1. Secondary avalanches in gas mixtures
Ö. ŞAHİN, İ. TAPAN and R. VEENHOF
Department of Physics, Uludağ University, 16059, Bursa - TURKEY
Abstract
Avalanche development in gas-based detectors relies not only on direct ionisation but also on excitation of noble gas atoms. Some quencher molecules can be ionised when they collide with excited atoms, a process on which we reported earlier [1]. Alternatively, excited atoms can decay by photon emission. If these photons are insufficiently absorbed by the quencher, yet capable of ionising, then they may escape from the avalanche region and start secondary avalanches. This process, called photon feedback, leads to an over-exponential increase of the gas gain which limits the working range. In this paper, we derive photon feedback parameters from published gain measurements for several gas mixtures and fit these parameters in a model which describes their dependence on the quencher concentration and the pressure.
Fig. 1. Mean free paths of photons in the quenchers considered in this work, at pgas = 1 atm and Tgas = 300 K. Orange lines show the energy of argon excited states. Solid lines correspond to radiative states. For clarity, not all of the excited states are shown on the plot. The cross sections are taken from the review of J. Berkowitz [5] and references therein.
Introduction
Feedback in different quenchers
Noble gas atoms can be excited by collisions with avalanche electrons. Radiative states can decay directly to ground under emission of VUV photons, thus contributing to feedback if suitable quenchers or surfaces are present.
VUV photons with a mean free path smaller than the avalanche merely increase the gain. If the quencher does not absorb the photons effciently, secondary avalanches may result. Radiative decays are moreover subject to radiation trapping [2, 3]. The apparent lifetime of such states is therefore substantially larger than their a natural lifetime. This opens the possibility of delayed avalanches.
Non-radiative states first emit lower energy photons when decaying to intermediate states. Such photons do not in general contribute to feedback because their energy is below the work functions of the gas and the metals used in the counters.
Many of the gain curves that we have used for our Penning study show signs of photon feedback. We have not discussed feedback in detail in the Penning study because the impact of Penning transfers on gas gain can easily be separated from the effect of photon feedback. Feedback is however of practical importance, and interesting in its own right. We have therefore a closer look at the effect here.
The data of P.C. Agrawal et al. [6, 7, 8] shows that βα1/fq, see figure 2. The decrease of feedback with increasing quencher fraction merely reflects the decreasing probability that a photon escapes from the avalanche region. What is surprising is that the relation between β and fq is not exponential.
C2H2 and C3H8 can both be ionised by 4s de-excitation photons but CH4 can not. The mean free path in C3H8 is smaller than in C2H2, and the latter as a result is more prone to discharge. CH4 is not sensitive to 4s radiation and can only be ionised by the much less abundant radiation from 3d and higher states. As a result, is smaller than in the other gases.
Total Gain
Photon feedback can be described with a single parameter β, the number of secondary avalanches started by one avalanche electron [4]. If the average avalanche size without feedback is G, then there will be β G secondary avalanches, producing β G2 electrons in the second generation. Summing, the total number of avalanche electrons is:
Fig. 2. Photon feedback versus quencher fraction. The circles are fits using equation 1 and the solid lines are proportional to 1/fq.
Fig. 3. Photon feedback β versus partial pressure (fp) of C3H8. The circles are the fitted feedback parameters and the lines are the fits with 1/ fp.
I. Krajcar Bronic´ and B. Grosswendt have measured the gain at pgas = 2-50 kPa in Ar-C3H8 mixtures [9]. This data shows that βα1/(fq pgas), see figure 3, confirming the reciprocity seen in the data of P.C. Agrawal et al.
(1)
Conclusions
We have investigated the parametrisation of the secondary avalanches with a simple model which explains the trends observed in several argon-based gas mixtures.
The sum converges only when βG  1/G, which can be interpreted as a stability condition.
Mean free path of excited argon atoms
Acknowledgment
The authors would like to thank Scientific Research Projects unit of Uludağ University and Turkish Atomic Energy Authority for their supports.
The mean free path λ() for de-excitation photons is related to the photo-absorption cross section of the quencher σpa():
References
[1] Ö. Şahin et al., Penning transfer in argon-based gas mixtures, J. Instr. 5 (2010) P –30.
[2] T. Holstein, Imprisonment of Resonance Radiation in Gases, Phys. Rev. 72 (1947) 1212–1233.
[3] T. Holstein, Imprisonment of Resonance Radiation in Gases. II, Phys. Rev. 83 (1951) 1159–1168.
[4] I. Krajcar Bronic´ and B. Grosswendt, Gas amplification and ionization coefficients in isobutane and argon-isobutane mixtures at low gas pressures, Nucl. Instr. and Meth. B 142 (1998) 219–244.
[5] J. Berkowitz, Atomic and Molecular Photoabsorption, ch. 6, pp. 246, 252. Academic Press, 2002.
[6] P.C. Agrawal and B.D. Ramsey, Use of propane as a quench gas in argon-filled proportional counters and comparison with other quench gases, Nucl. Instr. and Meth. A 273 (1988) 331–337.
[7] P.C. Agrawal and B.D. Ramsey, Penning gas mixtures for improving the energy resolution of proportional counters, IEEE Transactions on Nuclear Science 36 (1989) 866–870.
[8] P.C. Agrawal et al., Study of argon-based Penning gas mixtures for use in proportional counters, Nucl. Instr. and Meth. A 277 (1989) 557–564.
[9] I. Krajcar Bronic´ and B. Grosswendt, Ionization coecient in propane, propane-based tissue equivalent and dimethyl-ether in strong non-uniform electric fields, J. Phys. D: Appl. Phys. 32 (1999) 3179–3187.
(2)
where  is energy of the photon, fq the quencher fraction and n = pgas=(kBTgas) the number density of the gas. The mean free paths in mixtures of argon with 10 % quencher are in the range µm, heavier alkanes tend to have smaller mean free paths, see figure 1.
12th Pisa Meeting on Advanced Detectors, 20 – 26 May 2012, Elba – Italy