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Characterization of the MCPI sensors

1. Introduction

This documents describes the characterization of three 2p F.O.V sensors which were flown on the HEO satellite 1997-068. By use of the GEANT software, the efficiency of the sensors along with their angular sensitivity were evaluated. A data analysis protocole is suggested.

2. GEANT model

The three sensors are made of mushroom shaped silicon detectors under hemispherical aluminum shields. The inner radius of the aluminum shields are 1 cm and the outer radius are 0.0305, 0.126 and 0.319 cm, respectively. The GEANT model of the mechanical assembly is sketched in Figure 1, which also shows tracks of 50 MeV protons from an isotropic flux passing through the point at 45 polar angle and 90 azimuthal angle on the shielding dome surface.

Fig. 1: For each of the sensors, threshold levels of detected energy loss were set electronically at 0.3 MeV and 5 MeV.The channel which records particles with more than 0.3 MeV energy loss are named with a suffix L, whereas the channels for particles loosing more than 5 MeV in the detector are named with a suffix H. The shielding thicknesses given above (multiplied by 1000) appear as prefix in the channel names. Thus, the six channels are named 030L, 030H, 126L, 126H, 319L and 319H

3. Averaged efficiency over a 2p F.O.V solid angle

The three sensors are accomodated on a sufficiently massive satellite so that one can assume that no particle can reach the sensor from the rear side hemisphere. Therefore, the efficiency of the sensors were evaluated for particles of which the tracking was initiated at the hemispherical aluminum shields. The detection efficiencies of electrons, protons and a - particles for an isotropic flux are shown in Figure 2.

Fig. 2: One sees that the low energy channels are sensitive to electrons, whereas the high energy channels count protons and alpha - particles only.

4. Angular sensitivity

Using a complex well performing detection system, one should be able to give quantintative answers to the following queries:

+ Given a space direction, is it possible to calculate the energy spectrum of particles from that direction?
+ Given an energy interval, is it possible to evaluate the angular distribution of particles having that energy?



Obviously, such radiation detection systems should be designed with a number of energy channels and cover several field of view (solid angle channels).

To analyse data from simple detection systems, one has often to assume an angular distribution model for detected particles and deduce the energy spectrum parameters. On the other hand, one may assume an energy spectrum for detected particles and deduce their angular distribution, provided that the detector is sensitive to the particle incident angle. It may be shown that this last condition is fullfilled, when the product of the detection efficiency (averaged over the effective surface) and the effective surface is not constant for the channels of the detection system.This product (QA) is shown in Figure 3 for protons and for channel 126L and 126H.

Fig. 3 It is not constant for the low energy channel and for a proton spectrum characterized by a power law index equal to 2 detected by the channel 126L. However the variation of this product over the polar angle ranging from 0 to 90 deg. does not appear to be very significant for the high energy channel 126H.

5. Deconvolution formula

5.1. Energy spectra

The contribution of a given particle type to the counting rate in channel i of sensor j is given by:

where the geometrical factor appears and contains information on the integral (over the F.O.V solid angle and the aperture surface) of the angular distribution pji(E) is the intrisic detection efficiency and is the differential flux of particles.

Other parametrizations of the energy spectrum may be used Eth and Eu are the limit of channel i of module j.

The geometrical factor of an hemispherical aperture with a radius R for an isotropic flux is:

Departure from this values indicates that the flux is not isotropic. Thus, in a thorough data analysis process, the geometrical factor (gathering factor) is considered as a parameter to be determined on the basis of experimental data.

The parameters G, gamma, Jd0 characterizing the energy spectrum and the angular distribution of the particle flux are obtained by minimizing the function:

When the sensors detect many particle species, their contributions to the counting rate are summed up and the function changes accordingly. Unfortunately, with 6 energy channels from our 3 sensors, which corresponds to 6 constraints, it is only possible to deduce 6 parameters (the two energy spectrum parameters times three particle species). It will be necessary to make assumptions on the angular distributions, i.e. to give the value for G, for each type of particle. An isotropic flux will be assumed for electrons, protons and alpha - particles.



The efficiency of three sensors has been evaluated using the GEANT software. Possible uses of these sensors to deduce energy spectra and angular distribution of electrons, protons and a - particles were investigated. We conclude that

1.At least five such sensors are needed in order to deduce energy spectra of three particle species
and three gathering (geometrical) factors which contains informations about the angular distributions. Using three sensors, one may deduce three energy spectra for every counting rate sample, but angular distributions must be ussumed.

2.The sensitivity of the sensors to the particle incidence angle appears to be not significant enough for all the channels to allow extraction of parametrized angular distribution functions.

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