Measurement of the Z boson cross-section in - Harvard University ...

Chapter 3: Luminosity Measurement at the LHC and in ATLAS 74
cores.
The two cores are driven into saturation with a current at frequency Fmod in the
modulation windings. With no beam present, when equal but opposite modulation
currents are applied to the cores, the induced voltages on the detection windings are
also equal but opposite. However, when there is a beam, the beam current generates a
static magnetic field in the cores, which offsets the hysteresis loop for zero modulation
current. Consequently, since the modulation is opposite in the two cores, the time
spent in saturation is different for the two branches of the hysteresis loop. When the
induced voltages in the two detection windings are combined and demodulated, the
result is a series of voltage pulses with the pulse width being directly proportional to
the beam current.
Each LHC ring has two BCTCDs. Their current resolution is 2 µA, corresponding
to ≈ 10 9 protons [66]. At design luminosity, each LHC beam will have 4.8 × 10 14 pro-
tons [1], corresponding to a circulating current of 0.582 µA, so that the measurement
accuracy will be ≈ 10 −6 . A beam lifetime of about 25 hours because of pp collisions
implies a decay rate of ≈ 5 × 10 9 protons/s. With a measurement time of 10 s, the
BCTDCs are able to measure this rate, and therefore the expected beam lifetime,
with a precision of ≈ 1%.
Note that comparison between bunch-by-bunch current measurements from the
fast transformers, summed over all bunches, and the total beam current measured
with the DC transformers gives information about the size of longitudinal beam tails.