Cyclotron radiation and max speed of a cyclotron accelerator

Consider a proton undergoing 2d cyclotron motion (in the icy-plane) with initial velocity v0 in a magnetic field of magnitude 8 pointing out of the plane. Larmor's formula for the power radiated by an accelerating charge is: P = A. E. (4.2\"? 6.716063 What is the power radiated by a proton undergoing cyclotron motion with velocity v in a magnetic field B? Note that the power dKE radiated is related to the kinetic energy KE of the electron by: F = P. (ME Show that the kinetic energy, KE, of the proton satisfies a differential equation of the form: 7 = yKE, which has solution I KEG) = KEne_7' where KEG = mv is the initial kinetic energy. Determine the decay rate 1/ in terms of v. B and fundamental constants. Assuming that the decay constant is much less than the cyclotron frequencyhfgj y jg. we can approximate that the decay rate is constant over one cyciotron orbit. What is the change in KE of the proton per cyclotron period as a function of the velocity v? Cyclotron accelerator: A cyciotron accelerator applies an alternating voltage with amplitude V, and with a frequency that matches the cyclotron frequency of the proton, such that the proton gains energy: 6V during each cyclotron period. The maximum speed attainable by a cyclotron occurs when the KE gain from the accelerating voltage is equal to the KE loss due to the cyclotron radiation. What is the maximum speed, vmax, to which we can accelerate a proton using a cyclotron accelerator How would the maximum speed compare to the answer in Part D if we accelerated an electron with the same cyclotron? Express at! answers in terms of variables given (3. V. v0) and fundamental constants [proton charge (e) and mass (M) of proton, speed of tight (c), and dielectric constant of vacuum an]