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2011 | Buch

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Frontiers in Fusion Research

Physics and Fusion

verfasst von: Mitsuru Kikuchi

Verlag: Springer London

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik"

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Über dieses Buch

Frontiers in Fusion Research provides a systematic overview of the latest physical principles of fusion and plasma confinement. It is primarily devoted to the principle of magnetic plasma confinement, that has been systematized through 50 years of fusion research. Frontiers in Fusion Research begins with an introduction to the study of plasma, discussing the astronomical birth of hydrogen energy and the beginnings of human attempts to harness the Sun’s energy for use on Earth. It moves on to chapters that cover a variety of topics such as: • charged particle motion, • plasma kinetic theory, • wave dynamics, • force equilibrium, and • plasma turbulence. The final part of the book describes the characteristics of fusion as a source of energy and examines the current status of this particular field of research. Anyone with a grasp of basic quantum and analytical mechanics, especially physicists and researchers from a range of different backgrounds, may find Frontiers in Fusion Research an interesting and informative guide to the physics of magnetic confinement.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Sun on Earth: Endless Energy from Hydrogen

Abstract

The Big Bang created the universe 13.7 billion years ago. The universe is brimming with hydrogen, and the beautiful night sky is formed by hydrogen fusion. Here, the fusion is a nuclear reaction creating nuclei such as helium through reactions between light nuclei such as hydrogen.

The Sun is hot dense plasma confined by the gravity of its huge mass, bringing huge energy to the planetary system in the form of solar light produced by massive fusion reactions. All life on our planet depends on solar energy.

A large number of scientists in the latter half of the twentieth century challenged to the dream of creating a Sun on Earth to produce energy from fusion. To do this, we aimed to build ITER creating an energy-producing machine, a Sun on Earth, as well as helping to understand the physics.

A fusion reaction requires a temperature of a few hundred million degrees. Deuterium and tritium fuel take the “plasma state” – the fourth state of matter. Plasma exists in various forms around us. It is necessary to understand and control plasma to develop a usable form of fusion energy.

Mitsuru Kikuchi

Chapter 2. Hydrogen Fusion: Light Nuclei and Theory of Fusion Reactions

Abstract

Deuterium, tritium, neutron, and helium are the main players in the reaction (D + T → He + n + 17.6 MeV; see Figure 2.1) to realize the Sun on Earth. In the microworld of atoms and nuclei, particles exhibit wave characteristics, and nuclear properties and reaction mechanics are governed by the Schrödinger wave equation.

These players have interesting properties. An encounter between deuterium and tritium results in the formation of a compound nucleus through the tunnel effect at a fractional energy of 500 keV Coulomb barrier potential. The compound nucleus has a high reaction probability near 80 keV due to the resonance phenomenon. In this way, nature gives humans a chance to use this reaction.

Mitsuru Kikuchi

Chapter 3. Confinement Bottle: Topology of Closed Magnetic Field and Force Equilibrium

Abstract

In the natural fusion reactor, the Sun, dense hot plasma is confined by a gravitational field. Characteristic of this force is that it is a central force field and acts in the direction of field line. For this reason, the confinement bottle has the topology of a sphere (Figure 3.1 (a)). In the man-made fusion reactor, high temperature plasma is confined by trapping charged particles with the Lorentz force in a magnetic field to sustain reaction in a small dimension of 100 millionth of that of the Sun. Characteristic of this force is that it acts in a direction perpendicular to the field line. For this reason, the confinement bottle has the topology of a torus (Figure 3.1 (b)). In this chapter, force equilibrium is treated to confine high temperature plasma in the topology of a torus. Practically, the magnetic field line dynamics is treated using the methodology of analytical mechanics and symmetry involved in the force equilibrium is discussed.

Mitsuru Kikuchi

Chapter 4. Charged Particle Motion: Lagrange–Hamilton Orbit Dynamics

Abstract

The motion of light and objects in nature follows an orbit in which the path integral of the “action” becomes extremal. Fermat’s well-known optics principle tells us that light draws an orbit such that the time required becomes minimum between fixed point A and B. For example, Snell’s law describing refraction of light in media with different refractive indexes can be derived from Fermat’s principle (Figure 4.1). Nature is governed beautifully by the variational principle.

The variational principle for the object motion is expressed by Hamilton’s principle. The complex charged particle motion, a combination of Larmor and drift motions in the confinement magnetic field, can be simplified using the above variational principle.

Mitsuru Kikuchi

Chapter 5. Plasma Kinetic Theory: Collective Equation in Phase Space

Abstract

The motion of a large number of charged particles in plasma could be determined completely if the initial conditions are known since an individual particle follows Newton’s equations of motion. The flow of the probability distribution function of the system in 6N phase space consisting of the position and momentum of N particles shows incompressibility (Liouville theorem). This property leads to an important theorem of the isolated dynamical system “Poincare’s recurrence theorem,” which guarantees that the system will return to be arbitrarily close to the initial state. The kinetics equation represented by the Boltzmann equation is derived from reversible mechanics equations, but is often irreversible. In the Boltzmann equation, a statistical assumption “Stosszahl Ansatz” leads to a collision term exhibiting the arrow of time. Thus, there is a fundamental difference between the reversible dynamical equation and the kinetic equation.

In the kinetic equation for high temperature plasma, a strange phenomenon (called Landau damping) occurs where the oscillating electric field damps with time even when collisions are negligible through the mechanismof “phase mixing” in the velocity space, since the operator of the kinetic equation ν ∙ ∂f / ∂ x has a continuous spectrum. In this chapter, the basics of plasma kinetic equations including Coulomb collisions, the drift kinetic equation, and the gyro kinetic equations are introduced based on the orbit theories described in Chapter 4.

Mitsuru Kikuchi

Chapter 6. Magnetohydrodynamic Stability: Energy Principle, Flow, and Dissipation

Abstract

It is not easy to discuss general plasma stability since plasma is a nonlinear and dissipative medium. In this chapter, after a survey of the general stability, linear stability, in particular, ideal magnetohydrodynamic stability with an Hermitian (self-adjoint) linear operator is discussed. Then, nonlinear tearing forming a magnetic island by magnetic reconnection caused by the dissipation, and the stability of plasma flow with a non-Hermitian operator are outlined.

Mitsuru Kikuchi

Chapter 7. Wave Dynamics: Propagation and Resonance in Inhomogeneous Plasma

Abstract

Plasma is a dispersive medium and wave propagation can be described by the Eikonal equation derived by Landau.Wave energy is also defined. If there is no dissipation in the plasma, Lagrange–Hamilton formulation is applicable and the conservation law is obtained. The zero approximation as the dispersive medium is the dissipationless cold plasma approximation ignoring the thermal effect. Cutoff and resonance occurs in this approximation.

The wave propagation in non-uniform plasma is important in confined plasma and energy absorption occurs in the resonance layer. The drift wave appears universally in the confined plasma and is unstable above the critical temperature gradient, producing turbulence through wave–wave interactions.

Mitsuru Kikuchi

Chapter 8. Collisional Transport: Neoclassical Transport in a Closed Magnetic Configuration

Abstract

In high temperature confined plasma, the mean free path of the Coulomb collision becomes much longer than the geometric (torus) dimensions, and this is called a “collisionless regime.” In this case, the particles are categorized into particles trapped by a magnetic mirror and the particles not trapped by the magnetic mirror. The difference in these particle orbits produces distortion of the velocity distribution function and deviates from the Maxwell distribution.

This will affect the physical properties of the plasma. The thermal force produced by the trapped particle operates on untrapped particles to reduce the electrical conductivity or to produce a plasma current (bootstrap current), or to enhance the thermal diffusion across the magnetic field. They are collectively called neoclassical transport.

Mitsuru Kikuchi

Chapter 9. Turbulence in the Plasma: Self-organized Criticality and Its Local Breakdown

Abstract

Turbulent transport is at the frontier of plasma confinement research and is still under development. Here, the basic concepts of the dynamical system are introduced as a useful fundamental discipline. Thermal diffusion of the low confinement state can be explained by the self-organized criticality examined by complexity science and the transport barrier is formed by the local breakdown of self-organized criticality when a turbulent cell is torn by the flow shear.

Mitsuru Kikuchi

Chapter 10. Towards the Realization of Fusion Energy

Abstract

In this chapter, energy research and development in terms of fusion is overviewed, including energy and environment issues, progress of plasma confinement in the three major areas of fusion research, namely tokamak and helical by magnetic confinement, and laser fusion by inertial confinement. The experimental reactor ITER is aiming at DT fusion energy production and its control via the tokamak concept is described. A the broader approach is supplementing ITER towards DEMO. The possible role of fusion is also considered in terms of transforming the energy supply and demand structure with the goal of reducing carbon dioxide emissions during this century.

Mitsuru Kikuchi

Backmatter

Titel: Frontiers in Fusion Research
verfasst von: Mitsuru Kikuchi
Verlag: Springer London
Electronic ISBN: 978-1-84996-411-1
Print ISBN: 978-1-84996-410-4
DOI: https://doi.org/10.1007/978-1-84996-411-1