VI.Plasma Conduction Model(Classical) m0=aE-mv文-R n m昨=-qE-mvV-p dt n p.=n.kT,p.=n_kT k=1.38 x 1023 joules/K Boltzmann Constant A.London Model of Superconductivity[T→O,v±→O] m..m. dt =-q.E dv- j.q.n,v,J=-q.n.v. 0-品an)=ang-ana目-E m.m 0+e 票-是an)qn祭-qng周-E m.m 06_8 @.=an,of.-92n (plasma frequency) m.E m 8 For electrons:q-=1.6 x 1019 Coulombs,m.=9.1 x 1031 kg n.=1020/m3,e=8。÷8.854x10-12 farads/,m 0p.=1 g2n≈5.6x101rad/s m.8 =2 g=≈9x100Hz 6.641,Electromagnetic Fields,Forces,and Motion Lecture 7 Prof.Markus Zahn Page 9 of 276.641, Electromagnetic Fields, Forces, and Motion Lecture 7 Prof. Markus Zahn Page 9 of 27 VI. Plasma Conduction Model (Classical) + + + + ++ + + ∇ −ν − dv p m =q E m v dt n − − − − −− − − ∇ − −ν − dv p m = qE m v dt n p = n kT , p = n kT ++ −− k=1.38 x 10-23 joules/o K Boltzmann Constant A. London Model of Superconductivity [ T → ν→ 0, 0 ± ] dv dv m =qE , m = qE dt dt + − ++− − − + − + − ++ −− J =q n v , J = qnv − ( ) ( ) q E 2 dJ d dv q n q n v =q n =q n = E dt dt dt m m + + + + + ++ ++ ++ + + + = ω + ε 2 p ( ) ( ) q E 2 dJ d dv q n = qnv = qn = qn = E dt dt dt m m − − − − − −− −− −− − − − − − −− ε 2 + + − − + − + − ω ω ε ε 2 2 2 2 p p q n q n = ,= m m (ωp = plasma frequency) For electrons: q-=1.6 x 10-19 Coulombs, m-=9.1 x 10-31 kg n-=1020/m3 , 12 o 8.854 x 10− ε = ≈ ε farads/m − − − − ω ≈ ε 2 11 p q n = 5.6 x 10 m rad/s − − ≈ π ωp 10 pf = 9 x10 2 Hz − ωp