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Lectures
The present page gives a short introduction of the lectures of the 12th ITER Internation School. For detailed the program, please refer to the Program page.
Monday, June 26
William Heidbrink (University of California, Irvine, USA): Introduction of Energetic Particle Physics
Super-thermal energetic particles (EP) are produced by RF heating, neutral-beam injection, fusion reactions, and (in the case of runaways) by parallel electric fields. Because guiding-center drifts are proportional to energy, the EP orbits are necessarily large. Orbits are described by conserved constants of motion that define topological boundaries for different orbit types. The EP distribution function is governed by the competition between sources, wave heating, collisions, and transport processes. Collisions and electric and magnetic field perturbations produced by instabilities alter particle orbits, causing the constants of motion to change. The effect of collisions on the distribution function is well understood. When considering EP transport, a distinction is made between field perturbations that resonate with an aspect of the orbital motion and those that do not. Resonance occurs when the wave phase returns to its initial value after an integer number of orbits. In contrast, in the case of non-resonant perturbations, orbital phase averaging reduces transport. In summary, large orbits are a blessing and a curse: For non-resonant modes, orbit-averaging reduces transport but, for resonant transport, large orbits facilitate jumps across topological boundaries and enhance the number of resonances.
Lars-Göran Eriksson (Chalmers University of Technology, Sweden): Sources of EPs (NBI, ICH, fusion): theory & experiments
Energetic particles plays a crucial role in magnetically confined fusion plasmas. The most important type is clearly alpha particles born in D-T fusion reactions with an energy of around 3.5 MeV. The confinement of these particles is essential for the sustainment of the fusion burn. However, a number of other sources of energetic particles are also important. For example, in order to obtain the temperatures needed for a burning fusion plasma, auxiliary heating of tokamak plasmas is normally necessary. Examples of such heating systems include Neutral Beam Injection, Ion Cyclotron Resonance Heating and Electron Cyclotron Resonance heating. The first two of these produces energetic ions whereas the third leads to energetic electrons. In addition to heating, the resulting energetic particles can affect plasmas in a number of ways, including by driving currents (e.g. for current profile control), influencing/driving plasma instabilities and drive plasma rotation. Furthermore, energetic electrons can arise in tokamak disruptions, where the strong electric field resulting from the abrupt plasma current decrease (the current quench) can generate so-called runaway electrons. Such electrons have the potential to create severe damage to plasma facing components.
The purpose of the lecture is to provide a review of the main sources of energetic particles in tokamak plasmas and the impact they have on the plasma itself. It will cover both theoretical aspects of energetic particle physics and experimental results showing the presence and influence on fusion plasmas of such particles. Because the field is vast, the emphasis will be on covering a few key aspects of energetic particles in tokamaks without resorting to excessive mathematical detail.
Sergei Sharapov (CCFE, UK): EP instabilities: Linear physics near threshold
Energetic particle-driven (EP) modes are often observed in present-day tokamak experiments and they are of major importance for the next step burning plasmas such as ITER and DEMO. Alpha particles born in deuterium-tritium fusion at energy 3.5 MeV, as well as energetic ions from neutral beam injection (NBI) and ion cyclotron resonance heating (ICRH) in the MeV energy range will have all super-Alfvénic velocities and can resonate with Alfvén waves in ITER. The fundamental issues associated with the super-Alfvénic energy range of fusion-born alpha-particles and ions used in auxiliary heating are: what is the hierarchy of EP instabilities, and what transport of energetic particles they may cause beyond the neo-classical. This talk will review the main EP instabilities, from “fishbones” at rather low frequency range of tens kHz, to Toroidal Alfvén Eigenmodes (TAEs) in the range of 150 – 250 kHz, and to ion cyclotron instabilities in the frequency range of tens MHz. Free energy sources for such instabilities will be reviewed, and theory of TAEs will be presented in detail as an example of a wider class of the “gap” modes existing within the frequency gaps in Alfvén continuum due to plasma geometry. Soft and hard regimes of EP instabilities will be considered in the near-threshold approach satisfying the ordering |γL-γd|<< γL, γd, where γL and γd are linear growth and damping rates of the modes. The use of EP instabilities for so-called MHD spectroscopy on present-day tokamaks will be demonstrated then allowing solution of inverse problems of obtaining information about the plasma from the spectrum of EP modes excited in the plasma. An extrapolation of EP characteristics towards the next step burning plasma experiment will be discussed.
Tuesday, June 27
Mirko Salewski (Technical University of Denmark): Energetic particle diagnostics
Energetic particle diagnostics are crucial to hold up theory against experimental data. We will discuss the most widespread energetic particle diagnostics presently installed on magnetic confinement devices around the world, including neutron and gamma-ray spectroscopy, fast-ion D-alpha spectroscopy, neutral particle analyzers and imaging neutral particle analyzers, collective Thomson scattering, neutron and gamma-ray cameras, charged fusion product diagnostics, ion cyclotron emission spectroscopy and fast-ion loss detectors. The focus will be on physics principles of the diagnostics, rather than technology and hardware, with special attention to those diagnostics foreseen for ITER.
Experimental data from different fast-ion detectors are routinely combined to infer the spatial 2D distribution using tomography, for example to determine the spatial Alfven eigenmode structure using soft x-ray diagnostic or to determine the 2D spatial profile of neutron and gamma-ray emission using neutron and gamma-ray cameras. We will discuss mathematical principles of fast-ion tomography, highlighting the prior information used to measure these 2D images from the sparse data obtained in magnetic confinement plasma experiments. Finally, ultimately we are interested in the fast-ion phase-space distribution function in experiments. Emerging tomography techniques in phase-space allow the measurement of 2D velocity distribution functions and even of 3D phase-space distribution functions and can possibly be extended up to 5D phase-space. We will use key ideas relying on prior information such as the drift orbits and the physics of collisions in plasmas.
Sergei Sharapov (UKAEA, UK): Control of EP-related instabilities, e.g., sawteeth, AE
Abstract to be provided.
Wednesday, June 28
Michael Van Zeeland (General Atomics, USA): Diagnostics associtated with redistribution of confined EPs and the causes
Fast ions created in fusion reactions, neutral beam injection and RF heating are characterized by significantly larger energies than the bulk ion temperature and an often complicated and highly anisotropic distribution function. Through resonances with the periodic motion of fast ions, energy can be efficiently exchanged with an array of instabilities including Alfven eigenmodes and fishbones, leading to instability growth and eventual transport of the driving fast ions. Much has been learned about this process in part due to several innovative diagnostic techniques that probe not only details of fast ion phase space but also the modes responsible for the transport. Confined fast ion diagnostics take advantage of many different processes including charge-exchange reactions, nuclear reactions, wave scattering and even the fast ion contribution to equilibrium pressure. Each approach has a unique diagnostic weight function and phase space sensitivity which is key to understanding and validating models that capture the details of wave-particle interaction physics, something that often happens in localized regions of phase space. Tomographic inversion of data from multiple fast ion diagnostics has also been demonstrated and shows potential for reconstructing the local fast ion distribution function and impact of instabilities. Measurements of the waves are performed using diagnostics that probe the instability-induced perturbed density, temperature and magnetic field. Over the last decade, these measurements have moved from individual point measurements to beautiful 2D images of the mode structure and play a crucial role in the investigation of fast ion transport. This talk reviews key diagnostics of confined fast ions and energetic particle driven instabilities, gives examples of direct measurements of the impact of the instabilities on the confined fast ion profile, and discusses directions for future work.
*Supported by the US DOE under DE-FC02-04ER54698
Yasushi Todo (NIFS, Japan): Kinetic-MHD hybrid simulations of energetic-particle driven instabilities
Kinetic-magnetohydrodynamics (MHD) hybrid simulation is a combination of gyrokinetic particle-in-cell simulation for energetic particles and MHD simulation for the bulk plasma. The kinetic-MHD hybrid simulation is a useful tool for the understanding and the prediction of energetic-particle driven instabilities. The physical model and the recent progress of the kinetic-MHD hybrid simulations are presented with a focus on the validation studies of DIII-D, JT-60U, and LHD. In addition to the recent progress of the hybrid simulations, basic physics of the interaction between Alfvén eigenmodes (AEs) and energetic particles, for example, resonance condition, a conserved variable during the wave-particle interaction, wave-particle trapping, higher-order resonance, and resonance overlap is explained. It is demonstrated with surface of section plots (Poincaré plots) that the significant transport of energetic particles may take place due to both the resonance overlap of the multiple AEs and the overlap of higher-order resonances with a single AE. The nonlinear MHD effects on AE evolution are discussed including the generation of zonal flow.
Eric D. Fredrickson (Princeton University, PPPL, USA): Experimental observations of EP transport and loss (e.g., AE, 3D-fields, ripple, NTMs...)
Fast ion losses in ideal devices are typically easily predicted and negligible. However, the perfect magnetic geometries envisioned in conceptual machines are seldom achieved in practice. Necessary compromises in the design of coils, unavoidable errors in construction, and imperfect materials result in perturbations (error fields, ripple) to the idealized magnetic geometry. Further, instabilities driven by the inherent non-equilibrium nature of the thermal plasma (tearing modes, sawteeth, turbulence, disruptions, ELMs) and instabilities driven by the non-equilibrium fast ion populations themselves can all interact synergistically with each other and with field errors to result in significant losses of fast ions. Of particular concern for ITER, heating of the plasma with waves in the ion-cyclotron range of frequencies has also been seen to enhance losses. We describe here experiments which have documented the reduction of fast ion populations either by directly measuring the lost fast-ion flux, or by measuring the change in the confined fast ion population. The major concern is developing the ability to predict losses of fusion alphas in future ignited plasma devices such as ITER. Current and past experiments have studied the losses of D-D fusion products, beam ions, RF-generated ion “tails”, and some limited data on D- T fusion alphas (JET and TFTR). While alpha-driven TAE were seen on TFTR, their amplitude was low and the losses expected from those modes are presumed to be small. Measured losses have largely been found to be consistent with theoretical predictions (based, for example, on experimental estimates of mode amplitudes).
Thursday, June 29
Manuel Garcia-Munoz (University of Sevilla, Spain): Diagnosing the loss of EPs and causes
Supra-thermal (fast) ions must be kept well-confined until they slow down through Coulomb collisions to the thermal plasma. Fast-ions are, however, subject to transport by a large spectrum of electromagnetic perturbations due to their high energies and long mean free paths and slowing down times. While in quiescent axisymmetric tokamak, fast-ions are very well confined in tokamaks, MHD fluctuations can cause intense and sometimes localised losses that, if not abated could damage the integrity of the machine vacuum vessel. In the presence of MHD fluctuations, the nature of the fast-ion transport and loss mechanism is given by the wave-particle interaction. A net wave-particle energy and momentum exchange, i.e. transport and loss, typically happens if a wave-particle resonance condition is fulfilled. In tokamaks, wave-particle resonances are given by the particle orbital frequencies and wave properties, thus, to understand and identify the particle transport and loss mechanisms, the particle orbit topology, wave nature and time scales must be known. In this lecture, the requirements for a Fast-Ion Loss Detector will be presented together with the design and performance of the most common detectors in present devices. The main components required to construct a realistic synthetic detector within the FILDSIM code will be discussed, and applications for the design of the FILD system for different devices, including ITER will be presented. Tomographic reconstructions of the measured signals using the FILDSIM code will be presented and discussed.
Maxime Lesur (Institut Jean Lamour, Lorraine University, France): EP instabilities: nonlinear effects and consequences
Energetic Particles (EPs) drive macroscopic MHD modes, which transport EPs, and couple with background turbulence. They impact fuelling and the wall integrity, and ultimately the efficiency of a fusion reactor. Understanding the nonlinear evolution of EP-driven modes is crucial to predict and control these impacts. In a toroidal device, the structure, linear frequency, and linear growth rate of an EP-driven mode, which are determined by 3D calculations, evolve on a slow time scale of mean field evolution (∼100 ms). In contrast, nonlinear wave-particle interactions, which determine the saturated state in the single-mode limit, occur on a fast time scale (∼1 ms) and can be treated perturbatively by a 1D model: the Berk-Breizman model.
This model is a generalization of the simple bump-on-tail Vlasov-Poisson model for a single mode, with the addition of a prescribed damping of the wave energy, and a collision operator. It provides a basis for estimating the nonlinear saturation amplitude, and the qualitative nonlinear behaviour of an isolated EP-driven mode.
The apparent simplicity of the corresponding equation system hides surprisingly rich physics. In the unstable case, trapping of resonant particles significantly modifies the distribution function and an island structure appears in phase-space. The following nonlinear saturation features bifurcations between three kinds of behaviours. In particular, chaotic solutions can display significant shifting of the mode frequency (chirping), as holes and clumps are formed in the distribution function. This can lead to ballistic transport of EPs, and can drive subcritical instabilities. A subcritical instability is a nonlinear instability that occurs even as the system is linearly stable, but with a threshold in the amplitude of initial perturbations. Subcritical instabilities stay dormant until they are brought over their threshold by some interaction, drive, forcing, or even thermal noise. Investigating their onset conditions requires nonlinear calculations. They are of great interest because they open a new channel for tapping free energy and can have essential impacts on EPs.
Mario Podestà (Princeton University, PPPL, USA): Reduced models of EPs transport for scenario modelling
Energetic Particle (EP) transport and loss play a crucial role in scenario modeling, optimization and predictions for burning plasmas. Integrated simulations need to include models for EP transport, possibly at different levels of physics fidelity, to enable whole-discharge simulations with reasonable computation times. The main concepts of EP transport are first reviewed, along with an overview of the modeling frameworks presently available to describe EP physics in integrated simulations. EP models are introduced following a hierarchy of complexity, from simple (ad-hoc) models to phase-space resolved models, including models based on the “critical gradient” and “quasi-linear” approaches. The main assumptions, applicability range and limitations of each model are briefly discussed. Next, the importance of EP transport in integrated tokamak simulations for scenario modeling discussed with examples from existing tokamaks. A key point in the discussion, connecting to other specific EP-related topics (e.g. diagnostics), is the validation of EP transport models given available experimental data and limitations in the EP transport models, in view of the models’ application and projection to future scenarios such as burning plasmas. Finally, the integration of reduced EP transport models into time-dependent simulations for scenario prediction and optimization is discussed, with emphasis on open issues for projections from present-day tokamaks to ITER and future fusion reactors.
* Work supported by the U.S. DOE under contract number DE-AC02-09CH11466
Antti Snicker (AALTO University, Finland): Modelling of transport and loss of EPs due to low-frequency modes and 3D fields
In this lecture, we will go through the basics of the Monte Carlo methods used for fast particle simulations, in particular for 3D. Examples are given on what kind of problems Monte Carlo methods can solve. The bulk of the lecture discusses various non-axisymmetric (magnetic) perturbations that can exist in tokamak plasmas and how they affect the fast ion distribution and losses. In particular, we learn that even with static magnetic perturbations the resonant transport is the main channel for transport, together with the diffusive transport. A short overview of a role of low-frequency modes for fast particle transport is given.
Friday, June 30
Robert Granetz (MIT, USA): Physics of observations of runaway electrons
This lecture will present the physics of runaway electrons (REs) based on experiments and measurements. A sampling of topics that will be included
are:
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- REs in different phases of a discharge: startup, flattop, disruption
- survey of RE observations on several tokamaks (i.e. disruption damage)
- ITPA joint study of E/Ecrit during flattop
- RE energy loss mechanisms (e.g. synchrotron emission, etc)
- ITPA joint study of startup REs
- mitigation of disruption-triggered REs, including active intervention and proposed passive methods
Tünde Fülöp (Chalmers University of Technology, Sweden): Modelling of runaway electrons
We discuss the characteristics and consequences of runaway electron generation, as well as possible mitigation strategies in future fusion devices. We describe recently developed numerical tools for self-consistently simulating the evolution of temperature, electric field, and impurity densities, along with the generation and transport of runaway electrons in tokamak plasma initiation and termination scenarios. We show examples of modelling runaway dynamics in present-day devices, including how synthetic diagnostics can be used for benchmarking theoretical models and probing runaway dynamics.
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