Consider a plasma with cold protons and hot electrons with a 1 dimensional distribution function proportional to 1 (v 0 2 v 2 ), so the full 1 dimensional distribution function is (a) Show that the dispersion relation for Langmuir waves, with phase speeds large compared to v 0 , is (b) Compute the dispersion relation for ion acoustic waves, assuming that their phase speeds are much less than v 0 but are large compared to the cold protons thermal velocities Your result should be F(v) nvo (v v) n me 8(v) mp (22 45)

Question: Consider a plasma with cold protons and hot electrons with a 1-dimensional distribution function proportional to 1/(v 0 2 + v 2 ), so the

Consider a plasma with cold protons and hot electrons with a 1-dimensional distribution function proportional to 1/(v₀² + v²), so the full 1-dimensional distribution function is

F(v) = = nvo (v + v) +n me 8(v). mp (22.45)

(a) Show that the dispersion relation for Langmuir waves, with phase speeds large compared to v₀, is

(b) Compute the dispersion relation for ion-acoustic waves, assuming that their phase speeds are much less than v₀ but are large compared to the cold protons’ thermal velocities. Your result should be

F(v) = = nvo (v + v) +n me 8(v). mp (22.45)

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To derive the dispersion relation for Langmuir waves and ionacoustic waves we start with the given 1dimensional distribution function Fv nvo v v nme 8v mp 2 Equation 2245 where n is the electron numbe... View full answer

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