RADIATION ENVIRONMENT INDUCED DEGRADATION ON CHANDRA

Transcription

1 REPORT RADIATION ENVIRONMENT INDUCED DEGRADATION ON CHANDRA AND IMPLICATIONS FOR XMM Prepared by: R. Nartallo, H. Evans, E. Daly, A. Hilgers, P. Nieminen, J. Sørensen ESA Space Environments and Effects Analysis Section F. Lei, P. Truscott, DERA Space Department, U.K. S. Giani, J. Apostolakis, CERN, Switzerland S. Magni, INFN, Milan Reference: Esa/estec/tos-em/00-015/RN Issue: 1 Revision: 0 Date of Issue: March 16, 2000 Status: Final Document Type: Report Distribution: F. Jansen, D. Lumb

2 2 of 60 DOCUMENT APPROVAL Title: Date: March 16, 2000 Issue: 1 Revision: 0 Author: Name Organisation Date Signature Ramón Nartallo TOS-EMA March 16, 2000 Approved by: Name Organisation Date Signature DOCUMENT CHANGE LOG Issue Revision Date Reason for change DOCUMENT CHANGE RECORD Page(s) Paragraph(s) Reason for change

3 3 of 60 TABLE OF CONTENTS 1 Introduction Geant4 simulations XMM Particle generator Physics processes Tracking Parameters XMM spacecraft geometry The X-ray baffle The telescope mirrors The reflection grating The detector volumes Simulations Results Efficiency of the mirrors a) Scattered protons b) Direct hits EPIC and RGS detectors Effect of the EPIC baffle Arrival of protons in the vicinity of the RGS Effect of the entrance baffle Chandra Chandra spacecraft geometry Results Efficiency of the mirrors ACIS detector Comparison between XMM and Chandra Validation of Geant Comparison with TRIM Simulation set-up Comparison with Experiment RGS Grating Tests Mirror Shell Tests Analysis of opacity of baffle using the Sector Shielding Analysis Tool Background Simulations conducted a) Shielding analysis of the inner baffle b) Shielding analysis of the baffle from the mirror Independent Modelling of Mirror Acceptance Angles Environment Solar/heliospheric protons Statistically-Based Predictions Magnetospheric Environment Discussion Conclusions References... 60

4 4 of 60 1 Introduction Chandra has recently experienced unexpected degradation of the majority of the CCDs in the ACIS instrument. Since Chandra is in a similar orbit to XMM, which also has instruments based on CCDs, a concern exists over the effects on these instruments. This technical note represents a report of the analysis to date by the ESA Space Environments and Effects Analysis Section of the problem. It has become clear in the time since the symptoms were first observed on Chandra that the problems were due to low energy (~100keV) protons reaching the focal plane after scattering through the mirror shells. The observed damage characteristics are highly suggestive of largescale displacement damage. Furthermore, the damage was observed in front-illuminated devices where the sensitive channel is some microns from the surface while back-illuminated devices, where particles have to penetrate only some tens of microns further, are largely undamaged. Besides the Optical Monitor (not considered in this study), XMM has 5 CCD-based instruments for X-ray detection: two Reflection Grating Spectrometers (RGS), each with 9 back-illuminated MOS CCDs, and three European Photon Imaging Cameras (EPIC), two of which consist of 7 front-illuminated MOS CCDs and the third has a array of 12 p-n chips. For comparison, the ACIS camera on Chandra consists of 10 MOS CCDs, of which only two are back-illuminated. Figure 1 to Figure 4 show the focal plane detectors of these instruments This report analyses in detail the mechanism by which these protons can reach the CCDs and cause damage. In the introduction, some background on other lines of investigation is also provided. In the early phase of the analysis, the possibility that the damage was a result of energetic electron incidence was studied, along with other possibilities. The main tool used for the quantitative analysis has been the Geant4 Monte-Carlo toolkit, developed by a collaboration in the high-energy physics community, strongly supported by CERN and also including ESA. The physical process at the centre of the study, low-angle scattering of low-energy protons, is not one that has received much theoretical or experimental study. Therefore, an important element in the study was the validation of the Geant4 results by comparison with a well-established program, TRIM, which although it treats the interactions in three-dimensions, the medium in which the interactions themselves take place is planar. Further validation was sought by comparison with experimental results from Columbia University, carried out as part of the recent efforts to investigate the problem. We show that the X-ray optics of Chandra and XMM behave quantitatively in a very similar manner and that for every unit of omnidirectional flux on the mirror shells, something in the region of 10-6 to 10-5 particles reach the focal plane. Part of the reason for this high figure is that the optics can transmit particles that are incident off-axis at relatively high efficiency. Chandra is in a highly eccentric orbit (the orbit parameters are given on Table 1). With an argument of perigee of 270º, the apogee is the most northerly possible and is on average as clear of the radiation belts as it is possible to be in this orbit. Nevertheless, the orbit does cut through the radiation belts and is exposed to high fluxes of energetic electrons and low energy protons. Orbit parameters Chandra XMM Apogee km km Perigee 10000km 7000km Inclination 28 o 39 o Argument of Perigee 270 o 57 o Table 1. Orbit parameters of the Chandra and XMM spacecraft.

5 5 of 60 Figure 1. The EPIC MOS focal plane consists of 7 MOS type CCD detectors. Figure 2. The EPIC p-n focal plane consists of 12 p-n type CCD detectors.

6 6 of 60 Figure 3. The RGS focal plane consists of 9 MOS type CCD detectors. Figure 4. The ACIS focal plane consists of 10 MOS type CCD detectors.

7 7 of 60 While the orbit inclination is higher for XMM, the argument of perigee does not produce an extreme latitude for the apogee and this, combined with a lower apogee and perigee, results in a more severe environment than for Chandra. Figure 5 and Figure 6 confirm this. Integral Fluence (#/cm2) 1.E+14 1.E+13 1.E+12 1.E+11 1.E+10 1.E+09 1.E+08 1.E+07 1.E+06 Proton Fluence GEO CHANDRA G8 Fluence (#/cm2) G10 Fluence (#/cm2) XMM 1.E Energy (MeV) Figure 5. Proton fluences for 60 days BOM of Chandra and XMM: The XMM values are for the first 60 days and the Chandra values are with many orbits run to average out the varying geometry of radiation belt encounters. Fluences are integral in energy. Geostationary values are shown to compare GOES measurements during the Chandra period with models. 1.E+15 Electron Fluence 1.E+14 1.E+13 Integral Fluence (#/cm2) 1.E+12 1.E+11 1.E+10 1.E+09 1.E+08 1.E+07 1.E+06 GEO G8 Fluence (#/cm2) XMM 60d CHANDRA G10 Fluence (#/cm2) 1.E Energy (MeV) Figure 6. Electron fluence spectrum for 60 days. XMM, Chandra and Geostationary predictions made with AE-8 are shown alongside GOES geostationary flight data.

8 8 of 60 These figures represent predictions for the two missions of the orbit-averaged proton and electron fluences respectively, made using the standard AP-8 and AE-8 static models [1]. The fluences are integral in energy, omnidirectional (integrated over 4π Sr) and integrated over 60 days to represent the first two months of the mission. The units are (cm -2 ). The upper spectrum in Figure 5 is for XMM. The Chandra curve shows that above about 20MeV the integrated fluence of protons is very low. Also shown in Figure 5 are the measurements made at geostationary orbit by the GOES-8 and GOES-10 spacecraft along with the predictions of AP-8. This shows that while the AP-8 model falls off rapidly with energy at geostationary orbit, the predictions are broadly consistent with the measurements. More proton data are being investigated. The upper set of curves in Figure 6 represent the electron fluence in geostationary orbit from GOES-8 and GOES- 10, and the AE-8 predictions. The average environment is in agreement with the static model. The electron environments of XMM and Chandra are very similar. An obvious issue investigated was the actual environment during the early phase of the Chandra mission and whether it had been more severe than normal. In Figure 5 and Figure 6 we have shown that the geostationary sensors in the period were in line with expectations. Figure 7 shows a record of the daily fluences measured by GOES sensors from which it is clear that no special events had occurred. The outer radiation belt environment is characterized by rapid enhancements and decreases of electron fluxes as shown in the lower panel for >2MeV electrons. The upper panel shows proton fluxes at >1MeV (upper trace) and >10MeV (lower trace). The low flux of >10MeV protons indicates that there were no Earth-arriving solar particle events, although there was an X-class X-ray flare on the Sun on 28 August. Shortly after the opening of the telescope door in early August, an electron injection event occurred (see lower panel). Moreover on 21 September, there was a large flux dropout. Both these phenomena are normal magnetospheric occurrences. Figure 7. The Geostationary environment in August and September 1999 as measured by sensors on the GOES spacecraft. The top panel shows proton daily fluences while the lower panel shows electron daily fluences

9 9 of 60 CCDs, as well as other detectors, are well-known to be susceptible to radiation damage in space. Problems from radiation background have also been well-investigated [2]. The main damage problems are identified as: Energetic protons which could penetrate spacecraft shielding and cause displacement damage in CCDs, resulting in degradation of the Charge Transfer Efficiency (CTE). This non-ionizing energy loss (NIEL) of protons has been the main concern for CCD degradation. Much work has previously been done on characterizing the degradation of CCDs (as well as other optoelectronic components) with respect to the non-ionizing dose. Clearly any low energy protons directly reaching the CCDs will cause similar damage since the damage increases with decreasing energy until near the "Bragg peak", where the slowing proton deposits energy most rapidly. The energy dependence of the NIEL is shown in Figure 8. Clearly a 1MeV proton is about 10 times more damaging than a 10MeV proton. A proton of 0.1MeV is roughly 100 times more damaging. Electrons can also damage CCDs if arriving in sufficient numbers, although the characteristics of the damage are different from that caused by protons. Figure 8 shows that low energy electrons cause little displacement damage per particle compared to protons. While electrons penetrating the spacecraft shielding are a problem, an important concern, particularly for radiation background, is electrons scattering through the X-ray mirror system directly onto the CCDs. To prevent it, magnetic deflection systems are employed in both Chandra and XMM. Other sources of potentially damaging radiation include solar energetic particle events, magnetospheric and other ions, cosmic rays and secondary radiations of all sorts generated by interactions with the spacecraft shielding. Ions heavier than protons have higher NIEL and so potentially cause more damage. Figure 8. Non ionizing energy loss of various particles as a function of their energies Re-analysis of the shielding around the focal planes of Chandra and XMM have confirmed high levels of shielding, thus ruling out energetic protons as a problem. The enclosures of the detectors and the baffling was examined for efficiency in attenuating energetic protons, and augmented if necessary. In the case of the XMM EPIC camera, a shielding analysis by ESTEC showed that the minimum straight-line shielding to space from any CCD was about 2cm aluminium equivalent. An examination of the Chandra focal plane reveals a similar number. Baffling close to the detectors appears to screen the view of the telescope tube ("optical bench") which is made of a lightweight structure of the order of 2mm equivalent aluminium thickness. In addition, the chosen orbits have perigees that keep the spacecraft above the most energetic part of the proton radiation belt, which for >70MeV protons peaks at around 3000 km equatorial altitude[3].

10 10 of 60 The electron process is also unlikely to be the source because the observed damage signature is not like total dose damage. Although electron fluxes in the radiation belts can be very high, as shown in Figure 6 and Figure 7, and electrons can scatter through the mirror shells, divertors are included in both Chandra and XMM to remove these electrons. The non-ionizing damage from any undeflected electrons would be minimal. The ionizing dose is also very low and cannot generate ionizing dose effects observed during ground-based testing in ionizing dose environments of some kilorads. Only if an unforeseen damage mechanism is present can electrons be invoked. The electrons implicated would be stopping in surface layers of the CCDs. Another source of electrons is through the relatively thin (~2mm equivalent aluminium) telescope tube. In this case, the magnetic deflector design on Chandra is non-optimal and could divert electrons onto parts where they could "shower". The telescope tube area is 50m 2, so the number particles involved are large. However, with the considerable baffling of the detectors, the high fluxes needed at the focal plane seem to be difficult to achieve. As mentioned previously, one feature of the observed degradation on Chandra is that the front illuminated CCDs have been degraded while the back-illuminated CCDs have not. While there are probably some differences in sensitivities, the conclusion drawn is that the source of damage does not have sufficient energy to reach the sensitive regions of the back-illuminated CCDs that have some 40µm of extra Si in front of them. Although low-energy protons appear to be effectively screened by the available shielding, Figure 8 shows that they are highly damaging. Because of the shielding available, it is not possible to obtain sufficient low-energy protons from the high-energy population through slowing down in the spacecraft material to cause the observed degradation. However, Figure 5 shows that in unshielded situations there are large numbers of these protons. Apart from a hole in the structure, the only other possible access for particles is through the mirror shells. The geometry of the mirrors is essentially two co-axial sets of concentric shells as shown in Figure 9. While the presence of baffles (including one at the centre of the mirror assembly) precludes a direct penetration of radiation from the outside of the spacecraft to the focal plane, particles scattering from the surfaces of the mirrors may be able to reach the focal plane. As mentioned above, this was expected to be a problem with energetic electrons, which are well known to scatter easily, and for this reason the magnetic deflection systems were included. Figure 9. Illustration of the geometry of X-ray mirror shell optics.

11 11 of 60 What had not been appreciated is that low energy protons can also scatter. The main issue is how efficient this scattering is. Figure 10 shows simulations made with the TRIM code [4] of the scattering of low-energy protons as a function of incident angle. This shows that at low angles, the scattering efficiency is about 0.6 and increases with decreasing energy. Moreover, as shown by Figure 11, the angle at which the protons are backscattered can also be low. With incident protons at a 1 o angle to the surface, approximately half of the exiting particles have an exit angle below 3 o. In order to reach the focal plane, the particles must undergo at least 2 scatters. If they are assumed to mimic the X-ray double scatter behaviour, the field of view from the focal plane is a solid angle of 6x10-5 Sr for XMM [5] and 10-4 Sr for Chandra [6]. The unobscured aperture areas for the telescopes in the two missions are also similar: 1700cm 2 per mirror for XMM and 1145cm 2 for Chandra. Figure 10. Total backscattering of protons as a function of incident angle for 1000 incident protons and three different proton energies. Figure 11. The distribution of the angle of emergence of backscattered protons for 1000 incident protons at an angle of 1 o.

12 2 o 3 o e Page 12 of 60 Clearly, the region of most interest is that where the incident and exit angles are low. Performing the TRIM simulations with particles per incident angle for 100keV protons gives the scattering efficiency shown in Figure 12 and Figure 13. Clearly a better value for the 1 o incident into the [0,1 o ] scatter bin is now obtained: ~6.5%, quite close to the preliminary values for 1MeV shown in Figure 11. Figure 12. Fraction of particles in each 0.5 o scattered angle bin [0,0.5], [0.5,1] as a function of incident angle. 1 o Incident Angles 4 o Scatter Angle Figure 13. Fraction of particles scattering into each scattered angle bin for various incident angles.

13 13 of 60 Assuming these protons illuminate an area of the focal plane given by Ω L 2 where Ω is the acceptance solid angle and L the focal length, the fluence of particles of energies between E and de is: Q(E) 2 f(e)de S {Ω/4π} / ΩL 2 = Q(E) 2 f(e)de S /4πL 2 Where Q(E) is the scattering from a single encounter with a shell (either a single scatter of a "condensed" multiple scatter) and is a strong function of energy, S is the telescope acceptance area and f is the omnidirectional flux of particles, differential in energy. The values used for Q are those giving a scatter from 1 o into the 0-1 o scattered bin (Figure 11 and Figure 12). The process is clearly of increasing efficiency as the incident angle reduces, although the scatter angle is less specular as the energy is reduced. Further TRIM and Geant4 simulations are described later. However, it is clear from this simple analysis that sufficient numbers of damaging protons can arrive at the focal plane of both spacecraft to cause concern. Moreover, calculations using classical Rutherford scattering [7] (see Annex) imply a value close to 0.6 (although experimental tests of the low-angle scatter, discussed later, indicate that Rutherford scattering is not the process involved). It is rather multiple scattering. The resulting fluence values are only for grazing incidence scattering mimicking the X-ray scattering. There is a non-zero contribution from protons entering from outside the X-ray field of view and undergoing low angle scattering or similar non-optimal secondary or other scattering. All these factors point to the fluence values in Table 2 as being lower bounds. If Q is as high as 0.3, the 10MeV equivalent fluence from 100keV protons will be of the order of cm -2 in 60 days at the CCDs. Acceptance Area S (cm 2 ) Acceptance Angle (Sr) L (cm) E (MeV) Fluence interval (f(e) E) (cm -2 ) Q Fluence (cm -2 ) 10MeV Equivalent Fluence (cm -2 ) Chandra > ~ ~ > ~ ~ XMM 1700/mirror > ~ ~ > ~ ~ Table 2. Telescope parameters and orbit fluences for Chandra and XMM. Cosmic rays are permanently present on the Chandra and XMM orbits. Although he fluxes are low (~4/cm 2 /s for all ions), the NIEL of heavy ions is much greater than protons. Nevertheless, the number of particles is too low to cause problems. Over a long mission, they may become a factor. Protons of 4.4MeV energy can undergo a nuclear interaction with Carbon (present in the Chandra and XMM telescope tubes) that leads to emission of a γ-ray. This could potentially lead to showering, but again the source and efficiency are too weak to generate damaging doses. Apart from the low-energy protons, in the radiation belts there are also low-energy ions. There can be large fluxes of O + during storm-times. Tests with the TRIM code show that they can also scatter efficiently at low angles. These ions can cause more damage than protons and need to be carefully considered in forthcoming analyses. While there were no solar energetic particle events at Earth during the early phases of the Chandra mission, they will undoubtedly occur during the lifetime of both Chandra and XMM. Indeed it is quite remarkable to be so far into "solar maximum" with so few large energetic particle events

14 14 of 60 having occurred. A simple model for the fluence spectrum (differential in energy) of the October 1989 event as measured at geostationary orbit is: j(e) = E -1.7 for E<30MeV E -2.8 for 30MeV<E<150MeV E for E>150MeV where E is in MeV and j is in protons.cm -2.MeV -1. This may not represent the spectrum at 100keV in the magnetosphere, but it shows that the fluence levels are somewhat lower than the low energy radiation-belt fluences in Figure 5. At high energies they are important for direct penetration of shielding. XMM, having a lower perigee and a lower apogee will see a more severe environment than Chandra. Natural changes in XMM orbital perigee and apogee altitudes will not improve the situation for low energy particles as these are much more extended in the radiation belts than the high-energy component. Figure 14. RGS geometry showing scatter angles

15 15 of 60 On XMM, the EPIC cameras are able to take precautionary measures through use of a filter wheel position that blocks the view of the mirrors during belt passages. In view of this, RGS is more of a concern since it has no protection system. However, to reach RGS, protons have to undergo a subsequent scatter in the gold-coated Reflection Gratings, at a higher angle than they need to get through the mirrors. A first estimate of the efficiency of this scatter using the TRIM code is that the fluence at the RGS might diminish by a further factor 30 due to this scatter. However, as shown in Figure 14, the incident and scatter angle change across the gratings. It seems that the most obvious cause for the degradation is low energy protons (and possibly other ions) scattering through the mirror shells. The following sections analyse these issues in detail through Geant4 and TRIM simulations.

16 16 of 60 2 Geant4 simulations 2.1 XMM A 3D computer model of one of the XMM X-ray telescopes and its associated detectors has been implemented in Geant4. This model is used to simulate the response of the instrument to the radiation environment it will encounter on orbit, in particular the interactions of low energy protons and electrons with the telescope module (baffle, mirrors and grating) and the effects these will have on the performance and survivability of the EPIC-MOS and RGS CCD detectors Particle generator In the Geant4 simulation, the initial incident particles can be either protons or electrons. They can either follow a user supplied energy distribution, or have monochromatic energies as specified by the user. For their incident positions and directions, users can choose from a list of predefined options: isotropic, beam, aperture and point. In fact all the simulations in the current study were performed using the aperture option, where an isotropic distribution of particles 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 (normally matching to that of the opening of the telescope) from where they can enter the system. In order to simulate the response of the system to radiation originating at angles outside the nominal field of view, the user can also define any arbitrary angle of acceptance or source halfangle (the default acceptance angle is 1 degree). The position of the source is randomly sampled over an incident area which is specified as a disk, with minimum and maximum radii supplied by the user (the defaults for XMM are 14 and 36cm respectively). This disk is positioned just in front of the X-ray baffle, at a distance of 795.1cm from the XMM focal plane Physics processes A number of physics processes available in Geant4 routines, such as Compton scattering, Bremsstrahlung or the photo-electric effect, have been included in the model to represent accurately the interaction of protons and electrons with the various surfaces encountered, with special attention being paid to the gold coating on the mirrors. These routines are able to simulate the creation of secondary particles, track the trajectory of each individual particle and record their energy loss as they interact with the system. The processes included in this model are: Hadron ionisation, with knock-off electron (δ-ray) production Hadron multiple scattering, including the lateral displacement of the particle Electron ionisation Electron bremsstrahlung Electron-positron annihilation Muon ionisation Muon bremsstrahlung Muon pair production Photoelectric effect Compton scattering γ-conversion Of these, the first two are the most important ones for analysis of proton propagation in the XMM mirror system. For a detailed discussion on the physics and the implementation of the various processes, see the Geant4 physics reference manual [8].

17 17 of Tracking Parameters The tracking of the incident particle and its secondary in Geant4 is largely controlled by the parameters STMIN and DEMAX. STMIN is the minimum step size for the track and DEMAX is the maximum fraction of energy the tracked particle can lose in one step. STMIN in fact decides the cut-off energy threshold for the simulation. In general smaller DEMAX and STMIN lead to more detailed tracking of the particle but at the cost of simulation running time. Best performance can be obtained by using optimized DEMAX and STMIN values for a given simulation. One other factor needs taken into consideration in determining the DEMAX and STMIN values is the algorithms implemented for the chosen physical process. In the case of XMM/Chandra simulations, Multiple Scattering is one of the dominant processes and its implementation in Geant4 is tuned to reproducing the average effects after several scatterings. This places a requirement that the step size has to be bigger than several multiple-scattering interaction lengths. Using TRIM we learnt that for 100keV proton its average trajectory range is 0.4µm, and it undergoes more than ~30 scatters before being stopped. So the interaction length is in the order of ~nm. At small angles of incidence, however, the picture is rather different: most protons were scattered out after just a couple of interactions and the protons travelled for only ~10nm in the gold layer. We ran Geant4 simulations with a combination of STMIN and DEMAX values for 100keV protons onto gold layers at 1 degree incident angle. Figure 15 is a plot of the scattered proton energy spectra as produced by these simulations. From these spectra it is clear that STMIN= 0.1µm is inadequate as the spectrum showed an unrealistic cut-off above 50keV. This is supported by the angular distribution of the scattered protons as plotted in Figure 16, in which the STMIN = 0.1µm case is the odd one out compare to the others, as well as the distribution derived from TRIM calculations (see 2.4.1). On the other hand, the STMIN = 0.01, and 0.001µm cases produced a consistent result and it is similar to that produced by the TRIM code. One trend we can observe from these plots is that the smaller STMIN tend to make the angular distribution biased to small angles and at the same time leads to more protons scattered off at high energies. Although the spectrum and angular distribution of the scattered protons are largely determined by the STMIN parameter, the DEMAX factor also affects the results to some extent: a smaller DEMAX value tends to produce more protons scattered at smaller angles and at higher energies, i.e. the same effect as STMIN. However, if we compare the Geant4 results to that of the TRIM calculations (see 2.4.1), although the two are in general agreement, Geant4 tends to produce too many scattered protons at small angles and not enough at high energies. Our observation is that by adjusting DEMAX and STMIN we cannot achieve a perfect agreement between these two. The tracking process uses a complex formula based on STMIN and DEMAX to determine the actual step size. It is acknowledged [9] that for very low energies the step size used is approaching STMIN and the effective value of DEMAX becomes ~ 1. As for high energies, i.e. the range of the particles >> STMIN, the step size is simply DEMAX fraction of the particle range. For the Geant4 simulations presented here, we settled on STMIN = 0.01µm and DEMAX = This is a compromise choice as it gives reasonable agreement with the TRIM results in both the energy and angular distributions, and at the same time it meets the requirement of the Multiple Scattering process algorithm that the step size ought to be greater than a couple of interaction lengths.

18 18 of 60 Stmin = 0.1 um --- demax = demax = 0.01 Stmin = 0.01 um --- demax = demax = 0.01 Protons/Bin Stmin = um --- demax = demax = 0.01 Stmin = um --- demax = demax = 0.01 Scattered Energy / Incident Energy Figure keV protons onto Au layers at 1 degree incident angle. Scattered proton energy spectra for various STMIN and DEMAX values. stmin = 0.1 um --- demax = demax = 0.01 Stmin = 0.01 um --- demax = demax = 0.01 Protons/Bin Stmin = um --- demax = demax = 0.01 Stmin = um --- demax = demax = 0.01 Scattering Angle (degree) Figure keV protons onto Au layers at 1 degree incident angle. Angular distributions of the scattered protons for various STMIN and DEMAX values.

19 19 of XMM spacecraft geometry 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. A graphical representation of the model is shown in Figure 17. Figure 17. XMM telescope geometry, showing the baffle, mirrors and the grating. Note that the entrance baffle is excluded from the calculations so the calculated transmission, especially for particles arriving from large off-axis angles, is a worst-case value The X-ray baffle The X-ray baffle has been modeled as two 1mm thick plates 59mm apart. The material used is 1 part Ni for 2 parts Fe. The exact dimensions were obtained from [10][11] The telescope mirrors The telescope mirrors have been modeled 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 outer and inner radii of each conic section were obtained using the approximations given in [12]. Other detailed information on the construction of the mirrors were obtained from [13]. The overall length of the mirrors is 600mm, centred at a position 7.5 m 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 was filled by cylindrical nickel tubes leaving a 3mm gap with respect to the outer radius of the innermost mirror shell The reflection grating The reflection grating was modeled based on a computer file provided by the XMM team [14]. The grating plate structure consists of 200nm of Gold on top of 40 µm of epoxy and 1mm layer of carbon fiber. The effect of the "saw-tooth" surface on the grating plates has been neglected, although to a first order this should have little impact on the results (since there are 645 lines/mm

20 20 of 60 with 19nm saw-tooth elevation, this pattern corresponds to a tilt of 0.7º with respect to the nominal plane of the individual grating elements) The detector volumes Three dummy detector volumes (i.e. made of vacuum) were included in the XMM Geant4 model to record the number 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 Simulations A battery 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 protons when using narrow viewing angles (up to 2 degrees) to a maximum of 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 η defined by where η = Ω / 4π ( Asource / Adetector )( Ndetected / Nincident ) Ω is the solid angle that corresponds to the selected source half-angle θ and is given by 2π(1 - cosθ) A source is the area over which the isotropic particle distribution is generated A detector is the area of the detector volume on which particles are recorded N incident is the total number of particles generated over A source N detected is the number of particles recorded at a detector location within A detector The efficiency is the number that the omnidirectional 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. In the XMM simulations the areas involved in the efficiency calculations are: A source = cm 2 A mirror_detector = cm 2 A RGS_detector = cm 2 A EPIC_detector = 33.18cm 2 The size of the RGS collecting area was doubled to ensure detection of particles arriving outside the detector nominal position due to the approximation made by neglecting the "saw-tooth" surface.

21 21 of 60 For the estimation of errors in the calculated efficiencies, it is assumed that Poisson statistics apply, therefor the error in the number count of detected protons grows as the square root of the number Results The results of the simulations performed with the XMM Geant4 model are shown in Table keV protons Mirror (scattered) Mirror (direct) RGS EPIC θ ( ) N inc N det η ± N det η ± N det η ± N det η ± E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E keV protons E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E keV protons E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-06 1MeV protons E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E MeV protons E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E-07 Table 3. XMM simulation runs for protons in the energy range 0.1 to 1.5MeV for source half-angles θ and N inc number of incident particles. The number of protons recorded at each of the dummy detector volumes N det is used to calculate the efficiency η, its error is estimated assuming Poisson statistics apply Efficiency of the mirrors The efficiency with which protons propagate through the mirrors can be estimated from the number of protons recorded at the dummy detector volume placed behind the mirror. The energy of these protons indicate whether they have scattered on the mirror surfaces (hence losing some of their energy in the process) or if they still carry the initial energy, which indicates that they have not interacted with the mirrors. Figure 18 is a plot of the efficiency of the mirrors for scattering

22 22 of 60 protons in energy ranges between 0.1 and 1.5MeV as a function of the source half-angle (i.e. the solid angle over which the incident radiation is being sampled). The figure also shows the efficiency of the X-ray baffle and mirror combination in allowing protons to reach the interior of the XMM optical bench unhindered. 1.E-04 1.E-05 Efficiency 1.E-06 Scattered 0.1 MeV 1.E-07 Scattered 0.3 MeV Scattered 0.6 MeV Scattered 1.0 MeV Scattered 1.5 MeV Direct Hits 0.1 MeV 1.E-08 Direct Hits 0.3 MeV Direct Hits 0.6 MeV Direct Hits 1.0 MeV Direct Hits 1.5 MeV 1.E Source half-angle (deg) Figure 18. Efficiency of the mirrors is plotted against source half-angle for proton energies in the range 0.1 to 1.5MeV. Scattered protons and direct, unhindered protons are shown. a) Scattered protons The efficiency of the XMM mirrors in scattering protons varies more strongly with the angle of incidence of the radiation than its energy. Other than the 100keV protons (more readily absorbed), the efficiency of the more energetic protons all follow practically the same curve. The efficiency for a 1 degree source half-angle is , which increases by an order of magnitude for source half-angles of 10 degrees, from which point the efficiency remains constant. b) Direct hits These tests demonstrate that there is a "direct leak" in the system for radiation incident within an angular range of 2.5 degrees on the aperture plane of the parabolic mirror confirming the findings of the sector shielding analysis procedures carried out on the geometry (see 2.4.3). The efficiency of direct hits (protons reaching the dummy detector behind the mirror without interaction) increases sharply with source half-angle up to 2.5 degrees, for greater angles of incidence the efficiency becomes asymptotic with a value of EPIC and RGS detectors The efficiency of the protons in reaching the EPIC and RGS detectors have been plotted in Figure 19 and Figure 20 as a function of source half-angle (for each proton energy) and as a function of proton energy (for each source half-angle) respectively. The results largely reflect the behaviour caused by the interaction with the mirrors themselves: The efficiency is a stronger function of source half-angle than proton energy.

23 23 of 60 It increases sharply up to incidence angles of ~4 degrees, beyond which any increase is very shallow, or the efficiency even becomes asymptotic with a value for 600keV protons at the EPIC and at the RGS. 1.E-04 1.E-05 Efficiency 1.E-06 EPIC 0.1 MeV 1.E-07 EPIC 0.3 Mev EPIC 0.6 MeV EPIC 1.0 MeV EPIC 1.5 MeV RGS 0.1 MeV 1.E-08 RGS 0.3 MeV RGS 0.6 MeV RGS 1.0 MeV RGS 1.5 MeV 1.E Source half-angle (deg) Figure 19. Efficiency of the EPIC and RGS detectors is plotted against source half-angle for proton energies in the range 0.1 to 1.5MeV. 1.E-04 1.E-05 Efficiency 1.E-06 EPIC 0.5 deg EPIC 1 deg EPIC 4 deg 1.E-07 EPIC 2 deg EPIC 10 deg EPIC 30 deg RGS 0.5 deg RGS 1 deg 1.E-08 RGS 2 deg RGS 4 deg RGS 10 deg RGS 30 deg 1.E Proton Energy (MeV) Figure 20. Efficiency of the EPIC and RGS detectors is plotted against proton energy for each source half-angles in the range 0.5 to 30 degrees.

24 24 of Effect of the EPIC baffle An aluminium baffle of 57.2cm length that is part of the EPIC camera was not included in the original simulations. Tests carried out for various proton energies with this baffle in place showed that it had no noticeable effect on the number of protons reaching the EPIC CCDs Arrival of protons in the vicinity of the RGS A test run has been carried out where a detector volume centred on the actual RGS position but four times its size was used to collect protons arriving in the vicinity of the RGS. This test allowed us to investigate two different effects: the effect of neglecting the "saw-tooth" surface on the grating plates the ability of the grating (optimised for X-ray photons) to spread the incident protons over the area of the RGS. Figure 21 shows the distribution of detected protons arriving at both the EPIC and RGS detectors. The small rectangle on the figure indicates the real position of the RGS and the larger rectangle the area actually sampled. It is clear from this figure that the spatial distribution of protons on the EPIC detector is evenly spreadout over its entire area. On the RGS, however, they tend to concentrate towards the side closer to the EPIC (along the Z-axis) but are evenly distributed along the Y-axis. Y (cm) Z (cm) Figure 21. Spatial distribution of protons arriving at the EPIC and RGS (and its vicinity). Out of protons incident on the telescope (entrance baffle present in the simulation) only 90 protons are detected on the actual RGS area. If the size of the RGS collecting area is doubled along the Y-axis, the number of protons also doubles to 188 (100% increase). If the RGS collecting area is displaced by a half length along the Z-axis (towards the EPIC) instead, the increase in the number of protons collected is 150% (230 protons). If the collecting area is also doubled in width at this position, 474 protons are detected. The number of protons collected in the full area sampled (large rectangle) is 549. What this test seems to indicate is that the grating is not very efficient at spreading the protons along the Z-axis (on the surface of the RGS) as it would do with X-ray photons. This means that most of the protons scattering off the grating probably miss the RGS detectors, as they are spread out sideways and concentrate on the area between the RGS and the EPIC. However, most of the protons that do reach the RGS will tend to concentrate on the same corner CCDs. Figure 34 seems to indicate that any displacement on the arrival position of the protons at the RGS due to the neglect of the saw-tooth surfaces in our simulation, is compensated for by the somewhat smaller angle of incidence of the protons on the grating surfaces. Apparently these two factors cancel each other out and our efficiency results should stand Effect of the entrance baffle The entrance baffle placed before the XMM X-ray baffle is a cylindrical aluminium shell 90- cm in length and 87cm outer diameter. On its inner face it has 12 annular vanes with a clear

25 25 of 60 aperture greater than outermost X-ray baffle opening [15]. Although this structure has not been included in the simulations reported above (which can therefore be taken to illustrate the worst case scenario), a test run has been carried out with the entrance baffle present for 600keV protons and 1 degree source half-angle. The result of this test indicates that the presence of the entrance baffle may reduce the number of protons reaching the EPIC by 8% and the RGS by 17%. 2.2 Chandra A Geant4 model has also been implemented for the Chandra spacecraft, including the High Resolution Mirror Assembly (HRMA), optical bench, magnetic broom, internal baffles and ACIS camera detectors. The only difference between the XMM and Chandra simulations was the geometry of the spacecraft. Both simulations share the code responsible for generating a distribution of particles incident on the spacecraft, and the physics modules that govern the interactions between these particles and the materials that make up the telescope and detectors. In the Chandra simulation the radiation is generated using the aperture particle gun (see 2.1.1) over an annular area defined by inner and outer radii of 31.2 and 61.3cm respectively. The source is placed just in front the HRMA at a distance of cm from the focal plane Chandra spacecraft geometry The geometric model of the Chandra spacecraft has been implemented using some 400 individual elements, the bulk of which (352 elements) correspond to the HRMA alone. The forward collimator consists of 10 parallel plates, each with 4 annular apertures of varying width corresponding to each of the mirror shells. The mirrors themselves have been modeled 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 between the two mirror sections (parabolic ad hyperbolic), effectively blocking any stray-light. Further apertures are placed in the middle of each section of the innermost shell. An aft collimator with 6 parallel plates of similar construction to the forward collimator, but with annular gaps consistent with a converging annular beam follows the hyperbolic mirror. A graphical representation of the model is shown in Figure 22. Figure 22. Chandra telescope geometry, showing the HRMA and optical bench. The detector enclosure is at the focal plane end of the telescope. The materials used for the collimator plates and central apertures was SiO 2, 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 dimensions of all the components in the

26 26 of 60 HRMA have been calculated based on detailed information provided in [16]. 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 aluminum enclosure at the focal plane end of the telescope houses the ACIS camera. The CCDs of the ACIS camera are accurately modeled 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 modeled. The magnetic field of the magnetic broom placed in the middle of the optical bench can be turned on for electron tests but was not used for the protons tests reported here. The dimensions of all the components were obtained from [17][18][19][20] Results The results of the simulations performed with the Chandra Geant4 model are shown in Table 4. In contrast with the XMM case, no protons get through the mirror system without at least one interaction. The areas involved in the efficiency calculations for Chandra are: A source = cm 2 A mirror_detector = cm 2 A ACIS_detector = cm 2 100keV protons Mirror (scattered) ACIS θ ( ) N inc N det η ± N det η ± E E E E E E E E E E E E E E E E E E E E E E E E E keV protons E E E E E E E E E E E E E E E E E E E E E E E E E keV protons E E E E E E E E E E E E E E E E E E E E E E E E E-07 1MeV protons E E E E E E E E E E E E E E E E E E E E E E E E E MeV protons E E E E E E E E E E E E E E E E E E E E-07 This is mostly due to the presence of the aperture baffle placed between the parabolic and hyperbolic mirrors, with very narrow gaps for each mirror shell.

27 27 of E E E E E-06 Table 4. Chandra simulation runs for protons in the energy range 0.1 to 1.5MeV for source halfangles θ and N inc number of incident particles. The number of protons recorded at each of the dummy detector volumes N det is used to calculate the efficiency η, its error is estimated assuming Poisson statistics apply Efficiency of the mirrors The efficiency with which protons propagate through the Chandra mirrors can be estimated from the number of protons recorded at the dummy detector volume placed behind the mirror. Figure 23 is a plot of the efficiency of the mirrors for scattering protons in energy ranges between 0.1 and 1.5MeV as a function of the source half-angle (i.e. the solid angle over which the incident radiation is being sampled). 1.E-04 1.E-05 Efficiency 1.E-06 Scattered 0.1 MeV Scattered 0.3 MeV Scattered 0.6 MeV Scattered 1.0 MeV Scattered 1.5 MeV 1.E Source half-angle (deg) Figure 23. The efficiency of the Chandra mirrors for propagating protons is plotted against source halfangle for proton energies in the range 0.1 to 1.5MeV. As in the XMM case, the efficiency of the mirror is a strong function of the incident direction of the protons rather than their energy. Tests were conducted for source half-angles up to 10 degrees, where the efficiency starts to flatten out. The maximum efficiencies recorded (at 10 degrees) are for proton energies up to 600keV and for 1.5MeV protons. In Chandra no protons were detected behind the mirrors still with initial energy in any of the runs (i.e. there are no stray-light leaks) ACIS detector The efficiency of protons in reaching the ACIS camera at Chandra focal plane is plotted in Figure 24 and Figure 25 as a function of source half-angle (for each proton energy) and as a function of proton energy (for each source half-angle) respectively. The behaviour observed is, as for XMM,

28 28 of 60 a reflection of the interaction of the protons with the mirrors. In the ACIS case there is virtually no dependence on the proton energy (see Figure 25). For 600keV protons the efficiency is for 1 degree source half-angle and for 10 degrees.

29 29 of 60 1.E-04 1.E-05 Efficiency 1.E-06 ACIS 0.1 MeV ACIS 0.3 Mev ACIS 0.6 MeV ACIS 1.0 MeV ACIS 1.5 MeV 1.E Source half-angle (deg) Figure 24. Efficiency of the ACIS detector is plotted against source half-angle for proton energies in the range 0.1 to 1.5MeV. 1.E-04 1.E-05 Efficiency 1.E-06 ACIS 0.5 deg ACIS 1 deg ACIS 2 deg ACIS 4 deg ACIS 10 deg 1.E Proton Energy (MeV) Figure 25. Efficiency of the ACIS detector is plotted against proton energy for each source half-angles in the range 0.5 to 10 degrees.

30 30 of Comparison between XMM and Chandra A comparison between the results obtained for the EPIC and ACIS cameras shows that they will have very similar efficiencies to protons. In Figure 26 the efficiency for 600keV protons is plotted against source half-angle for the EPIC and RGS instruments on XMM and the ACIS camera on Chandra, as well as the efficiencies of the mirrors in both telescopes for scattering protons. In Figure 27 the efficiency of protons incident within a source half-angle of 1 degree are plotted against proton energy. 1.E-04 1.E-05 Efficiency 1.E-06 1.E-07 ACIS EPIC RGS Chandra Mirrors XMM Mirrors 1.E Source half-angle (deg) Figure 26. Efficiency of the EPIC, RGS and ACIS instruments and the XMM and Chandra mirrors plotted against source half-angle for 600keV protons. 1.E-05 1.E-06 Efficiency 1.E-07 ACIS EPIC RGS Chandra Mirrors XMM Mirrors 1.E Proton Energy (MeV) Figure 27. Efficiency of the EPIC, RGS and ACIS instruments and the XMM and Chandra mirrors plotted against proton energy for protons within incident within a source half-angle of 1 degree.

31 31 of 60 For 1 degree source half-angles, 600keV protons have almost identical efficiencies at the EPIC and ACIS, and respectively. For 10 degrees source half-angle, the efficiency of the EPIC is 70 % that of the ACIS camera, with 1 particle in 10 5 reaching the instrument. However, this gain is probably balanced out by the fact that the XMM orbit is a somewhat harsher environment. 2.4 Validation of Geant4 The condensed history method employed in Geant4 requires that the step length of the simulation be long enough to ensure multiple interactions will occur in a single step of the calculation. A long step length is preferred, as it reduces the compute time required for the simulation and follows the philosophy of the condensed history method. Small angle scattering requires a short step length, as the exit characteristics of a particle from a target vary strongly with the depth at which the particle is deflected. To ensure Geant4 was correctly treating these small scatter angles it was initially compared with a planar geometry model using the TRIM software [21]. TRIM provides for investigations of small angle (~1 o ) back scattered ions. The results from this comparison were used to tune the Geant4 parameters for the step length and maximum energy loss per step to provide similar exit energy and scatter angle distributions (see 2.1.3). Samples of the XMM mirror shells and RGS grating were subjected to proton tests at small scatter angles in the Harvard University Accelerator for Materials Science [22]. The data from these experiments provided a basis to validate further the tuning performed with the TRIM results Comparison with TRIM TRIM simulations using planar geometry formed the basis of tuning the Geant4 parameters to ensure it was providing realistic low angle scattering results Simulation set-up Simulations of the XMM mirror shell, XMM RGS grating and Chandra mirror shells were created both in Geant-4 and TRIM (see Table 5 below). The basic geometry is shown on Figure 28 and is derived from the TRIM co-ordinate system. α β θ Z Y X Figure 28. Basic geometry and co-ordinate system of the TRIM/Geant4 simulations. Runs for various angles of incidence (α) from 1 to 90 were performed for proton energy ranges from 100keV to 1MeV. A similar planar geometry was constructed using Geant4 and corresponding runs performed. To ensure good statistics, the runs consisted of particles.

32 32 of 60 XMM Mirror Thickness Material Gold 500 Å Au Nickel 0.4mm Ni XMM Grating Gold 250 Å Au Epoxy 4mm (H:47%, C:45%, O:7.5%) Chandra Mirror Iridium 300 Å Ir Chromium 100 Å Cr Zerodur 24mm Si (assumed) Table 5. Composition of the XMM mirrors and grating and Chandra mirrors. The exit vectors and energies of the back-scattered particles were binned in energy (E), elevation (θ) and azimuth (β) and the distributions compared. Figure 29 shows the intersection of the exiting particles with a unit sphere. The exiting energy and elevation distributions are shown in Figure 30 and Figure 31. Figure 29. Geant-4 simulation of 1MeV protons with an incident angle of 1 : points represent the projection of exit vectors on a unit sphere. The left panel is a projection in the X-Z (abscissa-ordinate) plane, while the right panel is the projection in the Y-Z (abscissa-ordinate) plane. Initially, Geant4 failed to produce a significant number of low elevation angle scattered protons, but the exit energy distribution provided a reasonable fit to the TRIM results. Attempts to fit the elevation angle distribution by tuning the Geant4 step-cut parameters (stmin=0.01 µm, demax=0.05) resulted in the exit energy distribution deviating further from the TRIM distribution, see figure below. Given the critical dependence of the low angle distribution on the penetration of particles through the mirror shells and grating to the CCDs it was considered more important to tune Geant-4 to fit its elevation angle distribution to the TRIM results at the expense of the energy distribution.

33 33 of 60 XMM - SRIM 1deg Incident 100 kev Protons Fraction of Incident Particles Exit Energy/Incident Energy SRIM 100 kev Incident Protons XMM - SRIM 1deg Incident, 500 kev Protons G4 100keV Fraction of Incident Particles Exit Energy/Incident Energy SRIM 500 kev Incident Protons XMM - SRIM 1deg Incident, 1 MeV Protons G4 500keV Fraction of Incident Particles Exit Energy/Incident Energy SRIM 1000 kev Incident Protons G4 1000keV Figure 30. A comparison of the exit energy distributions of the Geant4 simulation with the TRIM simulation of the XMM mirror shells.

34 34 of 60 XMM - SRIM 1deg Incident, 100 kev Protons Fraction of Incident Particles Exit Angle 12 SRIM 100 kev Incident Protons G4 100keV XMM - SRIM 1deg Incident, 500 kev Protons Fraction of Incident Particles Exit Angle 12 SRIM 500 kev Incident Protons G4 500keV XMM - SRIM 1deg Incident, 1 MeV Protons Fraction of Incident Particles Exit Angle 12 SRIM 1000 kev Incident Protons G4 1000keV Figure 31. Elevation angle distributions for TRIM and Geant-4 complementary simulations of the XMM mirror shells.

35 35 of Comparison with Experiment Proton reflectivity measurements of XMM grating and mirror samples were performed at the Harvard University Accelerator for Materials Science [22] by the Columbia group. This data (an example of which is shown in Figure 32) provided the means to empirically verify the tuning of the Geant-4 simulations RGS Grating Tests The grating plates simulated in the full 3-D model discussed in were a simplification of the actual plates. Instead of the saw-toothed grating surface, the plates were modeled as a smooth layer of gold on the carbon fiber/epoxy substrate. This difference can be accounted for by adding to the angle of incidence (α) for the Geant-4 results. Examination of the proton scatters in the target material showed that the protons were predominantly scattered near the surface in the gold layer and the number of protons scattered in the carbon fiber and epoxy layers were not significant. Figure 33 shows there is good agreement between the Geant4 simulation and the Columbia experiment. Both sets of data peak at similar scatter angles, although the Geant4 "reflection" efficiency was slightly higher than the experimental value, which should therefore provide more pessimistic figures for the full XMM geometry simulation. As the grating saw tooth angle correction is not applied to the full 3-D XMM geometry, the Geant4 data was also compared, uncorrected, to the experimental data. In the range of angles required to scatter into the RGS detector, the Geant4 simulation remained higher than experiment, as shown in Figure 34. For the purposes of the simulation, the agreement is regarded as very good. Data on the exiting energy spectra from the Columbia experiment were only available as a series of plots of protons as a function of pulse height, an arbitrary unit, an example of which is seen in Figure 32. Qualitatively, the protons don't loose much energy during the scatter, although a spread in energy is apparent. Without further information about the conversion of pulse height to energy, little more than a basic verification of the shape of the spectra is possible.

36 36 of 60 Figure 32. Plots provided from the Columbia experiment for 1.3MeV protons with a angle of incidence from the RGS grating (upper) and 0.3MeV protons at an angle of 0.75 on the mirror shard (lower). The piled-up protons (2xPH) give a measure of the dead time correction and also the zero energy position.

37 37 of Flux (#/cm 2 /st/inc. p+) 10 1 RGS Acceptance Range Scatter Angle (degrees) Columbia: 1.3 MeV, 1.576deg G4: 1.3 MeV, 1.576deg 100 Flux (#/cm 2 /st/inc. p+) 10 1 RGS Acceptance Range Scatter Angle (degrees) Columbia: 1.3 MeV, 1.826deg G4: 1.3 MeV, 1.826deg Figure 33. Comparisons of 1.3MeV proton measurements as a function of scatter angle with the equivalent Geant-4 results. The target material for these measurements was the XMM RGS grating. The scatter angle required for a hit on the RGS detector is indicated. It appears that the Geant-4 simulation provides slightly pessimistic results but the agreement is good.

38 38 of Flux (#/cm 2 /st/inc. p+) 10 1 RGS Acceptance Range Scatter Angle (degrees) 12 Columbia: 1.3 MeV, 1.576deg G4: 1.3 MeV, 1.576deg Figure 34. Comparisons of 1.3MeV proton measurements as a function of scatter angle with the equivalent Geant-4 results, uncorrected for grating angle. The scatter angle required for a hit on the RGS detector is indicated. While the peak of the flux is shifted right, the match between the Geant simulation and the experiment in the RGS scatter region is improved Mirror Shell Tests The Columbia experiment included reflection testing of a shard sample, 50mm wide, of the XMM mirrors. The detector, with an area of 7.9x10-5 cm, was positioned at three separate positions, representing scatter angles of 0.75, 1.4 and 2.38 and measurements taken at angles of incidence in quarter degree intervals between 0.0 and 1.75 for energies of 0.3, 0.5 and 1.3MeV. Not all combinations of detector position, angle of incidence and energies were investigated. The geometry of the Geant4 software used in the grating comparison was modified to represent the Nickel substrate with a Gold coating and runs were made of particles for energies and angles of incidence corresponding to the results of the Columbia experiment. Comparison plots are seen in Figure 35 -Figure 37. The back-scattered protons were binned at a resolution of 0.01 wide in azimuth and 0.1 in elevation and corrected for solid angle. As with the grating simulation, the mirror simulation fits the experimental data quite well. The fit is not as close in form as there is a divergence at smaller angles of incidence. The difference in magnitude of the BDRF at the maxima matches to within a factor of 2 to 3. From these results, it is expected that the full Geant4 simulations of XMM provide a pessimistic scattered fluence from the mirror shells for the higher energy particles, but may under-predict the scattered fluence for the lower energy particles, except at low angles of incidence. It is not fully understood if the drop in BDRF measured in the Columbia experiment at low angles of incidence is an experimental artifact, or whether further tuning of Geant4 is required to account for the decrease in reflective efficiency. The scatter angle was estimated by the angle of incidence at which the count rate dropped due to the occlusion of the mirror face by the mirror bulk, as seen from the detector position, i.e. the elevation angle becomes negative.

39 39 of MeV; Position 2: 0.75 deg. Columbia BDRF Geant 4 Monte-Carlo Columbia BDRF Uncor #/sr/inc. proton Angle of incidence 1.3 MeV; Position 1: 1.4 deg. Columbia BDRF Geant 4 Monte-Carlo Columbia BDRF Uncor #/sr/inc. proton Angle of incidence 1.3 MeV; Position 3: 2.38 deg. Columbia BDRF Geant 4 Monte-Carlo Columbia BDRF Uncor #/sr/inc. proton Angle of incidence Figure 35. Comparison of the 1.3 MeV scatter angle from Geant4 and the Columbia experiment for the three detector positions. The drop in fluence for higher angles of incidence is due to the occlusion of the mirror face by the mirror bulk as seen from the detector. The drop for lower angles of incidence for the Columbia data arises from the footprint of the 5mm diameter proton beam not fully intercepting the target material. An analytic correction has been applied to the "Columbia BDRF" curve [23].

40 40 of MeV; Position 1: 1.4 deg. Columbia BDRF Geant 4 Monte-Carlo Columbia BDRF Uncor #/sr/inc. proton Angle of incidence 0.3 MeV; Position 3: 2.38 deg. Columbia BDRF Geant 4 Monte-Carlo Columbia BDRF Uncor #/sr/inc. proton Angle of incidence Figure 36. As for Figure 35 but for 0.3 MeV protons. 0.5 MeV; Position 1: 1.4 deg. Columbia BDRF Geant 4 Monte-Carlo Columbia BDRF Uncor #/sr/inc. proton Angle of incidence Figure 37. As for Figure 35 but for 0.5MeV protons.

41 41 of Analysis of opacity of baffle using the Sector Shielding Analysis Tool The Geant4 analyses have shown a large contribution to the focal plane fluence from particles incident at angles above 1º from the axis direction. Efforts made to check the acceptance from all directions are reported here Background The Sector Shielding Analysis Tool (SSAT) performs ray tracing from a user-defined point within a spacecraft geometry to determine shielding levels (i.e. the fraction of solid angle for which the shielding is within a defined interval) and shielding distribution (the mean shielding level as a function of direction). To achieve this the tool utilises the fictitious geantino particle, which undergoes no physical interactions, but flags boundary crossings along its straight trajectory. Knowledge of the positions of these boundary crossings together with the density of the material through which the particle has passed can be used to profile the shielding (typically in g/cm 2 ) for a given point within the geometry. The shielding provided by the geometry can be sampled as a function of spherical polar coordinates θ and φ, and the user may control the extent of the solid angle sampled. The number of geantino histories followed, which determines the statistical accuracy of the results, is also set by the user. The SSAT outputs either 1-D or 2-D tabulated histograms that define the shielding levels and shielding distribution respectively. Associated with these is statistical information: Poisson errors for 1-D shielding data and standard deviation for 2-D histograms Simulations conducted The SSAT analysis to assess the opacity of the XMM baffle structure to an isotropic particle flux was conducted in two parts. The first examined the shielding presented by the inner baffle for particles incident upon a gap in the outer baffle. The second analysis has examined the shielding presented by both baffles from a point at the entrance to the mirrors. In both cases the shielding results were obtained as a function of direction and the fraction of the solid angle analysed that was unshielded was determined. a) Shielding analysis of the inner baffle The shielding effects of the inner baffle were analysed from a gap in the outer baffle (x = cm, y = 46.0cm, z = cm), for values of θ = 80 o -100 o and φ = 0 o. As expected, the inner baffle presents a comb shielding function and there are many angles for which incident protons will travel straight through (see Figure 39). What the baffle actually does, however, is to ensure those with angles (with respect to the optical axis) ~0 o 1 o and ~1.8 o 2.5 o do go through, whilst ~1 o 1.8 o are not transmitted. Therefore, if the acceptance angle for the mirrors is somewhere between 0 o 1.8 o, this will restrict the field-of-view (FOV) further to 0 o 1 o. Over a range of θ = 80 90º with respect to the geometry Z-axis (±10 o with respect to the optical axis), ~70% of the FOV is not blocked by the baffle. In a separate run θ was kept constant (θ = 90 o with respect to geometry Z-axis) and φ varied instead, i.e. the geometry was scanned ±10 o around the X-direction. These results showed that the geantinos encountered no shielding by the baffle.

42 42 of Sector Shielding Analysis of XMM Baffle (sampled at x= cm, y=46.0cm, z= cm, looking in direction θ= o deg, φ=0 o ) Coarse sampling Fine sampling Shielding by invar [cm] θ angle from z-axis [deg] Figure 38 Figure 39. Analysis of inner XMM baffle from gap in out baffle b) Shielding analysis of the baffle from the mirror In this simulation, the shielding from the baffle was analysed from a point on the entrance to the XMM mirrors (x= 780cm, y = 46.8cm, z = 52cm) over the 2π sky above the aperture (i.e. angles of θ = 0 o 180 o and φ = 90 o 270 o ). In practice, the analysis needs only to cover the sky between φ = 180 o and 270 o, since the shielding distribution of the other half of the sky is just a mirror image of the one shown in Figure 40 due to the symmetry in the baffle structure. The geantinos were fired from a point 25cm from the mirrors optic-axis, which is at the middle position of the nested mirror shells. From this position the solid angle extended by the baffle is around 1.5π, and the SSAT analysis revealed that ~25% of this solid angle is open. It is worth investigating in more detail the angles close to the optic axis (i.e. θ=90 o, φ=180 o ). Figure 41 shows the shielding distribution in a FOV of 10 o 10 o centred on the optical axis. The SSAT analysis shows that ~52% of the 10 o 10 o FOV is open and hence particles can clearly enter the system from adjacent baffle gaps.

43 43 of 60 Figure 40. Analysis of the XMM Baffles from the mirror aperture. Horizontal co-ordinate is the φ angle and the vertical one is the zenith angle θ, in the global co-ordinates system of the Geant4 model. The viewing point (i.e. where the geantinos were fired) is at x= -780cm, y= 46.8cm, z=52 cm. The colour table is in units of gm/cm 2 shielding materials.

44 44 of 60 Figure 41. Analysis of the XMM Baffles from the mirror aperture. The field-of-view (FOV) is 10 o 10 o centred on the optical axis of the mirrors. The colour table is in units of gm/cm 2 shielding materials.

45 45 of Independent Modelling of Mirror Acceptance Angles There are several off-axis ray paths through the mirror baffles. This has been investigated by [24]. It was found that from a point at the mirror entrance, the free space was visible within a solid angle varying between 0.1 and 0.23 steradian. This is a significant fraction of the whole space visible from the centre of the mirror system taking into account the mirror extension (0.86 steradian). As an example the intersection of the ray path accessible from the middle of a mirror entrance with a plane at the top of the mirror baffle extension is displayed in Figure 42. Figure 42. Intersection of the ray path through the middle of a mirror entrance with a plane at the top of the X-ray baffle.

46 46 of 60 3 Environment 3.1 Solar/heliospheric protons Data from the IMP and ACE spacecraft were analysed. Some of the IMP data are available via the OMNIWEB service, but the lowest energy channels of most relevance for the present analysis come from the EPAM instrument. Figure 43 shows these data for the three lowest channels ( , 0.5-1, 1-2MeV). The year shown is 1981 for which a large part of the year was at high flux levels, due to many cororating solar-related structures. 1E+6 1E E+4 flux (/cm2/s/sr/mev) 1E+3 1E+2 1E+1 1E+0 1E-1 1E-2 1E doy Figure 43. Solar proton fluence for energy ranges , 0.5-1, 1-2MeV. This makes identification of specific solar events (as is done with high-energy solar particle events) somewhat difficult and possibly meaningless. This "space weather" needs to be examined though a more customised analysis procedure. Figure 44 shows the number of days in the complete IMP-8 record ( ) in given flux ranges. What is more important in the context of damage, if protection methods such as aperture blocking are to be implemented, is the amount of time lost in preventing certain levels of fluence. For this, the number of days at a given daily flux level that contribute to the overall fluence is needed. Figure 45 shows the contribution to the total fluence from days of certain average flux and Figure 46 combines these two. It shows the contribution to the total fluence from each daily average flux range and the corresponding time in that flux range. Moving from points on the left to points on the right, the number of days lost on protecting against various fluence levels can be obtained. In terms of the total expected mission fluence, Figure 47 shows the annual fluence spectrum and for comparison the values from the ACE spacecraft. ACE is very useful since it provides data on protons of a more relevant energy and these data are provided in near real-time. It can be seen that the data are coherent with the IMP data.

47 47 of < 1 1 to to to to Average Flux (#/cm2/s/st) Figure 44. Number of days in IMP-8 EPAM record ( MeV) in given flux ranges. 1.E+12 Protons/cm2/day 1.E+11 1.E+10 1.E+09 1.E+08 < 1 1 to to to to Ave Daily Flux Range (/ cm2/ sr/ s) Figure 45. The contribution to the total fluence from days of certain average flux.

48 48 of 60 In terms of "events", it is found that compared to the total IMP record fluence in the MeV range of ~ /cm 2 /MeV, less than half comes from the biggest 20 events and only ~10% from the longest-lived. So in order to protect against a significant amount of observing time could be lost. For example, if protection against the largest class (with flux > 10000) is required, which contribute ~3x10 11 cm -2, about 10 days will be lost. If protection is needed against any events with flux above 10cm -2, with contributions to the total fluence from the , , and > 10 4 classes, about 2000 days will be lost. 1.E to Number Fluence Contribution from Range (#/cm 2) 1.E+11 1.E+10 > to to to 10 <1 1.E # days in range Figure 46. Fluence contribution against the number of days contributing. Annual Omnidirectional Fluence (/cm 2 /MeV) 1E E E E E E E E E E ACE Annual Flu 1E E (M e V) Figure 47. Annual differential fluence from the IMP EPAM and ACE.

49 49 of Statistically-Based Predictions Here, a method is described to evaluate the probability of exceeding Solar Proton Fluence in the range keV. From 23 years of IMP data (courtesy of JHU-APL) in the range keV one extracts 13 years corresponding to the maximum of solar activity. For these 13 years the yearly fluence appears to be well approximated by a log-normal distribution. Assuming that this results from a compound Poisson process, one can expect that the above property is conserved for n-year fluence distribution for which the following simple relations are supposed to hold according to [25]: and F n = n F 1 σ n 2 = σ 1 2 /n where F i and σ i are respectively the mean and the standard deviation of the i-year fluence. An uncertainty is attached to the derivation of the two parameters of the log-normal law because of the limited number of data. This uncertainty leads to a spread of the probability that one could derive from the above model. This can be taken into account via a Monte-carlo simulation based on the generation of 10 5 random sets of 13 values that lead to the same value of the inferred mean and variance. For each set, the probability of exceeding a given fluence over a period of 5 years and 10 years of high solar activity, has been derived using the above hypotheses. The final result shown in Figure 48 is the sum of these probabilities. Figure 48. Probability of exceeding a given proton fluence in the range keV during high solar activity. The vertical lines are located at the averaged value of the measured fluence over respectively 5 and 10 years during high solar activity.

50 50 of Magnetospheric Environment Until now predictions of the magnetospheric environment have been based on the AP-8 model. This model is static and at low energies it is known that the ion population is dynamic. Data from recent missions is now available to make estimates of the magnetospheric environment, although care must be taken in extrapolating these to the XMM orbit, which crosses very different parts of the magnetosphere. A detailed analysis has been made using data from Equator-S, launched in December 1997, a low-cost mission designed to study the Earth s equatorial magnetosphere. The Equator-S orbit was near-equatorial (4 inclination) hence subjected to higher particle fluxes, with a 500km perigee and 67000km apogee, reaching the outer parts of the magnetsophere. The orbit coverage of the Equator-S spacecraft is shown for the whole mission in GSE x-y plane in Figure 49, the position of the Earth and direction to the Sun are indicated and flux values are colour coded. Figure 49. Mission orbit coverage of Equator-S in GSE x-y plane (ecliptic) with colour-coded flux values. One of the Equator-S mission objectives was to provide high-resolution plasma and magnetic field measurements in the equatorial magnetosphere and across the low-latitude dayside magnetopause and boundary layer. Seven science instruments measured the ambient magnetic and electric fields and the density, velocity temperature and composition of the charged particles around the spacecraft. Of particular interest for this study is the output from the Energetic Particle Instrument (EPI), an array of solid-state telescopes that measured electrons and ions in the ranges keV and keV respectively, in 6 energy channels and 4 angle channels at a time. The data from the highest energy channel ( keV), covering the proton energies of interest for the EPIC-MOS instrument on XMM, is shown in Figure 50. The recorded proton flux and its mean value are plotted against radial distance in GSE co-ordinates.

51 51 of 60 Figure 50. The Equator-S highest energy proton channel ( keV) plotted against radial position, also showing the mean value. In an attempt to extrapolate the proton fluence measured by Equator-S to the outermost radial distances reached by the XMM orbit (114000km), models were fitted to the mean proton flux curve using two different extrapolations beyond the Equator-S apogee: a constant or asymptotic fluence level equal to that measured at the apogee of the Equator-S orbit, and a log fall-off from this point extending to the XMM apogee distance. These are plotted in Figure 51.

52 52 of 60 Figure 51. A fit to the mean proton flux with two alternative extrapolations above the Equator-S apogee, constant and log fall-off. Assuming that XMM would see the same proton fluence as predicted by these two models (i.e. the different orbit inclination is not taken into account at this point), the orbital fluence as a function of cut-off altitude (i.e. the point at which the FOV of the EPIC cameras becomes blocked/unblocked by the aluminium stop) can be calculated. This is shown in Figure 52, where the proton fluence at each cut-off point has been estimated for the time during which the EPIC detectors remain exposed in going from cut-off, through apogee to cutoff again. For the actual XMM orbit, the proton fluences are most likely to lie somewhere in between the values predicted by the two extrapolation models. Figure 52. Orbital proton fluence as a function of cut-off altitude for the constant and log fall off (extrapolation) models. The integration along the orbit is from cut-off, through apogee to cut-off again, i.e. the time during which the EPIC detectors are exposed. In order to check the magnitude and type of spectrum provided by the Equator-S data, the proton flux measured in three Equator-S energy channels at geostationary orbit altitude, has been plotted in Figure 53 for a number of days of 1998, together with similar data from other spacecraft on geostationary orbit. The data from the LANL instruments on US defense satellites shows that the proton energy spectrum falls off very steeply by three orders of magnitude between energy ranges keV and 1.2-5MeV. The Equator-S data shown in this plot correspond to energy channels 45-73keV, keV and keV. These data show a proton flux reduction by nearly two orders of magnitude between the lower and higher energy channels, confirming the steep spectrum fall off. This explains the closer agreement between the low energy LANL channel and the Equator-S 45-73keV channel, as it is these protons that make up most of the flux detected in the LANL instrument. The stripes seen in the Equator-S data are due to taking only the orbital sections as they pass close to geostationary altitude.

53 53 of 60 The >1MeV and >10MeV integral proton fluxes measured by the GOES-9 satellite are also shown in Figure 53. The main contributions to these integral flux values come from the low-energy end of each channel. It is clear for these data that the >10MeV flux is steady over a full month, in stark contrast with the keV data from Equator-S whose maximum variation over the same period can exceed well over one order of magnitude. Figure 53. Comparison of proton flux measured at geostationary orbit altitude by Equator-S in three separate energy channels and by other geostationary spacecraft. The data clearly show the very steeply falling energy spectrum, which makes it difficult to correlate high (>10MeV) and low (~200keV) energy proton population levels. The extreme variation in proton flux with proton energy is the reason why the correlation between measurements made by a high energy detector (>10MeV) and the low energy proton population (~200keV) is very poor. This means that it will be difficult to extrapolate the output from the radiation environment detector on board XMM to obtain estimates of the low energy proton flux surrounding the spacecraft because of this very steep spectrum.