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Notes on the development of a magnetic diverter the
SIMBOL-X X-ray telescope
Code:06/2009
INAF/OAB Technical
Report
Issue:
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Class
CONFIDENTIAL
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Istituto Nazionale di Astrofisica (INAF)
Via del Parco Mellini, 00100 Roma, Italy
Osservatorio Astronomico di Brera (OAB)
Via Brera 28, 20121 Milano, Italy
Via E. Bianchi 46, 23807 Merate, Italy
Notes on the development of a magnetic diverter for the
SIMBOL-X X-ray telescope
Issued by D. Spiga (INAF/OAB)
IDL simulation tools by D. Spiga
Support structure design by G. Parodi, M. Ottolina (BCV Progetti)
Support structure engineering and thermal tests by E. Mattaini (INAF/IASF Milano)
Magnetic field measurement by D. Spiga at the LABEX laboratory, thanks to the collaboration of
G. Sironi (Università Milano-Bicocca)
GEANT simulations by V. Fioretti (INAF/IASF Bologna) and A. Tiengo (INAF/IASF Milano)
Notes on the development of a magnetic diverter the
SIMBOL-X X-ray telescope
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INAF/OAB Technical
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Contents
1.!Introduction .................................................................................................................. 3!
2.!The properties of some hard magnetic materials..................................................... 5!
2.1.!General aspects ......................................................................................................5!
2.2.!Hard magnetic materials ......................................................................................... 7!
3.!Calculation of the magnetic field.............................................................................. 10!
3.1.!Outer magnetic field ..............................................................................................10!
3.2.!Internal magnetic field ...........................................................................................15!
4.!Measurements of the magnetization........................................................................ 16!
4.1.!Indirect measurement ...........................................................................................16!
4.2.!Direct B measurement ..........................................................................................18!
4.3.!Demagnetization curve .........................................................................................18!
5.!Resistance to thermal cycles.................................................................................... 21!
6.!Magnetic field predictions......................................................................................... 24!
6.1.!The Newton-XMM electron diverter case..............................................................24!
6.2.!The SIMBOL-X proton diverter magnetic field ......................................................25!
7.!Compliance with the background requirement....................................................... 27!
7.1.!Rejection rate ........................................................................................................27!
7.2.!Angular distribution of protons ..............................................................................31!
8.!Conclusions ............................................................................................................... 32!
Applicable Documents
[AD1] NHXM Phase A, Optical Payload Design Report, MLT note SX-RP-ML-003 (2008)
Reference Documents
[RD1] R. Willingale, An electron diverter for the Swift Telescope, XRA study note XRT-LUX-RE-011/1,
University of Leicester (2000)
[RD2] R. Nartallo et al., Radiation environment induced degradation on Chandra and implications for
XMM, ESA Report Esa/estec/tos-em/00-015/RN
[RD3] D. Spiga et al., A magnetic diverter for chaged particle background rejection in the SIMBOL-X
telescope, Proceedings of the SPIE Vol. 7011, 70112Y (2008)
[RD4] E. Mattaini, Spider per Magnetic Diverter, INAF/IASF Milano, technical report
Acronyms
HED High-Energy Detector
IASF Istituto di Astrofisica Spaziale e Fisica Cosmica/ Institute for Space Astroph. and Cosmic Physics
INAF Istituto Nazionale di AstroFisica / Italian Institute for Astrophysics
LED Low-Energy Detector
MD Magnetic Diverter
OAB Osservatorio Astronomico di Brera / Brera Astronomical Observatory
Notes on the development of a magnetic diverter the
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1. Introduction
Scope of this document is to report some details on the activities performed in the phase A of the
SIMBOL-X project [AD1] to develop a magnetic diverter (MD), aimed at reducing the background
due to the funnelling of high-energy (100 keV and above), charged particles, chiefly protons and
electrons. Like that of Newton-XMM, the orbit of SIMBOL-X was meant to be mainly outside the
Earth magnetosphere, where the flux of high-energy particles coming from the Sun is intense, non-
directional, unstable and seldom predictable. It therefore represents a major source of instrumental
background when they are collected by the mirror assembly and impinge the X-ray detectors.
A possible countermeasure is the adoption of a magnetic deflector to prevent the particles to
reach the detector. This solution was adopted for Swift-XRT [RD1] and Newton-XMM [RD2], with
the aim of deflecting electrons. However, the magnetic field level was insufficient to effectively
deviate protons, which are 2000 times as massive as electrons.
Fig. 1: the configuration of magnets for the SIMBOL-X proton diverter.
A higher and deeper magnetic field, however, can be suited to protect SIMBOL-X detectors.
This can be achieved with a proper arrangement of high-grade permanent magnets. The
motivations, the description of a preliminary magnetic configuration and the results of the
simulation, showing the expected performances are described in [RD3].
Such a MD, made of magnetic bars aligned on the 24 spokes of a radial structure, falling in
correspondence of the mirror module spider, acts effectively on protons and electrons up to 1 MeV.
Each spoke carries 3 magnets of decreasing thickness, with magnetic moments oriented in the
diverter plane, in the azimuthal direction. The resulting magnetic field is mainly azimuthally
oriented (see Fig. 1); the deflecting force is thereby oriented outwards for protons and inwards for
electrons (even though the deflecting force is so strong for electrons that they reverse their motion,
see Fig. 17).
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For feasibility reasons the sizes of the magnets are 60 mm of length, 18 mm of height, and
with variable thickness: 2.8 mm for the inner ring, 4 for the intermediate, 5 for the outer ring. They
span along the spokes from 13 cm from the axis to 33 cm, separated by 1 cm left for fixtures.
Actually, to improve the mounting stability, it is convenient to break the magnets into two parts, on
the two sides of the spider (as suggested by BCV). The new configuration then needs to be
simulated and its feasibility evaluated. In this report we describe some details, that could not be
included in [RD3], like the properties of permanent magnets (Sect. 2), the field computation (Sect.
3), the measurement of magnetization (Sect. 4), the resistance to thermal cycles of a part prototype
(Sect. 5), the prediction of the magnetic field (Sect. 6) and some simulations aimed at checking the
performances of the MD (Sect. 7).
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2. The properties of some hard magnetic materials
2.1. General aspects
The magnetization of permanently magnetic material is completely characterized by its hysteresis
cycle. This term can be intended as either
a) the variation of the magnetic induction, B, with the magnetic field, H, inside the material or
b) the variation of the magnetization (i.e. the density of magnetic dipole moment), M
(sometimes I or J), with the magnetic field, H, inside the material.
For a given ferromagnetic alloy, the hysteresis cycle depends on the magnetic history and on the
temperature: permanent magnets are produced from ferromagnetic alloys after a magnetic history
that sets them to a stable hysteresis cycle, still dependent on the temperature, but still reversible
until the Curie temperature is reached.
Consider a simple rectangular magnetic bar. If M is uniform and directed like the x axis, and
no electric current are present, H reverses its normal component at the faces yz (the tangential
component is continuous at the other faces). This is clear, as the surfaces normal to M have
magnetic poles that represent the sources of H (B is continuous and has no sources). Moreover, the
integral of H along a close loop must be zero. As in vacuum B and H are proportional and parallel,
H is anti-parallel to B. Then, the hysteresis cycle at which permanent magnets can work is the
second quadrant of the BH plane, called demagnetization curve (Fig. 2).
Fig. 2: some hysteresis cycles of Neodymium magnets (after www.neorem.fi).
In that branch, also H and M are anti-parallel. However, the magnetic susceptivity is not
negative since the derivative dM/dH is positive also in the demagnetization branch of the hysteresis
cycle. A very important property that can be read from a hysteresis cycle is the magnetic remanence
Br, corresponding to the maximum B in a permanent magnet, at H = 0. For hard magnetic materials,
it is of the order of 1 T (see Tab. 1), and very close to the saturation value (the maximum M value
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for H > 0). The remanence can be reached only by shaping the magnet in a toroidal configuration.
In this way, no poles are present and H = 0 everywhere, hence B = M.
If the torus has a gap, B decreases, while M remains almost constant. Therefore, H becomes
negative. Inspection of the demagnetization curves show that M is fairly constant in a wide interval
of H values, down to a maximum negative H called M-coercitive strength or anisotropic coercitive
field, HcM, strongly depending on temperature, at which M drops to zero. This is the field needed to
cancel the magnetization of the material. Therefore, the demagnetization curve of B is nearly linear
if H > HcM: moreover, there is a given HcB ≥ HcM at which also B vanishes, called B-coercitive
strength or isotropic coercitive field. This corresponds to a limit situation of zero B field inside the
magnets (and consequently outside), even though, in hard magnetic materials, M is still close to the
remanence. In such conditions we can approach HcB only if thickness of magnet tends to zero. In
other words, only the region of H > HcB can be explored. Clearly a high coercitivity is a factor of
merit since it allows intense magnetic field with magnets having small sizes.
Fig. 3: a rough schematization of the hysteresis cycle of a magnet. The greyed region is the regime where
permanent magnets operate.
Fig. 3 represents a rough schematization of an ideal hysteresis cycle. M is roughly constant
in a wide range of magnetic field values: moreover, ideally Br = µ0HcB. The region HcM < H < HcB
can be explored only by means of an intense, negative, external magnetic field generated via electric
coils. Only beyond HcM, a strong, external magnetic field can force M to a permanent, sudden
inversion. In other words, a permanent magnet cannot demagnetize itself, unless its temperature
becomes close to the Curie’s. If this happens, the magnetization can be lost also under the influence
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of a modest H: then HcM ≈ H
cB and the material can lose its magnetization even in absence of
external fields. The demagnetization curve of B then drops off at that value of H. It was, in fact, the
capability to produce magnetic materials with HcM >> HcB that made possible the great advance in
the magnetic grades that took place in the 80’s.
Finally, the region with H > 0 can be studied also in presence of electric currents to enhance
M. Nevertheless, this region is of interest only for electromagnets, and for materials characterized
by a low remanence and coercitivity, but high saturation (like pure Iron).
2.2. Hard magnetic materials
In Tab. 1 we report some interesting properties of hard magnetic materials. Apart from Ferrite,
abandoned nowadays, casting AlNiCo magnets (Coaniax) can be obtained from a fused magnetic
alloy of Cobalt (14%), Ni (14%), Aluminium (8%) and Iron (51 %), cooled at a slow rate in a
strong external magnetic field. They are the most resistant hard magnetic material at high
temperatures. This also makes them easy to manufacture, also with large sizes (> 250 mm). They
can be also sintered. They have, indeed, very low coercitive fields, and then they are suitable only
for industrial applications.
Tab. 1. Collected properties of some magnetic materials1
AlNiCo
Sm2Co17
Nd2Fe14B
Magnetic remanence (T)
0.5 ÷ 1
0.8 ÷ 1.1
1.22 ÷ 1.44 (N52)
M-Coercitive strength (kOe)
0.5 ÷ 1.8
12 ÷ 25
10.2 ÷ 11.5
B-coercitive strength (kOe)
0.2 ÷ 0.5
7.8 ÷ 10.3
6.8
Max Energy product (MGOe)
1.0 ÷ 5.0
14 ÷ 30
35 ÷ 50
Density (g/cm3)
6.8 ÷ 7.3
8.0 ÷ 8.5
7.4 ÷ 7.6
Vicker hardness (Hv)
-
450 ÷ 600
570
Tensile strength (Kg/mm²)
-
-
8.0
Flexural strength (Kg/mm²)
-
-
25
Young’s modulus (GPa)
-
-
160
Poisson’s ratio
-
-
0.24
Curie Temperature (°C)
810 ÷ 860
700 ÷ 850
310 ÷ 340
Max Working Temperature (°C)
400 ÷ 550
250
80 ÷ 180
CTE (10-6 °C -1)
-
-
5÷8 (//) -1÷-3 (⊥)
Temperature coefficient of Br (°C -1)
-0.02%
-0.05%
-0.11%
Temperature coefficient of Hc (°C -1)
-
-
-0.6%
1 Data after www.calamit.com
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.Samarium-Cobalt (Sm2Co17) magnets are generally sintered and fragile. However, they
exhibit high Curie temperatures (up to 250 °C), and are very resistant to corrosive agents.
Therefore, they are usually uncoated.
Neodymium-Iron-Boron (Nd2Fe14B) magnets are usually sintered or bonded. They get
quickly corroded by oxygen, salt, moisture. A Zinc cladding is well suitable to protect the magnet
from oxidization, even if Zinc is not suitable for applications in vacuum, since it tends to outgas
also at room temperature. For space applications, the cladding should be qualified, but not be
ferromagnetic (no Ni, Fe or Cobalt). Gold requires in general a Ni pre-coating. Epoxy resins should
also be qualified for space. A possibility might be Nickel-Kanigen alloy (that is non-ferromagnetic).
The magnet strength is often described along with the maximum energy product BHmax, i.e.
is the maximum value of BH inside the magnet, with B in gauss and H in oersted2. This also gives
an idea of the magnetic field that it can generate, because the total magnetic energy inside a magnet
equals the total magnetic energy that it generates in the outer space. The maximum energy product,
expressed in MGOe (106 G × Oe), is often referred to as magnetic grade. In addition, a letter is
added as a prefix to the magnetic grade: N, M, H… denoting the maximum operating temperature:
N = 80 °C, M = 100 °C, H = 120 °C, SH = 150 °C, EH = 180 °C, UH = 200 °C. E.g., a magnet with
M35 grade is a material operating up to 100 °C, with a maximum energy product of 35 MGOe.
Some examples for Neodymium magnets re reported in Tab. 2.
Tab. 2. Magnetic materials data of Neodymium-Boron-Iron magnets (after www.supermagnete.de)
Br
bHc
iHc
BHmax
(T)
(kOe)
(kA/m)
(kOe)
(kA/m)
MGOe
kJ/m³
N30
1.08 – 1.12
9.8 – 10.5
780 – 830
> 12
> 955
28 – 30
223 – 239
N33
1.14 – 1.17
10.3 – 11.0
820 – 876
> 12
> 955
31 – 33
247 – 263
N35
1.17 – 1.21
10.8 – 11.5
860 – 915
> 12
> 955
33 – 35
263 – 279
N38
1.22 – 1.26
10.8 – 11.5
860 – 915
> 12
> 955
36 – 38
287 – 303
N40
1.26 – 1.29
10.5 – 12.0
860 – 955
> 12
> 955
38 – 40
303 – 318
N42
1.29 – 1.32
10.8 – 12.0
860 – 955
> 12
> 955
40 – 42
318 – 334
N45
1.32 – 1.37
10.8 – 12.5
860 – 995
> 12
> 955
43 – 45
342 – 358
N48
1.37 – 1.42
10.8 – 12.5
860 – 995
> 12
> 955
45 – 48
358 – 382
N50
1.40 – 1.46
10.8 – 12.5
860 – 995
> 12
> 955
47 – 51
374 – 406
N52
1.42 – 1.47
10.8 – 12.5
860 – 995
> 12
> 955
48 – 53
380 – 422
2 1 A/m = 4π 10-3 Oe, where the Oersted is the magnetic field unit in the CGS system.
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The hysteresis cycle in the demagnetization branch is in general well linear (see Fig. 2):
.
The maximum BH clearly occurs at the point where the hyperbola BH = -K is tangent to the
hysteresis curve:
,
i.e., if and only if
,
so BHmax = BrHcB/4. Moreover, as in the assumed simplification Br = µ0HcB,
.
Substitution of values (see Tab. 2) shows that this computed energy product falls in the nominal
range of magnetic grades.
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3. Calculation of the magnetic field
3.1. Outer magnetic field
The magnetization of a material is not a property of the material itself. It depends strongly on the
magnet shape and size. In addition, it can be affected by the external magnetic field if it is very
intense, because it shifts the magnetic load on the hysteresis curve. Nevertheless, even if the B-H
demagnetization curve is rather steep, the M-H magnetization curve is not. Then we can
approximate the magnets to have a uniform magnetization, directed along the x-axis (see Fig. 4).
Let the magnetic bars to have sizes a, b, c along the three axes. Symmetry requires that
and the same relations hold for the H field. Therefore, the field can be studied only for x, y, z
positive. This will allow us to avoid singularities at the magnet’s edge. Each infinitesimal element
at r’ of the magnetic bar has a volume d3r’ and a magnetic moment oriented like x, d3m = M d3r’.
Fig. 4: geometry of a rectangular magnetic bar with uniform magnetization
The H field at r is the superposition of elementary dipolar fields,
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and the components of the field follow by integration over the volume of the bar,
Computation of Hy. We rewrite the integral as
,
and the integration over x’ is immediate:
the second integration is easy as well,
To complete the integration, we note that the 4 integrals have the generic form:
where A± = (x±a/2)2+(y±b/2)2 is a non-negative constant. It equals zero only along the lines passing
by the edges of the bar aligned as z. If it is positive, we make the position [A± + (z-z’)2]1/2 = t-(z-z’),
and we integrate the generic integral over z’
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where C is another constant. Using this result we obtain the final expression for the field,
that describes the field at all points of the outer space, but for x = ± a/2 and y = ± b/2. In these
points, indeed, the field can be obtained by passing to the limit. In fact, by repeating the
computation with A± =0 one obtains the same results (the integral is exactly ln(z-z’)). We note that:
• If x =0 we expect that Hy = 0 by symmetry, and in fact all terms cancel out (1 and 3, 2 and 4)
• If y = 0 and z ≠ 0 (the xz plane) Hy = 0 by symmetry, and in fact all terms cancel out (1 and
2, 3 and 4)
• If z = 0 but y ≠ 0 (the yz plane) Hy = 0 as expected.
Computation of Hz. Same computation as the y component after exchanging y and z, b and c.
Similar comments apply.
Computation of Hx. The computation is slightly more complicated. Firstly we recognize the
integrand as the derivative, with respect to x’, of
we thereby obtain
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Now we can execute the integration over y’, noting that the two integrals in the previous equation
have the generic form
where A± = (x±a/2)2+(z-z’)2 is a non-negative constant. The substitution [A± + (y-y’)2]1/2 = t-(y-y’)
yields
and, re-substituting, after some passages,
that can be substituted into the expression for Hx. We then obtain
to execute the last integration, we write A± = (x±a/2) and B± = (y±b/2). The generic integral then
reads
that can be solved along with the usual substitution [A±2 + B±2 +(z-z’)2]1/2 = t-(z-z’). We obtain,
with some algebra,
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that is easy to integrate:
that is,
we thus evaluate the integrals and obtain the final expression for Hx,
it is easy to see, using the relation arctan(1/x) = π/2- arctan x, that singularities can be eliminated.
Note that Hx does not vanish at x = 0, as expected.
The total magnetic field at r, due to the entire magnets assembly whose centres are located
at r1, r2… rN is obtained from a vector sum of the individual contributions Bk, k = 1, 2…N,
computed as above:
€
B(r)=M(
ϕ
k,
θ
k,
ψ
k)⋅Bk(r−rk)
k
∑
where M is the 3D rotation matrix relative to the Euler angles,
ϕ
,
θ
,
ψ
, describing the orientation of
the kth magnet in the adopted reference frame.
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3.2. Internal magnetic field
The use of the integral of dipolar elementary fields to calculate the external magnetic field of a
magnetic bar is equivalent to describe a magnetized material along with (fictitious) magnetic
monopoles distribution, based upon the scalar potential, rather than the vector potential. Therefore,
the magnetic bar appears to be similar to a magnetic capacitor, with uniform σ = ±M pole
distributions at the yz faces. Since these poles are the sources of the H field (unlike B, that has not
any), H reverses its direction at the yz interfaces, as expected, but it is continuous at the other ones.
Hence, the result of the integration returns the correct H field either inside or outside the magnetic
bar. Then B follows from B = µ0(H+M), inside or outside the material.
Nevertheless, we can derive the internal field using an approximate, but more interesting
method. Consider a circular loop intersecting N magnets (like in the arrangement of Fig. 1, N = 24)
along the direction of M: the terminal faces (perpendicular to M) are also perpendicular to B. Since
its normal component is continuous at interfaces, Bv = Bm: instead, H has a discontinuity. Hv + Hm =
M. Clearly, if the loop is oriented as Hv in vacuum, Hm and the loop have opposite orientations.
Now use Ampere’s law (no conduction current is present),
.
For a guessed M value, we can compute the B field at all points of the loop in the vacuum, hence
the integral can be easily computed: this enables the computation of H in the magnets,
,
where N is the number of magnets and τ is their length in the magnetic dipole direction. Note that,
were the entire loop were filled with magnetic material, Hm would vanish, as expected. Then B in
the material is easily obtained from
,
where Bm equals the B normal component at the magnet boundary, computed in vacuum. This sets a
relation between the average B in vacuum and the B at magnet’s surface, and then we can derive M
by requiring the point (Hm, Bm) to fall on the hysteresis cycle, which – in linear approximation – we
should know from the tabulated magnetic remanence and the coercitive strength. We will see an
application of this method in Sect. 4.3, for isolated magnets and for the magnet assembly.
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4. Measurements of the magnetization
4.1. Indirect measurement
To maximise the magnetic field, the maximum magnetic grade should be selected. N52 magnets
purchased from www.supermagnete.de are well suitable to return the magnetization needed. We
report here some magnetization measurements.
We measured the attraction force of two magnets, by approaching them until it balances their
weight (beware! they crash when suddenly collide and the debris can seriously injure):
1) two parallel magnets 4 mm thick (32 g weight, density 7.4 g/cm³) attract each other with a
force equal to their weight, 32 gp = 0.31 N when separated by 7.2 cm (see Fig. 5). When
separated by 8 cm, the repulsive (measured with scales) force becomes 22 gp = 0.216 N.
2) two magnets 5 mm thick (40 g weight) attract each other with a force equal to their weight,
40 gp = 0.39 N when separated by 7.7 cm.
3) two magnets 2.8 mm thick (22.4 g weight) attract each other with a force equal to 22.1 gp =
0.219 N when separated by 6.6 cm.
4) a 5 mm and a 2.8 mm thick magnets attract each other with a 0.219 N force when separated
by 7.7 cm, and a 0.39 N force when separated by 6.4 cm.
Fig. 5: magnetic field intensity for an assembly of 2 magnets (4 mm thick) of the described type, separated by
a 7.2 cm distance.
These results constrain the magnetization of the material (the force is, in fact, proportional to
M²), so it can be determined quite easily. The total force acting between the two (see Fig. 5) is
,
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where the labels 1 and 2 can also be exchanged. Now place the center of the 1st magnet at x = -(D-
c/2) = -(7.2cm-0.2 cm) = - 7 cm, where D is the distance between the two magnets’ center, with the
magnetic moment toward the origin (which is shifted with respect to Fig. 5). As the magnetization
of the 2nd magnet is uniform and directed along x, the same does Bx. The force is purely directed
along x. The 2nd magnet is placed with a face at x = 0 and the other at x = c (c = 0.4 cm). The
integration along x is easy:
Then Fx < 0, i.e. it is attractive because Bx decreases with the distance from the magnet 1. As the
magnetic field is numerically computable from the shape of the magnet and M, we derive for M =
1.36 T = 1080 kA/m.
An even simpler result could have been obtained noticing that the x component of a dipolar
field is
where θ is the polar angle with the magnetic moment direction. Substituting in the previous
expression, this yields, approximating at the first order,
Fig. 6: (left) magnetic intensity for a 4 mm thick magnetic bar, in the mid-plane. (right) the magnetic field,
viewed sideways. Some asymmetry is due to the terrestrial magnetic field.
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that is, solving and collecting a ab factor for 4 mm thick magnets at D = 7.2 cm,
,
Vs. 3.1 N measured, a good approximation considering that we retained D = 7.2 cm as a constant
(while it is sensitively variable with x and z and larger than 7.2 cm!).
4.2. Direct B measurement
The comparison of the measured (using a PASCO instrumentsTM Hall probe at LABEX laboratory,
Milano-Bicocca University) magnetic field with the computed one along the axes x, y, z as a
function of the distance from the magnet’s center is plotted in Fig. 7 for the 4 mm thick magnet.
The component parallel to the direction of magnetization was measured along the three axes
(refer to Fig. 6 for a description of the reference frame). Also plotted are the theoretical predictions
(solid lines), assuming a uniform magnetization of 1.36 T. The agreement between the model and
the measurement is very good, also for the 2.8 and 5 mm thick magnets (not shown), within the
uncertainty due to the positioning of the probe (a few millimetres). The experimental setup is not
sufficiently accurate to allow a determination of the value of M better than to a few percent.
Fig. 7: measured vs. computed magnetic field (x component) along the three axes, assuming M = 1.36 T.
4.3. Demagnetization curve
The found value of ~1.36 T for the magnetization now allows us to trace a branch of the hysteresis
cycle. Adopting as remanence the nominal one of N52 magnets, 1.45 T, we see that the
magnetization decreases slowly as H decreases (i.e. becomes more negative). A linear trend down
to HcM is then reasonable. Applying the method described in Sect. 3.2 for the computing the internal
magnetic field for a 4 mm thick magnet, H is -930 kA/m and B is 1955 G, in the magnet. This is the
H value corresponding to M = 1.36 T on the H-M curve. Tracing B = µ0H +M, we obtain the
demagnetization curve for B, which is nearly linear. The extrapolation to B = 0 returns the value of
HcB = -M(HcB) = -1070 kA/m, in good agreement with the specification (see Tab. 2).
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Fig. 8: the demagnetization curve for (isolated) N52 magnets under test. The computed H and B intensity
(squares) are consistent with the model, assuming a slowly decreasing magnetization (red curve).
For the magnets the magnetization is between 1.36 (2.8 mm thick) and 1.37 T (5 mm thick). H ranges
between -970 and -900 kA/m, B between 1370 and 2420 G.
From the continuity of the normal component of B then follows that the found B is also the
induction inside the magnets. Moreover, since M slowly changes, their magnetization can be
computed assuming initially 1.36 T. Then we can compute H and B in the magnet; in general they
will fall (approximately) on a different point of the hysteresis cycle, but not exactly. Reading the
actual value of M in correspondence to the last H value, we obtain a new M. Then we repeat the
computation for H and B until the calculation converges.
The results for the isolated magnets under test are reported in Fig. 8: they fit well the
demagnetization curve initially assumed. The magnetization changes only for a 1% for the three
sizes, while B increases (and H becomes less negative) more rapidly as the thickness of magnets is
increased.
The situation changes, indeed, when the magnets are placed in the actual arrangement
foreseen for the SIMBOL-X magnetic diverter. In that case, the loop length is increased in
proportion with r, but also the thickness of magnets, τ, does the same to follow the thickness of the
spider. Then, the magnetization is expectedly much more constant throughout the MD, even if the
demagnetization curve in Fig. 8 remains the same. The computation of the actual magnetization for
the different rings then returns:
M = 1.360 T = 1080 kA/m, Hm = -955 kA/m, Bm = 1560 G in the magnets of the inner ring,
M = 1.365 T = 1085 kA/m, Hm = -920 kA/m, Bm = 2020 G for the magnets of the intermediate ring,
M = 1.370 T = 1090 kA/m, Hm = -893 kA/m, Bm = 2460 G for the magnets of the outer ring.
One can see that the magnetization has been changed – for the better – only by 1% for the thicker
magnets. The variation of the working point on the demagnetization curve is represented in Fig. 9.
There is a sensitive gain in the internal magnetic field for the magnets of the inner ring, a modest
effect for the magnets 4 mm thick and almost no effect for the magnets of he outermost ring.
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Fig. 9: the working point displacement for magnets of the three rings for the MD of SIMBOL-X (circles),
with respect to the isolated magnets (squares like in Fig. 8). The blue line is the demagnetization
curve of the N52 magnets.
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5. Resistance to thermal cycles
The magnets to be used need proper fixtures to make them able to withstand the launch and the
operation conditions. Fixtures of the magnets aimed at enclosing them completely are being
designed: such enclosures would avoid that, in case of breaking of some magnets, some debris
move to the surrounding space and eventually impact or stick to some ferromagnetic part of the
telescope (like the Nickel optics), with potentially catastrophic consequences for the whole
telescope. Moreover, the magnets should also be fixed at their positions, because their equilibrium
of their magnetic forces is very unstable: if a single magnet is removed from its location, the
attraction/repulsion between magnets can dramatically increase (Sect. 6), with an increasing risk of
failure of the fixtures or magnet breaking, or, in the most optimistic case, a structural
tensioning/deformation of the support. Some spoke prototypes in Aluminium (Al 7075 alloy), with
grooves drilled in them, are displayed in Fig. 10. In a first version (Fig. 10, left), the magnetic bars
are completely embedded in the Aluminium support structure. In a second version (Fig. 10, right),
only the upper half of the magnets is enclosed in the grooves. The minimum thickness of the
support (3 mm) is sufficient to house the 2.8 mm – thick magnets leaving a 0.1 mm Aluminium
wall. The magnets have been glued in their grooves using a space-qualified epoxy resin (3M
Scotch-Weld 2216 B/A, 24 h curing time).
Fig. 10: Aluminium support structure (by E. Mattaini, [RD4]) for a spoke of the magnetic diverter prototype
(left) first prototype: magnets (not shown) are to be completely inserted in the structure. (right)
second prototype: only half-height of the magnets is covered.
As the Magnetic Diverter will be located outside the thermal blankets (that will keep the
optical module at a constant temperature of 20 °C, with minimized temperature gradients), the MD
will be exposed to extremely low temperatures (-80 °C). This can potentially be a problem, since
the mechanical stability of sintered magnets can be compromised by the exposure to low
temperatures. On the other side, the exposure to high temperatures can degrade the magnetization
(N-grade magnets cannot work at temperatures higher than 80 °C, even if the Curie’s is much
higher). Therefore, the endurance of the magnetic assembly for the MD of SIMBOL-X has to be
checked.
This has been done at IASF-MI [RD4], along with several thermal cycles. At this regard,
tests have been performed on two prototypes: the first one (Fig. 10, left), with magnets completely
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enclosed in the spoke structure, was mounted by mistake with the central magnet with reversed
magnetization (we will refer to this wrong configuration as up-down-up or antiparallel). This is
unessential, indeed, for this qualification test since we were only interested in the endurance of the
material to low temperatures and to the invariance of the magnetization after a thermal cycle. The
second prototype (Fig. 10, right) was correctly mounted with parallel magnetizations.
Fig. 11: magnetic field measurement for the two prototypes along a line parallel to the spoke, 2 cm distant.
(left) component parallel to the magnetization, i.e. parallel to the azimuthal direction in the final
MD.(right) transverse component, i.e. radial in the final MD, along the same line. The models
assume a uniform magnetization of 1.36 T.
The first prototype was exposed several times to temperatures from -25 °C to +65 °C for a
60 h time, then from room temperature to -78°C for a 10 h time. The second prototype was exposed
only to the low temperature part of the qualification cycle. After this treatment, no sign of structural
damaging or fixture failure was observed in both cases. We have then measured the magnetic field
at the LABEX laboratory of the two assemblies in order to detect some possible decay of the
magnetization degree, along with the same Hall probe used for the field measurements reported in
Sect. 4.2.
Fig. 12: magnetic field measurement for the two prototypes along a line parallel to the spoke, 5 cm distant.
(left) component parallel to the magnetization, i.e. parallel to the azimuthal direction in the final
MD.(right) transverse component, i.e. radial in the final MD, along the same line. The models
assume a uniform magnetization of 1.36 T.
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The results of the measurements are reported in Fig. 11 and Fig. 12. Solid lines represent the
computed magnetic field component parallel (along the x axis, see Fig. 5 for the axes orientation) or
perpendicular (along y) to the direction of the magnetization, computed assuming the same
magnetization of 1.36 T before the thermal cycles. The magnets assembly is laid on the y-axis and
centred on the origin, with the 5 mm magnet in the positive y-axis half-plane. The magnetic
moments are oriented towards (i.e. the North poles are on) the positive direction of the x-axis (in
the antiparallel configuration the 2.8 and 5 mm thick magnets were oriented in the positive x
direction). Computation and measurements have been performed along a line parallel to the y-axis
at a 2 cm distance (Fig. 11) and 5 cm (Fig. 12).
The agreement between measurement and prediction is very good, meaning a correct
description of the magnetic field and the invariance of magnetization (Sect. 4.3) after thermal
cycles. Some deviations, nevertheless, can be observed in the scan at 2 cm distance in the parallel
component, where the magnetic field if higher. This is due to the very high B gradient, therefore
any positioning error of the probe results in a measurement error. The error might be reduced by
adopting a mechanical system of alignment with a larger precision and stability than a positioning
“by hand”.
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6. Magnetic field predictions
6.1. The Newton-XMM electron diverter case
Fig. 13: (left) field lines for the electron diverter of Newton-XMM, at z = 0 cm, i.e., in the diverter mid-
plane. (right) the magnetic field magnitude along a mid-sector, in the mid-plane and z =2 cm.
Even though the magnetic field measurements are consistent and experimentally verified, we have
performed another check by comparing the prediction of formulae in Sect. 3 with the measured
field values of the electron diverter of Newton-XMM, reported in [RD1]. The MD onboard
Newton-XMM is similar to that of SIMBOL-X, but the magnetic bars are not monolithic. They are
made of small blocks embedded in the supporting spokes, and kept in place with a resin.
Nevertheless, they are in mutual contact, hence their magnetic field can be computed as if an
assembly on a spoke were a single, magnetic bar. The magnets assumed for the simulation have
thereby 32 magnetic bars along 16 spokes, sized 208 mm (radial) x 6 mm (axial) x 4 mm
(azimuthal), one below and one above the mid plane, separated by a 4.5 mm axial gap. The magnet
arrangement and some field lines are drawn in Fig. 13, left.
The magnetization of these magnets deserves a few words. The magnetic material is a rare
earth one qualified for space, the Vacodym 383 HR by Vacuumschmeltze, though it is out of
production nowadays. This material has a remanence of 1.22 T and a coercitive field for B close to
950 kA/m. Following the procedure described in Sect. 4.3, we can derive that the magnetization on
the working point is close to M = 1.16 T. This is much higher than the specification for the MD
diverter of Mac > 140 G cm3 / cm (expressed as magnetic moment per unit length along the radius,
where ac is the section of the bar, refer to Fig. 4), that returns M = 460 kA/m.
With the actual magnetization value of 1.16 T, we can compute the magnetic field for the
diverter of Newton-XMM. Our algorithm yields the solid lines of Fig. 13, right, along a mid-sector
line in the mid-plane of the diverter and at z = + 2 cm. The experimental points (after [RD1]) are in
excellent accord with the theory.
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6.2. The SIMBOL-X proton diverter magnetic field
Using the formulae of Sect. 3.1 to compute the magnetic B field outside the magnets, using the
magnetization values determined in Sect. 4, the magnetic field resulting from the arrangement
described in Sect. 1 can be computed in any point of the space as a vector superposition of B as
generated by the each magnet, after a proper 3D rotation. In this section we describe the resulting
field.
Fig. 14: (left) field lines for the SIMBOL-X magnetic diverter, at z = 2 cm, i.e. in the middle of the second
level of magnets. (right) the magnetic field magnitude along a mid-sector, at z =2 cm. The arrows
denote the range covered by SIMBOL-X mirror shell radii.
In Fig. 14, left, we show some field lines, as viewed from top, in a mid plane of the second
level of magnets. Note that the field is essentially azimuthal, even if it tends to bend out in the gaps
between the magnetic bars, and at the edges of the MD. For this reason, at a radial distance from the
axis in front of the magnetic bars the magnetic field is stronger. It is also stronger close to the
magnets’ surface (500 G and more) while it exhibits a minimum in the mid-sector region. In the
axial direction, it also has a minimum in the diverter mid-plane and reaches a maximum around z =
± 2 cm. At this z, along a mid-sector line, the B magnitude varies as shown in Fig. 14, right. It can
be seen that the field is zero on the z axis, starts to increase just outside the innermost ring of
magnets, reaches a maximum of 600 G, then it passed by two further (lower) maxima, in
correspondence of the middle and outermost ring, then drops to zero. At a 40 cm distance from the
axis, the magnitude of B is already comparable with that of the terrestrial magnetic field.
In Fig. 15 we can instead see the contour plot of the magnitude of B in a (left) transversal
and (right) radial section. We see in particular that, moving off the diverter plane, B reaches a
maximum around 2 cm, then it rapidly drops in the first 10 cm to values close to the Earth magnetic
field. It is then sufficient to keep the MD at 10-15 cm distance from the mirror module exit to avoid
a mirror shell magnetization, with a potential impact on the imaging quality. On the other side, The
magnetic field at the detector spacecraft distance of 20 m is less than 10-15 G, then it will not harm
its equipment, since it can stand up to 1 mG to work properly.
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Fig. 15: (left) B field intensity for the whole MD of SIMBOL-X, 2 cm above the mid-plane. (right) the
magnetic field, viewed sideways along a mid-sector plane.
From the magnetic field one can derive the force acting on each of them (Sect. 4.1), by
computing the gradient of B generated by all the magnets but the one under test. Due to the axial
symmetry, in the position where they are fixed the force is always in a radial plane: the axial
component is always repulsive. The magnets of the outer ring tend to be pulled out of the axis,
those of the inner and middle ring are attracted toward the axis.
These are the calculated force components for a magnet in the upper part (z >0) of the MD.
A + sign indicates a force directed outwards, a – sign an attractive force.
Inner ring: Ft = 0 N, Fz = +0.35 N, Fr = -1.7 N
Middle ring: Ft = 0 N, Fz = +1.23 N, Fr = -1.5 N
Outer ring: Ft = 0 N, Fz = +2.20 N, Fr = +2.3 N
It should be noted that the equilibrium in the azimuthal direction is highly unstable (1 mm
displacement of a magnet of the inner ring along the azimuth would, e.g., cause a 0.4 N lateral force
to arise).
500 G
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7. Compliance with the background requirement
In this section we will check the effectiveness of the magnetic field generated by the MD designed
for SIMBOL-X. The maximum acceptable background, N, for SIMBOL-X is
N < 1.2x10-5 sec-1 cm-2 keV-1 for E < 10 keV (LED)
N < 2.3x10-6 sec-1 cm-2 keV-1 for 10 keV < E < 80 keV (HED)
7.1. Rejection rate
Firstly, we have to set some limit to the maximum kinetic energy to run in the simulation of the
MD. We note that the proton contribution to the background involves only the LED, because the
HED is largely screened against the proton flux, and the few protons that can reach it can be
rejected using an anticoincidence system. In contrast, the LED is directly exposed to the proton
flux, and, since a proton event cannot be distinguished from an X-ray photon one, all protons
having energies in the sensitivity band of the LED (< 30 keV) are a certain source of background.
Nevertheless, also protons of higher energies are dangerous, due to possible inelastic
collisions that release only a part of their kinetic energy. These can be still observed as events in the
LED, and contribute to the background.
Fig. 16: GEANT simulation on the interaction of protons in the LED of SIMBOL-X. Most protons are
detected without inelastic effects (black). Proton events at lower energy (blue) are important only
above 500 keV. Secondary events (red) like electrons emission and proton leaks are discarded by
the anticoincidence system.
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It is then apparent that we cannot simply set E < 30 keV in the simulation. In order to
determine the maximum energy to use in the simulation, we simulated the interaction of protons in
the LED using the GEANT libraries installed at INAF/IASF Bologna. The simulation results are
reported in Fig. 16: almost all protons below 500 keV are detected with their energy. At 50 keV
there is an important fraction of inelastic events, but the MD deflects these protons very effectively.
Beyond 500 keV, indeed, the fraction of inelastic events becomes evident, even though they
still involve less than 1% of the total events. The simulation did not return the spectra of scattered
protons, and then we cannot determine exactly how these protons affect the background in the LED
energy band. It seems, indeed, that for increasing energy the ratio of inelastic scattering tends to
saturate to a few percent. Moreover, we know, from the Equator-S data, that the actual spectrum of
protons (in quiet Sun regime) outside the radiation belts is a steep power-law,
,
even if it may become up to 10 times higher during a solar flare. Anyway, there are probably few
high-energy protons that will impinge the LED, when compared to those at lower energy. We then
deal with the simulation up to 2 MeV. Beyond this energy, as we will see, the proton incidence rate
on the LED would almost be below the tolerable background level in quiet Sun regime, also
without the action of the MD.
Another important point to be considered in the simulation is the initial angular spread of the
proton beam. This is still unknown because the process responsible for the proton reflection off
grazing-incidence optics is not clarified yet. Some guess is obtained from GEANT simulations,
which return an angular spread of σ ≈ 3 deg at 500 keV; actually, GEANT simulations performed
by Nartallo [RD2] underestimate the proton background on XMM by a factor of 5. Therefore, the
angular spread of protons must be smaller than predicted by GEANT by a factor of 5, yielding
σ ≈ 0.6 deg at 500 keV, as per Turner’s estimates. At lower energies, σ is expectedly larger: 1 to
1.6 deg.
It should be noted that a larger angular spread causes the MD to be less effective: even
though the proton beam is less focused toward the detector, which would make the irradiation less
severe, in presence of the magnetic field there is a finite likelihood that an off-axis particle is re-
deflected towards the detector field. In the theoretical limit of a completely isotropic velocity
distribution, the effectiveness of the MD would be zero because the field would simply remix the
direction of incoming protons, which would thereby remain isotropic.
Assuming then σ ≈ 2 deg, the simulation of the MD acting on a proton beam and an electron
beam with a 200 keV kinetic energy is displayed in Fig. 17. Note that protons are deflected
outwards, while electrons are repelled. The outcome of the simulation for protons with a flat energy
spectrum from 1 to 2000 keV is posted in Fig. 18.
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Fig. 17: the proton diverter action on 200 keV protons (left), and 200 keV electrons (right). Electrons are
repelled because in a > 300 G (average) tangential field the radius of curvature is < 5 cm, that is
less than the field depth (approx. 6 cm). Therefore, after a half-loop, they go back.
The simulation results in Fig. 18 can be summarized as follows: the utilization of the MD
reduces of the irradiation from a 5.9% to a 0.12%, for a flat energy spectrum at 1 to 2000 keV.
Moreover, the particles impinging the detector area are mostly high-energy ones (> 300 keV),
which represent a minor fraction of the proton background population.
Fig. 18: the result of a simulation for a proton beam with a flat energy spectrum from 1 to 2000 keV with an
initial Gaussian beam spread of 2 deg rms. The inner square is the LED detector. (left) 1000
protons, without MD, (right) 5000 protons, with MD.
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Running the simulation adopting the actual Equator-S energy spectrum of protons at 1 to
2000 keV (shown in Fig. 19, left) confirms that the proton background is heavily reduced by the
magnetic field action by a factor of 2 × 10-4, even if the estimate is made uncertain by the poor
statistics. In order to check whether such attenuation would be sufficient to keep the proton
background below the acceptable limits (1.2x10-5 sec-1 cm-2 keV-1), we plot the expected
background without and with magnetic diverter (Fig. 19, right), using the Equator-S spectrum, I(E).
An acceptance angle of 5 deg at the optic entrance (as from Nartallo’s simulation), yielding an
entrance solid angle
Ω
= 0.024 sterad, and a collecting area Aeff =1000 cm2 have been adopted. The
spectrum is then attenuated by a factor T(E). Without MD the beam attenuation (T = 5.9%) is
constant and due only to the beam divergence after the reflection on the optics. With MD, T(E)
results from the combined effect of geometrical divergence and the magnetic force. The attenuation
with the MD, as a function of the kinetic energy E, is derived from the simulation with the flat
spectrum (Fig. 18). The moderating effect of thermal blankets, that would ease the MD operation if
located outside them, has not been included. The background curves are then obtained from
€
N(E)=IEq.−S(E)⋅ Ω5 deg
Aeff
ALED
⋅T(E)
,
where ALED is the area of the LED.
The effectiveness of the MD is then apparent from Fig. 19, right: the angular spread of the
beam (red line) is insufficient to keep the proton background below the limit for the LED (dashed
line), up to a 2 MeV kinetic energy. In other words, even assuming that all protons impinging the
detector contribute to the background (and this is a very pessimistic assumption, see Fig. 16), we
have to deflect only protons with kinetic energies up to 2 MeV. These protons are effectively
discarded by the action of the MD (blue points). Even within the error bars due to statistics, all
protons below 200 keV are blocked by the magnetic field: beyond this energy, they generate a
background lower than the instrumental one.
Fig. 19: (left) the same simulation of Fig. 18, right, with 10000 launched protons, assuming the actual
distribution of kinetic energies, as measured by the Equator-S satellite. (right) the proton
background reduction on the LED with the Magnetic Diverter.
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7.2. Angular distribution of protons
The simulation performed in the previous section can be repeated to describe the angular
distribution of protons around the LED. To do this, we adopt a flat spectrum at 10 to 1000 keV
kinetic energies, to increase the statistical significance. 10000 protons have been launched with a
Gaussian distribution of angles with a 2 deg rms.
The radial distributions (integrated over 4 cm wide circular coronae and divided by the
coronal area) at a 20 m distance are extracted for the configuration with and without the MD, in 4
energy bands (10-100, 100-250, 250-500, 500-1000 keV). The distributions (see Fig. 20) were
renormalized to the proton rate expected from the Equator-S spectrum, as collected by a 1000 cm2
optic area, within an acceptance angle of 5 deg off-axis, averaged over the energy bands of interest.
Fig. 20: spatial distribution of protons scattered by the MD on the focal plane (at radii much higher than
half-size of the detector), as simulated in four energy bands. The oscillations are due to the poor
statistics.
Neither energy loss in the interaction with the optics nor energy loss of protons at thermal
blankets crossing has been assumed. As expected, the spread of protons is much higher for the
softer band, i.e. 10-100 keV, which overlaps the LED sensitivity range (the oscillations is probably
due to statistics effects, due to the smaller energy band). In particular, the radial distribution without
MD is peaked at r = 0, while the simulation with the MD has a minimum there. The LED edge is
very close to the minimum. For the other energy bands, the deflection is smaller and, in fact, the
distributions with/without B resemble each other much more, even if there is always a sharp
minimum at r = 0.
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8. Conclusions
The notes above can be summarized as follows:
• A magnetic diverter for protons for the SIMBOL-X telescope can be manufactured using
commercially available Neodymium magnets with a N52 magnetic grade.
• The magnetic field generated by a proper assembly of magnetic bars that would not obstruct
the X-ray flux can be computed analytically in a fast and reliable way.
• The calculated magnetic field is in excellent agreement with experimental measurements
and with the measured field of previous MDs for electrons onboard X-ray telescopes, like
those of Newton-XMM.
• A support system can be designed and seems to withstand the orbital temperatures. The
magnetic field seems to be unaffected by thermal cycles from + 65 oC to -80 oC.
• The MD should be located after the optic exit, at a 15 cm minimum distance from the
minimum diameter of mirror shells, in order to not harm the shape of X-ray Nickel mirrors.
• The magnetic field deflects effectively protons and repels electrons up to 2 MeV, keeping the
proton background below the instrumental noise of the LED.
