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Rev. Sci. Instrum. 90, 124502 (2019); https://doi.org/10.1063/1.5120410 90, 124502
© 2019 Author(s).
Design and implementation of electron
diverters for lobster eye space-based X-ray
optics
Cite as: Rev. Sci. Instrum. 90, 124502 (2019); https://doi.org/10.1063/1.5120410
Submitted: 17 July 2019 • Accepted: 15 November 2019 • Published Online: 05 December 2019
V. Aslanyan, K. Keresztes, C. Feldman, et al.
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Design and implementation of electron diverters
for lobster eye space-based X-ray optics
Cite as: Rev. Sci. Instrum. 90, 124502 (2019); doi: 10.1063/1.5120410
Submitted: 17 July 2019 •Accepted: 15 November 2019 •
Published Online: 5 December 2019
V. Aslanyan,1,a) K. Keresztes,1C. Feldman,1J. F. Pearson,1R. Willingale,2A. Martindale,1S. Sembay,2
J. P. Osborne,2S. S. Sachdev,1C. L. Bicknell,1P. R. Houghton,1T. Crawford,1and D. Chornay3
AFFILIATIONS
1Space Research Centre, Department of Physics and Astronomy, University of Leicester, University Road,
Leicester LE1 7RH, United Kingdom
2Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
3University of Maryland, College Park, Maryland 20742, USA
a)Electronic mail: v.aslanyan@leicester.ac.uk
ABSTRACT
Micropore optics have recently been implemented in a lobster eye geometry as a compact X-ray telescope. Fields generated by rare-earth
magnets are used to reduce the flux of energetic electrons incident upon the focal plane detector in such a setup. We present the design
and implementation of the electron diverters for X-ray telescopes of two upcoming missions: the microchannel X-ray telescope onboard
the space-based multiband astronomical variable objects monitor and the soft X-ray instrument onboard the solar wind magnetosphere
ionosphere link explorer. Electron diverters must be configured to conform to stringent limits on their total magnetic dipole moment
and be compensated for any net moment arising from manufacturing errors. The two missions have differing designs, which are pre-
sented and evaluated in terms of the fractions of electrons reaching the detector, as determined by relativistic calculations of electron
trajectories. The differential flux of electrons to the detector is calculated, and the integrated electron background is determined for both
designs.
©2019 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(http://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/1.5120410
., s
I. INTRODUCTION
X-ray telescopes use grazing incidence optics to focus pho-
tons onto a detector. Micropore Optics (MPOs) reflect X-rays
from the walls of regular arrays of microscopic square chan-
nels. Such a geometry requires a direct line of sight from the
focal plane to the immediate space environment of the telescope,
allowing charged particles (either trapped in the magnetic field
of the Earth or comprising solar wind, etc.) to reach the detec-
tor directly. Electrons with energies of 0.01–10 MeV can deposit
significant energies into silicon based devices,1,2 causing elevated
background levels. Mitigation against electrons is possible using
permanent magnets which alter the electron path (i.e., magnetic
diverters) away from the detector to some other part of the tele-
scope structure. Various configurations of magnets have been used
or proposed to protect X-ray instruments from electrons3,4 and
protons.5
Micropore Optics (MPOs) have been recently developed as a
compact and lightweight method to focus X-rays.6Arrays of thou-
sands of microscopic square glass channels focus soft X-rays by
grazing incidence reflection. Metals (such as iridium) are used to
coat the inner channel walls to improve X-ray reflectivity at the
relevant energies. The individual MPOs are spherically slumped
to a radius Rrelated to their focal length by f=R/2. Numer-
ous MPOs are assembled onto a spherical surface of radius Rto
make up a so-called lobster eye geometry; rays are focused onto
a sphere of radius R/2. A lobster eye can potentially cover an
arbitrarily large field of view, provided that the detector could be
made spherical, or suitable arrangements be made for a planar
detector.
Space-based multiband astronomical Variable Objects Mon-
itor (SVOM)7,8 is a Chinese-French mission due to be launched
at the end of 2021 into a 600 km altitude circular orbit with
an inclination of 30○. It is designed to study gamma-ray bursts
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and so has crystal scintillator (GRM) and coded mask (ECLAIRs)
instruments to detect and locate them. These are complemented by
the Micropore X-ray Telescope (MXT) and the Visual Telescope
(VT). The satellite slews rapidly and autonomously in response to
new gamma-ray bursts (GRBs) detected onboard, and new GRB
locations are transmitted to the ground promptly via a dedicated
VHF network. SVOM has similarities to Swift,9with some additional
capabilities, although it is smaller in length and mass. SVOM com-
pensates for its smaller size by operating at lower energies where the
source photon flux is greater.
The MXT is a lobster eye optic made up by MPOs arranged in
a 5 ×5 grid for a focal length f= 1.125 m and 64′×64′Field Of
View (FOV), limited by the CCD detector. The central 9 MPOs have
a thickness of 2.4 mm, and the surrounding 16 MPOs have a thick-
ness of 1.2 mm, optimized to detect point sources in their FOV. The
back-illuminated CCD detector consists of an array of 256 ×256
square pixels, with a width of 75 μm. The CCD detector is config-
ured for photon energies in the range 0.2–10 keV. An electron which
strikes a detector pixel can either appear as a photon if the energy
deposited is below 10 keV or cause a “dead” pixel for the duration
of one frame if the energy deposited exceeds 10 keV. The back-
ground radiation budget sets a limit on the integrated electron flux of
10−3cm−2s−1at the detector to achieve the science goals; reduction
below this value is desirable. The limit is derived assuming a worst-
case absorption profile so that electrons of all energies arriving at the
focal plane are assumed to cause undesirable effects and must be mit-
igated. A switchable filter wheel is installed as part of the focal plane
assembly to allow for calibration and pursuit of secondary science
objectives and to shield the CCD detector from transient radiation
effects.
Solar wind Magnetosphere Ionosphere Link Explorer (SMILE)10
is a joint mission between the European Space Agency and the Chi-
nese Academy of Sciences, due to launch in November 2023. The
aim of SMILE is to image charge exchange X-ray emission from the
boundary of the magnetopause using the soft X-ray imager, in addi-
tion to monitoring the aurorae with the Ultraviolet Imager (UVI),
the solar wind magnetic field with the Magnetometer (MAG), and
solar wind particles with the Light Ion Analyzer (LIA). The SMILE
satellite will have a highly elliptical orbit ranging from around 1
Earth Radius (RE) altitude at perigee to around 19 RE altitude at
apogee, with an inclination of 60○. The Soft X-ray Instrument (SXI)
optic is composed of two optic frames, each containing 16 MPOs
with 1.2 mm thickness, slumped to achieve f= 0.3 m and to give a
wide 26.5○×15.5○FOV.
The SMILE SXI focal plane will accommodate two CCD detec-
tors manufactured by Teledyne e2v, designated CCD370, butted in
close proximity. The CCDs are back-illuminated and thinned to
have a sensitive silicon thickness of approximately 16 μm, detect-
ing photons in the range ∼0.15 to 2.5 keV. The CCDs have 4510
×4510 native pixels of 18 μm size but will be operated with a fac-
tor 6 binning to give effective pixels of 108 μm. The CCDs have
an asymmetric frame transfer architecture, with approximately a
6:1 ratio. The CCDs have a charge injection circuit which will be
used to minimize the effect of charge transfer inefficiency caused
by radiation damage. The scientific objectives require an inte-
grated electron flux be limited to below 0.1 cm−2s−1at the detec-
tor during normal operation. The limit is obtained assuming that
incoming electrons of all energies cause either elevated photon
background levels or “dead” pixels, both of which lead to image
degradation.
A. Orbit electron flux
The orbit for SVOM has a relatively gentle electron back-
ground, with the exception of the South Atlantic Anomaly where
fluxes of energetic charged particles rise dramatically. A recent
study of the electron fluxes in low Earth orbit undertaken by
DEMETER-IDP11 found the peak inside this region to be five or
six orders of magnitude higher than the flux outside the region.
Based on its inclination and orbital period, SVOM is expected
to pass through the South Atlantic Anomaly several times per
day, inducing an overall dead-time of 13%–17%. To compute the
expected differential electron flux for SVOM, outside the exclu-
sion region, we use the AE9 model12 (version 1.5). We take
the mean differential flux density over several complete, repre-
sentative orbits which do not pass through the South Atlantic
Anomaly. The model is restricted to electron kinetic energies
EK>40 keV, so we approximate the differential flux below
this threshold by a simple extrapolation; the result is shown in
Fig. 1.
The SMILE spacecraft is expected to experience high and vari-
able charged particle fluxes. A shutter mechanism within the SXI
telescope will protect the instrument during extreme solar wind
conditions and passage through the radiation belt of the Earth.
Representative differential electron flux densities expected for the
SMILE mission are taken from data acquired by the 3DP instrument
onboard the WIND spacecraft during the solar maximum between
March and August 2001,13 as shown in Fig. 1. Two electron flux
densities are indicated: the peak of the observation period occur-
ring during a coronal mass emission and the ambient time average
excluding elevated transients.
FIG. 1. Incident differential electron flux density for the two missions considered
here. For SVOM, the mean over several orbits outside the South Atlantic Anomaly
is taken from the AE9 model. For SMILE, we use the electron density in the
solar wind, as measured by the WIND/3DP instrument at ambient and peak con-
ditions. The corresponding dotted lines indicate extrapolations to higher and lower
energies, respectively, based on the closest available data.
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II. MAGNET SELECTION
The MPOs considered in this article are square with an area
of 40 ×40 mm2, as shown in Fig. 2. The channels are between
1 and 3 mm deep (as specified below) and 40 μm wide, giving a large
aspect ratio. The pore wall thickness is approximately 11 μm, giv-
ing an open area fraction of 61%. In order to filter unwanted visible
light, the outer faces of MPOs are coated with a 70 nm aluminum
film (to prevent direct illumination) and the MPOs themselves are
bonded to the optic frame by opaque adhesive (to prevent scattered
light entering via outer edges of the MPOs).
Electron diverters are constructed by bonding permanent mag-
nets to a rigid metal diverter frame. In order to maximize the
effectiveness of magnets at deflecting the trajectories of electrons,
they are ideally placed at the greatest possible distance from the
focal plane. For a lobster eye geometry, the diverter frames are
mounted close to the MPOs to achieve this while minimizing X-ray
vignetting. The diverter frames are self-standing and rigid enough to
withstand magnetic stresses on the magnets and vibrations during
launch.
The selection of the material for the diverter magnets is a trade-
off between the magnetic remanence (and hence field strength)
and other physical characteristics. The remanence
Brdetermines
the magnetic dipole moment through
m=
BrVμ0, where Vis
the volume of the magnet and μ0is the permeability of free space.
With a larger achievable remanence, the size of the magnets can be
made smaller; hence, the payload mass and vignetting effects can
be reduced. Conversely, mission requirements may dictate a large
operating temperature range so driving the choice of the magnetic
material.
The two leading choices of the magnetic material are
neodymium iron boron (Nd2Fe14B, hereafter abbreviated to
NdFeB)15 and samarium cobalt (most usually Sm2Co17, hereafter
abbreviated to SmCo),14 both of which have been used on previ-
ous space missions; their key properties are summarized in Table I.
NdFeB magnets have the highest field strength of the commer-
cially available rare-earth magnets (we assume a mean remanence
of
Br=1.415 T) but require special treatment to avoid corro-
sion. SmCo magnets have slightly lower, but, nonetheless, high field
strengths (we assume a mean remanence of
Br=1.09 T although
higher values are possible), are resistant to corrosion, and are suit-
able for spacecraft expected to experience high temperatures. The
effectiveness of both types of magnets is evaluated in Sec. IV.
FIG. 2. (Left) A single spherically slumped, aluminum-coated Micropore Optic
(MPO), with linear dimension 40 mm. (Right) details of glass square micropores of
inner width 40 μm.
TABLE I. Summary of the relevant properties of neodymium iron boron (NdFeB) and
samarium cobalt (SmCo) magnets. Note that both types have been successfully used
on previous space missions.
Property NdFeB SmCo
Mean remanence (T) 1.415 1.09
Maximum temperature (○C) 90 350
Corrosion resistant No Yes
Thermal expansion coefficient (K−1) 7.5 ×10−61.1 ×10−5
The geometry of the magnets is dictated by the restrictions of
the optics as they must fit between two adjacent MPOs without sig-
nificantly obscuring the line of sight. We have selected large aspect
ratio magnets with dimensions 38 ×6×3 mm3so that the long edge
is approximately equal to the linear dimensions of MPOs. The mag-
nets are chamfered on each edge nominally by 0.5 mm for a total
volume of 660 mm3.
NdFeB magnets have a Curie temperature of 310 ○C and in
certain configurations operate reliably15 up to 120 ○C, while SmCo
magnets can operate up to 350 ○C. Both materials are therefore com-
patible with the operational conditions of the two missions discussed
in this article, where the temperature will not exceed 90 ○C. The lin-
ear temperature expansion coefficient of the magnets is compatible
with the mechanical properties of the diverter frames to which they
are bonded.
During diverter assembly, magnets are cleaned, vacuum baked
at 80 ○C, and bonded to the metal diverter frames using Scotchweld
2216 epoxy. This bonding agent is widely used in space applications,
and testing has confirmed its suitability for this purpose. Care must
be taken with NdFeB magnets in particular, which rapidly corrode
or rust if left untreated. To prevent corrosion, these types of magnets
must be coated with Mapsil 213-B encapsulating resin, if possible
immediately after bonding. Mapsil 213-B is certified and widely used
to conformally coat printed circuit boards on spacecraft. However,
the adhesive resin can trap particle contaminants and subsequently
release them to degrade the performance of the optics and detector;
investigation into contamination is ongoing. Figure 3 shows opti-
cal micrographs of two magnets which have been coated by encap-
sulating resin. Both magnets were kept in a humidity-controlled
environment before bonding and application of the coating, with
the one on the left in the nominal condition, while the one on the
FIG. 3. Micrographs of neodymium iron boron (NdFeB) magnets for use in electron
diverters. Both magnets have been coated with protective Mapsil 213-B but display
differing amounts of corrosion: on the left, the magnet retains its surface finish; on
the right, it is discolored by corrosion. White regions in both cases are reflections
from the Mapsil 213-B coating.
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right has been discolored by corrosion during storage. Note that
the effect of corrosion on the magnetic moment is negligible
in this case.
III. DIVERTER DESIGN AND ERROR FIELD
COMPENSATION
The magnetic field
Bfrom a magnetic dipole
mis given by
B=μ0
4π
r3[3ˆ
r(
m⋅ˆ
r)−
m], (1)
where
ris a vector from the dipole to the measurement point
and ˆ
r=
r
r. For the magnets considered in Sec. II, the mean
magnetic moment
m=743 mA m2. The total dipole magnetic
moment of a configuration of magnets is the vector sum of the
constituent moments,
mT=∑j
mj. There is a limit on the mag-
netic cleanliness of the electron diverter, with the dipole moment
of the magnetic field typically limited to
mT≲100 mA m2; this is
imposed so as to prevent torque on the spacecraft in the magnetic
field of the Earth. As a result, any possible configuration of dipoles
must be designed symmetrically with net zero magnetic moment;
any resulting moment arises from manufacturing or alignment
errors.
Three possible configurations of magnets (with net zero mag-
netic moment) to be located close to MPOs in order to deflect
electrons are shown in Fig. 4. Pairs of opposing magnets form a
quadrupole, which can be extended outward by adding more mag-
nets orientated toward the center. For multiple MPOs, a quadrupole
configuration can be achieved with relatively few magnets, com-
pared to the other methods (see discussion below). Conversely, the
quadrupole produces a magnetic null, i.e., the magnetic field van-
ishes in the center of the MPO leading to degraded performance.
Provided that the magnetic axis can be aligned with the long dimen-
sion of the magnets, a Halbach array16 can be assembled. This con-
figuration produces an almost uniform field across one or more
MPOs and can be tiled to arbitrary size, provided that the resul-
tant pattern is square (such as a 2 ×2 or 3 ×3 MPO arrange-
ment); a rectangular pattern (such as 2 ×3 MPOs) does not have
net zero magnetic moment. Another approach to constructing an
electron diverter discussed in this article is two identical subassem-
blies, each with a finite magnetic moment; the two subassemblies
are then counteraligned to achieve cancellation of the magnetic
moment.
The MPOs for the MXT instrument onboard the SVOM mis-
sion, arranged into a lobster eye geometry, are shown in Fig. 5(a);
only the top portion of the whole 1.125 m telescope tube is pic-
tured (note that Xis the optical axis). The assembled electron
diverter for the Qualification Model (QM) of the MXT is shown
attached to the rear plane of the optic frame in Fig. 5(b). The
QM differs from the final flight version by a slightly shorter focal
length, slightly thinner MPOs in some cases, and with the four cor-
ner MPOs replaced by opaque blanks. For the QM, NdFeB mag-
nets have been bonded and encapsulated, as described in Sec. II,
but the possibility of using SmCo magnets for the flight version is
being considered. The magnets appear as the long dark sections,
coated with reflective resin, the MPOs appear as gray squares, and
the Aluchrom blanks appear as light brown squares. The diverter
is of a quadrupole design, with the magnets’ orientations and the
resultant magnetic field shown in Figs. 5(c) and 5(d), respectively.
The design offers good magnetic coverage of the MPOs with the
exception of nine magnetic nulls which extend outward, perpen-
dicular to the plane of the diverter. The design consists of 36
magnets bonded to an Aluchrom frame; the quadrupole design is
economical in terms of the number of magnets, minimizing the
vignetting due to the diverter frame. A comparable Halbach array
would require each MPO to be surrounded on all sides and there-
fore require 60 magnets. The magnet economy of the quadrupole
design can be seen in Fig. 5(b) through the light brown edges of
the diverter frame (for example, in each of the corners), where
no magnet is installed; for the Halbach design, each of these
edges would require a magnet to be installed and hence increase
vignetting.
For the SVOM MXT, the magnetic moment requirement is
mT<50 mA m2. The magnets are nominally orientated only in
the plane of the diverter, and as a result, the error moment is also
expected to be predominantly within the plane. In order to satisfy
the magnetic cleanliness requirement for the total residual mag-
netic moment, a set of smaller compensating magnets is included
in the diverter design. There are two mounting points at oppo-
site ends of the diverter for holders to which smaller compensating
magnets are bonded. Compensating magnet holders can accommo-
date one or two magnets, each with
m≃74 mA m2(one tenth
of one larger magnet), and are free to rotate in the plane of the
diverter. The number and orientation of the compensating magnets
must be selected after determining the strength and direction of the
error moment, and the compensating magnets must then be fixed
in place.
The SXI onboard the SMILE mission, as shown in Fig. 6(a),
has two separate optic arrays, each of 4 ×4 MPOs, to give a wide
field of view (note that, unlike the MXT, Zis the optical axis). The
optics’ design naturally lends itself to the dipole pair design in Fig. 4.
FIG. 4. Examples of three diverter configurations with total
zero dipole moment. The magnetic moments are marked on
each magnet by the arrows (blue) along with representative
magnetic field lines. Square MPOs are shown in gray. Mag-
netic nulls, or regions of near-vanishing magnetic field, are
indicated by a red cross (×).
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The electron diverter is split into two titanium frames, as shown
in Fig. 6(b), with magnets bonded in the locations indicated. Both
magnetic materials described in Sec. II are being explored for the
mission. Each diverter frame is curved to structurally match the rear
of the optic frame onto which it is bolted (i.e., inside the telescope
tube), which has a radius of curvature R= 60 cm. The diverter frames
are rotationally symmetric about their common center, and con-
sequently, the net magnetic moments of the two frames are equal
and opposite; the resultant field, for the case of NdFeB magnets,
is given in Figs. 6(c) and 6(d). Magnetic nulls exist between the
two frames but are covered by the optic frames and stray light baf-
fles. Electrons passing through the thin MPOs are deflected out-
ward from the center, toward the two outer sections of the tele-
scope tube. Each electron experiences a magnetic field of at least
5 mT/7 mT for SmCo/NdFeB on its trajectory, which is enough
to completely deflect electrons with energies below 30 keV/50 keV
(see below).
The radial component of the magnetic field of a dipole located
at the origin is given by
B⋅ˆ
r=μ0
2π
r3
mcosθ−θ, (2)
whereθis the angle between the magnetic moment and the principal
measurement axis. Measurements to determine the dipole moment
are typically made by a Hall probe kept at a constant distance to the
magnetic configuration under test, which is then rotated. As a result,
B⋅ˆ
ris measured at regular intervals in θwhile keeping
rconstant.
The N-point Discrete Fourier Transform (DFT) of such a set of mea-
surements (scaled by the angular interval Δθat which measurements
are taken) is
bj=2
N−1
k=0
B⋅ˆ
rexp−2πi
NjkΔθ. (3)
By comparing Eqs. (2) and (3), the dipole moment can be deter-
mined from the Fourier decomposition through
m=2π
r3b1μ0,
while its orientation is θ=arg(b1). In practice, the circle over
which
B⋅ˆ
ris measured will not be coplanar with the vec-
tor
m, i.e., the magnetic moment will be slightly out of the
plane of measurement. Consequently, measurements are made in
three orthogonal planes, yielding the projection of the magnetic
moment onto each plane; for example,
mY−Zrefers to the com-
ponents of the magnetic moment in the Y–Zplane. For a spa-
tially extended magnetic configuration, as for a realistic diverter,
the origin of the measurement axis must be precisely colocated
on the axis of symmetry of the system. Conversely, even an ideal
quadrupole would exhibit a fictitious dipole moment if such mea-
surements are not performed about the geometric center of the
quadrupole.
FIG. 5. (a) Upper end of the SVOM MXT
instrument (lower section of the tele-
scope tube and detector not pictured),
showing lobster eye MPO geometry. (b)
Photograph of the rear side (view from
the detector plane out) of the assem-
bled Qualification Model (QM) of the
MXT optic, with the diverter installed.
The NdFeB magnets, which are darker
than the diverter frame, can be clearly
seen. (c) Schematic of the magnet ori-
entation and location within the diverter
frame (magnets are not to scale).
(d) The resulting magnetic field strength
in the midplane of the diverter, with pro-
jections of the edges of the MPOs (which
are above the plane of the diverter). If
SmCo magnets were to be used, the
field strength would be scaled down by
an appropriate amount, while the field
direction would remain unchanged.
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Measurements were performed on the assembled SVOM MXT
Qualification Module (QM) diverter at the J.-B. Biot Amagnetic
Laboratory as described above. The radial field component
B⋅ˆ
r
measured at r= 1.211 m in the Y–Zplane of the diverter (before
and after installation of the compensating magnet) is shown in
Fig. 7(a). The quadrupole moment contribution
B⋅ˆ
r∼cos(2θ)is
dominant at this measurement distance. The quadrupole compo-
nent can be obtained from the Fourier expansion in Eq. (3) through
Re{b2exp(2iθ)}; the residual obtained by subtracting the contribu-
tions of the b0(average) and b2terms from the total field is shown in
Fig. 7(b). In the uncompensated case, the cosθ−θterm is clearly
visible, with Fourier analysis yielding
mY−Z=91 mA m2and
θ=121○(where θ=0 corresponds to the +Yaxis). Based on
this measurement, a single compensating magnet was chosen and
installed to oppose the error moment, as shown in Fig. 7(c) and
also visible in the lower center of Fig. 5(b). After installation, the
error moment in the plane of the diverter frame is reduced to
mY−Z
=17 mA m2and the total moment to
m=34 mA m2. Subsequent
image analysis shows that the compensating magnet was installed
at an angle of 115.8○, opposing the measured error moment as
required.
The SVOM MXT instrument is designed to be kept within
an operating temperature range of 20 ±10 ○C by a set of resistive
heaters. The heaters (light and dark brown) and the applicable cables
are visible in Fig. 5(b). The magnetic moment of a closed current
loop in a plane is given by
m=IA
n, (4)
where Iis the current, Ais the area enclosed by the loop, and
nis
a unit vector normal to the plane of the loop. MXT heaters oper-
ate with a near-constant current I= 380 mA, enclosing an esti-
mated area of 0.013 m2and hence giving a magnetic moment of
m=4.94 mA m2; this is far below the relevant limit.
The above procedure for error moment compensation is
planned to be repeated for SXI. The error moment from the curved
SXI diverter frame is more challenging to compensate as the mag-
nets are not confined to a single plane: four mounting points for
FIG. 6. (a) SMILE lobster eye optics inside the SXI. (b) SMILE SXI diverter frames, looking out from the instrument’s CCD detector, showing the position of magnets (gray)
and the net magnetic moment of each frame; smaller, adjustable correcting magnets are also visible at the top and bottom of the assemblies. (c) Magnetic field strength on
a plane through the center of the SXI (X= 0), with an indicative instrument cross section (black) and the detector at the bottom (orange). (d) Magnetic field on a spherical
surface which defines the midpoints of the magnets. Projections of MPOs are also indicated (note that the diverter frame is offset from the MPOs). The field strength is given
for NdFeB magnets, but if SmCo magnets were to be used, it would be scaled down.
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FIG. 7. (a) Measurements of the MXT diverter’s radial field component at
r= 1.211 m in the Y–Zplane, before and after installation of the compensating
magnet. (b) Residual field, obtained by removing the constant and quadrupole
components of the field; the dashed line indicates the contribution of the uncom-
pensated dipole moment. (c) Compensating magnet installed in position, showing
angle to the Yaxis.
compensating magnet holders and two midway along the outside of
each of the frames, as shown in Fig. 6(b). Each compensating mag-
net holder is free to rotate in a single plane about its mounting point;
multiple holders are prefabricated with varying elevations out of the
rotation plane, allowing the correct elevation angle to be chosen at
compensation time.
IV. ELECTRON DEFLECTION EFFICIENCY
A. General considerations
The incoming spectrum of electrons extends to kinetic energies
EK>100 keV, approaching or exceeding the rest energy of electrons.
In the absence of an electric field (as is the case in the optics’ rest
frame), a particle’s energy is a constant of motion. The relativistic
expression for the acceleration of an electron in a pure magnetic field
is given by
d
v
dt =qe
γme
v×
B, (5)
where qeand meare the charge and mass of an electron and
the relativistic factor γ≡(1−
v2c2)−1/2=1 + EKmec2is
constant.
We solve the resulting set of equations using the common
4-step Runge-Kutta method17 with a minimum time step Δt= 10−13
s; this yields an acceptable Courant number and allows for rapid
evaluation of electron trajectories. The topologically complicated
diverter magnetic field is obtained by direct interpolation of the vec-
tor field on a precomputed grid. Electrons are initialized at random
positions on the inner surface of individual MPOs, inside the open
areas of the corresponding micropores, with a fixed kinetic energy
and a velocity close to an inward-facing normal vector to the face
of the given MPOs. The direction of the initial velocity is charac-
terized by a polar angle θ(inclination from the normal vector) and
azimuthal angle ϕ(rotation around the normal vector), where, for an
isotropic electron distribution, cos2θand ϕtake uniform randomly
distributed values due to geometric effects.18
Neither a detailed model nor experimental measurements for
the passage of electrons through an MPO exist at present. Studies
of micropores as electron multipliers19 have found the probability
of scattering of primary electrons along the channel to be negligi-
ble, while secondary electrons are reabsorbed unless a sufficiently
large voltage is applied. Therefore, a simplifying assumption is made
that electrons which strike the channels of MPOs are immediately
absorbed and do not cause emission of secondary electrons. The ini-
tial velocities of the electrons are uniformly distributed into a cone
with an open angle θmax = 3○around the normal to the correspond-
ing MPO; at higher open angles, the trajectory always intersects a
square micropore of width 40 μm and depth ≥1.2 mm. This implies
that any electron with a polar angle exceeding 3○is certain to strike
the MPO channels, and therefore, only electrons in a cone with this
open angle must be considered. In the first time step, a check is made
to determine if the trajectory of the electron intersects one of the
walls of the microchannel; the electron proceeds if this is not the
case.
We assume in this model that when an electron strikes a
solid surface, it is immediately absorbed. Those electrons which
are not absorbed by the micropores must either strike the diverter
frame, the telescope tube (including the mechanical structures in
the focal plane), and the CCD detector or be deflected by the mag-
netic field back into the optics assembly (and therefore out of the
instrument).
The efficiency of an electron diverter as a function of elec-
tron energy is then determined by the fraction of total electrons
which strike the detector. For each of a number of fixed kinetic
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energies, we simulate 3 ×107electrons with random initial posi-
tions and velocities within the constraints outlined above and cal-
culate the detector hit fraction. Note that those electrons which
are absorbed by the micropores and those with trajectories orien-
tated away from the detector are included in the total; consequently,
the hit fraction even in the absence of a magnetic field is below
unity.
The differential flux of electrons at the detector (expressed in
s−1keV−1) is given by
Φ=ηopenNMPO AMPOΘηhit F, (6)
where ηhit is the calculated detector hit fraction, Fis the differential
electron flux density (see discussion in Sec. I), ηopen = 0.61 is the
open fraction of individual MPOs, NMPO is the number of MPOs,
AMPO = 4 ×4 cm2is the area of a single MPO, and Θ=πsin2(θmax)
sr is a geometrical factor18 for isotropic flux through a cone of open
angle θmax; for all simulations, θmax = 3○as outlined above. The total
electron flux at the detector is computed by direct integration of Φ
for each diverter design.
Electrons deflected away from the CCD detector can nonethe-
less lead to the emission of secondary electrons and undesirable
luminescent x-rays from the solid surfaces inside a lobster eye tele-
scope. For the MXT, most secondary emission is expected at the
upper end of the telescope tube (where the density of primary elec-
tron impact is greatest), far from the CCD detector. For SXI, it is
planned to include baffles installed on the inner walls of the tele-
scope tube to block direct line of sight for a significant fraction of
secondary emissions.
B. MXT diverter efficiency
For the SVOM MXT, we approximate the telescope tube by
a cylinder with radius 14.8 cm, although in reality, some sections
throughout its length are slightly narrower due to stiffening rings
inside the tube. The optics assembly is an appropriate spherical sec-
tor at the top of the tube. The detector in the model is taken to be
the active CCD area of 1.92 ×1.92 cm2, centered within the tube
at the focal length of the telescope. The trajectories of 200 electrons
which hit the CCD detector (chosen randomly) with NdFeB mag-
nets are shown for each of two electron energies: EK= 10 keV and
EK= 100 keV in Figs. 8(a) and 8(d), respectively. These trajecto-
ries have been projected onto the X–Zplane (i.e., motion in Yis
not shown), and a cross section of the MXT model taken at Y= 0
is also shown. The points in the midplane of the diverter (X= 0)
through which these electrons pass are shown in Figs. 8(b) and
8(e); the magnetic field strength and the simulated surface defined
by the telescope tube are also shown. Most electrons in these sim-
ulations which emerge from the micropores are deflected into the
telescope tube.
It is clear that the overwhelming majority of electrons which
hit the detector pass through the magnetic nulls intrinsic to the
quadrupole design of the diverter, especially at higher energies.
There is an asymmetry in the results: the orientation of the mag-
netic field deflects a small number of electrons emerging from the
upper right and lower left MPOs inward, to the detector; at the lower
right and upper left MPOs, the field direction is reversed so that elec-
trons can reach the detector by completing a circular orbit at lower
energies, or through the magnetic null at high energies. This trend
is shown in Figs. 8(c) and 8(f), where the number of electrons from
each MPO which hit the detector is given. The hit location of each
electron on the surface CCD detector is also shown, demonstrating
an even distribution; note that the plot is not indicative of the size of
CCD pixels.
The detector hit fraction is given for a range of electron kinetic
energies in Fig. 8(g) for magnetic materials as indicated. The over-
all hit fraction exhibits a power-law trend with increasing energy;
a small shoulder is seen at 10 keV. The corresponding differential
flux at the detector calculated from Eq. (6) is shown in Fig. 8(h);
initially, this quantity rises due to the dominant growth of the hit
fraction but subsequently rapidly falls off as a result of the decreas-
ing input electron spectrum. The hit fraction for SmCo magnets is
higher than that of NdFeB magnets by a consistent factor across the
energy range.
The electron flux to the entire detector and per unit area is
given in Table II for energies between 1 and 1000 keV, above which
the differential flux becomes insignificant. Electrons between 1 and
10 keV are expected to be fully absorbed by the CCD detector and
appear as photons of the appropriate energy so that this energy
range is the most detrimental; the integral for this energy range
is also given. In addition to computing the electron hit fractions
with the nominal magnetic field of the diverter described above,
a hit fraction ηhit = 1.4 ×10−3has also been determined for the
magnetic field set to zero everywhere while keeping the geometry
unchanged (i.e., the diverter frame is still simulated). This value
is independent of EKbecause the electrons take ballistic trajecto-
ries; integrating Eq. (6) with this hit fraction gives an estimate for
the flux in absence of a diverter. The calculated electron fluxes
can be compared to the operational limit stemming from science
requirements, which is also given in Table II; the figures imply
that the electron flux exceeds the required limit without a diverter
but is comfortably below the limit with the quadrupole design
presented here.
C. SXI diverter efficiency
We model the two adjacent CCD detectors of SXI as a sin-
gle rectangular active area of 16.8 ×8.3 cm2centered in the focal
plane. The remaining components of the model are taken from the
geometry in Fig. 6. For the nominal magnetic configuration in the
diverter design of SMILE SXI with NdFeB magnets, examples of tra-
jectories of electrons for EK= 100 keV are shown in Fig. 9. Note
that electrons which hit the diverter frames or escape out through
the MPOs are not shown. Some trajectories of electrons appear to
stop without intersecting a surface: these electrons hit the other two
faces of the tube not shown in the figure. The majority of electrons
are deflected toward the telescope tube as intended, with only some
electrons coming through the central rows of MPOs striking the
CCD; in total, only ∼0.1% of electrons with this kinetic energy hit
the CCD.
The detector hit fractions for a range of energies and the two
magnetic materials considered are given in Fig. 10. For energies of
30 keV and below, none of the simulated electrons hit the detec-
tor; we deduce that the hit fraction is <10−7. Simulations suggest
a hard cutoff below this energy for SmCo magnets, unlike the
MXT diverter discussed above, because there is a finite minimum
magnetic field over the whole open region of the optic (i.e., there
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FIG. 8. For NdFeB magnets: trajectories of a sample of electrons (projected onto the X–Zplane) with representative kinetic energies of (a) 10 keV and (d) 100 keV which
pass through the MXT optic and hit the detector. Cross sections of the simulated telescope tube and electron diverter frame are shown (black) with the CCD detector
emphasized (orange). The points where these electrons pass through the diverter midplane are shown for the two kinetic energies in (b) and (e), respectively, with the
simulated telescope tube (black circle). The number of electrons from each MPO which hit the detector and the distribution of all electrons over the surface of the CCD
detector (1.92 cm on each side) are given for each respective energy in (c) and (f). For magnets as indicated: (g) the total fraction of electrons which hit the detector is
shown as a function of electron energy, with a total of 3 ×107electrons simulated for each energy. (h) Differential flux density of electrons which hit the detector, with input
from Fig. 1.
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TABLE II. Total flux and flux density of electrons over the MXT detector, for the cases specified. The operational limit is set
by the mission science constraints by the total allowed background count rate. The flux of electrons at the detector for the
magnetic field set to zero everywhere (nonfunctioning diverter) and for the nominal diverter described above is obtained by
integrating over the energy ranges indicated.
Magnets Energy range (keV) Total flux (s−1) Flux density (cm−2s−1)
Operational limit ... All 3.69 ×10−310−3
No
Bfield ... 1–1000 6.82 ×10−31.85 ×10−3
Nominal diverter NdFeB 1–10 7.77 ×10−72.11 ×10−7
SmCo 1–10 1.22 ×10−63.30 ×10−7
Nominal diverter NdFeB 1–1000 9.51×10−52.58 ×10−5
SmCo 1–1000 1.47 ×10−43.99 ×10−5
are no accessible magnetic nulls for low energy electrons to pass
through); for NdFeB magnets, the minimal field is higher, and con-
sequently, the cutoff is higher, at around 50 keV. The hit fraction
rises very rapidly above this cutoff energy but quickly saturates as the
energy rises, and the electrons’ trajectories become effectively ballis-
tic. The expected differential flux of electrons is also given in Fig. 1.
The hit fraction saturation is identical for both magnetic materials,
and hence, it is only at low electron energies where the differen-
tial flux with SmCo magnets significantly exceeds that with NdFeB
magnets.
The integrated electron flux, up to an energy of 10 MeV (above
which the differential flux falls rapidly), is given in Table III for both
magnetic materials. The integrated flux in the absence of a mag-
netic field (with the diverter frame) is also computed. Without a
diverter, the flux exceeds the required limits even for ambient con-
ditions. The nominal diverter geometry with two magnets of the
FIG. 9. Trajectories of 100 keV electrons inside SMILE SXI with NdFeB projected
onto the Y–Zplane; electrons hitting the telescope tube and the focal plane outside
the CCD are shown in red, and those hitting the CCD are shown in blue. A cross
section of the SXI (black) is shown, with the CCD detector (orange) and the central
divider between two optic frames (gray) emphasized.
types considered is sufficient to meet the operational limits under
ambient solar wind conditions. During a coronal mass emission,
however, the electron flux cannot be sufficiently mitigated under any
conditions.
FIG. 10. Fraction of electrons coming through MPOs (top) which hit the detector of
SMILE SXI, based on simulations of 3 ×107electrons in each energy group and
magnetic materials as indicated. Note that, for energies <30 keV, this fraction is
zero (see discussion), as denoted by the downward triangle. The flux of electrons
hitting the detector per energy group (bottom), with the incoming flux as the ambi-
ent flux taken from Fig. 1; the solid and open symbols correspond to known and
extrapolated values, respectively.
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TABLE III. Total flux and flux density of electrons over the SXI detector, for conditions indicated. The operational limit is set
by the mission science constraints. For the energy ranges indicated, the flux is computed with the nominal magnetic field
described above and with the magnetic field set to zero everywhere.
Solar Energy range Total flux Flux density
Magnets wind (keV) (s−1) [cm−2s−1]
Operational limit . . . . . . All 13.9 0.1
No
Bfield ... Ambient 1–10 000 15.7 0.11
Nominal diverter NdFeB Ambient 1–1 000 0.87 6.21 ×10−3
SmCo Ambient 1–1 000 1.18 8.44 ×10−3
Nominal diverter NdFeB Ambient 1–10 000 1.38 9.92 ×10−3
SmCo Ambient 1–10 000 1.71 1.22 ×10−2
Nominal diverter NdFeB Peak 1–10 000 1.16 ×1038.34
SmCo Peak 1–10 000 1.65 ×10311.8
V. CONCLUSION AND OUTLOOK
Lobster eye type X-ray optics are protected from undesirable
energetic electrons by electron diverters. Electrons are deflected
from the detectors by a set of high aspect ratio rare-earth mag-
nets installed between individual MPOs. Two magnetic materials are
considered: neodymium iron boron (NdFeB) maximizes the mag-
netic field but must be protected from corrosion by careful appli-
cation of encapsulating resin; samarium cobalt (SmCo) has a lower
remanence but does not require encapsulation. The effective tem-
perature range of both materials is compatible with the two missions
considered here. Three possible orientations of the magnets allow
the net magnetic moment to be minimized, as required by mag-
netic cleanliness limits. A quadrupole design is chosen for the square
arrangement of MPOs on the MXT instrument of SVOM. For SXI
onboard SMILE, the optic frame is split into two mutually opposing
halves.
Manufacturing errors and the mismatch of opposing dipoles
can lead to an undesirable net magnetic dipole moment. The pro-
cedure for determining the residual magnetic moment by means of
a series of radial field measurements has been outlined. Detailed
knowledge of the magnetic moment allows for the installation of
correcting magnets in one of a number of mounting points on the
diverter frame.
The effectiveness of an electron diverter design has been deter-
mined by calculating the trajectories of relativistic electrons inside
the X-ray telescope. The fraction of electrons which hit the CCD
detector is computed for a range of kinetic energies. Hence, the
differential and integrated flux of electrons at the CCD detector is
determined. These quantities are computed for both magnetic mate-
rials considered here, as well as for zero magnetic field which would
be seen in the absence of a diverter. For both the MXT and SXI,
the integrated flux with zero magnetic field exceeds desired limits;
nominal magnetic field strengths produced by both magnetic mate-
rials reduce the electron flux at the detector by several orders of
magnitude, to acceptable levels.
The diverter of MXT is effective at deflecting electrons with the
relevant kinetic energies; the long focal length of the instrument is
also favorable in this regard. Most of the electrons which hit the CCD
detector pass through magnetic nulls intrinsic to the quadrupole
diverter design. The flux at the detector is well below the scientific
limits for both magnetic materials. The diverter of SXI deflects all
electron trajectories away from the CCD detector below kinetic ener-
gies of ∼30 keV. A large fraction of electrons reach the detector at
higher kinetic energies due to the compact size of SXI and the large
CCD area.
Future Monte Carlo simulations may answer the remaining
questions about the passage of energetic electrons through square
micropores and the emission of secondary electrons and photons
from the inner surfaces of X-ray instruments. The magnetic field
strengths of the diverters of the MXT instrument and SXI are not
sufficient to impactfully alter the trajectories of protons over the
compact dimensions of the two lobster eye telescopes considered
here.
ACKNOWLEDGMENTS
This research used the SPECTRE and ALICE High Perfor-
mance Clusters at the University of Leicester. The authors acknowl-
edge part funding from the United Kingdom Space Agency (UKSA)
through Grant No. ST/R002282/1.
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