To this point of view this book, at least the first few chapters, may be used as a very good complement to other textbooks for plasma physics Masters students or even PhD beginners and engineers who are looking for some specialization in this domain. It should be noticed here, and this is highly appreciated, that in all cases the author starts by treating the full problem and then continues with a case-study of different, commonly accepted situations.

He then continues with charged-neutral interactions with special mention of charge transfer reactions.

## Transport Processes in Multicomponent Plasma - CRC Press Book

The cases of the Coulomb potential and shielded Coulomb potential are discussed for the description of interactions between charged particles. Last, but not the least, other types of interactions described by the Lennard-Jones and Born-Mayer potentials are also stated and discussed. This very methodical way of description is used in all chapters of this book-this is highly appreciated! This book fills a gap in the literature of this subject-to my knowledge, during the last years very few new studies have been published in the crucial domain of multicomponent plasmas.

However, the author systematically gives a critical comparison between the two methods; this is very useful for the reader who has to decide which one of these formalisms is convenient for him. Besides all the positive points stated in the above paragraphs, there are, ineluctably, some negative points: the text in this book is really very dense, only three to four figures are included for the full book. This may have an offputting effect on the reader. Fortunately, the organization in chapters and paragraphs is very clear and easy to follow.

Thus, after reading the first chapter which includes all necessary symbol conventions and notations the reader may go directly to the chapter which interests him. In my opinion, reading this book from the first to the last page is rather improbable!

Finally, a table summarizing the notations and symbols used in this book could be of great help for the user, but, unfortunately this is missing for this edition. This book is, for all the above reasons, a necessary complement to a plasma physicist's library. This site uses cookies. By continuing to use this site you agree to our use of cookies. To find out more, see our Privacy and Cookies policy. There are extensive investigations of the different physical processes in solar loops, both, observational and theoretical [1].

The transport processes in the solar loops are relatively poorly studied because of their complex structure and the necessity of taking into account a large amount of physical processes present in them. The solar loops have different shapes, indeed some of them just rise above the surface of the sun while others look like the toroidal configurations of fusion devices Priest , page [2].

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Fortunately, the theory of plasma dynamics in toroidal configurations has been rather well developed in connection with the research of thermonuclear fusion. Specifically, it is supposed that the ion transport is neoclassical i. Indeed, the neoclassical theory consistently includes the collisional regime, when the mean free path is small in comparison with the typical longitudinal size of the system, the weakly collisional one the ''plateau'' regime, when the transport coefficients do not depend on the collision frequency , and the ''banana'' regime, when it is necessary to take into account the so-called trapped particles, [4].

- Plasma Transport Theory.
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- Callen: Paleoclassical Transport Model.

The electron dynamics in a collisional regime can be also described in the framework of the neoclassical theory. A comprehensive review of the neoclassical transport theory has been published by Hinton and Hazeltine [5]. The plasma of solar loops, in some cases, is collisional with high longitudinal particle flow velocities, not far from the plasma sound speed. Under these conditions, we can neglect the radial gradients of the magnetic field in the equations describing the plasma dynamics.

The solar loops transverse cross-section can differ from a circular one and the temperature is high enough for the plasma to be considered as fully ionized [6]. Here, we want to construct the transport processes theory valid for solar loops as in toroidal magnetically confined collisional two-component ions and electrons plasma configurations, with high longitudinal along the torus particle flow velocities and elongated elliptical transverse cross-section.

Previously, such a problem was solved for axisymmetric plasma columns with circular cross-section, in cases in a plateau [7], collisional [8], [9], and all transport regimes [10]. Of course, there are fundamental differences between the solar loops and tokamaks. The first difference is the sun strong gravitational field.

The second is the vertical position of the many loops. The third is the absence of strong inductive currents in the loops, as in the case for tokamaks. Finally, the feet of solar loops is on the surface of the Sun. These differences need special considerations. We confine ourselves to consider only the local characteristics of the plasma dynamics, such as the local plasma transport.

The sun gravitational field affects primarily the plasma longitudinal flow. Simplifying the problem, we average the evolution equations only over the azimuthal angle, at the same coordinate along the loop.

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In some sense, we replace the flow velocity, depending on the longitudinal coordinate, by the mean flow velocity. In this case, as a first approximation, we neglect the dependence of the macroscopic plasma parameters on the longitudinal coordinate, along the torus. There is a similarity between tokamaks with the poloidal divertor, where the magnetic field lines are unclosed, and the solar case with the feet of the loops tied to the solar surface. Furthermore, the longitudinal transport dominates the energy and particles balance in many kinds of solar loops, however, for interpretation of the observational data, it is necessary to evaluate the particle and energy amount crossing the solar loop surface.

In some kinds of solar loops such as shown in the book by Priest, page [2] , the transverse transport can dominate the longitudinal one because of the solar loop large outer surface, in comparison with the transversal area of the feet. We are aware that, even for strongly toroidal solar loops, we do not take into account all possible ranges of variation of the plasma parameters.

In some kinds of solar loops, the effects of radial gradients, curvature of the magnetic field, and the derivatives of the plasma parameters along the torus can be of the same order of the effects considered here.

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These problems can be the subject of future investigations. In this paper, we confine ourselves to consider only the comparatively simple case of solar loops with the complicated geometry of the magnetic field.

The model equilibrium magnetic field and the associated coordinate system and metric are described in section 2 to 4. The particle and heat fluxes are derived in sections 5 and 6, respectively. The ambipolarity condition is discussed in section 7. Using this condition, the final expressions for the transport fluxes are obtained and evaluated, for some cases of interest, in sections 8 and 9. Finally, the conclusions are presented in section First of all, we need to choose the coordinate system convenient to evaluate the heat and particle fluxes in the elliptical plasma torus.

For a smooth torus no dependence of the plasma macroscopic parameters on the coordinate along the toroidal column , it is convenient to take two coordinates in a transverse cross-section of a plasma column a radial coordinate and a azimuthal, poloidal, coordinate and an angle coordinate along torus. The coordinates should be chosen so that the dependence of the plasma macroscopic parameters on them should be as simple as possible. For example, the plasma macroscopic parameters should depend mainly on the radial coordinate and be approximately constant along the magnetic surfaces for a torus with a small inverse aspect ratio the ratio between the small and large radii of the plasma column.

It can be shown, from the approximate equilibrium equation [3], that. Multiplying this equation by B , we have. Thus, it is convenient to choose the radial coordinate so that it is constant on a magnetic surface. Possible candidates for this coordinate are the plasma volume inside the magnetic surface V , the toroidal f or poloidal c magnetic fluxes, and any functions of these values.

## Transport Processes in Multicomponent Plasma

If a radial coordinate does not coincide with the magnetic surface, strong angle dependence will appear in dynamic equations and the calculations will be highly complicated. In a toroidal magnetic configuration with elliptic transverse cross-section, it is possible to take a function of semi minor and major axes as the radial coordinate, as will be done in the sequel.

Using the Maxwell equation. Then, integrating the second equation of Eqs. Then, integrating the first equation of Eqs. From Eq. Using Eqs. As a result, we have. The definition of the safety factor q , which plays an important role in a plasma stability theory, is. We see from this equation that q depends only on the radial coordinate r , i.

Now, we can find the metric and the coordinate dependence of macroscopic plasma values in the coordinate system with straight magnetic field lines. At first, we take the orthogonal coordinates r ', w ' and z where r ' is the ''radial'' coordinate, w ' and z are the poloidal and toroidal angles respectively to be attached to some points on the magnetic surfaces and to the geometric center of their transverse cross-section. The length element in this orthogonal coordinate system is. Here, R is the torus major radius.

The next step is the encircling of the magnetic surfaces by means of the transformation. Although, as it will be shown below, the ellipticity usually does not give a substantial contributions to the final expressions for the transport fluxes, we believe that it is useful to take the ellipticity into account methodically for future investigations in this direction, for cases, where the ellipticity may be substantial. Then, we focus on the geometric center of the solar loop cross-section and straighten the magnetic line of force by means of small variations of the poloidal angle with the help of the parameter d q , r , introduced by the expressions.

We make this approximation as the first step to solve the problem under investigation. Of course, this model needs further investigation, taking into account the longitudinal along torus derivatives of macroscopic values in the dynamic equations. To find the metric tensor components g ik and their determinant, we substitute Eqs.