Discuss the implications of Liouvilles theorem on the focusing of beams of charged particles by considering the

Question:

Discuss the implications of Liouville’s theorem on the focusing of beams of charged particles by considering the following simple case. An electron beam of circular cross section (radius R0) is directed along the z-axis. The density of electrons beam (px and py) are distributed uniformly over a circle of radius p0 in momentum space. If some focusing system reduces the beam radius from R0 to R1, find the resulting of the transverse momentum components. What is the physical meaning of this result? (Consider the angular divergence of the beam.)
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...