•• Many particle accelerators, including the cyclotron and the synchrotron (Sections 17.11...

•• Many particle accelerators, including the cyclotron and the synchrotron (Sections 17.11 and 18.11), hold charged particles in a circular orbit using a suitable magnetic field. The centripetal acceleration, a = υ2/r, can be very large and can lead to serious energy loss by radiation, in accordance with Eq. (11.1). (a) Consider a 10-McV proton in a cyclotron of radius 0.5 m. Use the formula (11.1) to calculate the rate of energy loss in eV/s due to radiation, (b) Suppose that we tried to produce electrons with the same kinetic energy in a circular machine of the same radius. In this case the motion would be relativistic and formula (11.1) is modified by an extra factor* of γ4:

Find the rale of energy loss of the electron, and compare with that for a proton. (Your answer for the electron should be enormously larger than for the proton. This explains why most electron accelerators are linear, not circular, since the acceleration in a linear accelerator — once υ ~ c — is far smaller than the centripetal acceleration considered here.)

*Note that this is for the case of circular motion. For linear motion the factor is γ6.