A ring of fixed bending radius could in principle carry either electrons or protons…

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 ring of fixed bending radius r=1000 mr = 1000\,\mathrm{m} could in principle carry either electrons or protons at the same momentum, p=50 GeV/cp = 50\,\mathrm{GeV}/c. The energy radiated per turn by an ultra-relativistic electron in such a ring is U0 [GeV]≈8.85×10−5 E4[GeV]/r[m]U_0\,[\mathrm{GeV}] \approx 8.85\times10^{-5}\,E^4[\mathrm{GeV}]/r[\mathrm{m}], and at fixed energy and radius the loss scales as 1/m41/m^4. ((a)) Estimate the energy lost per turn by a 50 GeV50\,\mathrm{GeV} electron beam in this ring, and by a 50 GeV50\,\mathrm{GeV} proton beam in the same ring. ((b)) If this same ring were instead run as an electron-positron collider at an instantaneous luminosity L=2×1032 cm−2 s−1\mathcal{L} = 2\times10^{32}\,\mathrm{cm^{-2}\,s^{-1}}, for a process of cross section σ=10 nb\sigma = 10\,\mathrm{nb}, estimate the interaction rate.

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