parallel, fully gyrokinetic Vlasov codes are used, both including electromagnetic effects. Somewhat surprisingly, and unlike in the analogous case of ion-temperature-gradient-driven (ITG) turbulence, we find that the turbulent electron heat flux is significantly underpredicted by simple mixing length estimates in a certain parameter regime (ŝ∼1, low α). This observation is directly linked to the presence of radially highly elongated vortices (“streamers”) which lead to very effective cross-field transport. The simulations therefore indicate that ETG turbulence is likely to be relevant to magnetic confinement fusion experiments.

Progress, since the ITER Physics Basis publication (ITER Physics Basis Editors et al 1999 Nucl. Fusion 39 2137-2664), in understanding the processes that will determine the properties of the plasma edge and its interaction with material elements in ITER is described. Experimental areas where significant progress has taken place are energy transport in the scrape-off layer (SOL) in particular of the anomalous transport scaling, particle transport in the SOL that plays a major role in the interaction of diverted plasmas with the main-chamber material elements, edge localized mode (ELM) energy deposition on material elements and the transport mechanism for the ELM energy from the main plasma to the plasma facing components, the physics of plasma detachment and neutral dynamics including the edge density profile structure and the control of plasma particle content and He removal, the erosion of low- and high-Z materials in fusion devices, their transport to the core plasma and their migration at the plasma edge including the formation of mixed materials, the processes determining the size and location of the retention of tritium in fusion devices and methods to remove it and the processes determining the efficiency of the various fuelling methods as well as their development towards the ITER requirements. This experimental progress has been accompanied by the development of modelling tools for the physical processes at the edge plasma and plasma-materials interaction and the further validation of these models by comparing their predictions with the new experimental results. Progress in the modelling development and validation has been mostly concentrated in the following areas: refinement in the predictions for ITER with plasma edge modelling codes by inclusion of detailed geometrical features of the divertor and the introduction of physical effects, which can play a major role in determining the divertor parameters at the divertor for ITER conditions such as hydrogen radiation transport and neutral-neutral collisions, modelling of the ion orbits at the plasma edge, which can play a role in determining power deposition at the divertor target, models for plasma-materials and plasma dynamics interaction during ELMs and disruptions, models for the transport of impurities at the plasma edge to describe the core contamination by impurities and the migration of eroded materials at the edge plasma and its associated tritium retention and models for the turbulent processes that determine the anomalous transport of energy and particles across the SOL. The implications for the expected performance of the reference regimes in ITER, the operation of the ITER device and the lifetime of the plasma facing materials are discussed.

The phenomenology of edge localized modes (ELMs), an MHD instability occurring in the edge of H-mode plasmas in toroidal magnetic fusion experiments, is described. ELMs are important to obtain experimental control of the particle inventory of fusion plasmas. From an analysis of the ELM behaviour of different magnetic fusion experiments, three distinct types are identified, namely dithering cycles, type III and type I ELMs. A physical picture of these phenomena is established on the grounds of theoretical models put forward to describe the different ELM phenomena.

SIMNRA is a Microsoft Windows 95/Windows NT program with fully graphical user interface for the simulation of non-Rutherford backscattering, nuclear reaction analysis and elastic recoil detection analysis with MeV ions. About 300 different non-Rutherford and nuclear reactions cross-sections are included. SIMNRA can calculate any ion-target combination including incident heavy ions and any geometry including transmission geometry. Arbitrary multi-layered foils in front of the detector can be used. Energy loss straggling includes the corrections by Chu to Bohr’s straggling theory, propagation of straggling in thick layers, geometrical straggling and straggling due to multiple small angle scattering. The effects of plural large angle scattering can be calculated approximately. Typical computing times are in the range of several seconds.

For interpreting fusion rate measurements in present fusion experiments and predicting the fusion performance of future devices or of d-t experiments in present devices, it is important to know the fusion cross-sections as precisely as possible. Usually, it is not measured data that are used, but parametrizations of the cross-section as a function of the ion energy and parametrizations of the Maxwellian reactivity as a function of the ion-temperature. Since the publication of the parametrizations now in use, new measurements have been made and evaluations of the measured data have been improved by applying R-matrix theory. The authors show that the old parametrizations no longer adequately represent the experimental data and present new parametrizations based on R-matrix calculations for fusion cross-sections and Maxwellian reactivities for the reactions D(d,n)3He, D(d,p)T, T(d,n)4He and 3He(d,p)4He

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

The 'Progress in the ITER Physics Basis' (PIPB) document is an update of the 'ITER Physics Basis' (IPB), which was published in 1999 [1]. The IPB provided methodologies for projecting the performance of burning plasmas, developed largely through coordinated experimental, modelling and theoretical activities carried out on today's large tokamaks (ITER Physics R&D). In the IPB, projections for ITER (1998 Design) were also presented. The IPB also pointed out some outstanding issues. These issues have been addressed by the Participant Teams of ITER (the European Union, Japan, Russia and the USA), for which International Tokamak Physics Activities (ITPA) provided a forum of scientists, focusing on open issues pointed out in the IPB. The new methodologies of projection and control are applied to ITER, which was redesigned under revised technical objectives. These analyses suggest that the achievement of Q > 10 in the inductive operation is feasible. Further, improved confinement and beta observed with low shear (= high βp = 'hybrid') operation scenarios, if achieved in ITER, could provide attractive scenarios with high Q (> 10), long pulse (>1000 s) operation with beta <no-wall limit and benign ELMs.

This book, first published in 2000, provides a comprehensive introduction to the theory of magnetic field line reconnection, now a major subject in plasma physics. The book focuses on the various reconnection mechanisms dominating magnetic processes under the different plasma conditions encountered in astrophysical systems and in laboratory fusion devices. The book consists of two major parts: the first deals with the classical resistive approach, while the second presents an overview of weakly collisional or collisionless plasmas. Applications primarily concern astrophysical phenomena and dynamo theory, with emphasis on the solar and geodynamo, as well as magnetospheric substorms, the most spectacular reconnection events in the magnetospheric plasma. The theoretical procedures and results also apply directly to reconnection processes in laboratory plasmas, in particular the sawtooth phenomenon in tokamaks. The book will be of value to graduate students and researchers interested in magnetic processes both in astrophysical and laboratory plasma physics.

A general picture of magnetic reconnection in the framework of 2-D incompressible resistive magnetohydrodynamic theory is presented. Numerical studies of (quasi-) steady-state driven reconnection reveal current sheet formation for Mach numbers M=u/vA exceeding the Sweet–Parker reconnection rate MSP=(η/LvA)1/2. Since the thickness δ of the current sheet is found to be invariant to a change of the resistivity η, its length Δ increases rapidly with decreasing η or increasing M, which can be written in the form Δ∼(M/MSP)4, so that Δ reaches the global system size L within a short range of the parameter M/MSP. The results are rather insensitive to the particular choice of boundary conditions. Because of the presence of a current sheet, the overall reconnection process is quite slow. This picture essentially agrees with Syrovatsky’s [Sov. Phys. JETP 33, 933 (1971)] theory and disproves Petschek’s [AAS/NASA Symposium on the Physics of Solar Flares, (NASA, Washington, DC, 1964) p. 425] mechanism of fast magnetic reconnection. A theory of the solution in the external and in the diffusion region is developed and analytical expressions in agreement with the simulation results are obtained by means of a variational principle. For sufficiently long current sheets the tearing mode becomes unstable in spite of the stabilizing effect of the inhomogeneous flow. The tearing mode contributes to the overall reconnection process, but a general assessment of this effect in the asymptotic regime of almost vanishing η is difficult.

This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate students and researchers working in turbulence theory, plasma physics and astrophysics.

• Reviews the fundamental physics aspects of the first ITER W divertor and defines the required operational lifetime within the Staged Approach. • Uses the ITER divertor SOLPS simulation database to establish the target peak heat flux and neutral pressure burning plasma operating domain. • Assesses consequences of narrow SOL heat flux channels, fluid drifts, component shaping and 3D magnetic fields for ELM control. • Uses W recrystallization to define an operational budget and shows that heat fluxes ∼50% higher than previously assumed may be acceptable. • Shows that Ne and N should be equally good as seed impurities and suggests that very strong ELM mitigation will be required at high performance. • Provides a list of key outstanding R&D areas to consolidate the divertor physics basis in the period up to ITER operation. On the eve of component procurement, this paper discusses the present physics basis for the first ITER tungsten (W) divertor, beginning with a reminder of the key elements defining the overall design, and outlining relevant aspects of the Research Plan accompanying the new “staged approach” to ITER nuclear operations which fixes the overall divertor lifetime constraint. The principal focus is on the main design driver, steady state power fluxes in the DT phases, obtained from simulations using the 2-D SOLPS-4.3 and SOLPS-ITER plasma boundary codes, assuming the use of the low Z seeding impurities nitrogen (N) and neon (Ne). A new perspective on the simulation database is adopted, concentrating purely on the divertor physics aspects rather than on the core-edge integration, which has been studied extensively in the course of the divertor design evolution and is published elsewhere. Emphasis is placed on factors which may increase the peak steady state loads: divertor target shaping for component misalignment protection, the influence of fluid drifts, and the consequences of narrow scrape-off layer heat flux channels. All tend to push the divertor into an operating space at higher sub-divertor neutral pressure in order to remain at power flux densities acceptable for the target material. However, a revised criterion for the maximum tolerable loads based on avoidance of W recrystallization, sets an upper limit potentially ∼50% higher than the previously accepted value of ∼10 MW m −2 , a consequence both of the choice of material and the finalized component design. Although the simulation database is currently restricted to the 2-D toroidally symmetric situation, considerable progress is now also being made using the EMC3-Eirene 3-D code suite for the assessment of power loading in the presence of magnetic perturbations for ELM control. Some new results for low input power corresponding to the early H-mode operation phases are reported, showing that even if realistic plasma screening is taken into account, significant asymmetric divertor heat fluxes may arise far from the unperturbed strike point. The issue of tolerable limits for transient heat pulses is an open and key question. A new scaling for ELM power deposition has shown that whilst there may be more latitude for operation at higher current without ELM control, the ultimate limit is likely to be set more by material fatigue under large numbers of sub-threshold melting events.

The state of the art in the field of electron cyclotron emission and absorption of fusion plasmas confined by a magnetic field is reviewed. The general theory is described concisely, explicit results being given mainly for plasmas in local thermodynamic equilibrium. Moreover, the practical implications of these effects with respect to cyclotron radiation losses, the use of cyclotron emission as a diagnostic tool, and electron cyclotron heating and current drive are discussed with emphasis on tokamak plasmas.

A multi-machine database for the H-mode scrape-off layer power fall-off length, λq in JET, DIII-D, ASDEX Upgrade, C-Mod, NSTX and MAST has been assembled under the auspices of the International Tokamak Physics Activity. Regression inside the database finds that the most important scaling parameter is the poloidal magnetic field (or equivalently the plasma current), with λq decreasing linearly with increasing Bpol. For the conventional aspect ratio tokamaks, the regression finds , yielding λq,ITER ≅ 1 mm for the baseline inductive H-mode burning plasma scenario at Ip = 15 MA. The experimental divertor target heat flux profile data, from which λq is derived, also yield a divertor power spreading factor (S) which, together with λq, allows an integral power decay length on the target to be estimated. There are no differences in the λq scaling obtained from all-metal or carbon dominated machines and the inclusion of spherical tokamaks has no significant influence on the regression parameters. Comparison of the measured λq with the values expected from a recently published heuristic drift based model shows satisfactory agreement for all tokamaks.

We present the first comprehensive study of r-process element nucleosynthesis in the ejecta of compact binary mergers (CBMs) and their relic black-hole (BH)-torus systems. The evolution of the BH-accretion tori is simulated for seconds with a Newtonian hydrodynamics code including viscosity effects, pseudo-Newtonian gravity for rotating BHs, and an energy-dependent two-moment closure scheme for the transport of electron neutrinos and antineutrinos. The investigated cases are guided by relativistic double neutron star (NS-NS) and NS-BH merger models, producing ~3-6 Msun BHs with rotation parameters of A~0.8 and tori of 0.03-0.3 Msun. Our nucleosynthesis analysis includes the dynamical (prompt) ejecta expelled during the CBM phase and the neutrino and viscously driven outflows of the relic BH-torus systems. While typically ~20-25% of the initial accretion-torus mass are lost by viscously driven outflows, neutrino-powered winds contribute at most another ~1%, but neutrino heating enhances the viscous ejecta significantly. Since BH-torus ejecta possess a wide distribution of electron fractions (0.1-0.6) and entropies, they produce heavy elements from A~80 up to the actinides, with relative contributions of A>130 nuclei being subdominant and sensitively dependent on BH and torus masses and the exact treatment of shear viscosity. The combined ejecta of CBM and BH-torus phases can reproduce the solar abundances amazingly well for A>90. Varying contributions of the torus ejecta might account for observed variations of lighter elements with 40<Z<56 relative to heavier ones, and a considerable reduction of the prompt ejecta compared to the torus ejecta, e.g. in highly asymmetric NS-BH mergers, might explain the composition of heavy-element deficient stars.

On the basis of an analysis of the ITER L-mode energy confinement database, two new scaling expressions for tokamak L-mode energy confinement are proposed, namely a power law scaling and an offset-linear scaling. The analysis indicates that the present multiplicity of scaling expressions for the energy confinement time τE in tokamaks (Goldston, Kaye, Odajima-Shimomura, Rebut-Lallia, etc.) is due both to the lack of variation of a key parameter combination in the database, fs = 0.32 R a−0.75 k0.5 ∼ A a0.25k0.5, and to variations in the dependence of τE on the physical parameters among the different tokamaks in the database. By combining multiples of fs and another factor, fq = 1.56 a2 kB/RIp = qeng/3.2, which partially reflects the tokamak to tokamak variation of the dependence of τE on q and therefore implicitly the dependence of τE on Ip and ne, the two proposed confinement scaling expressions can be transformed to forms very close to most of the common scaling expressions. To reduce the multiplicity of the scalings for energy confinement, the database must be improved by adding new data with significant variations in fs, and the physical reasons for the tokamak to tokamak variation of some of the dependences of the energy confinement time on tokamak parameters must be clarified.

A model describing film growth from hyperthermal (\ensuremath{\sim}1--${10}^{3}$ eV) species impinging on substrates is presented. The model involves a shallow subsurface implantation process called ``subplantation,'' energy loss, preferential displacement of atoms with low displacement energy ${\mathit{E}}_{\mathit{d}}$, leaving the high-${\mathit{E}}_{\mathit{d}}$ atoms intact, sputtering of substrate material, and inclusion of a new phase due to incorporation of a high density of interstitials in a host matrix. Epitaxial or preferred orientation may result from the angular dependence of the ${\mathit{E}}_{\mathit{d}}$ and the boundary conditions imposed by the host matrix, i.e., the ``mold'' effect. The discussion focuses on deposition of carbon diamondlike films, but examples of other systems, such as Si, Ge, and Ag, are provided as well. The model is supported by classical-ion-trajectory calculations and experimental data. The calculations probe the role of ion range, local concentration, backscattering coefficient, sputtering yield, and ion-induced damage in film evolution. The experimental data emphasize in situ surface-analysis studies of film evolution. The physical parameters of the deposition process that are treated are as follows: (i) nature of bombarding species (${\mathrm{C}}^{+}$ versus ${\mathrm{C}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{C}}^{\mathrm{\ensuremath{-}}}$ versus ${\mathrm{C}}_{2}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{C}}_{\mathit{n}}$${\mathrm{H}}_{\mathit{m}}^{+}$, ${\mathrm{Ar}}^{+}$, and ${\mathrm{H}}^{+}$), (ii) ion energy, (iii) type of substrate, and (iv) substrate temperature during deposition.

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvenic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfven eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfven eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfven eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions.

A self-contained introduction to magnetohydrodynamics (MHD), with emphasis on nonlinear processes. Chapters 2 to 4 outline the conventional aspects of MHD theory, magnetostatic equilibrium and linear stability theory, which form a natural basis for the topics in the subsequent chapters. The main part, chapters 5 to 7, presents nonlinear theory, starting with the evolutions and saturations of individual ideas and resistive instabilities, continuing with a detailed analysis of magnetic reconnection, and concluding with the most complex nonlinear behaviour, that of MHD turbulence. The last chapters describe three important applications of the theory: disruptive processes in tokamaks, MHD effects in reversed-field pinches, and solar flares. In the presentation the focus is more on physical mechanisms than on special formalisms. The book is essential reading for researchers and graduate students interested in MHD processes both in laboratory and in astrophysical plasmas.