Basics of Plasma Astrophysics by Claudio Chiuderi, Marco Velli (auth.)

By Claudio Chiuderi, Marco Velli (auth.)

This ebook is an creation to modern plasma physics that discusses the main correct contemporary advances within the box and covers a cautious collection of purposes to numerous branches of astrophysics and area technological know-how. the aim of the ebook is to permit the scholar to grasp the elemental techniques of plasma physics and to carry her or him modern in a couple of appropriate parts of present learn. subject matters coated contain orbit idea, kinetic conception, fluid versions, magnetohydrodynamics, MHD turbulence, instabilities, discontinuities, and magnetic reconnection. a few earlier wisdom of classical physics is needed, specifically fluid mechanics, statistical physics, and electrodynamics. The mathematical advancements are self-contained and explicitly designated within the textual content. a couple of workouts are supplied on the finish of every bankruptcy, including feedback and solutions.

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If, for instance, we consider a rarefied plasma dominated by collective effects, we may neglect collisions and equate the rhs of Eq. 7) to zero, leading to the Vlasov equation: e0 1 ∂f + v · ∇ f + (E + v × B) · ∇ v f = 0. 7) If we adopt the Boltzmann collision model (binary elastic collisions) we will get the Boltzmann equation, where the collisional term is given in terms of an integral that involves the product of two distribution functions. The Boltzmann equation is particularly important for neutral gases, where binary collisions are dominant, but it is not the most appropriate to describe plasmas.

However, in this case too we have ∇v · F = e0 c i ∂(v × B)i =0 ∂vi since the i-th component of v × B does not depend on vi . Keeping all this in mind Eq. 30) becomes: F ∂f + v · ∇ f + · ∇ v f = 0. 4) So far we have implicitly assumed that all the particles occupying the same cell of phase space are subject to the same acceleration. e. those due to the simultaneous action of all the particles of the plasma, but may not be true for collisions, namely for interactions involving only two particles at a time.

However, the case E = B has particular importance since it is related to the motion of a particle in the field of an electromagnetic wave. The method of a Lorentz boost, used to treat the cases with E = B, is no longer applicable and we must solve directly the equation of motion of special relativity in the laboratory frame. The more familiar non relativistic case can be easily obtained by taking the appropriate limit. We shall consider a particle of mass m and charge e0 , initially at rest at the origin of the coordinates, acted upon by a linearly polarized electromagnetic wave of frequency ω.

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