Turbulent Transport In Magnetized Plasmas

Wendell Horton

• Publisher: WSPC
• Year: 2012
• ISBN:
  9789814483889
• Topic: Ciencias físicas
• Subtopic: Física nuclear

The book explains how magnetized plasmas self-organize in states of electromagnetic turbulence that transports particles and energy out of the core plasma faster than anticipated by the fusion scientists designing magnetic confinement systems in the 20th century. It describes theory, experiments and simulations in a unified and up-to-date presentation of the issues of achieving nuclear fusion power.

Contents:

• Basic Concepts and Historical Background
• Alfvén and Drift Waves in Plasmas
• Mechanisms for Drift Waves
• Two-Component Magnetohydrodynamics
• Laboratory Experiments for Drift Waves
• Magnetohydrodynamics and Magnetic Confinement Geometries
• Laboratory Plasma Experiments for Waves and Transport
• Turbulence Theory for Drift and Alfvén Waves
• Impurity Transport Studies
• Coherent Structures in Plasmas
• Fluctuating Magnetic Fields and Chaotic Orbits
• Toroidal Confinement Systems
• Temperature Gradient Driven Instabilities
• Electron Temperature Gradient Driven Turbulence
• Magnetic Reconnection Instabilities
• Ignition Physics in Multiscale Plasma Turbulence
• Rotational Instabilities
• Transport Simulations with Multiscale Codes for Internal Transport Barrier Formation
• Gyrokinetic Simulations of Drift Wave Turbulence

Readership: Graduate students, researchers and academics interested in confinement of plasmas, instabilities, transport and turbulence in plasmas.

Chapter 1

Basic Concepts and Historical Background

Plasmas are created by heating gases through the absorption of ionizing radiation in the visible through the ultraviolet part of the electromagnetic spectrum and through collisional ionization of molecules with energetic electrons. The absorption and heating processes are typically localized in space so that large spatial gradients occur in the plasma density, temperature and other characterizing parameters. Due to the high electrical conductivity of ionized gases, large electrical currents typically flow and produce substantial self-generated magnetic fields in the plasma. In other plasmas strong magnetic fields exist, produced by external currents such as those flowing in the cores of the planets or those in the conducting coils designed to produce plasma confinement in laboratory machines. Thus, the focus of this book is on the transport processes in magnetized plasmas.

Due to the 40 years of intense international pursuit of the laboratory confinement of high temperature (T > 10⁷ K) hydrogenic plasmas for the purpose of obtaining controlled nuclear fusion, there is an enormous resource to be found in the scientific literature on the experiments, the theory, and now, the numerical simulations of the plasma transport processes. While there are some books, most notably those by Mikhailovskii (1992), Wakatani (1998), Weiland (1999), and Wesson (2004), developing the subject, and numerous review articles on the transport problem, there is need for a book suitable for the first stages of transport research. Thus, in this work we attempt to provide a general presentation starting from elementary considerations, while including the most recent results that one may view as firmly established in the understanding of the nonlinear transport processes in ionized gases. The collisional transport produced by the binary Coulomb interactions between the charges in a plasma is a well-developed subject treated in the works of Balescu (1988) and Helander and Sigmar (2002). When the plasma temperature is high and density is low, the distance between these nearby encounters is long and the orbits of the particles between the collisions are complicated. The mean distance between Coulomb collision is called the mean-free-path and complex orbits have names like “banana” and “potato” particle orbits [Helander and Sigmar (2002)]. In general, the turbulent transport greatly exceeds the collisional transport in tokamaks. The exceptions are discussed in Chapter 14 of Helander and Sigmar (2002).

A clear and reliable way to understand transport in fluids and plasmas is to follow the evolution of test particles, or a passive field, typically called a dye or trace impurity, in the system. Test particle transport theory, simulations, and experiments are emphasized here, perhaps more than is traditional in the existing plasma literature. The limitations of the test particle method are serious, however, which accounts for their being less well developed in earlier works on plasma transport. The limitations arise because the motion of the charged particles modifies the electric charge and current distributions in the plasma. These changes in the electric charge density ρ_q(x, t) and current density j(x, t) in turn modify the electromagnetic fields E(x, t) and B(x, t) in the plasma. Thus, the orbits of the particles are themselves changed again due to the collective effect of the accumulated charges and currents from the fields, due to their motions in these same fields. This problem is known as the self-consistent field problem. The self-consistent field problem forms the essence of the theoretical and simulation modeling of plasma dynamics. It is this circular sequence of interactions of the motion of the charged particles in the self-consistent electromagnetic fields that contains both the externally-applied fields and those generated by the particle motions that determine the actual transport of the plasma. Thus, the large body of works on plasma transport theory and modeling have their complexity rooted in the problem of determining, as clearly as possible, the solutions of the orbital equations with the self-consistent plasma electric and magnetic fields. Obviously, many different theoretical approaches can be and have been made to extract key transport information from this problem. Often, the approach is set by a priori assumptions about the nature of the fields; coherent waves or vortices, weak turbulent fields or states of strong turbulence, for example.

While the most practical information desired may be contained in turbulent transport coefficients such as the particle diffusivity D and the electron and ion thermal diffusivities

and

respectively, there are important processes where no such simple diffusivities exist. In such regimes there can be bursty in time large transport events, the dominance of coherent structures such as streamers, zonal flows, the existence of long flights of the particles through small gaps in transport barriers, and other exotic transport processes.

1.1 Space and Astrophysics

Early plasma physics research began in about 1900 when scientists puzzled over the high altitude lights in the northern sky and the systematic deflections of the magnetic compass needle in careful measurements taken across the northern latitudes of the Scandinavian countries. Birkeland, whose name is attached to the large plasma currents known to flow into and out of the northern ionosphere from the magnetosphere, pioneered this research by building models of the magnetosphere in the laboratory, in an effort to reproduce the auroral observations. The properties of the Birkeland plasma currents are now measured with spacecraft that are equipped with high-resolution particle and field instruments [Kivelson and Russell (1995)]. Birkeland set up a laboratory magnetic confinement experiment and reproduced the effect of the auroral rings, but uncovered many more problems of complicated physics than could be answered with the knowledge and equipment of that era. Alfvén and Falthammer, along with Stoermer, pursued these complex issues and realized that these were generic problems for the solar system and what they called the cosmos in their subsequent books that give many of the basic plasma physics concepts used today. Two of these concepts developed by Alfvén that are used extensively in the drift wave transport of plasmas are the low frequency electromagnetic Alfvén plasma waves and the guiding center drift of the guiding centers for describing the trajectories of charged particles in the confining magnetic fields in plasmas. For these and other important discoveries, Hannes Alfvén received the Nobel Prize in 1970 in plasma physics.

The plasma physics of the solar corona [Aschwanden (2006)] has similarities to that of the toroidally confined in tokamaks. The flux ropes observed with high resolu...