Computer Simulations
Introduction
A computer model to simulate the interaction of particles
encountered in orbit (protons and electrons) with X-ray telescope
mirrors, of the type used in XMM-Newton and Chandra, at low
angles of incidence, has been implemented in
Geant4.
Geant4 is an object-oriented Monte-Carlo tool-kit developed
in C++ by an international collaboration (of which ESA is
a member) lead by the high-energy physics community. Its modules
have been used to construct independent 3D models of the XMM-Newton
and Chandra geometries. The models, however, shared the same
code for generating isotropic particle populations ‘just
outside’ the telescope aperture and for tracking the
interaction between the protons and the telescope optics and
detectors through the relevant physical processes. For all
protons reaching the focal plane CCD detectors, the momentum
and energy of the particle is stored for each interaction.
This information is used to find the number of scatters each
proton undergoes in the mirrors and other surfaces and the
energy with which it reaches the CCDs. Independent laboratory
tests exposing XMM-Newton mirror and grating samples to grazing-incidence
beams of low energy protons, conducted by Columbia University
were used to validate the simulations.
Geometry
XMM-Newton
The mass model of one of the XMM telescope mirrors, X-ray
baffle and grating systems, consisting of more than 1000 individual
elements, has been implemented in Geant4. At the focal plane
the EPIC-MOS and RGS detectors are represented by simple collecting
areas. A further dummy volume was placed between the mirror
assembly and the grating to estimate the efficiency of the
mirror system at allowing particles through it. The X-ray
baffle has been modelled as two 1mm thick plates 59mm apart.
The material used is 1 part Ni for 2 parts Fe. The telescope
mirrors have been modelled as 58 shells, each of which is made
of four contiguous conic sections: two representing the parabolic
shaped mirror and a further two representing the hyperbolic
shaped mirror. The overall length of the mirrors is 600mm,
centred at a position 7.5m from the focal plane. The surface
of the mirrors is a 50nm gold layer deposited on a nickel
shell of ~1mm thickness. The core of the telescope is filled
by cylindrical nickel tubes. The reflection grating has
been modelled as a grid of plates. Each grating plate structure
consists of 200nm of Gold on top of 40mm of epoxy and 1mm
layer of carbon fiber. Three dummy detector volumes are
included to record the momentum and energy of the particles
reaching the locations of interest:
- A circular detector volume placed immediately behind the
mirror (before the grating) to calculate the efficiency
of the mirrors for scattering protons and to evaluate the
size of the ‘direct leak’ (protons getting through
without any interaction).
- A rectangular detector volume at the location of the RGS.
- A circular detector volume (6.5cm diameter) at the location
of the EPIC.
In order to simulate the EPIC p-n camera, the reflection grating
is removed from the geometry.
Chandra
The geometric model of the Chandra spacecraft comprises
some 400 individual elements, the bulk of which (352 elements)
correspond to the High Resolution Mirror Assembly (HRMA)
alone. There is a forward collimator consisting of 10 parallel
plates, each with 4 annular apertures of varying width corresponding
to each of the mirror shells. The mirrors themselves have
been modelled as 4 shells made of 20 conic sections: the first
10 approximate the shape of the parabolic mirrors and the
remaining 10 sections approximate the hyperbolic mirrors.
A set of central apertures are placed at the centre of the
HRMA, effectively blocking any stray-light. Further apertures
are placed at the centre of the mirrors innermost shell's.
A further collimator is placed behind the HRMA, with 6 parallel
plates of similar construction to the forward collimator,
but with annular gaps consistent with a converging annular
beam. The materials used for the collimator plates and central
apertures was SiO2, PYREX glass was used for the
mirror shells structure, coated with 10nm of Chromium and
32.5nm of Iridium. The whole HRMA is enclosed in a sheath
of carbon fiber. The rest of the spacecraft model consists
of the optical bench, made of two layers of carbon fiber enclosing
a layer of aluminium, and carbon fiber end disks. An aluminium
enclosure at the focal plane end of the telescope houses the
ACIS camera. The CCDs of the ACIS camera are accurately modelled
in size and position. The stovepipe baffle made of tantalum
and carbon fiber and the titanium baffle in front of the ACIS
camera have also been included in the model.
3D VRML graphics of the XMM-Newton
and Chandra model geometries
can be visualised with a VRML viewer.
Particle generator
The particles incident on the telescope can be mono-energetic
isotropic distributions of protons or electrons, although
an energy spectrum representative of the environment crossed
by the spacecraft orbit can also be supplied. Particles are
generated using the ESA sponsored General Particle Source
module, which can also specify the shape of the area or volume
over which the particle population is generated. In order
to maximise the number of particles entering the system, the
isotropic radiation is generated within a cone, the half-angle
of which corresponds to the field of view of the mirror. This
is an optimised way of concentrating a large number of particles
over a restricted area from where they can enter the system
(and hence reduce the CPU time required to achieve good statistics).
In order to simulate the response of the system to radiation
originating at angles outside the nominal field of view, any
arbitrary angle of acceptance or ‘source half-angle’
can be specified. The position of the source is randomly sampled
over an incident area defined as an annulus with minimum and
maximum radii normally matching the telescope aperture. The
source is positioned a very short distance from the telescope
aperture.
Physics processes
The main physics process involved in the simulation is the
scattering of particles with low angles of incidence at the
mirror gold surfaces. The Geant4 Multiple Scattering and Low
Energy Ionisation are the main physics modules used in the
proton simulations and for the electron simulation Bremsstrahlung
is also included. Other processes such as Photoelectric Effect,
Compton Scattering and Gamma Conversion are also included
for dealing with secondary particles.
Simulation runs
A series of simulation runs have been performed for protons
of various energies in the range 100keV to 3MeV. The number
of particles incident on the external side of the X-ray baffle
ranged from a minimum of 5×106 protons when using
narrow viewing angles (up to 2 degrees) to a maximum of 40×106
protons for the most demanding wide angle tests. These relatively
high numbers of incident particles require large amounts of
CPU time to process, but guarantee a statistically significant
number of particles reaching the detectors in all cases. For
each proton energy, a series of runs were conducted, where
the angular distribution of the protons was sampled isotropically
over different conical half-angles, ranging from 0.5 to 30
degrees, representing the particles contained within a solid
angle range from 2.4x10-4 to 8.2x10-1
steradians.
The number of counts registered at each of the detector volumes
is converted to an efficiency measurement "h" defined by:
h = W/4p (Asource/Adetector)(Ndetected/Nincident)
- W is the solid angle that corresponds to the selected
source half-angle q and is given
by 2p(1 - cosq)
- Asource is the area over which the isotropic
particle distribution is generated
- Adetector is the area of the detector volume
on which particles are recorded
- Nincident is the total number of particles generated
over Asource
- Ndetected is the number of particles recorded
at a detector location within Adetector
The efficiency is the number that the omni-directional incident
flux must be multiplied by to derive the flux at the "target".
For each run four different efficiencies have been calculated:
- The efficiency of protons to scatter (at least once) off
the mirror surfaces.
- The efficiency of protons to travel through the X-ray
baffle and mirror surfaces without a single interaction.
- The efficiency of protons in reaching the RGS detector.
- The efficiency of protons in reaching the EPIC-MOS detector.
Results
The results of the Geant4 simulations are best represented
in terms of efficiency h as a function of proton energy.
Figure 1 shows a summary of the efficiencies obtained for
the ACIS, EPIC MOS and RGS instruments.
Figure 1 Efficiency of protons reaching
the CCD detectors on Chandra and XMM-Newton as a function
of their incident energy. The proton population at the telescope
aperture is sampled out to a 10 degree source half-angle.
The efficiency of protons in reaching the ACIS detectors
is about 1 in every 105 incident on the telescope
aperture, at least a factor 2 greater than that for the EPIC
camera, especially at the lower proton energies. The efficiency
on the RGS is one order of magnitude less than that on the
EPIC.
Figures 2 shows the proton impacts on the XMM-Newton focal
plane (the position of the EPIC and RGS detectors is also
shown) and Figure 3 shows the proton impacts on ACIS.
Figure 2 Schematic of the position of
the EPIC (circle) and RGS (small rectangle) detectors on the
focal plane, showing the impacts of 200 keV protons from a
simulation where 5×106 protons were generated at
the telescope aperture within a 1 degree source half-angle.
Figure 3 Schematic of the focal plane
layout of the CCDs on the ACIS instrument, showing the impacts
of 200keV protons from a simulation where 5×106
protons were fired at the telescope aperture within a 1 degree
source half-angle.
The spatial distribution of the protons impinging on the
XMM-Newton CCD detectors is not uniform but falls off with
distance from the optic axis. This is in good agreement with
what has been measured on the actual instruments in orbit.
The distribution of protons reaching the ACIS in the simulation
appears to be uniform, but non-uniform distributions have
been reported from the instrument in orbit.
The fall-off with radial distance from the optical axis
in the proton numbers reaching the XMM-Newton detectors (often
referred to as "vignetting") is being further investigated.
Figure 4 shows this effect on both EPIC cameras as obtained
from running simulations where 20x106 200keV protons
are incident on the telescope aperture.
Figure 4 Proton impacts per cm2
on EPIC MOS and PN cameras from Geant4 simulations where an
isotropic distribution of 20x106 200 keV protons
were generated at the telescope aperture within a 1o
source half-angle.
The fall-off from the centre to the edge of the EPIC detectors
obtained from the simulation does not appear to be gradual
but in both cases it shows a structure similar to a fringing
pattern.
Conclusions
The investigations carried out in the course of this study
show that protons can propagate through grazing-incidence
mirrors designed to focus X-rays and reach focal plane detectors.
Besides contributing to the background radiation levels on
the detectors, at certain proton energies NIEL damage may
lead to severe degradation of the instrument. The predictions
made with the above models triggered the adoption of protective
measures (i.e. shield closure) to protect the EPIC instruments
during radiation belt passages, which has prevented significant
damage from occurring to their CCDs. The prediction for the
CCDs on the RGS instruments, for which no protective measures
can be taken, was that the level of damaging proton fluence
expected would not lead to significant radiation damage, as
it has indeed proved to be the case.
Geant4 has proven to be a powerful tool for modelling the
interactions between spacecraft and their orbital environments,
as it allows to build complex geometries, model the physics
and the radiation processes in 3D.
Current Developments
The XMM-Newton Geant4 model is being further refined to
investigate the background radiation level provided by protons
encountered in radiation belt passages and those produced
in solar event, for all CCD detectors. For this work, the
geometry model will include a full description of the focal
plane instruments (optics and detectors) and the physics models
will be extended to lower proton energy regimes.
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