PROBLEM SET 6
Due Friday, March 19, 1999
Reading: Jackson, Secs. 14.6䎣.3
Problems: Jackson, 14.17, 14.26ad and addition; LD 9
14.17: The "fundamental frequency"
is
defined as the repetition frequency of the pulses of radiation seen by a
distant observer. This would appear as the fundamental frequency in a
Fourier decomposition of the periodic signal. Do not set
in the calculation of , but keep the first
correction in powers of to see what
happens.
14.26d, addition: Explain how one could show through observation that the high frequency component of the radiation from the Crab nebula is synchrotron radiation rather than thermal (black body) radiation. Give at least two tests. |
Work to first order in . The Fourier integral involves only a finite interval in t' or z', and the phase factor can be simplified under the conditions given by dropping the term in . After you evaluate the integral, you will see that one term has a denominator that can vanish, while the other term does not. Drop the second term for simplicity. The final result should look like a standard expression for radiation by a relativistic particle multiplied by a "grating factor". |
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© 1997, 1998, 1999 Loyal Durand