A proposal to study gas gain fluctuations in Micromegas detectors M. Chefdeville 15/05/2009 We present two methods to measure gas gain fluctuations in Micromegas detectors and the experimental setup that would be needed for such a study. 1 Introduction The development of an electron avalanche in gas is a stochastic process that is governed by probabilities. As a result, the total number of electrons produced in an avalanche fluctuates. The gain fluctuations impact on the performance of amplification-based gaseous detectors such as Micromegas. In a TPC for instance, several primary electrons are multiplied above a few pads of a given pad row. The center of gravity of the primary electrons would ideally be determined with an equal weigth for each electrons. Gain fluctuations, however, modify the weigths which results in a worse precision on the c.o.g. and hence in a degradation of the spatial resolution. The intrinsic limit of the energy resolution of a gaseous detector is set by the flucutations in the primary number of electrons and by the gain flucutations. Neglecting all secondary effects (electronic noise, limited collection of the primary electrons, field non-uniformity...), the resolution R can be expressed as: R 2 = F + b (1) N where F is the Fano fator, b the relative variance of the gain distribution and N the number of primary electrons. The gain distribution (also called single electron response SER) has been already measured for various detector geometry (Micromegas, GEM, PPC). It can be parametrized by the Polya distribution: ( ) m 1 p m (g) = mm 1 g exp( mg/g) (2) Γ(m) G G where G is the mean gain and m is a parameter that relates to the relative variance of the distribution b = 1/m. The Polya distribution for various integer values of m (1 5) is shown in Figure 1. At m = 1 the distribution is a decreasing 1
exponential. When m increases a maximum appears at non-zero values of the gain and the variance decreases. 1 m = 1 m = 2 m = 3 m = 4 m = 5 10-1 10-2 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 g/g Figure 1: Polya distribution for various values of m. Gain fluctuations can be studied by measuring the single electron response. This is realized by releasing single electrons in the gas (generally by focusing a low intensity UV laser on a photocathode) and measuring the individual signals after multiplication. This technique requires very low noise electronics and relatively high gas gains (larger than 10 4 ). Such studies have been conducted twice with Micromegas: in He/iC 4 H 10 0/30 at G = 10 5 and more recently in Ne/iC 4 H 10 95/5 at G = 10 4 10 5. The shape of the gain distribution can be investigated indirectly. Under the assumption that it is Polya-like, a measurement of G and m fully determined p(g) (Equation 2). In opposition to G, measuring m is not straightforward as it relates to the signal variance which can be influenced by several effects. We propose in this paper two simple measurements of m which can be performed with an 55 Fe source. Hence, the shape of the gain distribution in Micromegas detectors can be determined in several gas mixtures, which has never been done before. Our results are important for the basic understanding of Micromegas and useful as input for detector simulation. Also, they can be compared to GARFIELD predictions (common gas detector simulation program). Eventually our study could very well be accepted for publication. 2
2 Measurements of gain fluctuations 2.1 Measurement principle Our mesurements are based on a more complete form of Equation 1 which takes intot account the effect of the collection efficiency on the energy resolution. Each primary electron has a probability p to reach the amplification gap and (1- p) not to do so. Accordingly, if we consider a fixed number of primary electrons N, the number of collected electrons N c follows a Binomial distribution: p(n c ) = N! N c!(n N c )! pnc (1 p) N Nc (3) Calling p = η the collection efficiency, the mean of N c is equal to: N c = ηn (4) where we omitted the average bar (N c ), and its variance is given by: σ 2 N c = Nη(1 η) (5) The fluctuations in the number of primary electrons, number of collected electrons and gas gain are independent. Their relative variance can be summed and Equation 1 becomes: which yields: R 2 = F N + b Nη(1 η) + ηn (ηn) 2 () R 2 = F 1 + (b + 1)/η N From this Equation, the gain relative variance b (and hence m) can be adjusted onto the measured trends of R(η) or/and of R(N ). In the first case the collection efficiency is varried while in the second it is the number of primary electrons. In the next two sections, we describe how these measurements could be performed. A design of a gas box housing a Micromegas of small size that would fulfil the measure requirements is proposed in section 3. 2.2 Energy resolution and collection efficiency The electron collection of Micromegas depends on the compression of the field lines at the entrance of the mesh holes. More precisely, it is an increasing function of the field ratio E A /E D because the electrons are more strongly focused towards the center of the holes. As an example the trend of the position of the photopeak from 55 Fe 5.9 kev X-ray conversions in an Ar-based mixture as a function of field ratio is shown in Figure 2 (a). The energy resolution, defined as the relative r.m.s. of the peak, decreases with the field ratio as the collection efficiency improves (Figure () 3
2 (b)). The correlation between resolution and efficiency is made clearer in Figure 3 where R is plotted as a function of η. Here the assumption is made that the collection efficiency is equal to 1 when the peak position is maximum. According to Equation it can be parametrized as: p0 1 R = + p 2 + 1 1 (8) p 1 p 1 η with p 0 = F, p 1 = N and p 2 = b. Hence, b can be adjusted to the data points, fixing F and N to values found in litterature. In Ar-based mixtures, the Fano factor has been measured to be around 0.2 while N = E 0 /W is equal to 230 electrons for 5.9 kev X-ray conversions by the photoelectric effect (using W = 25. ev). In Ar/iC 4 H 10 9.2/2.5, we thus obtain (b ± b)= (0. ± 0.02) which corresponds to gain relative variations of 90 % r.m.s.. peak position (ADC) 140 130 120 110 100 90 80 0 0 Ar 2.5% ic 4 H 10 50 40 0 50 100 150 200 250 field ratio energy resolution (%) 11 10 Ar 2.5% ic 4 H 10 9 8 5 0 50 100 150 200 250 field ratio (a) (b) Figure 2: 55 Fe peak position (a) and energy resolution at 5.9 kev (b) as a function of field ratio. 2.3 Energy resolution and number of primary electrons The energy resolution is a decreasing function of the number of primary electrons N (cf. Equation 1). At full collection efficiency the trend of the resolution with N depends on F and b which can hence be determined from a measurement of the resolution at various X-ray energies. An 55 Fe source emits 5.9 and.5 kev X-rays in the ratio 8.5/1. The absorption of an X-ray by the photoelectric effect on an argon atom results in the emission of a photoelectron. The excited atom can emit a fluorescence photon which likely escape the detection volume (the fluorescence yield of argon is equal to 0.13) or an Auger electron (actually several Auger electrons). 4
11 10 9 χ 2 / ndf 31.48 / p0 0.2 ± 0 p1 230 ± 0 p2 0.49 ± 0.0202 R (%) 8 Ar 2.5% ic 4 H 10 5 0.4 0.5 0. 0. 0.8 0.9 1 1.1 η Figure 3: Energy resolution at 5.9 kev and electron collection efficiency. As a result, the 55 Fe spectrum in Ar-based mixtures contains four peaks: K α photopeak at 5.9 kev K α escape peak at 2.9 kev K β photopeak at.5 kev K β escape peak at 3.5 kev Assuming W =25. ev, these four energies correspond to 230, 113, 253 and 13 primary electrons respectively. The K α and K β lines are close to each other ( E = 0.5 kev) and therefore the double peak structure of the escape peak and photopeak can only be measured with a detector of very good energy resolution. This structure is visible in the spectrum shown in Figure 4 where a small peak from Al fluorescence at 1.5 kev (channel number 45) is also observed. This spectrum was recorded in an Ar/CH 4 90/10 mixture with an integrated Micromegas (50 µm gap Ingrid at V grid = 390 V). The sum of four gaussians is fitted to the spectrum. Doing so, the gaussian means are constrained by the energy ratios while the integrals and sigmas are free parameters of the fit. Ignoring the escape peak of K β X-ray conversions which contains too little events, the measured energy resolution is determined at each energy (Figure 5). According to Equation 1, we use the following parametrization of the resolution R and the peak position p: p0 + p 1 R = p (9) 5
where p 0 = F and p 1 = b. Adjusting p 1 to the data points we obtain (b ± b)= (0.33 ± 0.01) in Ar/CH 4 90/10 which corresponds to gain relative variations of 58 % r.m.s.. This value is significantly lower than the one obtained in Ar/iC 4 H 10 9.2/2.5 (cf. section 2.2). A different InGrid was used for the two measurements and this observation can probably be explained by a better amplification gap uniformity of the InGrid used in the P10 mixture. 3 10 5.9 kev.5 kev 2.9 kev 3.5 kev 10 2 0 50 100 150 200 250 300 MCA channel Figure 4: 55 Fe spectrum in a P10 gas mixture (a) energy resolution (%) 8.5 χ 2 / ndf 10. / 2 8.5.5 p0 0.2 ± 0 p1 0.3323 ± 0.004 5.5 80 100 120 140 10 180 peak position (ADC) Figure 5: Energy resolution and peak position for 2.9, 5.9 and.5 kev (b).
3 Experimental setup The main requirement to perform the measurements presented previously is to minimize all sources of signal fluctuations other than primary and gas gain fluctuations, for instance electronic noise and amplification uniformity. Concerning the first requirement, a Micromegas of small area (a few cm 2 ) and a low noise electronics (ORTEC 142B preamplifier or the one used at NIKHEF) are well suited. A uniform amplification gap can be obtained with an InGrid or, with larger areas, a Micro-Bulk which is a round-shaped Bulk Micromegas of about cm diameter and a continous anode. Both achieve a very good energy resolution probably due to the uniform gap. A design of a test chamber is shown in Figure. The drift gap should be of a few mm to have a uniform field between the mesh and the cathode and to allow low field ratios (that is high drift fields) at voltages smaller than 2 kv. The cathode could be a mesh with high transparency so that the chamber inside can be looked at during operation (during cooking of the mesh for instance). The window should be transparent to X-rays, in that respect a thin kapton or mylar foil should be fine. The distance from the window to the cathode should be small (about 5 mm) to minimize X-ray absorption in this gap. Two HV connections are needed to bias the cathode and mesh. These connections can be made through a few mm thick PCB maintained by screws and an O-ring on one chamber side. Figure : Design of a test chamber.