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phys documents (dragged) 63 - g + 1 n e g e h 3 (2 m e kT e...

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Chapter 11: Plasma physics 57 11.4 Thermodynamic equilibrium and reversibility Planck’s radiation law and the Maxwellian velocity distribution hold for a plasma in equilibrium: ρ ( ν ,T ) d ν = 8 π h ν 3 c 3 1 exp( h ν /kT ) - 1 d ν ,N ( E,T ) dE = 2 π n ( π kT ) 3 / 2 E exp ± - E kT ² dE “Detailed balancing” means that the number of reactions in one direction equals the number of reactions in the opposite direction because both processes have equal probability if one corrects for the used phase space. For the reaction ³ forward X forward ³ back X back holds in a plasma in equilibrium microscopic reversibility: ´ forward ˆ η forward = ´ back ˆ η back If the velocity distribution is Maxwellian, this gives: ˆ η x = n x g x h 3 (2 π m x kT ) 3 / 2 e - E kin /kT where g is the statistical weight of the state and n/g := η . For electrons holds g =2 , for excited states usually holds g =2 j +1=2 n 2 . With this one ±nds for the Boltzmann balance, X p +e - X 1 +e - +( E 1 p ) : n B p n 1 = g p g 1 exp ± E p - E 1 kT e ² And for the Saha balance, X p +e - +( E pi ) X + 1 +2e - : n S p g p = n + 1
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Unformatted text preview: g + 1 n e g e h 3 (2 m e kT e ) 3 / 2 exp E pi kT e Because the number of particles on the left-hand side and right-hand side of the equation is different, a factor g/V e remains. This factor causes the Saha-jump . From microscopic reversibility one can derive that for the rate coefcients K ( p, q, T ) := v pq holds: K ( q, p, T ) = g p g q K ( p, q, T ) exp E pq kT 11.5 Inelastic collisions 11.5.1 Types of collisions The kinetic energy can be split in a part of and a part in the centre of mass system. The energy in the centre of mass system is available for reactions. This energy is given by E = m 1 m 2 ( v 1-v 2 ) 2 2( m 1 + m 2 ) Some types of inelastic collisions important for plasma physics are: 1. Excitation: A p + e- A q + e-2. Decay: A q A p + hf...
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