MDT resolution

Context

Both the EDIT and the Marie Curie schools use a set of monitored drift tubes (MDT) as one of their demonstrations. Cosmic muons are used as ionising charged particles. Four layers of thin (7 mm radius) tubes are placed between plastic scintillators which act as trigger.

The experimental setup measures the drift time spectrum (time delay between the scintillator signal and the discriminator signal) and the spatial resolution (through autocalibration). This demonstration is accompanied by a simulation that tries to reproduce the measurements.

Fields

The tubes and wires are round and sufficiently long for the end-plug effects to be limited to small sectors of the tubes which are not covered by the scintillators. The field for such a configuration is trivial and is built in Garfield.

Gas

Transport properties

Plots of the drift velocity and transverse diffusion as function of the argon fraction help in understanding the way the timing spectrum and resolution depend on the gas composition. The drift velocity for low-energy electrons in pure argon is exceedingly small because these electrons bounce back when colliding with the argon atoms, keeping nearlt all their energy. The electrons build up high energies until they have sufficient energy to excite and ionise argon atoms. As a result, the electrons move fast, but they do not necessarily move along the electric field. Adding a quencher makes that also slow electrons can lose energy, thanks to the rotation, vibration and polyad states of the quencher.

A uniform rainbow is used between 0 % (red) and 100 % argon (purple). The plots were made from the gas files below using the following scripts:

• Velocity
• Transverse diffusion
• Townsend coefficient (plot not shown)

Gas files

MDTs are normally filled with Ar 93 % CO₂ 7 % at 3 bar but the CO₂ fraction can be increased to 10 %, which changes the time spectrum and the resolution.

The gas transport files can be calculated using Magboltz and Heed:

• mixing script

To save time, the following can be copied instead:

• Ar 0 % CO₂ 100 % at 3 bar
• Ar 1 % CO₂ 99 % at 3 bar
• Ar 2 % CO₂ 98 % at 3 bar
• Ar 3 % CO₂ 97 % at 3 bar
• Ar 4 % CO₂ 96 % at 3 bar
• Ar 5 % CO₂ 95 % at 3 bar
• Ar 6 % CO₂ 94 % at 3 bar
• Ar 7 % CO₂ 93 % at 3 bar
• Ar 8 % CO₂ 92 % at 3 bar
• Ar 9 % CO₂ 91 % at 3 bar
• Ar 10 % CO₂ 90 % at 3 bar
• Ar 20 % CO₂ 80 % at 3 bar
• Ar 30 % CO₂ 70 % at 3 bar
• Ar 40 % CO₂ 60 % at 3 bar
• Ar 50 % CO₂ 50 % at 3 bar
• Ar 60 % CO₂ 40 % at 3 bar
• Ar 70 % CO₂ 30 % at 3 bar
• Ar 80 % CO₂ 20 % at 3 bar
• Ar 90 % CO₂ 10 % at 3 bar
• Ar 91 % CO₂ 9 % at 3 bar
• Ar 92 % CO₂ 8 % at 3 bar
• Ar 93 % CO₂ 7 % at 3 bar: nominal mixture
• Ar 94 % CO₂ 6 % at 3 bar
• Ar 95 % CO₂ 5 % at 3 bar
• Ar 96 % CO₂ 4 % at 3 bar
• Ar 97 % CO₂ 3 % at 3 bar
• Ar 98 % CO₂ 2 % at 3 bar
• Ar 99 % CO₂ 1 % at 3 bar
• Ar 99.1 % CO₂ 0.9 % at 3 bar
• Ar 99.2 % CO₂ 0.8 % at 3 bar
• Ar 99.3 % CO₂ 0.7 % at 3 bar
• Ar 99.4 % CO₂ 0.6 % at 3 bar
• Ar 99.5 % CO₂ 0.5 % at 3 bar
• Ar 99.6 % CO₂ 0.4 % at 3 bar
• Ar 99.7 % CO₂ 0.3 % at 3 bar
• Ar 99.8 % CO₂ 0.2 % at 3 bar
• Ar 99.9 % CO₂ 0.1 % at 3 bar
• Ar 100 % CO₂ 0 % at 3 bar

Electronics

Bipolar shaping is used in this setup, to ensure the baseline remains stable when signals pile up:

Associated files:

• Delta response
• Plotting script

Timing spectra

To simulate the response of an MDT tube to the passage of a muon, the following steps are taken:

• Generation of a track at a random distance from the wire, with an ionisation pattern. We do this with the Heed program, a photo-absorption and ionisation model which in addition takes care of the relaxation of the excited atoms that have been produced.
• Tracking of the ionisation of electrons to the anode wire, allowing for diffusion. Since the geometry is symmetric, we do not need Monte Carlo methods. Instead, we use the faster Runge-Kutta-Fehlberg integration method to determine the mean drift time, then integrate the diffusion coefficient along the mean drift path to find the time spread.
• Simulation of the avalanche process near the wire, with the production of ions. In these calculations, we use the Townsend and attachment coefficients to calculate the avalanche profile and add exponential fluctuations. This is a particularly simple model which is only adequate at low gain.
• Calculating the current induced in the anode wire by the moving electrons and ions. For this, we use the weighting field method.
• Convoluting the current with the delta response.
• Noise should be added to the signal at this stage. This is not done in the example below, but there are provisions in Garfield for adding noise.
• Discriminating the shaped signal. In the examples, the threshold was chosen visually - for quantitative calculations, the threshold should be computed from the noise levels and the signal amplitude.

Applied to a mixture with 93 % (left) and 90 % (right) argon, the following time spectra are obtained:

These plots can be produced with scripts that at regular intervals display a sample signal before and after folding with the response function:

• 93 % argon
• 90 % argon

Spatial resolution

The same technique can be applied to simulate resolution curves. The main difference is that tracks are repeatedly generated at a fixed distance from the wire. From the width of the timing distribution at each distance, and the local electron drift velocity, one derives the spatial resolution for that distance. The procedure is repeated for a number of distances.

The dependence on the discrimination threshold is easily understood: when the threshold is set too high, occasionally a late electron will be triggered upon, whereas low thresholds in principle yield better resolution, but they would suffer from noise. Adding the noise term is left as an exercise for the reader. The resolution is better near the tube wall since the path length distribution from there to the wire is more narrow than it is for a track passing near the wire. Diffusion tends to outweigh this effect ib tubes with a larger diameter.

The brown points show the Gaussian width of the timing distributions and the green points represent the RMS of these distributions. The difference is an indication of the frequency of missing the earliest electrons (late timing) and of triggering on delta electrons coming nearer to the wire than the track (early timing). The plots were made for 93 % argon at 3 bar and with a low threshold (left, no noise) and a higher threshold (right):

These plots can be produced with the following scripts:

• (too) low threshold
• regular threshold
• high threshold
• (too) high threshold

Last updated on 6/4/11.