A proton ring currently holds a beam at momentum with a dipole field

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 proton ring currently holds a beam at momentum

p_1 = 3.5\,\mathrm{TeV}/c

with a dipole field

B_1 = 3.8\,\mathrm{T}

. Someone argues: "To reach

p_2 = 7.0\,\mathrm{TeV}/c

we should just double the dipole field to

7.6\,\mathrm{T}

and switch off the radiofrequency cavities to save power, since it is the magnets that speed the particles up." ((a)) Find the error in this reasoning, explaining what actually increases the beam's energy and what the dipole field does instead. ((b)) Using

r = p/(qB)

in collider units,

r[\mathrm{m}] = p[\mathrm{GeV}/c]/(0.2998\,B[\mathrm{T}])

, find the ring's bending radius from the stated momentum and field, and hence find the dipole field actually required to bend a

7.0\,\mathrm{TeV}/c

beam around the same ring. ((c)) Suppose the physics goal instead is to search for a very rare, previously unseen decay at a known, moderate collision energy, where the priority is the largest possible event rate rather than reaching a new energy at all. State, with a reason, whether raising the beam energy (as proposed) or raising the luminosity is the more relevant upgrade, and whether a fixed-target experiment could reach the required rate more simply.

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