passive magnetic cylindrical shielding at gauss-range static fields
TRANSCRIPT
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567
Contents lists available at ScienceDirect
Nuclear Instruments and Methods inPhysics Research A
0168-90
doi:10.1
$ Wo
FPA 200�Corr
E-m
journal homepage: www.elsevier.com/locate/nima
Passive magnetic cylindrical shielding at gauss-range static fields$
E. Calvo, M. Cerrada, I. Gil-Botella, C. Palomares, I. Rodrıguez �, F. Toral, A. Verdugo
Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas (CIEMAT), Avda. Complutense 22, 28040 Madrid, Spain
a r t i c l e i n f o
Article history:
Received 10 December 2007
Received in revised form
16 December 2008
Accepted 23 December 2008Available online 4 January 2009
Keywords:
Passive magnetic shielding
Cylindrical shielding
Photomultiplier
Low magnetic field
Helmholtz coils
Mumetal
Double Chooz
Reactor neutrino experiments
02/$ - see front matter & 2009 Elsevier B.V. A
016/j.nima.2008.12.186
rk supported by Spanish Ministry of Educatio
7-65107.
esponding author. Tel.: +34 914962554; fax: 3
ail addresses: [email protected], ikerrg
a b s t r a c t
A study has been performed in order to find the optimal solution for the magnetic shielding of the 10 in.
photomultipliers which will be used in the Double Chooz neutrino experiment under a very low
magnetic field (less than 2 G). The results obtained with analytical and numerical calculations are
compared with measurements made using test prototypes of several magnetic materials, with different
dimensions and from different manufacturers. An exhaustive analysis of the magnetic materials was
needed to understand the observed disagreement between calculations and test results obtained at low
field values.
& 2009 Elsevier B.V. All rights reserved.
1. Introduction
In each of the two Double Chooz detectors [1] a total of 390Hamamatsu R7081 [2] photomultipliers (PMTs), with dimensionsas shown in Fig. 1, will be installed inside a stainless steel buffer inorder to detect the photons resulting from neutrino interactionstaking place in the inner target volume filled with liquidscintillator. The magnetic field in the PMT region, induced bythe remanent magnetization of the external steel cylinderand also due to the Earth’s magnetic field, is expected to be lessthan 2 G.
It is well known that large-area PMTs are very sensitiveto magnetic fields because of the long path followed bythe photoelectrons to reach the first dynode under the effectsof the Lorentz force (shown in Fig. 1). A signal loss of about 10%has been measured for the R7081 Hamamatsu PMTs with a125 mG transverse magnetic field, while the loss increases up to60% at 500 mG (value close to the Earth’s magnetic field) [3].Therefore, a magnetic shield will be required for the operation ofthese PMTs in order to ensure that, in the presence of externalmagnetic fields up to 2 G, the average field in the PMTphotocathode region is less than 125 mG.
ll rights reserved.
n and Science under Project
4 913466068.
@gmail.com (I. Rodrıguez).
Active shielding compensating coils are currently used toshield low magnetic fields. Since detector constraints do not allowone to use this method, the only available option left is toimplement a passive shield design. The challenges of such anapproach, as will be discussed in the following sections, arerelated to the very low external magnetic fields, the large PMTsize, the large openings required to avoid losses of incomingphotons and the small shield thickness required in order tominimize weight and cost.
2. Analytical calculations
Both analytical and numerical calculations have been made inorder to obtain a first approximation of the dimensions of theshield, assuming a cylindrical shield with openings at each end.
The transverse shielding factor ST, defined as the ratio betweenthe external and internal transverse fields, has been calculatedusing the following expression (valid for an infinitely long cylinderin a uniform transverse field [4]):
ST ¼mr � d
Dþ 1 (1)
where D is the diameter of the cylinder, d is the thickness ðd5DÞ
and mr is the relative permeability of the shield material. Thesmaller the diameter, the better the shielding factor obtained. Onthe other hand, a large diameter is convenient to increase the PMT
ARTICLE IN PRESS
Fig. 2. CO-NETIC AAs alloy B–H an-hysteretic plot [5] used in the numerical
calculations.
Fig. 3. Magnetic field lines in the wall of a long cylindrical shield (cross-section).
Fig. 1. Hamamatsu R7081 [2] PMT dimensions and Lorentz force (courtesy of
Hamamatsu Photonics K.K.).
E. Calvo et al. / Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567 561
angular acceptance of photons. As a compromise we haveassumed 300 mm as the value for the shield diameter.
Eq. (1) also shows that a material with very large permeabilityand limited thickness can maximize ST. However, it has to be takeninto account that high permeability materials usually saturate atlow fields. A good example of high permeability material isMumetals1 [5], which has typical maximum values for therelative permeability of around 400 000 (Fig. 2). Increasing themagnetic flux yields an increase in permeability up to a saturationlimit. The linear range extends up to BE2400 G in the case of CO-NETIC AAs alloy [5].
The internal magnetic flux (Bin) inside a long cylindrical shieldimmersed in a transverse homogeneous field (Bext) has been
1 Mumetals is a registered trademark of Magnetic Shield Corp., Bensenville, IL
60106, USA (Tel.: +1630 766 7800, www.magnetic-shield.com) widely used as
reference to any nickel–iron alloy with very high magnetic permeability. For
optimum magnetic properties, the material requires thermal annealing.
calculated considering that the field lines contained within aregion of twice the cylinder diameter are collected by the shield asshown in Fig. 3. Therefore, both fields are related through [4]:
2 � D � Bext � 2 � d � Bin. (2)
Assuming an external transverse field of 2 G, the minimumthickness (d) of a mumetal shield operating at the maximumpermeability point (Bin=2400 G) is about 0.25 mm, which isavailable from most mumetal manufacturers. The correspondingrelative permeability for this saturation value is about 400 000[5]. However, this is only valid in the highest flux zones of thecylindrical shield (zone B of Fig. 3). A mean relative permeabilitymr equal to 200 000 has been used in the calculations in order toaverage for the different magnetic flux zones (from 2 to 2400 G)with different permeabilities in the shield.
Commercial mumetal sheets of Magnetic Shield Corp. (CO-NETIC AAs [5]) are 381 mm wide, long enough to cover the fullPMT. Therefore, we used as dimensions of the first shieldprototype 300 mm in diameter, 0.25 mm thick and 381 mm high.
The total transverse shielding factor (STeff) in the centre of amagnetic cylinder shield with openings can be computed as [4]:
1
STeff¼
1
STþ
1
STop(3)
where ST is the infinite cylinder component (Eq. (1)) and STop theopenings component. STop has been calculated using Eq. (4), withthe experimental value of the Bessel factor kT=3.52 [4], being L thelength of the cylinder. It is important to note that the contributionof the openings to the shielding factor is totally independent ofthe shield material, and only depends on geometrical parameters.
STop ¼ 1:5 � ekT �ðL=DÞ (4)
For an external transverse and homogeneous field of 2 G, theinternal field in the centre of our prototype should reduce to27 mG (STeff=73), in the same direction as the external field.
The shielding factor along the whole axis of the cylinder can becomputed using Eq. (5), where Bext and BTin are the fields outsideand inside the shielded volume, respectively. The coordinatesystem is centred in the lower opening of the cylinder with theZ-axis along the cylinder axis.
STeff ðzÞ ¼Bext
BTin¼
1
3� e�kT ðz=ðD=2ÞÞ þ
1
3� e�kT ððL�zÞ=ðD=2ÞÞ þ
1
mr � d
Dþ 1
0BB@
1CCA
�1
.
(5)
ARTICLE IN PRESS
Fig. 4. Magnetic flux inside the shield material for transverse external 2 G field
(parallel to the cut plane).
E. Calvo et al. / Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567562
If the top of the PMT is placed at 136 mm below the upper shieldopening,2 the field along the Z-axis in the photocathode area(z between 195 and 245 mm) is always less than 41 mG. This morethan fulfils our shielding requirements. The shielding factor isabout three in the openings.
3. Numerical simulations
An ANSYS [6] model has also been developed in order to cross-check the results of the analytical calculations. There are someadvantages in a finite element simulation:
�
the
The manufacturers’ real B–H non-linear plot is used (Fig. 2),thus there is no need to estimate the relative permeability.
� The resultant field is obtained in the full volume, not onlyalong the axis, and therefore, the field values can be plottedeverywhere to check for critical zones.
The shield dimensions used for the ANSYS model were identical tothe ones used for the analytical calculations. The finite elementsmodel design and calculation is quite challenging because theshield thickness is very small compared to the other dimensions.
Fig. 4 shows the result of the simulation when a uniformmagnetic field of 2 G perpendicular to the shield axis is applied.The magnitude of the field inside the mumetal is indicated incolours.
The effective shielding factor obtained in the centre of thecylinder is about 85. Table 1 shows the analytical and numericalresults at different tilt angles of the cylinder (01 means thatthe field is transverse to the cylinder axis), and at two points(centre of the shield and top of the photocathode at Z=245 mm).Since the highest value of the residual field occurs at a tilt angleof 01, only this configuration will be considered in our analysis.The agreement between analytical and numerical calculations isvery good.
Considering a shielding factor value of 85 in the centre of thecylinder obtained from numerical calculations, the equivalentrelative permeability from Eq. (5) yields a value of 290 000, not
2 The distance of 136 mm corresponds to the cylinder length (381 mm) minus
PMT length (245 mm), according to Fig. 1.
very far from the initial estimated average of 200 000. If this newrelative permeability is used instead of the initial estimate, theanalytical and numerical results are similar.
4. Experimental tests of a first prototype
4.1. Experimental set-up
Helmholtz coils provide a straightforward way to producea uniform field. In order to compensate the Earth’s magneticfield and to create a homogeneous field in any direction, threeHelmholtz coils (six solenoids) were aligned along three perpen-dicular axes. All the pairs of coils are different in size to allow thephysical assembly without interference (Fig. 5). The field has to behomogeneous in a large volume around the shield, thus the coilsmust be large enough for this purpose (�1.2 m diameter).
The relationship between the coil current and the field insidewas, in our case, 1 A/2 G. The coils were fed by three DC currentsources (max. 2 A, 30 V) and an AC variable autotransformer wasused to degauss the shields.
A magnetic sensor (Honeywell magneto-resistive sensorHMR2300) [7] was used for measuring the very low magneticfields inside the shield from �2 to 2 G, with a resolution betterthan 70mG. It was encapsulated in an aluminium case in order tostabilize the temperature and to fix the sensor to the positioningsystem inside the shield. The magneto-resistive probe has someinternal misalignments (non-perfectly perpendicular sensors,small offset). These were measured and found to be very small,on average less than 20 mG.
4.2. Shielding factor measurements at the centre of the cylinder
The first shield prototype (Fig. 5) was built by rolling a sheet ofmumetal (CO-NETIC AAs), overlapping the edges by severalcentimetres, and joining them with small aluminium rivets.The material was previously annealed by the manufacturer(at a temperature of 1121 1C for a period of 4 h in a pure, dryhydrogen atmosphere) to obtain optimum magnetic properties.Cooling proceeded at a rate of 222 1C/h until a temperatureof 600 1C was reached, after which the cooling rate could beaccelerated.
The shield was placed in the centre of the coils and, aftercompensating the Earth’s magnetic field, a transverse B-field wasapplied using one of the coils. The intensity of the external B-fieldwas increased from 0 to 2 G and the internal B-field at the centreof the shield was measured. The results are shown in Fig. 6 andcompared with the expected field values obtained from analyticalcalculations. The relative permeabilities considered in thecalculations were m=100 000 up to 0.5 G, m=150 000 from 0.5 to1 G and m=200 000 from 1 to 2 G.
The most important point to notice in Fig. 6 is thatthe measured field is much higher than that expected fromthe theoretical results. For example, at 2 G external transversefield, the expected inner field from calculations is about 30 mGwhile the measurements show fields larger than 180 mG.The corresponding shielding factor, shown in Fig. 7, is also muchless (about a factor 7) than the expected one for a 2 G externalfield. Moreover, the maximum shielding value corresponds to alower field close to 1 G. These results are, therefore, in strongdisagreement with the analytical calculations and do not fulfil theperformance requirements for the Double Chooz PMTs.
It can also be noticed in Fig. 7 an improvement of the shieldingfactor when the external field increases as a consequence of theincrease of the permeability with the magnetic flux. However,
ARTICLE IN PRESS
Table 1Comparison between analytical and numerical results for B-field inside a cylinder in the presence of an external 2 G field at different angles of incidence.
Angle of incidence 01 301 601 901
Measurement point Centre Top Centre Top Centre Top Centre Top
Residual field (mG) (analytical results) 27.2 41.4 23.5 35.9 13.5 20.7 0.0 0.0
Residual field (mG) (numerical results) 23.5 39.7 20.8 35.2 11.8 19.6 0.0 0.0
Fig. 5. Set of Helmholtz coils with the positioning system and magnetic sensor.
0
20
40
60
80
100
120
140
160
180
200
0External field (Gauss)
Fiel
d in
side
(mG
auss
)
0.25 0.5 0.75 1 1.25 1.5 1.75 2
Fig. 6. Field measured at the centre of the cylinder (diamonds) versus the external
transverse field. The analytically expected field values are also shown (circles).
0
2
4
6
8
10
12
14
0External field (Gauss)
Shi
eldi
ng fa
ctor
0.25 0.5 0.75 1 1.25 1.5 1.75 2
Fig. 7. Shielding factor measured at the centre of the cylinder.
0123456789
101112
0Axis position (mm)
Shi
eldi
ng fa
ctor
50 100 150 200 250 300 350
Fig. 8. Shielding factor measured along the longitudinal axis of the first prototype
shield for an external transverse 2 G field.
E. Calvo et al. / Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567 563
between about 1.2 and 1.4 G, the shielding factor starts to slowlydecrease. This is not compatible with a saturation of the material,as discussed in Section 2. This must be caused by a smaller
permeability than that expected in zone A of Fig. 3. This effectallows an increase of the internal field which cannot becompensated by the increase of permeability in zone B.
4.3. Shielding factor measurements along the longitudinal axis
Several measurements along the cylinder longitudinal axishave been made in order to compare not only the results in thecentre of the shield, but also the results from analytical andnumerical calculations along the full axis of the cylinder.
Fig. 8 shows the shielding factor corresponding to differentpositions along the longitudinal axis of the cylinder. The shieldingfactor in the openings of the cylinder (positions 0 and 381 mm) is
ARTICLE IN PRESS
Table 2Measurement of the shielding factor in the centre of cylinders with different
diameters, same height (381 mm) and thickness (0.25 mm).
Shield diameter (mm) 280 300 320 340
External transverse field (G) 1 2 1 2 1 2 1 2
Internal field (mG) 85 170 90 187 95 217 100 240
Measured shielding factor 11.9 11.8 11 10.7 10.4 9.2 9.7 8.5
Expected shielding factor 77.1 90 64.2 73.5 53.9 60.8 45.6 50.8
The expected analytical shielding factor is calculated with m=150 000 for 1 G and
m=200 000 for 2 G.
Fig. 9. An-hysteretic and first magnetization curves [8]. m0 is the free space
permeability, H is the magnetic field intensity, B is the magnetic flux density, Br is
the remanent magnetic flux, Hc is the coercitive force and Ms is the magnetization
at saturation.
E. Calvo et al. / Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567564
in good agreement with the analytical and numerical calculations.However, the disagreement is strong in other regions of the axis(up to a factor 7 less than expected).
Although off-axis measurements across the diameter have alsobeen taken, they are not significant because the field remainspractically constant when moving the sensor along theX- and Y-axes (perpendicular to the shield axis at its centre).The transverse magnetic field is always slightly larger onthe axis. Therefore, the value of the field on the axis can be usedto validate the results in the whole photocathode volume(conservative value).
4.4. Additional measurements
Several factors have been considered in trying to find the originof the discrepancy between calculations and measurements:
�
Cylinder overlapping: Four types of overlapping have beentested throughout the study, very similar results beingobtained in all cases: aluminium rivets, spot welding, edgewelding (without overlapping) and sticking with adhesivetape. � Mumetal remanent magnetization: An AC field has been appliedto the shield in order to remove the magnetization of thematerial after measurements. The results of the measurementsafter the demagnetization have not shown any significantchange.
�3 X and Y are the transverse directions and Z is the longitudinal direction.
Influence of shield diameter: Several cylinders of differentdiameters have been built using the same mumetal sheet.The effect of the end openings is more significant for largerdiameters as expected from Eq. (3) (Table 2). However, themeasurements show qualitatively the same behaviour as theprevious ones (shielding factors are much lower thanexpected) and the internal versus external field plots aresimilar to Fig. 6.
4.5. Discussion of the results
The value of the shielding factor in both openings of all thetested cylinders matches the analytically and numerically calcu-lated value; it is around 3. This value is independent of the shieldmaterial (Eq. (4)), thus indicating that the origin of thediscrepancy is linked to the mumetal characterization, and notto the theoretical calculations.
However, the numerical calculations are in agreement withanalytical formulae. ANSYS does not estimate a relative perme-ability value for the mumetal; it calculates the exact workingpoint of each element using the manufacturers’ B–H plot. Hence, adiscrepancy would occur if the B–H plot (Fig. 2) used for thecalculations does not correspond to the real behaviour of thematerial at very low static magnetic field values.
Magnetic material manufacturers usually give the an-hystere-tic B–H curves, which are calculated by hysteretic cycles of themagnetic material in AC fields (joining the peaks of the hystereticcycles as it is qualitatively shown in Fig. 9).
However, in the present case, the material is immersed ina very low DC field, and its performance is governed by thefirst magnetization curve. An-hysteretic curves are much steeperthan first magnetization curves, especially at lower fields. Thisbehaviour has its basis on the domain orientation of the metallicstructure crystals at microscopic level. When a pristine magneticmaterial (randomly magnetised) is exposed to a low frequency ACmagnetic field, the magnetic domains start shaking, lowering thefriction between them and allowing more domains to be orientedfor a given field level (increased permeability) [9]. However, whenthe field is a slowly increasing DC field, the domains cannot orientthemselves in the best way at low flux, because the magnetic forceis not strong enough to overcome the static friction betweendomains (low permeability). When the external field is taking themumetal close to saturation, AC and DC field behaviours aresimilar because the magnetic field is powerful enough to orientateall the domains in both cases.
This phenomenon has been confirmed in our cylindricalmumetal shields by applying a 50 Hz AC field. An external DChomogeneous field of 2 G was applied in one of the transversedirections3 (X-axis), corresponding to a shielding factor of about10.5, while one of the other Helmholtz coils was fed by a 50 Hz ACcurrent to ‘‘shake’’ the mumetal domains, and so improve theirorientation (and thus the permeability) by removing the staticfriction between them. The results of these measurements aregiven in Table 3, where a significant improvement of the shieldingfactor can be observed after application of an AC field of very lowamplitude (RMS is about 8 G).
It is also observed that the remanent magnetization afterapplying the AC field is much higher than before ‘‘shaking’’ thedomains. This also indicates that the domains have been welloriented, even using the same external 2 G static field.
It can be concluded that the B–H curve provided by themanufacturers is not valid to predict the magnetic behaviour ofthe materials immersed in very low magnetic fields. Experimental
ARTICLE IN PRESS
Table 4Magnetic field measurements at the centre of 0.5 mm thick and 305 mm height
Magnetic Shield Corp. mumetal shields.
Shield diameter (mm) 280 320
External field (G) 1 2 1 2
Internal field (mG) 31.9 55.1 45.4 81.5
Shielding factor 31.3 36.3 22 24.5
Table 3Shielding factors before and after AC excitation of the 300 mm diameter, 0.25 mm
thick Magnetic Shield Corp. cylinder.
External field Shielding factor Remanent magnetization (mG)
2 G 10.5 57
2 G+AC (Y-axis) 16.5 80
2 G+AC (Z-axis) 17.7 85
The remanent magnetization values are also indicated.
Table 5Magnetic field measurements at the centre of 0.5 mm thick and 305 mm height
Meca Magnetic shields.
E. Calvo et al. / Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567 565
measurements, like the ones reported in this paper, becomemandatory to characterize the materials.
0
5
10
15
20
25
30
35
40
45
0External field (Gauss)
Shi
eldi
ng fa
ctor
0.25 0.5 0.75 1 1.25 1.5 1.75 2
Fig. 10. Shielding factor measured at the centre of Meca Magnetic mumetal shield
(0.5 mm thick, 280 mm diameter, annealed during 3 h at 1080 1C).
Material Mumetal Supermimphy
Shield diameter (mm) 280 280 280 320
Thermal treatment 1070 1C 1 h 1080 1C 3 h 1080 1C 3 h 1080 1C 3 h
External field (G) 1 2 1 2 1 2 1 2
Internal field (mG) 34.3 59.7 26.9 47.4 16.2 45.3 37.7 69.9
Shielding factor 29.1 33.5 37.1 42.2 39.7 44.1 26.5 28.6
5. Optimization of the shield design and new prototype tests
The first cylinder prototype, built according to the theoreticalcalculations, did not fulfil the shielding requirements for theDouble Chooz PMTs. Significant discrepancies between theexperimental measurements and expectations were observed.Therefore, further options were considered in order to improvethe performance of the shield.
5.1. Increase of the shield thickness
The option of increasing the thickness of the shield seemed tobe the most convenient one in terms of simplicity and cost. Animprovement of a factor of two in the shielding factor is inprinciple enough for our purposes. Two new 0.5 mm thickMagnetic Shield Corp. mumetal shields, with different diameters,280 and 320 mm, were built. The only differences with previouscylinders were that their edges were directly welded withoutoverlapping and the height of the shields was smaller (305 mm).The magnetic measurements in the centre were very slightlyaffected by the new height. The thermal annealing after weldingwas similar to the one used for the 0.25 mm metal sheets(described in Section 4.2).
The measurement results are shown in Table 4. The shieldingfactor is about three times better than for the 0.25 mm thickshields. However, the analytical Eq. (1) in Section 2 predicts thatdoubling the shield thickness, would produce only a factor twohigher shielding factor. Unexpectedly, for these extremely lowmagnetic fields, the magnetic properties of the mumetal changewhen the thickness is increased. Before doing a more detailedanalysis of the mumetal properties, other materials manufacturedby another company were tested.
5.2. Tests of other materials
Two new 0.5 mm thick mumetal prototypes produced byMeca Magnetic4 were used for these tests. The manufacturingprocess included overlapping and spot welding of the edges, andthermal annealing in vacuum at 1080 1C during 1 or 3 h. Anotheralternative material of the same firm, named Supermimphy5 wasalso tested in order to compare its magnetic properties withmumetal.
The B-field in the centre of these shields was measured fortransverse external fields of 1 and 2 G. The measurement results
4 Meca Magnetic, Mr. Vincent BORIEL, 490 Rue de la Fontaine, 45200 Amilly,
France, Tel.: +33 238 07 13 13, www.mecamagnetic.com.5 Supermimphy [10] is a high purity, high permeability magnetic material,
mainly composed of Nickel and Iron. Its permeability is expected to be higher than
the one of mumetal.
are listed in Table 5. They confirm the previous observationthat a better shielding factor than that expected is achievedincreasing the thickness. In addition, the shielding factor dependssignificantly on the thermal treatment. It varies in the range33–42 for the several types of 280 mm diameter cylinders testedat 2 G. Table 5 also shows that the performance of Supermimphy isslightly better than the one of mumetal for these extremely lowmagnetic fields.
The shielding factor as a function of the external field for themumetal shield from Meca Magnetic, annealed for 3 h, is plottedon Fig. 10. The shielding factor at the origin is very high (about 25),and no shielding drop is observed beyond 2 G.
Fig. 11 also shows the shielding factor measured at differentpoints along the longitudinal axis of the shield, for an externalfield of 2 G. The value of the shielding factor in the openings isabout three, the same as for the previous shields of different types,and in agreement with the analytical formulae and the argumentsabout the permeability given in Section 4.
The Meca Magnetic mumetal shield of 0.5 mm thickness and280 mm diameter fulfils our shielding requirements. If the topof the PMT photocathode is placed 50 mm below one of theopenings, the average field in the photocathode area (from 200 to
ARTICLE IN PRESS
E. Calvo et al. / Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567566
250 mm in the longitudinal axis) is below 125 mG for an externalB-field of 2 G.
These measurements also show that, independently of themumetal manufacturer, thicker mumetal shields have largermagnetic permeability at low DC fields. This behaviour could beexplained by differences in the microscopic structure of mumetalsheets of different thickness [11,12].
5.3. Composition and crystallographic analyses of the materials
Two microscopic analyses of the different materials wereperformed to try to understand the unexpected magneticbehaviour of these materials at low static fields.
The analysis of the shield composition, based on the energydispersive X-ray spectroscopy technique [13], showed no majordifference between the various samples. However, the crystal-lographic analyses were very revealing.
Fig. 12 shows three crystallographic images of the samemumetal (Magnetic Shield Corp.) with different thicknesses
Fig. 12. Optical microscope images of 0.1 mm (a), 0.25 mm (b) and 0.5 mm (c) thick
Fig. 13. Optical microscope images of 0.5 mm thick mumetal Meca Magnetic of 1 h
0
5
10
15
20
25
30
35
40
45
0Axis position (mm)
Shi
eldi
ng fa
ctor
50 100 150 200 250 300
Fig. 11. Shielding factor as a function of the axis position for the 0.5 mm thick,
280 mm diameter mumetal shield, annealed for 3 h, from Meca Magnetic in
presence of a 2 G external field.
(0.1, 0.25 and 0.5 mm). The large difference in the grain sizeof the mumetals can be observed in the pictures. Although allmumetals have similar composition, the 0.1 mm sample has amean grain size of 20mm, while the grain size of the 0.25 and0.5 mm mumetal samples are 75 and 127mm, respectively.
The same comparison was made for Meca Magnetic 0.5 mmthick sheets (Fig. 13). The microscopic analysis reveals thatthe Supermimphy material, which showed the best magneticbehaviour in previous tests, has the largest mean grain size. Thisanalysis also shows that a longer thermal treatment (TT) allowsthe grains to grow more.
Mumetal samples from different manufacturers can also becompared from Figs. 12 and 13. The grain size is larger in MecaMagnetic with 3 h TT and Supermimphy than in Magnetic ShieldCorp. 0.5 mm mumetal, the magnetic behaviour being better forthe first two samples, as shown in Section 5.1.
Table 6 summarizes the crystallographic analysis. There is aclear correlation between the grain size and the measuredshielding factor. The shielding factor increases with the grainsize, independently of the material manufacturer. A possibleexplanation for this behaviour is to assume that the static frictionis smaller for larger domains making their orientation easier atlow magnetic fields.
The thicker sheets allow the growth of grains with larger sizeinside their crystalline structure. Hence, the expected improve-ment of the shielding factor with the thickness of the mumetalsheet is further enhanced by the increase of the grain size.
Magnetic Shield Corp. mumetal. The minimal scale is indicated in every picture.
(a), 3 h (b) thermal treatment and Supermimphy of 3 h thermal treatment (c).
Table 6Grain size vs. shielding factor at 2 G for different magnetic shields.
Material and manufacturer Thickness
(mm)
Grain size
(mm)
Shielding
factor
Mumetal Magnetic Shield Corp. 0.1 20 7
0.25 75 12
0.5 127 36
Mumetal Meca Magnetic 1 h TT 0.5 125 33
Mumetal Meca Magnetic 3 h TT 0.5 180 42
Supermimphy Meca Magnetic 3 h
TT
0.5 250 44
ARTICLE IN PRESS
E. Calvo et al. / Nuclear Instruments and Methods in Physics Research A 600 (2009) 560–567 567
6. Conclusions
In this paper, the design and calculation of the passivemagnetic shielding for the Hamamatsu R7081 PMTs of the DoubleChooz experiment has been reported. Magnetic shields arerequired in order to limit the average magnetic field in the PMTphotocathode area to below 125 mG, in the presence of externalfields below 2 G. A cylinder of about 300 mm diameter made from0.5 mm thick mumetal, thermally annealed for 3 h at 1080 1C, withan upper opening 50 mm above the PMT photocathode, will beable to fulfil these requirements.
Several prototypes with different dimensions and materialsfrom different manufacturers, were tested under low DC magneticfield in the Gauss range. These studies confirmed that the B–Hcurves provided by the manufacturers are not unique for everymaterial and TT but they also depend on the thickness of thespecific material. This is particularly critical for a cylindricalgeometry in presence of low magnetic fields, where very differentregions of magnetic flux appear inside the shield.
The experimental measurements reported in this paper can beused as a reference for the design of cylindrical passive magneticshields at low external magnetic fields.
Acknowledgements
We want to thank the manufacturers Magnetic ShieldCorporation and Meca Magnetic for the technical support andinformation. We are also grateful to Serviciencia S.L.,6 especiallyAlberto Marino for the support and manufacturing of the
6 Serviciencia S.L., Isabel II, 22, Polıgono Industrial ‘‘Sector 23’’ – Nave 70,
45210 Yuncos, Toledo, Spain. Tel.: +34 925 536154, www.serviciencia.es.
Helmholtz coils and to Gonzalo De Diego (CIEMAT) for theanalysis of the metal microscopic structure. We acknowledgefinancial support from the Spanish Ministry of Education andScience under Project FPA 2007-65107.
References
[1] F. Ardellier, et al., Double Chooz Collaboration, Double Chooz: a search for theneutrino mixing angle y13, Preprint arXiv:hep-ex/0606025v4, 2006.
[2] Hamamatsu Photonics K.K., 314-5, Shimokanzo, Iwata City, Shizuoka Pref.,438-0193, Japan /http://www.hamamatsu.com/resources/products/etd/pdf/LARGE_AREA_PMT_TPMH1286E05.pdfS.
[3] F.J. Valdivia, Master Thesis, Universidad Complutense de Madrid, 2007.[4] A.J. Mager, IEEE Trans. Magnetics MAG-6 (1) (1970) 67.[5] Magnetic Shield Corporation, Sheet and foil material selection
guide, Catalogue MG-7B /http://www.magnetic-shield.com/literature/pdf/mg-7.pdfS.
[6] ANSYS 10.0 Documentation, 2005 SAS IP, Inc. All rights reserved.[7] Honeywell Sensor Products, Smart Digital Magnetometer HMR2300, 900139
02-04 Rev. H, Solid State Electronics Center (800), pp. 323–8295 /www.magneticsensors.comS.
[8] S. Russenschuck, Electromagnetic design and mathematical optimizationmethods in magnet technology, CERN, AT-MEL-EM 1211, Geneva 23, Switzer-land, 2005.
[9] R.P. Feynman, Mainly electromagnetism and matter, in: The FeynmanLectures on Physics, vol. 2, Addison-Wesley, Reading, MA, 1964 (Chapters 36and 37).
[10] ArcelorMittal, Stainless & Nickel Alloys, Mumetal—Permimphy Supermim-phy, MAG/Mumetal/UK1—October 07 /www.imphy.comS.
[11] F. Pfeifer, C. Radeloff, J. Magnetism Magnetic Mater. 19 (1980) 190.[12] Dr. Heike Hattendorf, Soft magnetic Ni–Fe base alloys, ThyssenKrupp VDM
Report no. 27, June 2004.[13] An Introduction to Energy-Dispersive and Wavelength-Dispersive X-ray
Microanalysis, Oxford Instruments NanoAnalysis, Halifax Road, HighWycombe, Buckinghamshire HP12 3SE, UK, July 2006.