Calculating Primary Ionizations of Cosmic Muons in a Detector

[Blidaru Bogdan]

I am currently studying the MicroMEGAS detector principle. Ionizing particles traverse the space of around 6 mm of Ar:Co2 mixture in the detector (10x10cm² x 6mm) like in the picture below. A cosmic muon (4GeV) enters this space and ionizes along its path. I assume the longest path it can take (probabilistic) is alongside opposing diagonals of the rectangular parallelipiped (aprox. 142 mm) and the shortest is downstream (6mm).

Such a particle (minimum ionizing particle) loses energy following Bethe-Bloch formula at a rate of -dE/dx = 2 MeV/ (g/cm²). The density of the mix of Ar:CO2 is aprox. 1.7 kg/m³. This being said, a cosmic muon can deposit in 6mm and 142 mm or Ar:CO2 (-dE/dx * rho * x) 2.051 keV, respectively 48.536 keV.

It is normal that alongside its path, the muon ionizes in different points. My difficulty arises now assessing the number of such points (probabilistic). Given the above values of travel distances and energy values (and if possible given the configuration of the detector - that has a drift region where just a few primary ionizations occur, and an amplification region 40 kV/cm where electrons form avalanches), how can I calculate how many primary ionizations occur along the path of the cosmic muon?
And how can I be sure that the muon I am observing is a singular event at that particular time of the observation? (given the flux of about 1 cosmic muon per square centimeter per minute)

Thank you very much!

 

[mfb]

You'll need the average energy loss per ionization event in your gas mixture, probably a value to look up.
Travel distances from 6 to ~10 mm will be far more common than longer ones, especially if your detector is horizontal.

And how can I be sure that the muon I am observing is a singular event at that particular time of the observation? (given the flux of about 1 cosmic muon per square centimeter per minute)

How good is your timing? Do you have a second detector layer to veto radioactive decays in the detector? You can never be 100% sure, but with good timing and a second detector also seeing the event at the same time and at the right place your background becomes negligible.

 

[Blidaru Bogdan]

The only values I could found about the mixture are as follows:

The number of primary electron pairs per cm: 25.42
The total number of electron-ion pairs per cm: 93.7
Excitation energy: 11.6 eV
Ionization energy: 15.7 eV
Average energy required to produce electron-ion pairs: 26 eV

Now, I know the muon deposits in 6 mm a total of 2.051 keV. How can I distinguish from this total energy loss, the energy of the primary ionizations and their number?

Regarding the timing, I have just a configuration of just one horizontal detector. I am still only modelling it. In a laboratory setup, I cannot acquire another detector, so I am to rely on laboratory instrumentation.

 

[mfb]

26 eV/pair * 93.7 pairs/cm * 6 mm = 1460 eV, so the numbers don't match. Do they refer to the same temperature, pressure and gas composition? If yes, they are probably more reliable than the Bethe-Bloch approximation.

How can I distinguish from this total energy loss, the energy of the primary ionizations and their number?

You have the number of electron ion pairs per length, and the length, that is everything you need (if the numbers apply here).

Regarding the timing, I have just a configuration of just one horizontal detector.

Then background radioactivity will be a large problem, much more than two muons hitting the same spot at the same time.
You can look at the hits and their arrival time at the individual detector components if the time resolution allows that.

 

[Blidaru Bogdan]

26 eV/pair * 93.7 pairs/cm * 6 mm = 1460 eV, so the numbers don't match. Do they refer to the same temperature, pressure and gas composition?

The data I calculated was extracted from different sources treating minimum ionizing particles that revolve around 2 MeV/(g/cm²). Seems I was off. The latest reliable source I found (Atomic Data and Nuclear Data Tables, Vol. 76, No. 2, July 2001) states that this energy is more like 1.54 MeV/(g/cm²), which would lead to 1.613 keV being lost.
That would amount to about 60 ionizations along the path.
I was curious if without that data provided there was any way to know those numbers. Any idea?

 

[mfb]

Which numbers with data from where?

 

[Blidaru Bogdan]

Which numbers with data from where?

I got data regarding : the number of primary electron pairs per cm, excitation energy, the values in that post from Atomic Data and Nuclear Data Tables, Vol. 76, No. 2, July 2001.
If I only possessed my initial energy (4GeV), the energy loss inside (around 2 keV) and the path (6mm) is there any theoretical way to find out the number of primary ionizations along the path of the particle :)?
I tried to work with Loschmidt's number, a diameter for interaction with other particles and ionizing potential for Ar and amounted to 300 keV which is way off.

I am not sure which track to follow as they all lead to different results. If the results were in the range of an order of magnitude it would be a good start, but I'm way off :).

 

[mfb]

If I only possessed my initial energy (4GeV), the energy loss inside (around 2 keV) and the path (6mm) is there any theoretical way to find out the number of primary ionizations along the path of the particle :)?

Not with some information about the gas. And estimating those values with a simulation is probably very hard and way beyond the scope of your project. Take the values from the database. You should get consistent results with them.

 

[Blidaru Bogdan]

You are right! Thanks for the insight!
I am currently trying the Magboltz program developed at CERN for identifying properties of gases.
Seems it does the job. If anyone else is interested they should check it out.