Optimizing ³He tube design for various operational conditions: A review of the design parameters of ³He gas proportional counters used for neutron detection

ABSTRACT

Gas filled cylindrical proportional counters are long established and widely used for the detection of thermal neutrons. The practical and pragmatic issues involved in the construction of such counters remains partly as the undocumented lore and art of a few manufacturers. In this paper we present our experience as a guide to a better understanding of the constraints within which counters and their gas fillings may be chosen to satisfy operational requirements for a wide range of conditions including high count rates and high gamma backgrounds.

INTRODUCTION

This paper considers the constraints within which the gas mixtures used in neutron sensitive ³He gas filled proportional counters may be varied for gross neutron counting. The material extends the general discussions given in text books.

A neutron moderator is used to exploit the 1/v cross section allowing fast neutrons to be detected with higher efficiency. After moderation the neutron has negligible kinetic energy and so in interacting with a 3He nucleus a proton with an energy of 573 keV and a triton of 191 keV are emitted back to back and they ionize the gas in the counter as they are slowed down and stop. A single track is formed but the ionization is denser at the ends due to the Bragg effect [1]. The ionization created may be collected by an electric field allowing neutrons events to be detected.

The electrons move about 1000 times faster than the positive ions so we can ignore the movement of the positive ions over the timescale in which the electrons are collected. Near the cathode the electric field is weak so the electrons drifting towards the central anode wire do not gain sufficient energy between collisions to ionize the gas. If the gas contains electronegative impurities such as oxygen, then the electrons can attach themselves to these gas atoms to form slow moving negative ions - i.e., they are effectively lost from the drift process. This is why gas purity is so important in proportional counters – it is essential to keep the concentrations of oxygen and other electronegative species below 10 ppm (and preferably below 1 ppm).

As the electrons drift nearer to the anode, the electric field in a cylindrical proportional counter becomes stronger. At a radius of about twice that of the anode the electron gains enough energy between collisions to ionize another gas atom (i.e. a second free electron is obtained along with a positive ion). The two electrons continue to drift towards the anode, (while the positive ion goes slowly to the cathode), and each gains enough energy to ionize two more atoms and so on until the electrons reach the anode. In the last stage of multiplication before reaching the anode (which accounts for roughly half the total number of ion-pairs produced) the number of electrons liberated per primary electron can be as high as 10,000. Although this figure is not uncommon for low energy primary events such as soft X-rays in gas filled proportional counters for X-ray spectrometry it is unusual for neutron counters to go this high. For neutron counting application a gas multiplication in the range 10 to 100 is typical and rarely values approaching 1000 will be used. The reason for this is that, for ³He counters, experience shows that good pulse height resolution can be obtained if the total gas gain is kept between 10 and 100. Above this the resolution deteriorates but it may be advantageous to operate outside this range for particular reasons (for example to reduce the pulse rise time when event timing is of interest). The gas gain depends on the voltage on the anode. Together with the anode diameter and the cathode diameter this defines the electric field gradient. The other important variables are the gas mixture and the fill pressure. Space charge effects set the limit on gas gain. When the total number of ion-pairs approaches 10⁸ the multiplication process begins to lose proportionality [2] due to the sheath of charge around the anode reducing the multiplication, impairing full collection and allowing greater recombination.

If we examine the electrical disturbance i.e., the induced charge signal at the anode, we note that although a large number of electrons arrive, most are produced very close to the anode and so have only moved through a small electric field in reaching the anode. The signal produced is therefore very small. However, the positive ions now (i.e. they hardly moved during the electron collection) drift towards the cathode, most of them moving through virtually the whole voltage drop V. This induces a large signal on the anode. The initial fast rise is due to the ions moving through the stronger field near the anode: as the ions approach the cathode they slow down because of the weaker field and they have to travel further to produce the same effect at the anode. The value of the ion collection time is of the order of l ms (it depends upon counter size, gas pressure, anode diameter, voltage and gas composition) [3].

The signal is usually differentiated with a shaping time constant of l to 4 m s to give an analog signal which is directly proportional to the number of electrons (equal to the number of positive ions) formed in the avalanche which in turn is directly proportional to the number of primary ions pairs formed by the interaction of the incident radiation with the counter gas. If very high counting rates are required then shorter time constants must be used to utilize the fast electron pulse, but as the amplitude of this signal is much less than that due to the positive ion movement there can be signal/noise problems. However, shorter time constants are used routinely to improve the rejection of gamma ray events in the counter. Typically the energy deposition in the gas resulting from a gamma ray interaction is low because the electrons produced are lightly ionizing and can pass across the gas volume with the loss, at most, of only a few tens of keV. If neutron spectroscopy is required (i.e., analysis of the energy deposited by fast neutrons incident directly on the counter without moderator as opposed to simply total neutron event counting) then longer shaping time constants have to be used. Longer shaping times are needed in order to obtain a signal that is truly proportional to the total energy release. The count rates that can be achieved in spectroscopy mode are considerably reduced from those used for total event counting.

Ricker and Gomes [18] present the general principles and important parameters behind the formation of the detector signal that Ramsey first correctly described from empirical results. They set out the nine principal physical assumptions involved six of which are generally met. We comment on three:

i) Only the avalanche electrons and positive ions contribute to the formation of the anode pulse. This is satisfied for counters with substantial gains (> 100), for which the effects of the positive ions produced by the original photoelectron prior to the avalanche can be neglected.

ii) The time required for the high voltage supply to restore the drop in voltage caused by positive ion collection is long compared to the time of positive ion collection. Although often not satisfied, but a suitable correction for it can easily be made. In actual practice this assumption is deliberately violated; otherwise, pulse pile-up would render the counter useless as an energy analyzer. Furthermore, the maximum practical restoration time is limited by the counter capacitance and the coupling resistor required by the high voltage power supply for signal generation. The counter capacitance in series with the coupling resistor acts to differentiate the counter output pulse together defining a roll-off time constant.

iii) The ionic mobility, K₀, is a constant independent of ion velocity. For counter designs using very high voltages V₀ or very small wire radii, a, this assumption is invalid, since K₀ does vary weakly with the electric field E. However, the precise nature of this function depends in a rather involved way on the counter gas and its effect on the counter pulse shape will be not discussed here.

Ricker and Gomes go on to calculate the voltage pulse at the amplifier input (i.e., after passing though the high voltage coupling capacitor). They show that the pulse rise time can be calculated if the electron drift velocity and the ionic mobility K₀ for the appropriate charge carrier in the gas mixture are known. For ³He p + t tracks the situation is complicated because the specific ionization is not constant along the track and the distribution of tracks is not uniform within the counter because of neutron absorption near the cathode. Furthermore, the near isotropic nature of the ³He tracks considerably increases the difficulty of the calculation. The problem, and time involved, of carrying out the calculations is not justified here because it is still necessary to obtain experimental data. It is therefore simpler to directly measure the pulse rise time for the counter in the required experimental configuration. One consequence of the extended track of ions, which, because of the Bragg effect are concentrated at each end, is that tracks perpendicular to the anode can create markedly bi-modal signals. This is because the charge density is dumb-bell shaped and as each lobe is collected a peak in the signal is created. The possibility of double pulsing due to tracks that are almost perpendicular to the anode is discussed in the Appendix .

Brown and Jenson [19] have shown that the minimum time for electrons to travel from the cathode to the anode is a function of the value of E/p (electric field strength divided by fill pressure) at the cathode. They showed that for Ar/CH 4, the fastest gas measured by them, the minimum transit time (divided by the cathode radius) was about 0.15 μs.cm -1, i.e. for a 2 cm cathode radius a minimum of 0.3 μs. A typical value would be nearer to 1 μs. The important point to note here is that the minimum transit time from cathode to anode is inversely proportional to the counter radius, i.e. small diameter counters will have faster electron transit times. For long track events (neglecting collisions with the cathode) the final counter electrical output pulse (formed by movement of the positive ions away from the anode) will be increased as the cathode radius increases.

The gas multiplication factor in a cylindrical proportional counter is important if absolute values of incident particle energy (e.g., in spectroscopy) or w (mean eV deposited required to create an ion pair) are required. It is also of interest during the design and in operation in order to ensure that a sensible operating point can be established. For most uses of ³He counters the exact gas gain is not important. However, it is useful to understand the factors controlling gas gain if batches of counters are to be connected in parallel or are to be operated from the same voltage supply. The gas gain has been considered by many authors, e.g., Kiser [6]. There is a considerable volume of literature on this subject (see for example [8, 9]. Harling [14] showed that scaling laws can be used to predict the properties of a counter based on the known characteristics of another counter. If the gas gain is the same for both counters then the operating voltage, V, is given by: V = K₁ + K2 .p.a.ln(b/a) where K₁ and K₂ are appropriate constants and b is the cathode radius. Harling gives values of K₁ and K₂ for Helium/CO₂ mixtures. If it is desired to have two physically different counters operate at the same gas gain then Harling showed that the product between the pressure and anode diameter, p.a, must be constant and V/ln(b/a) must also be constant and both conditions must be satisfied independently. In practice with standard tube dimensions and gas mixtures matching may be approximate.

The experimental time involved in obtaining the appropriate constants for a given ³He/quench mixture is high so that for many purposes (if published data is not available) it is sufficient to obtain data over a limited range and then select the most suitable and convenient formula for interpolation calculations.

As the gas gain in a counter is increased there comes a point at which space charge effects start to become important. These effects lead to variations in gas gain between different avalanches i.e. non-linearity in the proportionality of the counter. The effect is particularly severe for detectors designed for low energy X-rays (or other high specific ionising particles e.g. alphas) operated at very high gas gains (e.g., > 10 5). Because of the long p + t track lengths in ³He counters the avalanche is spread out and space charges effects are less likely to be a problem (except for ionising tracks perpendicular to the anode wire). So as the relatively large signal does not require the use of high gas gains it is recommended that they are kept well below 4000 ( » 10⁸ /(765000 eV/30 eV.ip -1).