An electron-positron ring of bending radius first runs at the pole

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

An electron-positron ring of bending radius

r = 3000\,\mathrm{m}

first runs at the

Z

pole, with each beam at

E = 45.6\,\mathrm{GeV}

. The energy loss per turn to synchrotron radiation for an electron ring obeys

U_0\,[\mathrm{GeV}] = 8.85\times10^{-5}\,\frac{E^4\,[\mathrm{GeV}]}{r\,[\mathrm{m}]}

as quoted for LEP. ((a)) Find the loss per turn

U_0

45.6\,\mathrm{GeV}

on this ring. ((b)) The ring is then run at

E = 80.0\,\mathrm{GeV}

per beam (to make

W^+W^-

pairs), on the same radius. Find the new loss per turn and the factor by which it has increased. ((c)) To bring the loss back down, the radius is enlarged to

r = 6000\,\mathrm{m}

at the same

80.0\,\mathrm{GeV}

beam energy. Find the loss per turn on the enlarged ring.

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