Penning transfer
If one of the components in a gas mixture (typically a noble gas) has excited states above the ionisation energy of another component (typically a quencher), the transformation of excitation energy into ionisations (known as Penning transfer) can contribute significantly to the gas gain.
This effect can be described in terms of a probability \(r_{\text{P}}\) that an excited state eventually results in ionisation. The transfer probability for a given gas mixture and pressure can be determined by comparing measured gain curves with Magboltz simulations. Provided that sufficient experimental data are available, \(r_{\text{P}}\) can be parameterised as function of the concentration c of the admixture and the pressure p. The following table lists the gas mixtures for which \(r_{\text{P}}\) values have been determined from gain curve fits in recent years and the publications in which they can be found.
| Gas mixture | Reference | Comment |
|---|---|---|
| Ar/CO2 | NIM A 768 (2014), 104 | rP(c) at atmospheric pressure |
| Ar/CO2 | JINST 12 (2017), C01035 | rP(c, p) |
| Ar/CH4 | JINST 5 (2010), P05002 | rP(c, p) |
| Ar/C2H6 | JINST 5 (2010), P05002 | rP for 10% C2H6 at atmospheric pressure |
| Ar/C3H8 | JINST 5 (2010), P05002 | rP(c) at atmospheric pressure |
| Ar/iC4H10 | JINST 5 (2010), P05002 | rP for 10% iC4H10 at atmospheric pressure |
| Ar/C2H2 | JINST 5 (2010), P05002 | rP at atmospheric pressure |
| Ar/Xe | JINST 5 (2010), P05002 | rP(c) at atmospheric pressure |
| Ne/CO2 | JINST 16 (2021), P03026 | rP(c, p) |
| Ne/N2 | JINST 16 (2021), P03026 | rP(c, p) |
| Xe/TMA | JINST 13 (2018), P10032 | rP(p) for 5% TMA |
When simulating a detector that uses one of the gas mixtures in this list, the simplest way to switch on Penning effects is to call the function EnablePenningTransfer() of MediumMagboltz.
MediumMagboltz gas("ar", 80., "co2", 20.);
gas.EnablePenningTransfer();
The transfer probability will then be calculated using pre-implemented parameterisations. Alternatively, one can also set the Penning transfer probability explicitly, either globally (i. e. for all excitation levels in the gas mixture) or for a specific gas mixture. In the snippet of code below we set the transfer probability for all excited levels of Argon that exceed the ionisation potential of CO2 to \(r_{\text{P}} = 0.51\).
MediumMagboltz gas("ar", 80., "co2", 20.);
const double rP = 0.51;
const double lambdaP = 0.;
gas.EnablePenningTransfer(rP, lambdaP, "ar");
The second parameter (lambdaP), which defaults to zero, can be used to specify the spatial extent of Penning transfer. When using microscopic tracking, the starting point of an ionisation electron produced by Penning transfer will then be distributed uniformly inside a sphere of radius λ around the point where the excitation occured.
Macroscopic electron transport
The Penning transfer probabilities are not taken into account directly when generating a gas file using Magboltz. Instead, the collision frequencies \(f_{\text{exc}}, f_{\text{ion}}\) for each excitation and ionisation level in the mixture are saved to the gas file.
When switching on Penning transfer (using EnablePenningTransfer), the Townsend coefficient is scaled using
where \(\alpha', \alpha\) are the Townsend coefficients with and without Penning transfer.
For an illustration see this example.