Plasma fluid equations

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PHYS 7500 Plasma Transport Theory #3 c○Jeong-Young Ji 10 where we have used n i τ ie = n e τ ei m e v Te m i v Ti θ (66) for the ion-electron coefficients. Problem 3-4 (20 pts). Ignoring all other coefficients not listed in Eqs. (50-59), express R e and R i in terms of moments with nonvanishing collision coefficients Â ei , Â ie , and ˆB ie and show the momentum conservation law, R e + R i = 0. Assuming n 0k e = 0 for k > 0, show that Q i = −3µn e τ −1 ei (T i − T e ) and (the energy conservation law) Q e = −Q i − V ei · R e . Homework due: 10/19/2009
PHYS 7500 Plasma Transport Theory #3 c○Jeong-Young Ji 11 Appendix: how to write the moment equations (0,1) equation: √ √ √3 σ1 1 = 5 4 , ˆΞ 0 10 = − 2 , Û0 c10 = − 2 3 , ˆΨ 0+ 11 = 5 6 , ˆΦ 0+ 11 = √ 15 2 √ , 2 Û0+ 10 = − 2 √ 3 ∞∑ ˆD 1kn 0 0k = d t }{{} n 01 +(d t lnT)(ˆΞ 0 11 }{{} n 01 +ˆΞ 0 10n 00 ) + ∇ · V(Û0 c11 }{{} n 01 +Û0 c10n 00 ) 0 0 0 k=0 ∑ k +(∇V) · Û0 l1k n 0k + (∇V) · }{{} Û0 r1k }{{} 0 0 3 = −√ 2 n 1 √ √ 2 2 T d tT − 3 n∇ · V = − 1 3 T (3 2 nd tT + nT ∇ · V) ˆD 0+ 1k · n1k = v T ∇ · (ˆΨ 0+ 11 n11 + ∑ k ∑ k = = ˆΨ 0+ 10 n10 }{{} 0 +v −1 T [ q m (E + V × B) − d tV] · ˆD 0++ 1k : n 2k = ∇V : Û0+ 10 n20 = − 2 √ 3 ∇V : ˆD 0− 1k n−1k = 0, (1,0) equation: σ0 2 = 1 1− 2 , ˆΘ 00 = −√ 2, ∑ k k n 0k ) + v T ∇ lnT · (ˆΦ 0+ ˆΘ 0+ 10 n10 }{{} 0 11 n11 + ˆΦ 0+ 10 n10 √ √ √ 5 15 5 6 v T ∇ · n 11 + 2 √ 2 v T ∇ lnT · n 11 = 6 v T √ √ 5 1 2 6 vT 2 ∇ · (vT 3 1 n11 ) = − 3 T ∇ · q √ √ 2 2 2T π = − 1 3 T ∇V : π ∑ ˆD 0−− 1k n −2k = 0 1− ˆΨ 00 = √ 1 1− 2 , ˆΦ 00 = √ 1 2 , ˆΨ 1+ 00 = 1, ˆΦ 1+ 00 = 1 ∞∑ ˆD 0k 1 n1k = d t }{{} n 10 +(d t lnT)ˆΞ 1 00 }{{} n10 +∇ · VÛ1 c00 }{{} n10 k=0 0 0 0 +(∇V) · Û1 l00 }{{} n10 +(∇V) · Û1 r00 }{{} n10 = 0 0 0 ˆD 1+ 0k · n2k 1+ = v T ∇ · ˆΨ 00 n20 1+ + v T ∇ lnT · ˆΦ 00 n20 + v −1 = v T ∇ · n 20 + v T T }{{} 0 (∇ · n 11 + 3 ∇ lnT · n11) 2 T [ q m (E + V × B) − d tV] · ∇T · n20 a = v √ T 2 T ∇ · (Tn20 ) = ∇ · π mv T ) ˆΘ 1+ 0k }{{} 0 n 2k
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Plasma fluid equations

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