Transcription of Chapter 5 Electromagnetic Waves in
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Chapter 5 Electromagnetic Waves in
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, ).
Electromagnetic Waves in Plasmas ... Think of this equation as a matrix e.g.: ... Group velocity of wave, which is the velocity at which information/energy travel is dω v g = = 0 !! (5.51) dk In a way, these oscillations can hardly be thought of as a ‘proper’ wave because they do
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