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Unformatted text preview: 22. Synchrotron radiation Reading: Shu, Vol. 1, Ch. 18 22.1 The energy loss rate Electrons are accelerated in magnetic fields and as a result emit synchrotron radiation. We can write down the electron equation of motion d dt ( m~v ) = e c ~v ~ B d dt ( mc 2 ) = e ~v ~ E = 0 (22 . 1) Obviously =const and therefore m d~v dt = e c ~v ~ B (22 . 2) The wellknown solution to this equation is a helical motion with angular velocity and acceler ation g = eB mc a = g v ~a ~v (22 . 3) The acceleration is thus perpendicular to the velocity vector and to the magnetic field. Inserting this into Eq.21.17 for the total radiated power we obtain P = 2 e 2 3 c 3 4 ( a 2 + 2 a k 2 ) = 2 3 e 4 m 2 c 4 2 2 B 2 (22 . 4) As we have seen, relativistic electrons scatter efficiently on lowfrequency electromagnetic waves and will therefore assume an isotropic distribution. We may average over angle then and obtain P = 4 3 T c U B 2 2 U B = B 2 8 T = 8 r 2 3 = 8 e 4 3 m 2 c 4 (22 . 5) The total radiated power per particle is the energy loss rate, which we here find to have a...
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.
 Fall '08
 RABE
 Physics, Energy, Radiation

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