Transcription of Chapter 5 Electromagnetic Waves in - MIT OpenCourseWare
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Chapter 5 Electromagnetic Waves in - MIT OpenCourseWare
Chapter 5 Electromagnetic Waves in Plasmas General Treatment of Linear Waves in Anisotropic Medium Start with general approach to Waves in a linear Medium: Maxwell: 1 E B ; ( ) B = oj + c2 t E = t we keep all the medium s response explicit in j. Plasma is (infinite and) uniform so we Fourier analyze in space and time. That is we seek a solution in which all variables go like exp i( t) [real part of] ( ) It is really the linearised equations which we treat this way; if there is some equilibrium field OK but the equations above mean implicitly the perturbations B, E, j, etc. Fourier analyzed: ik B = oj + i c2 E ; ik E = i B ( ) Eliminate B by taking k second eq. and 1st i 2 ik (k E) = oj c2 E ( ) So 2 k (k E) + E + i oj = 0 ( ) 2cNow, in order to get further we must have some relationship between j and E(k, ).
Longitudinal Waves (B o = 0) Dispersion relation we know is nq2 1 = 0 = 1 − (5.40) m o ω2 [Strictly, the we want here is the total including both electron and ion contributions to
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