F. S. Zaitsev

Analyses of substantially different plasma current densities and safety factors reconstructed from magnetic diagnostics data

The problem of plasma current density and safety factor reconstruction using magnetic field measurements is considered. In the traditional formulation, the problem is strongly ill-posed. In particular, substantially different current densities and safety factors can be equally well attributed to the same set of measurements, given their experimental errors. In other words, the problem can be strongly unstable with respect to the input data. Different constraints are used in practice to make the problem more stable. This paper presents an accurate mathematical formulation of the inverse problem and its variants. A numerical algorithm is provided, which permits us to study the stability with respect to variations in the input data, to find all substantially different solutions, or to prove their absence, and to determine the confidence intervals of the reconstructions. The proposed method also allows establishing the maximum error for a given diagnostic (additional constraint), below which the diagnostic efficiently extracts one solution among several substantially different ones. Examples of very different current density and safety factor reconstructions for measurements with finite accuracy are presented for the original formulation of the inverse problem. Cases of MAST, JET and ITER-like plasmas are considered. It is shown that including the motional Stark effect (MSE) measurements as a constraint, provided the accuracy of MSE measurements is sufficient, allows identifying one solution among several very different ones, obtained without such a constraint. The maximum MSE diagnostics error for efficient identification of this solution is estimated for JET. The approach of this paper can be used for a wide range of ill-posed problems in physics and can help in selecting additional conditions, which can identify the most likely solution among several.

The numerical solution of the self-consistent evolution of plasma equilibria

An advanced mathematical model is developed for a self-consistent description of the evolution of free boundary toroidal plasmas. New numerical algorithms for the solution of the appropriate non-linear system of integro-differential equations are presented. An unusual feature of the system is that time derivatives enter only one of the equations. The model and algorithms are implemented in the SCoPE code. Examples of numerical modelling for tokamak plasmas are given.

Perturbations to deuterium and tritium distributions caused by close collisions with high-energy alpha-particles

The effect of nuclear elastic scattering (NES) of deuterium and tritium in close collisions with hot alpha-particles is considered. Calculations of the perturbed deuterium and tritium distribution functions are based on numerical solution of the three-dimensional trajectory averaged kinetic equation. The equation includes the full drift trajectory averaged Coulomb collision operator and the NES particle source. Modelling is carried out for parameters relevant to JET DT experiments and results of calculations are compared with typical measurements of NES deuterons. In addition, we evaluate the maximum achievable NES perturbation to the DT plasma. Finally, a potential opportunity for estimation of alpha-particle pitch-angle anisotropy, using measurements of NES perturbed deuterium or tritium distributions is discussed. We show that it is important to account for NES effects in order to accurately diagnose the alpha-particle distribution.

Automating Computations in the Virtual Tokamak Software System

We describe the concept, functional capabilities, graphic user interface (GUI), and operating technique of a specialized system for distributing the computational burden encountered in solving typical problems of controlled thermonuclear fusion. The system is employed in the Virtual Tokamak simulation modeling complex to automate the distribution of computing on a network of computers, making it possible to dramatically improve the productivity of a researcher’s work. The system is useful in various applications that require massive multivariate calculations using one or more application codes, and for supporting websites that provide computing services using locally stored science-intensive application software.

A New Method to Identify the Equilibria Compatible with the Measurements Using the Technique of the ε-Nets

In tokamaks, the problem of plasma current density and safety factor reconstruction, given the available measurements, can be strongly unstable with respect to the input data. Different constraints are used in practice to make the problem more stable. Traditionally, methods for equilibrium reconstruction search for one solution of the Grad-Shafranov equation with a set of constraints. However, the questions of the efficiency of a constraint in selecting a solution; the required accuracy of the measurements; the existence of very different solutions, which are compatible with the measurement errors; and the detailed assessment of the reconstruction confidence intervals are not addressed. This paper presents a numerical algorithm, based on the ε-net technique, which provides answers to all these questions. Examples of application of the method to the analysis of ITER- and JET-like plasmas are given.

The ScopeShell graphic interface: Support for computational experiments and data visualization

We consider problems of the visualization and automation of routine tasks that arise in the process of a computational experiment. We describe ScopeShell, a state-of-the-art universal platform independent graphic interface for computational codes that includes data visualization and the monitoring of calculations on distributed computing systems. We describe the concept behind ScopeShell, along with the interface’s functionality and methods of application. The ScopeShell system is used to support computational experiments in the field of controlled thermonuclear fusion. The system considerably increases the efficiency of research requiring the application of voluminous computer codes.

The problem of evolution of toroidal plasma equilibria

Abstract This paper is devoted to an advanced mathematical model for a self-consistent description of the evolution of free boundary toroidal plasmas, with a description of numerical algorithms for the solution of the appropriate nonlinear system of integro-differential equations, and discussion of some results from the model.

The effect of sawtooth oscillations on the alpha particle distribution and energy balance in the ITER plasma

The mixing of toroidal plasma under the conditions of sawtooth oscillations is considered using the Kadomtsev model. A new mixing formula for the averaged distribution function of fast transit and trapped particles is proposed in the methodology of a kinetic equation averaged over drift trajectories. The proposed formula generalizes the known results for the case of non-circular magnetic surfaces, an arbitrary aspect ratio, and charged particle drift trajectories significantly deviating from the magnetic surfaces. The formula is applicable for a sufficiently wide class of instabilities. The 3D kinetic equation is numerically solved using the FPP- 3D computation code for parameters close to the ITER inductive scenario. The alpha particle distribution function and the power introduced by alpha particles in plasma when sawtooth oscillations occur are calculated. It is shown that such oscillations may change the energy input of a thermonuclear reaction in certain areas by several times.

The Sawtooth Oscillation Effect on Fast-Ion Energy Spectra in ITER Plasma and Neutral Particle Analyzer Measurements

ITER plasma with parameters close to those with the inductive scenario is considered. The distribution functions of fast ions of deuterium D and tritium T are calculated while taking into account the elastic nuclear collisions with alpha particles 4He using the code FPP-3D. The D and T energy spectra detected by the neutral-particle analyzer (NPA) are determined. The plasma mixing effect on these spectra during sawtooth oscillations is studied. It is shown that the NPA makes it possible to detect sawtooth plasma oscillations in ITER and determine the percentage composition of the D‒T mixture in it both with the presence of instabilities and without them. A conclusion is drawn on the prospects of using NPA data in automatic controllers of thermonuclear fuel isotopic composition control and plasma oscillation regulation in ITER.

Constructing hidden Markov models for processing plasma magnetic diagnostics

A new approach to analyzing and interpreting magnetic measurements is proposed, based on hidden Markov models. This approach enables us to reduce the amount of discharge data from tens of gigabytes to several kilobytes, and to find the probability of the transition between states in plasma discharge. It becomes possible to compare data from other diagnostics or video images to the characteristic magnetic states of plasma. The proposed method makes the comprehensive study of plasma dynamics much easier. The new technique can also be used to design navigation systems for large diagnostic databases.