1) The bunches of particles in an accelerator will expand laterally because of the mutual Coulomb repulsion of particles with like charges as they move between the focussing magnets situated at intervals around the accelerator ring. In the Tevatron proton accelerator at Fermilab the particles are injected in bunches of 2 x 1011 in the form of cylinders of radius of 36 x 10-6 m and length 0.5 m. Obtain a relationship between the radius of the bunch and time in its rest frame in the absence of focussing.