Fundamentals of Plasma Physics
370 Chapter 12. Magnetic reconnection and using Eq.(12.36), the current density becomes J 1 z∼− ∆′ ǫμ 0 √ π A 1 z(0). (12.48) We ...
12.5 Generalization of tearing to sheared magnetic fields 371 The Alfvén time is the characteristic time of ideal MHD and is typ ...
372 Chapter 12. Magnetic reconnection which in turn can be thought of as the straight cylindrical approximationof a toroid withz ...
12.5 Generalization of tearing to sheared magnetic fields 373 Thus, ifx=0is defined to be the location of the reconnection layer ...
374 Chapter 12. Magnetic reconnection Continuing this discussion of the ramifications of the antisymmetry ofk·B 0 about x=0,we n ...
12.5 Generalization of tearing to sheared magnetic fields 375 this equation provides the essential dynamics offluid vortices tha ...
376 Chapter 12. Magnetic reconnection Thus, Eq.(12.80) becomes γ=0.55(∆′a)^4 /^5 τ−R^3 /^5 τ−A^2 /^5 ( na^2 R q′ q ) 2 / 5 (12.8 ...
12.6 Magnetic islands 377 It is seen that B⊥·∇Az 0 =0 (12.93) whereB⊥is the component perpendicular toz.Thus, the surfacesAz=con ...
378 Chapter 12. Magnetic reconnection 12.7 Assignments (a) (b) (c) z z poloidal flux surface current loop (^12) (^34) 5 (^123) 4 ...
12.7 Assignments 379 (b) Define privateflux to be aflux surface that links only one of the current loops (examples are theflux s ...
380 Chapter 12. Magnetic reconnection (current-sheet) as shown in Fig.12.6(c). Show that in order to have an X-point geometry an ...
12.7 Assignments 381 sheet. Note that( Bout∼∆ψ/ 2 πrLandBin∼∆ψ/ 2 πrδ;also note that∇· r−^2 ∇ψ ) can be expressed in terms ofBin ...
13 Fokker-Planck theory of collisions 13.1 Introduction Logically, this chapter ought to be located at the beginning of Chapter ...
13.1 Introduction 383 Adding Eqs.(13.1a) and (13.1b) gives (mT+mF)R ̈=mT ̈rT+mF ̈rF=0 (13.3) showing that the center of mass vel ...
384 Chapter 13. Fokker-Planck theory of collisions 13.2 Statistical argument for the development of the Fokker-Planck equation T ...
13.2 Statistical argument for the development of the Fokker-Planck equation 385 invoking Eq.(13.13) this can be recast as ∂f ∂t ...
386 Chapter 13. Fokker-Planck theory of collisions the respective relative velocities before and after the collision, then vrel ...
13.2 Statistical argument for the development of the Fokker-Planck equation 387 This result was for a particular value ofvFand s ...
388 Chapter 13. Fokker-Planck theory of collisions θ^2 .Thus, we obtain ∆vrel∆vrel|allb,φ = v^3 rel∆tfF(vF)dvF ∫^2 π 0 dφ λ∫D bπ ...
13.2 Statistical argument for the development of the Fokker-Planck equation 389 in which case 〈 ∆v ∆t 〉 = q^2 TqF^2 lnΛ 4 πε^20 ...
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