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Chapter 11: Plasma physics 59 2. The Doppler broadening is caused by the thermal motion of the particles: Δ λ λ = 2 c 2 ln(2) kT i m i This broadening results in a Gaussian line profile: k ν = k 0 exp( - [2 ln 2( ν - ν 0 ) / Δ ν D ] 2 ) , with k the coefficient of absorption or emission. 3. The Stark broadening is caused by the electric field of the electrons: Δ λ 1 / 2 = n e C ( n e , T e ) 2 / 3 with for the H- β line: C ( n e , T e ) 3 · 10 14 ˚ A - 3 / 2 cm - 3 . The natural broadening and the Stark broadening result in a Lorentz profile of a spectral line: k ν = 1 2 k 0 Δ ν L / [( 1 2 Δ ν L ) 2 + ( ν - ν 0 ) 2 ] . The total line shape is a convolution of the Gauss- and Lorentz profile and is called a Voigt profile . The number of transitions p q is given by n p B pq ρ and by n p n hf σ a c = n p ( ρ d ν /h ν ) σ a c where d ν is the line width. Then follows for the cross section of absorption processes: σ a = B pq h ν /cd ν . The background radiation in a plasma originates from two processes: 1. Free-Bound radiation, originating from radiative recombination. The emission is given by:
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