Advances in High Energy Physics

Volume 2016 (2016), Article ID 8561743, 8 pages

http://dx.doi.org/10.1155/2016/8561743

## Analytic Approximation of Energy Resolution in Cascaded Gaseous Detectors

Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics of the HAS, 29-33 Konkoly-Thege Miklós Street, Budapest 1121, Hungary

Received 3 February 2016; Accepted 28 March 2016

Academic Editor: Ming Liu

Copyright © 2016 Dezső Varga. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

An approximate formula has been derived for gain fluctuations in cascaded gaseous detectors such as Gas Electron Multipliers (GEMs), based on the assumption that the charge collection, avalanche formation, and extraction steps are independent cascaded processes. In order to test the approximation experimentally, a setup involving a standard GEM layer has been constructed to measure the energy resolution for 5.9 keV gamma particles. The formula reasonably traces both the charge collection and the extraction process dependence of the energy resolution. Such analytic approximation for gain fluctuations can be applied to multi-GEM detectors where it aids the interpretation of measurements as well as simulations.

#### 1. Introduction

The energy resolution of gaseous detectors, that is, the precision with which a specific energy deposit can be measured, is a fundamental parameter and indication of instrumental quality. From the broad literature of gaseous detectors, such as classical [1] or recent review documents [2, 3], one can understand the key contributing factors to the energy resolution. The fluctuation from the ionization process defines the “intrinsic” limit, quantified by the “Fano factor.” The main contribution however stems from the fluctuation of the amplification of single electrons: as avalanches are formed, the amplitude (detected signal) fluctuates.

The energy resolution formula includes the single avalanche fluctuation: the signal amplitude , usually expressed in units of input electrons, will have the following relative precision:

Here the key is , the single electron avalanche fluctuation, defined as the standard deviation relative to the mean value. depends not only on gas composition but on amplification geometry. The energy resolution scales with the primary electron number from the ionization, whereas instrumental effects further broaden the response.

Assuming that an avalanche process (which can be quite complicated) initiated by a single electron finally results in detected electrons with probability of , one can express . The mean gain is the mean value of the probability distribution. If the standard deviation is , the relative fluctuation is defined as . As an example, if the electron number distribution is purely exponential, then .

Experimental and theoretical estimates for have been a subject for many studies. For proportional chambers, Alkhazov predicts around 0.8 [4], depending on gain. A classical calculation was proposed by Legler [5]. Micropattern Gaseous Detectors (MPGDs) perform considerably better in energy resolution, due to the smaller values: this is true for GEMs (Gas Electron Multipliers) [6], whereas micromesh detectors are particularly outstanding [7] in this respect.

For GEM detectors involving multiple amplification layers, is referring to the whole process of the cascaded amplification. The electrons undergo various steps until the avalanche reaches the readout anode: they can be lost before entering the GEM holes or may end up on the other side of the GEM, following the field lines. The question addressed in this paper is as follows: can we approximate for a cascaded process? How can we include collection and extraction (in) efficiencies? This question not only is related to detector physics, but has relevance for practical instrument design, where simulations and measurements have a very broad range of parameters. Direct calculation can help in finding guidelines and assist search for optimized designs. We will find that the approach can be applied to any cascaded gaseous detectors, including hybrids of different MPGD types.

#### 2. Collection and Extraction from a GEM Layer

The avalanche process in a GEM detector takes place in the high field of the GEM holes. The focusing field geometry guides the electrons to the holes, whereas the field lines which emerge from the hole extract a certain fraction of the electrons [8]. The situation is shown in the cartoon of Figure 1. In this sense the avalanche formation can be separated in four steps:(1)Collection: the (single) electron from an ionization process drifts towards the GEM, being focused to a hole after leaving the approximately homogeneous drift region with field strength of . As some field lines end up on the GEM, the probability of entering the hole is . This means that fraction of the electrons is lost for the subsequent amplification.(2)Avalanche: those electrons which arrive in the high field region undergo a Townsend-avalanche. The total number of electrons coming out of the avalanche is , with relative fluctuation of .(3)A fraction of electrons is extracted: with a probability of , depending strongly on the transfer field below the GEM, the electron leaves the vicinity of the hole and drifts towards the subsequent gain stages. Actually most of the electrons ( fraction) end up on the bottom of the GEM.(4)The extracted electrons will be further amplified leading to signal formation in the detector. For this step, the relative fluctuation will be denoted by .