A design report for an electron ring of fixed bending radius plots the energy lost…

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Particle Physics & Quantum Fields · Particles, interactions and experiment

Particle Physics, Ch Accelerators and colliders: energy, luminosity and reach

Problem

A design report for an electron ring of fixed bending radius

r = 2000\,\mathrm{m}

plots the energy lost per turn,

U_0

, against the beam energy

E

on log-log axes. The curve is a straight line of slope

4

, passing through the point

E = 100\,\mathrm{GeV}

U_0 = 4.43\,\mathrm{GeV}

. ((a)) Write

U_0

as a function of

E

for this ring and use it to find the loss per turn at

E = 150\,\mathrm{GeV}

. ((b)) The radiofrequency system can replace at most

2.5\,\mathrm{GeV}

per turn per beam. Find the maximum beam energy this ring could sustain. ((c)) Run at that maximum energy, the ring collects

75\,\mathrm{fb^{-1}}

in one year, for a process of cross section

\sigma = 0.15\,\mathrm{pb}

. How many such events are produced in that year?

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