0.3 mW/K, roughly an order of magnitude worse than the thermal strap. At equilibrium, however, the temperature gradient is only 10 mK. SinceBicep2operates 40 mK above the base temperature of the fridge, this thermal gradient is tolerable.
The passive thermal filter is effective at attenuating high to mid-frequency thermal excitations.
The thermal transfer function has been measured, achieving > 40 dB attenuation at frequencies above 0.1 Hz (Kaufman et al. 2013a). Low frequency thermal fluctuations are filtered with an active thermal filter byBicep1-style temperature control modules. The module is a PID-controlled thermometer and resistive heater. Together, the active and passive thermal control achieve a focal plane temperature stability of better than±0.2mK rms during typical telescope scans. The thermal performance of the instrument will be discussed in more detail in later sections.
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To reduce the susceptibility to ambient fields, theBicep2SQUIDs provided by NIST are gradio- metric, counter-wound into a cloverleaf pattern. This reduces the effective loop area of the SQUID.
Even with this improvement, the SQUID response to a uniform DC field is non-zero, in part be- cause a uniform field is naturally distorted by the local magnetic environment. This gives rise to higher-order spatial gradients in the field to which the SQUID is sensitive. The two-dimensionality of the SQUIDs naturally give rise to a direction of maximum sensitivity to magnetic fields. For this reason, magnetic simulations are focused largely on the field amplitude in the direction normal to the plane of the SQUIDs.
We can calculate the sensitivity to magnetic fields at SQ1 as:
✓RTESMin
Ae↵
◆ I TCMB
. (2.12)
HereRTES is the TES current responsivity (⇠2⇥106 A/W),Min is the mutual inductance at the SQ1 input coil (475 pH), Ae↵ is the effective area of the SQ1 (measured to be 882 µm2 in Stiehl et al. 2011), and I/ TCMB is the CMB power conversion (derived in Appendix A.2). Entering these values into Equation 2.12, we find a field sensitivity of 0.1 pT/µKCMB, a factor of 2000 more sensitive than the TESs. Thus, to suppress magnetically induced signal to<0.1µKCMB, attenuation of 60dB or larger is required. This, of course, assumes no cancellation or subtraction. In practice, Bicep2’s ground subtraction technique (whereby a template of ground-fixed signal is generated and subtracted) reduces common-mode magnetic pickup. Additionally, the pickup will average down over detectors and coverage (since the signal is assumed to be ground-fixed). Our goal is to achieve as much attenuation as possible, keeping in mind the fact that further reduction will be possible in analysis and data averaging.
The second and third stage SQUIDs’ magnetic pickup is less concerning than pickup at the first stage. SQ2 is less sensitive, as it has a smaller effective area. Additionally, since the pickup is common-mode within a column, it can be subtracted using either common-mode rejection (pair differencing) or by subtraction of the dark SQUID response. Similarly, while the SSA magnetic sensitivity is high, the response is common to a column. Also, because of their location, the SSAs can be more easily shielded than the first and second stages.
The first line of defense in the Bicep2magnetic shielding design is a high-permeability nickel- iron alloy (manufactured under the trade name Cryoperm), formed into an open-ended cylinder that surrounds all of the 4 K components. The shield was manufactured by Amuneal.6 The material is annealed to improve the magnetic susceptibility at cryogenic temperatures.
The focal plane assembly sits within a niobium superconducting “spittoon” that serves as a second stage of magnetic shielding. The geometry was optimized in a series of COMSOL7magnetic
6http://www.amuneal.com
7http://www.comsol.com/
-10 dB
-20
-30
-40
-50
-60
-70
-80 ˆ
z ˆ x
(a)|B|~
-10 dB
-20
-30
-40
-50
-60
-70
-80 ˆ
z ˆ x
(b)|B~·z|ˆ
Figure 2.14: Attenuation of ambient DC fields within theBicep2sub-Kelvin superconducting mag- netic shield. Color scale reflects the field density amplitude, while blue lines show magnetic field lines. Left: Attenuation of the total field. Right: Attenuation of the zˆcomponent of the field.
shielding models performed by Talso Chui at JPL, Marcus Runyan at Caltech, and myself.
The third stage of shielding is the niobium backplane, as pictured in Figure 2.11. The first and second stage SQUIDs lie roughly 1 mm above the niobium backplane. The Meissner effect expels field in the direction normal to the surface, which is the same direction as the direction of maximum sensitivity of the SQUIDs. Because of the boundary conditions imposed by superconductivity, the field normal to the plane,B~ ·z, approaches zero near the surface. With this design,ˆ Bicep2models predict an attenuation factor of 40dB or larger for the total field amplitude, and 60to 50dB ofB~ ·z. In later sections, we will discuss the characterization of this magnetic shielding.ˆ
The design of the niobium backplane was optimized for magnetic performance. All fastener holes in the niobium are blind, so as to avoid supercurrents and pinned vortices in the material.
Similarly, early designs of the backplane included extrusions for the SQUID chips. While seemingly favorable, simulations of this topology predicted large increases in thezˆcomponent of the field, due to distortions caused by the corners of the extrusions. As a result, in later designs, the backplane was made to be as planar as possible. Additionally, a multi-layer sheet of Metglas,8 a high-permeability metallic foil, was added between the skyward side of the focal plane PCB and the copper detector plate. This additional shielding was not included in our magnetic modeling.
Since the SSAs are physically removed from the focal plane (sitting below in the 4 K “camera tube”), the shielding of these devices was implemented separately. Also, the SSAs are in a self- contained package that is much more easily shielded than the SQUIDs on the focal plane. The SSA module is contained within a niobium box that surrounds the SSA boards on five sides. The niobium can is then covered with multiple layers of Metglas. Because of the physical location of the SSAs, they see little attenuation from the open-ended cylindrical Cryoperm shield. However, the
8http://www.metglas.com
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Figure 2.15: TheBicep2telescope mount. The blue steel structure enables sub-arcminute pointing in three axes of motion: azimuth, elevation, and boresight rotation.
combination of the Metglas wrap and the niobium box achieve excellent magnetic attenuation, the characterization of which we describe in Section 3.5.