An Introduction To The Theory Of Plasma Turbulence – Tsytovich

In this post, we will see the book An Introduction To The Theory Of Plasma Turbulence
by V. N. Tsytovich.

About the book

This book is based upon lectures given by Professor Tsytovich at Culham Laboratory. The preceding text can only represent the present state of the development of the theory of plasma turbulence. The author has tried to follow the logic, but not the history of this field and, therefore, the references are very fragmented and not by any means complete. The essential physical statements that the author wants to emphasise finally are:
  1. The plasma properties in the turbulent region are mostly non-linear. This raises the possibility of universal plasma properties like a universal spectrum that can be independent of the type of instability.

  2. Nevertheless, the turbulence is often weak: W/nT << 1, and when describing the properties of the turbulent oscillation interactions it is not possible to expand the non-linear interactions in terms of the turbulent energy. The elementary excitations such as plasmons and “dressed” particles have thus a finite lifetime which is connected with their non­-linear interactions.

  3. The small low-frequency perturbations in a turbulent plasma have quite a different nature because of the frequent turbulent collisions, and the dielectric constant that describes such perturbations cannot be expanded in terms of the turbulent energy.

  4. The development of a turbulent state is very probable for a plasma as a result of the fact that the energy applied has a tendency to disperse to the greatest possible degree of freedom. Innumerable numbers of different plasma instabilities can bring the plasma to a turbulent state. The plasmas in astrophysical conditions must, therefore, often be turbulent. This can lead to a way of explaining cosmic-ray origins with a universal power-type spectrum.

  5. The development of plasma turbulence can occur as a result of development, firstly, of one or a small number of collective modes, with a subsequent spread of the energy to other modes by non-linear inter­actions as well as by the excitation of many modes at the first stage. For the case of the excitation of one mode, the first stage is not turbulent and the turbulence develops as the energy is spread, if the system is ergodic. The plasma collective motions seem to be the best test for an investigation of the general problems of the development of the random­isation process, as well as of the general problems of the possibility of a statistical description of a system.

The book was translated from Russian and was published in  1972.

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You can get the book here.

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1. Comparison of plasma and liquid turbulence 1
2. General Problems of the Theory of Plasma Turbulence 14
3. The Balance Equation for a Turbulent Plasma 27
4. Turbulent Collisions and Resonance Broadening 44
5. The Spectrum and Correlation Functions of Ion-sound Turbulence 62
6. The Spectrum and Correlation Functions of Langmuir Turbulence 74
7. Electromagnetic Properties of a Turbulent Plasma 93
8. The Cosmic-ray Spectrum 105

Conclusions 128

References 130

Index 133

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