By Patrick H. Diamond
This three-volume sequence provides the tips, types and techniques necessary to realizing plasma dynamics and self-organization for researchers and graduate scholars in plasma physics, managed fusion and comparable fields equivalent to plasma astrophysics. quantity I develops the actual kinetics of plasma turbulence via a spotlight on quasi-particle versions and dynamics. It discusses the basic physics strategies and theoretical equipment for describing susceptible and robust fluid and part house turbulence in plasma platforms faraway from equilibrium. The ebook connects the generally 'plasma' subject of susceptible or wave turbulence thought to extra commonplace fluid turbulence idea, and extends either to the area of collisionless section house turbulence. this offers readers a deeper knowing of those comparable fields, and builds a origin for destiny purposes to multi-scale procedures of self-organization in tokamaks and different limited plasmas. This e-book emphasizes the conceptual foundations and actual instinct underpinnings of plasma turbulence concept.
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In the regime of kλDe 1, a high and sharp peak appears near the eigenfrequency ω ∼ ωk . Owing to the very weak damping, the line width is narrow. As the mode number becomes large an in the regime of kλDe ∼ 1, the bandwidth becomes broader, and the fluctuation intensity becomes high. 21c) so we finally obtain D 2 k,ω 4π = which is in precise agreement with the statement of the FDT for a classical, plasma at temperature T . It is important to reiterate here that applicability of the FDT rests upon to the applicability of linear response theory for the emission and absorption of each mode.
23b) 2|k| |F | 2 So, yes, the electric field energy for plasma waves is indeed at equipartition. e. Ekin = Ek ), the total wave energy density per mode Wk is constant at T . 23b) does not imply the divergence of total energy density. Of course, some fluctuation energy is present at very small scales (kλDe 1) which cannot support collective modes. However, on such scales, the pole expansion is not valid and simple static screening is a better approximation. A short calculation gives, for k 2 λ2De > 1, Ek ∼ = (T /2)/k 2 λ2De , so that the total electric energy density is E2 = 8π = dk Ek ∞ −∞ T /2 dk ∼ 2π 1 + k 2 λ2De nT 2 1 .
11), we obtain f˜(1)f˜(2) = f n dv i dx i N [δ(x 1 − x i (t)) i,j =1 × δ(x 2 − x j (t))δ(v 1 − v i (t))δ(v 2 − v j (t))]. 12) Since the product of δs is non-zero only if the arguments are interchangeable, we obtain immediately the discreteness correlation function f δ(x 1 − x 2 )δ(v 1 − v 2 ). 13) gives the discreteness correlation function in phase space. Since the physical model is one of an ensemble of discrete, uncorrelated test particles, it is no surprise that f˜(1)f˜(2) is singular, and vanishes unless the two points in phase space are coincident.