Electromagnetic Waves for Thermonuclear Fusion Research

The following sections are included:

• DEDICATION
• PREFACE
• ABOUT THE AUTHOR
• CONTENTS

The target of research on controlled thermonuclear fusion (CTF) is the conundrum of how to find a new source of energy capable of satisfying the needs of a growing world population without destroying the environment. The goal is to control the large amount of energy that is released when two light atomic nuclei fuse to form a heavier one.

In this book, the plasma theory behind some of the most important diagnostics used in thermonuclear fusion research on magnetically confined plasmas will be presented. Since most of these tools have been developed for diagnosing tokamak plasmas, we will often use examples taken from tokamak experiments for illustrating the problem under discussion.

In this chapter, the state of the art of CTF Research is briefly summarized together with a description of the main feature of the magnetic configuration of tokamaks.

In most applications of electromagnetic waves to plasma diagnostics, it is sufficient to consider waves propagating in cold plasmas with frequency much larger than the ion cyclotron frequency, i.e., neglecting the ion dynamics. In this chapter, we will review the theory of propagation of these waves in homogeneous plasmas.

In laboratory experiments, one deals with confined plasmas that — by definition — are not homogeneous media. In this chapter, we first review the standard approximation of geometrical optics for wave propagation in inhomogeneous plasmas, where the wave is viewed as composed of independent rays, each propagating along a trajectory where the local dispersion relation is satisfied everywhere

This approximation provides a simple and elegant technique for accounting refractive effects in non-homogeneous plasmas, and plays an important role in the interpretation of measurements using electromagnetic waves. However, just because of the independence of rays, this approximation may lead to non-physical results, such as the focusing of the wave on a single point. This is obviously due to the fact that diffraction is not included in the geometrical approximation. In the second part of this chapter, we discuss a refinement of the theory of geometrical optics including lowest-order diffractive effects.

As we have seen in Chapter 2, the propagation of electromagnetic waves in plasmas has a strong dependence on both density and magnetic field. This is why measurements of the plasma refractive index have found extensive use in magnetic fusion research and are expected to play a role in future burning plasma experiments. In this chapter, we shall discuss some of these applications.

As already mentioned in Chapter 1, particle and heat losses in magnetically confined plasmas exceed by several orders of magnitude the predictions of classical collisional diffusion. According to plasma theory [1–3], this is caused by a short-scale turbulence originating from a variety of collective modes which are driven unstable by the inevitable inhomogeneity of confined plasmas — from the ion temperature gradient mode (ITG) and the trapped electron mode (TEM) with the scale of the ion Larmor radius, to the electron temperature gradient mode (ETG) with the scale of the electron Larmor radius. In typical magnetized plasmas of fusion research, we expect the wavelength and frequency of these fluctuations to be in the range of a few centimeters and hundreds of kHz, respectively…

The scattering cross-section that we derived in the previous chapter was the result of the hidden assumption that the plasma reacted to the probing wave as a fluid rather than a collection of random particles. In other words, we assumed that the scattered fields of individual electrons were correlated, and thus the average of the square of their vector sum was much larger than the average sum of their square. As a result we got a cross-section scaling like the square of the amplitude of electrons fluctuations. This is why this type of scattering goes under the name of collective scattering of electromagnetic waves. In this chapter we will deal with the opposite case — non-collective scattering — where the probing wave samples the electrons on a scale length where they appear free. From plasma theory we know that this would occur when the wavelength of fluctuations we try to detect is smaller than the electron Debye length , since no collective oscillations can exist with wavelengths appreciably shorter than λ _De [1], i.e., when

Density measurements play an essential role in the study and operation of magnetically confined plasmas. In existing large devices, such as tokamaks, the canonical tools for the measurement of the electron density are laser multichannel interferometry (Chapter 4) and Thomson scattering (Chapter 6), two of the most reliable methods in thermonuclear fusion research. Unfortunately, these are also two of the most demanding techniques for plasma accessibility, which ironically is a problem that seems to escalate with the plasma size. Indeed, plasma accessibility will become extremely difficult in a fusion reactor, where only the simplest diagnostics will survive…

In the previous chapter we have seen how relativistic effects on both the Hermitian and anti-Hermitian components of the dielectric tensor have profound effects on reflectometry. For this reason, and also in preparation for the subject of the next chapter, here we will review the relativistic theory of wave propagation in a collisionless and uniform plasma imbedded in a constant and homogeneous magnetic field. We will consider waves in the electron cyclotron range of frequencies for which ions can be treated as a static background, providing charge neutrality to the plasma equilibrium.

The measurement of plasma emission near harmonics of the electron cyclotron frequency is a ubiquitous diagnostic of electron temperature in present magnetically confined plasma experiments, and will certainly continue to play a major role in the next generation of fusion devices. It is based on the fact that, as we have seen in the previous chapter, a hot plasma imbedded in a magnetic field is a good absorber of electron cyclotron waves and thus, because of the Kirchhoff's law [1], it is also a good emitter of the same waves. Under certain conditions, the intensity of the emission is directly related to the electron temperature by the Planck law. Since the magnetic field of toroidal plasmas is not homogeneous, the electron cyclotron emission (ECE) is a function of position and therefore its measurement can provide a localized value of plasma temperature. In addition, the excellent temporal resolution of the state-of-the-art radiometers allows the detection of temperature fluctuations from both large and small-scale turbulent phenomena. In this chapter, we will review the physics of ECE measurements.

The following section is included:

• INDEX