Past exam of the sub-atomic physics course of the University of Oxford 2016 2 c c Solution 2026-10-25
The beam energy is a total pion energy, so the momentum follows the relativistic relation . Taking the standard charged-pion rest energy MeV,[ref]For motion perpendicular to a uniform magnetic field, the Lorentz force supplies the transverse momentum change and gives . With the stipulated eV s m,The unit cancellation leaves length after dividing by in metres per second. Equivalently, the usual magnetic-rigidity conversion is for unit charge. The sign of the pion charge chooses the bending direction, while the radius uses its magnitude. Treating the pion as massless would give about m and is not a good approximation at this modest total energy. The production target does not determine the downstream orbit once the pion momentum and magnetic field are specified.