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
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:
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).
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.
contribution of a given particle type to the counting rate in channel
i of sensor j is given by:
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.
parametrizations of the energy spectrum may be used Eth and
Eu are the limit of channel i of module j.
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:
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.
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
1.At least five
such sensors are needed in order to deduce energy spectra of three
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.
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.