Fundamentals of Plasma Physics
50 Chapter 2. Derivation offluid equations: Vlasov, 2-fluid, MHD This means that, as shown in Fig.2.5, a tube of plasma initiall ...
2.5 Magnetohydrodynamic equations 51 whereP⊥^2 D is the 2-D perpendicular pressure, and has dimensions of energy per unit area, ...
52 Chapter 2. Derivation offluid equations: Vlasov, 2-fluid, MHD equations is multiplied byqσand then summed over species to obt ...
2.7 Sheath physics and Langmuir probe theory 53 and the equation of motion is ρ DU Dt =J×B−∇P. (2.100) (b) Double adiabatic regi ...
54 Chapter 2. Derivation offluid equations: Vlasov, 2-fluid, MHD metal wires used to diagnose low temperature plasmas. Biasing a ...
2.7 Sheath physics and Langmuir probe theory 55 to denote a potential measured relative to the plasma potential, i.e., φ ̄(x) =φ ...
56 Chapter 2. Derivation offluid equations: Vlasov, 2-fluid, MHD one-dimensional Poisson’s equation d^2 ̄φ dx^2 =− e ε 0 (ni(x)− ...
2.7 Sheath physics and Langmuir probe theory 57 and so the electron current collected at the probe is Ie=−n 0 eA √ κTe 2 πme e−e ...
58 Chapter 2. Derivation offluid equations: Vlasov, 2-fluid, MHD 2.8 Assignments Prove Stirling’s formula. To do this first sho ...
2.8 Assignments 59 this ratio constant or not (explain your answer)? Let this ratio be denoted byλ (this is called a Lagrange mu ...
60 Chapter 2. Derivation offluid equations: Vlasov, 2-fluid, MHD Normalize the collision frequency, thermal velocity, and mean f ...
2.8 Assignments 61 (i) By taking the second moment of the Vlasov equation for each species (i.e., use v^2 / 2 ) and summing over ...
3 Motion of a single plasma particle 3.1 Motivation As discussed in the previous chapter, Maxwellian distributions resultwhen co ...
3.2 Hamilton-Lagrange formalism v. Lorentz equation 63 containsallinformation about the particle dynamics for a given situation ...
64 Chapter 3. Motion of a single plasma particle Sinceηi(t 1 , 2 ) = 0the integrated term vanishes and sinceηiwas an arbitrary f ...
3.2 Hamilton-Lagrange formalism v. Lorentz equation 65 be used as the canonical coordinates in which case Eq.(3.8) gives the can ...
66 Chapter 3. Motion of a single plasma particle 3.3 Adiabatic invariant of a pendulum Perfect symmetry is never attained in rea ...
3.3 Adiabatic invariant of a pendulum 67 The assumption of slowness is thus at least self-consistent, for ifω(t)is indeed slowly ...
68 Chapter 3. Motion of a single plasma particle so Eq.(3.31) becomes S = ∫t 0 +τ t 0 ω(t′)^2 { x(t 0 ) √ ω(t 0 ) ω(t′) cos (∫ t ...
3.4 Extension of WKB method to general adiabatic invariant 69 where ∇=Qˆ ∂ ∂Q +Pˆ ∂ ∂P (3.37) is the gradient operator in theQ−P ...
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