Optimization of an Adiabatic Demagnetization ... - COMSOL.com

Optimization of an Adiabatic Demagnetization Refrigerator’s 

Superconducting Magnet Shield for the Micro-X High-Resolution 

Microcalorimeter X-ray Imaging Rocket 

Enectali Figueroa-Feliciano 1,* , Mark Cavolowsky 2 , Chester Macklin 2 , Zhipeng Li 1 , Angela 

Sharer 2 , Ash Walker 2 

1 

Massachusetts Institute of Technology, Cambridge, MA 

2 

Olin College, Needham, MA 

*77 Massachusetts Ave. 37-664C, Cambridge, MA 02139, enectali@mit.edu 

Abstract: We are working on the design of a 

sounding rocket payload to do high-resolution 

imaging spectroscopy of the Puppis A supernova 

remnant. This rocket payload uses Transition- 

Edge-Sensor Microcalorimeters, which are 

superconducting detectors that obtain very high 

(2 eV FWHM at 6 keV) imaging spectra. These 

devices need to be cooled to 50 mK, for which 

we are designing an adiabatic demagnetization 

refrigerator. These refrigerators require the use 

of a high-field superconducting magnet which 

must be shielded to protect the sensitive TES 

detectors from the strong magnetic fields. Since 

this is a rocket payload, weight and impact 

resistance are very strong design factors. We are 

using COMSOL and MATLAB to model and 

optimize the shield to obtain a design that has the 

best shield-to-weight ratio. 

Keywords: Magnetic shielding, cryogenic 

refrigerators, x-ray 

1. Introduction 

Excerpt from the Proceedings of the COMSOL Users Conference 2006 Boston 

We are developing a sounding rocket 

adiabatic demagnetization refrigerator for the 

Micro-X sounding rocket mission [1]. This 

refrigerator needs to shield its magnet from the 

sensitive detectors in the focal plane, a few cm 

from the bore of the magnet. We are basing our 

design on the flight dewar for the University of 

Wisconsin’s X-ray Quantum Calorimeter 

(XQC), an instrument very similar to our Micro- 

X detector [2]. The XQC’s energy resolution is a 

factor of 3-6 times worse than our payload but 

their detectors are not sensitive to magnetic 

fields. We have used Comsol and MATLAB to 

model different designs with passive and active 

magnetic shields. In the next section we provide 

an overview of the science to by done by Micro- 

X. In Section 3 we discuss the technology behind 

Micro-X. In Section 4 we describe the problem 

and in Section 5 and 6 we present our work. We 

conclude with some discussion of our results and 

prospects for future work in this direction. 

2. Micro-X Science 

Our main science objective is to obtain a 

high spectral resolution image of the Bright 

Eastern Knot of the Puppis A supernova remnant 

(Figure 1). High-resolution spectroscopy 

provides a wealth of diagnostics (temperature, 

ionization, kinematics, density and abundance) 

of astrophysical plasmas. The X-ray band is 

home to the inner shell transitions of all the 

abundant elements besides H and He. With high 

spectral resolution data, looking at individual 

lines for the atomic transitions of these plasmas 

(and technique called plasma diagnostics) 

enables the measurement of the density, 

temperature and composition of a plasma, as 

well as measure velocities (via Doppler shifts) 

and turbulence (from excess broadening of the 

spectral lines due to the higher random velocities 

induced by the turbulent flow). 

Figure 1. The Puppis A supernova remnant. The box 

represents the 14.4’ FOV for observation of the Bright 

Eastern Knot by Micro-X


Figure 2. Simulation of the integrated Puppis A spectrum assuming a 300 sec observation by Micro-X with 2 eV 

FWHM spectral resolution. There are 92,000 counts in this simulation. 

The Puppis A supernova remnant (SNR) is a 

bright, middle-aged Galactic supernova remnant 

(~ 4000 years old) straddling the division 

between young SNRs that are totally dominated 

by their own ejected debris (from the SNR 

explosion) and older remnants that have lost all 

trace of their ejecta and now are seen through 

their inteaction with the local interstellar 

material. Puppis A still shows evidence of its 

explosion ejecta while at the same time being 

very strongly shaped by its interactions with a 

complex interstellar environment. The Bright 

Eastern Knot (BEK) region of Puppis A is the 

brightest, and perhaps most complex example of 

these interactions, with multiple shocked clouds 

plus evidence for ejecta in its vicinity. Figure 1 

shows a picture taken by the Rosat X-ray 

satellite of Puppis A. 

The main sciece goal of Micro-X is to 

unravel the kinematic, temperature, and 

ionization characteristics of the cloud shock 

interactions at the BEK and search for traces of 

the original ejecta of SNR (Figure 2). Crucial to 

both of these efforts will be determining the 

temperature distribution of the X-ray emitting 

gas. This is important for understanding ejecta 

enrichment because multi-temperature gas can 

mimic enriched abundances (the sign of ejecta 

material) in lower resoluition spectra. Our 

expected high energy reolution will allow us to 

unambiguously determine the state of the plasma 

through the identification and analysis of its 

spectral lines. 

3. The Micro-X instrument 

At this time, two X-ray space telescopes in 

orbit – the XMM-Newton and Chandra space 

telescopes – are capable of high resolution X-ray 

spectra through grating spectrometers. Grating 

spectrometers work well at lower energies (.2 - 2 

keV) but are degraded when looking at extended 

sources. Although some progress has been made 

in analyzing extened sources with XMM- 

Newton, the very high resolutions available for 

point sources remain unattainable for low surface 

brightness extended objects. 

Micro-X will use a 11 X 11 array of X-ray 

microcalorimeters designed and developed at the 

NASA Goddard Space Flight Center. Figure 3 

shows a schematic for an X-ray 

microcalorimeter. The device operates at 

cryogenic temperatures to minimize noise from 

thermal fluctuations. It senses the temperature


Figure 3. Basic Microcalorimeter. An X-ray 

absorber cooled by a refrigerator and connected to a 

cold bath senses a photons energy by the increase in 

temperature from the photon’s thermalization. 

pulse caused by a photon thermalization event 

and estimates the energy of the photon based on 

the pulse height of the temperature pulse. 

Microcalorimeters use one of the world’s most 

sensitive thermometers, the Transition-Edge 

Sensor (TES). A TES is a superconducting film 

biased in its transition. Changes in temperature 

cause changes in the resistance of the TES film. 

4. The Micro-X Adiabatic Demagnetization 

Refrigerator and the Shielding 

Problem 

In order to cool the mircrocalorimeter, we are 

designing a rocket-flight-qualified Adiabatic 

Demagnetization Refrigerator (ADR) for Micro- 

X. This unit will need to survive 17 g’s of 

acceleration during launch, and up to 200 g’s of 

deceleration during landing. An ADR uses a 

powerful 4 Tesla magnet to orient the spins in a 

salt and then adiabatically cools the salt by 

removing the field and allowing the spins in the 

salt to randomize. Our TES detectors are very 

sensitive to magnetic fields, so a shield is needed 

to protect the TESs from the ADR’s magnet. The 

requirements of the design are to minimize the 

ADR’s magnetic field in the region around the 

TES detectors while minimizing the weight of 

the shield. Because we must withstand high g 

forces, the larger the mass, the more stress is 

placed on the ADR during acceleration. Thus the 

parameter we wish to optimize is the reduction in 

field at the detector stage per unit mass of shield. 

5. Solution 1: Passive Shielding 

We have simulated several passive shield 

designs using COMSOL. Passive shielding refers 

to using high-permeability materials around the 

magnet to keep the magnetic field close to the 

magnet and provide shielding. Passive shielding 

works very well in low field environments, but 

in high-field environments the saturation effect, 

where the material’s permeability changes nonlinearly 

to that of free space as the field 

approaches some critical value, makes the design 

of passive shields very complex. We have 

successfully modeled this non-linear 

permeability in COMSOL and have written 

MATLAB scripts to iterate on different designs 

to obtain the best sielding for a given amount of 

mass. 

Figure’s 4 and 5 show a simulation for an 

axially symmetric model in COMSOL. In Figure 

5 the field for a 5 Tesla magnet is shown. The 

image is stretched to show regions above 2.5 

Tesla in white. 2.5 T is the saturation field of the 

Vanadium Permadur, so areas of the shield that 

are white are fully saturated. Many iterations on 

this design were attempted to try to find 

geometries where saturation did not occur. We 

defined the shield efficiency as the value of the 

magnetic field attenuation at the detector divided 

by the mass of the shield. This design had an 

efficiency of around 40. 

Figure 4. A model for the Micro-X ADR shield. R2 is 

the magnet, and R3 is the salt pill, which has its 

permeability set to 1 for this simulation. R6 and C02 

are Vanadium Permadur shields, and R4 is the 

detector region of interest.


Figure 5. The magnetic field for the model in Figure 

4. Shield sections in white are fully saturated. 

Figure 6. Best design for passive shielding. A 

combination of both Vanadium Permadur (thick 

shield) and Cryoperm (thin washer-style shield) 

provides a very low field in the detector region. 

After running many simulations by changing 

the geometry of the shield and using both 

Vanadium Permadur and Cryoperm (which has a 

higher permeability but lower saturation field 

than Vanadium Permadur) we arrived at the 

design on Figure 6. In this design there is a thick 

cylinder of VP that wraps under the magnet, with 

two flat large washers of cryoperm on the top 

and bottom of the shield. This high permeability 

material is placed farther away from the magnet 

so it does not saturate during full field. 

Although these designs will provide small 

enough fields to work, their mass is still larger 

than we desire. To try to bring the field around 

the detector down when at full magnet field, we 

looked at active shielding. 

6. Solution 2: Active Shielding 

Active shielding consists of placing a so 

called “bucking coil” (a magnet wound in the 

opposite direction of the main magnet) at a 

location nulls the field at the desired low-field 

region while maintaining the large field at the 

magnet bore. The advantage of active shielding 

is that the current through the bucking coil is 

proportional to the current in the main coil, so 

the attenuation is linear in current. There is not 

saturation effect, so active shields are very 

competitive at high fields. The drawback to 

active shields is that at low currents their 

attenuation is usually lower than what can be 

achieved with the high permeability materials. 

We modeled a series of bucking coils with 

different geometries but keeping the total mass 

of the bucking coil constant. To do this a 

MATLAB routine was created that kept the 

volume of the bucking coil constant while 

changing its geometry. In this model our target 

field in the detector volume was less than 0.05 

Tesla at full magnet field. This would allow the 

design of a superconducting shield around the 

detectors that would not saturate during the 

magnet cycle. Figure 7 shows one of the 

optimization designs that has a tubular style 

bucking coil. The colors have been stretched so 

that any region above 0.05 Tesla is white. The 

large horizontal box below the magnet is the 

desired low field area. As can be seen, this 

bucking coil design meets the requirements. 

Figure 8 shows another bucking coil with the 

same volume as that in Figure 7, but in a more 

horizontally spread out washer design. This 

design creates a more homogeneous low field 

region.


Figure 7. Bucking coil design for Micro-X. Here the 

bucking coil is fairly tubular, but creates a low field 

region within the 0.05 T requirements in the detector 

area (long rectangular region below the magnet. 

Figure 8. Best design for active shielding. This 

washer-style bucking coil has the same volume at the 

bucking coil in Figure 7, but its more horizontally 

spread out shape creates a more uniform low field 

region. 

7. Conclusions and Future Work 

We have begun the design of a active/passive 

shield for the Micro-X sounding rocket payload. 

We successfully implemented a non-linear solver 

and simulated saturation effects in highpermeability 

materials using COMSOL. 

MATLAB was used to step through different 

geometries and iterate designs. Output from 

COMSOL for each iteration was evaluated by 

MATLAB to provide feedback and metrics for 

the performance of each design. 

Our next step is to combine both approaches 

and design a low-mass active and passive shield 

that keeps the detector area field low at full 

magnet field while having a large attenuation 

factor at lower magnet fields when the detector is 

operating. We will continue using COMSOL and 

MATLAB as an effective platform for magnetic 

shield design. Future designs may incorporate 

non-axially symmetric elements which will 

require a 3D simulation to be done. 

8. References 

1. Figueroa-Feliciano, E et al., Science with 

Micro-X: The TES microcalorimeter x-ray 

imaging rocket, SPIE, 6266, 62660A (2006) 

2. McCammon, D. et al., A High Spectral 

Resolution Observation of the Soft X-Ray 

Diffuse Background With Thermal Detectors, 

The Astrophysical Journal, 576, 188-203 (2002)

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