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problem_6 - AST 822 Electromagnetic Radiation Problem Set 6...

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AST 822: Electromagnetic Radiation Problem Set 6: due Wednesday, November 23 1) A highly relativistic electron initially has Lorentz factor γ 0 1. It is moving in a magnetic field of constant flux density ~ B with a pitch angle α . What is γ ( t ) as the electron radiates away its energy in the form of synchrotron radiation? What is t 1 / 2 , the time required for the electron to radiate away half its initial energy? If α = π/ 2 and B = 10 - 6 gauss (a typical interstellar value), for what values of γ 0 is t 1 / 2 10 Gyr (the approximate age of the Galaxy)? 2) A high energy cosmic ray proton is emitted at the center of the Galaxy, then starts to orbit in the Galaxy’s magnetic field, of strength B = 10 - 6 gauss. a) If the proton is on a circular orbit, what is the orbital radius as a function of the proton energy ² ? At what energy is the orbital radius equal to the distance of the Sun from the Galactic center? b) If the Galactic center emitted cosmic ray protons with energy ² = 10 21 eV, and if ~ B
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