Modelling of the space-to-drift-time relationship of the ATLAS monitored drift-tube chambers in the presence of magnetic fields

The ATLAS muon spectrometer uses tracking chambers consisting of up to 5 m long drift tubes filled with Ar : CO 2 ( 93 : 7 ) at 3 bar. The chambers are run in a average toroidal magnetic field of 0.4 T created by 8 air core coils. They provide a track-point accuracy of 40 μ m if the space-to-drift-time relationship r ( t ) is known with 20 μ m accuracy. The magnetic field B influences the electron drift inside the tubes: the maximum drift time t max = 700 ns increases by ≈ 70 ns / T 2 B 2 . B varies by up to ± 0.4 T along the tubes of the chambers mounted near the magnet coils which translates into a variation of t max of up to 45 ns. The dependence of r ( t ) on B must be taken into account. Test-beam measurements show that the electron drift in case of B ≠ 0 can be modelled with the required accuracy by a Langevin equation with a friction term which is slightly non-linear in the drift velocity.