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Unformatted text preview: 18. Thermal bremsstrahlung Reading: Shu, Vol.I, Ch.15 Bremsstrahlung is the result of the acceleration of an electron in the Coulomb field of an ion. One can say that this is a small inelasticity effect in Coulomb scattering. Using the dipole approximation, i.e. Larmors formula, we can infer the total radiated power and hence the spectrum per Fourier transformation. dW dt = 2 e 2 3 c 3 v 2 ( t ) W = 2 e 2 3 c 3 Z - dt v 2 ( t ) = 2 e 2 3 c 3 Z - d | v ( ) | 2 (18 . 1) where we have used Parsevals Theorem for the Fourier components v ( ). Since v is real, it follows that v (- ) = v * ( ) and we obtain W = 4 e 2 3 c 3 Z d | v ( ) | 2 dW d = 4 e 2 3 c 3 | v ( ) | 2 (18 . 2) The electron will approach the ion with a certain impact parameter b . Though we know the path of the electron in the Coulomb field of the ion, it is identical to a Kepler orbit for positive total energy, we will use a straight-line approximation here, that is we assume the electron is only weakly deflected. Obviously this corresponds to assuming that b is large, which appears justified because most interactions will happen at large...
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