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# sess18 - 18 Thermal bremsstrahlung Reading Shu Vol.I Ch.15...

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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. Larmor’s 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 ∞-∞ dω | ˜ ˙ v ( ω ) | 2 (18 . 1) where we have used Parseval’s Theorem for the Fourier components ˜ ˙ v ( ω ). Since ˙ v is real, it follows that ˜ ˙ v (- ω ) = ˜ ˙ v * ( ω ) and we obtain W = 4 e 2 3 c 3 Z ∞ dω | ˜ ˙ v ( ω ) | 2 ⇒ dW dω = 4 e 2 3 c 3 | ˜ ˙ v ( ω ) | 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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sess18 - 18 Thermal bremsstrahlung Reading Shu Vol.I Ch.15...

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