By Ernesto Mazzucato
The technology of magnetically restricted plasmas covers the full spectrum of physics from classical and relativistic electrodynamics to quantum mechanics. over the past sixty years of study, our preliminary primitive realizing of plasma physics has made outstanding growth due to a number of experiments — from tabletop units with plasma temperatures of some hundreds of thousands of levels and confinement instances of lower than a hundred microseconds, to massive tokamaks with plasma temperatures of as much as million levels and confinement instances forthcoming one moment. We came across that plasma confinement is impaired through numerous instabilities resulting in turbulent methods with scales starting from the plasma measurement to a couple millimeters. figuring out those phenomena, that have bogged down growth in the direction of a fusion reactor, calls for using very refined diagnostic instruments, lots of which hire electromagnetic waves.
the first goal of this booklet is to debate the basic physics upon which the appliance of electromagnetic waves to the learn of magnetically restricted plasmas is based.
Readership: complicated scholars and pros who're attracted to thermonuclear plasmas.
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Additional info for Electromagnetic Waves for Thermonuclear Fusion Research
B1735-ch03 Inhomogeneous Plasmas 41 where Γ = [Y 4 sin4 θ + 4Y 2 (1 − X)2 cos2 θ]1/2 , and the ± sign corresponds to the ordinary (+) and the extraordinary (−) mode. 19) in the form dr 1 dr = = −sgn ds vG dt dk 1 dk = = sgn ds vG dt ∂D ∂ω ∂D ∂ω ∇k D , |∇k D| ∇r D . 28) ∂D ∂θ ∇θ . 29) G = A/Bm , where m = ±1, and thus k 2 c2 − G. 30) February 24, 2014 42 14:14 Electromagnetic Waves for. . 9in x 6in b1735-ch03 Electromagnetic Waves for Thermonuclear Fusion Research ∂G ∂G ∂Γ ∂D ∂G ∂G ∂Γ ∂D =− − , =− − , ∂X ∂X ∂Γ ∂X ∂Y 2 ∂Y 2 ∂Γ ∂Y 2 4Y 2 (1 − X) ∂G ∂Γ 1 ∂G + = 2 2(1 − 2X)Bm + 2A + mA cos2 θ , ∂X ∂Γ ∂X Bm Γ ∂G ∂G ∂Γ A Y 2 sin4 +2(1 − X)2 cos2 θ 2 , sin + = θ − m 2 ∂Y 2 ∂Γ ∂Y 2 Bm Γ 2k 2 c2 2X ∂D = + ∂ω ω3 ω + ∇X = X ∇θ = − 2Y 2 ω ∇ne , ne ∂G ∂G ∂Γ + ∂X ∂Γ ∂X ∂G ∂G ∂Γ , + ∂Y 2 ∂Γ ∂Y 2 ∇Y 2 = 2Y 2 ∇B , B B 1 ∇ k· , k sin θ B where in the last equation the gradient acts only on the magnetic ﬁeld.
In this chapter, we will review the theory of propagation of these waves in homogeneous plasmas. 4) where B and E are the magnetic and electric ﬁelds, and j and ρ are the current and space charge densities induced by the wave. 5) F=q E+ ×B , c 17 February 24, 2014 18 14:14 Electromagnetic Waves for. . 9in x 6in b1735-ch02 Electromagnetic Waves for Thermonuclear Fusion Research deﬁnes the physical meaning of E and B. 4) yields the conservation of charge ∂ρ + ∇ · j = 0. 2), we get the equation involving only E and J ∇×∇×E+ 4π ∂J 1 ∂2 E =− 2 .
1, in which B0 is along the x3 direction and k is in the (x1 , x3 ) plane . 1. Cartesian coordinate system with magnetic ﬁeld B0 along the x3 axis and wave vector k in the (x1 , x3 ) plane. February 24, 2014 14:14 Electromagnetic Waves for. . 9in x 6in b1735-ch02 Electron Waves 21 by 180o about the x2 axis. 25) 0, 0 0 −1 the Onsanger relation can be written as R · ε · RT = ε T , where the superscript T indicates the transpose. 26) ε (ω, k, B0 ) = −ε12 . 26) is valid only for the reference frame of Fig.
Electromagnetic Waves for Thermonuclear Fusion Research by Ernesto Mazzucato