Exploring Cosmic Origins with CORE: The Instrument

TL;DR

This paper presents the design of CORE, a space-based polarimeter for precise measurement of CMB polarization, optimized for budget constraints and capable of multi-band observations with high sensitivity.

Contribution

It introduces a novel, no-moving-parts instrument with diffraction-limited detectors covering 60-600 GHz, suitable for medium-size space missions within ESA's Cosmic Vision.

Findings

Projected survey sensitivity of 1.7 μK·arcmin after foreground removal

Design flexibility for a downscoped version with 3.2 μK·arcmin sensitivity

Use of Kinetic Inductance Detectors across 19 frequency bands

Abstract

We describe a space-borne, multi-band, multi-beam polarimeter aiming at a precise and accurate measurement of the polarization of the Cosmic Microwave Background. The instrument is optimized to be compatible with the strict budget requirements of a medium-size space mission within the Cosmic Vision Programme of the European Space Agency. The instrument has no moving parts, and uses arrays of diffraction-limited Kinetic Inductance Detectors to cover the frequency range from 60 GHz to 600 GHz in 19 wide bands, in the focal plane of a 1.2 m aperture telescope cooled at 40 K, allowing for an accurate extraction of the CMB signal from polarized foreground emission. The projected CMB polarization survey sensitivity of this instrument, after foregrounds removal, is 1.7 {\mu}K$\cdot$arcmin. The design is robust enough to allow, if needed, a downscoped version of the instrument covering the 100 GHz to 600 GHz range with a 0.8 m aperture telescope cooled at 85 K, with a projected CMB polarization survey sensitivity of 3.2 {\mu}K$\cdot$arcmin.

Tables

Table 1. Table 1 : Proposed \coremfive  frequency channels. The baseline aperture of the telescope is 1.2m in diameter. The detectors are cooled at 0.1K and their sensitivity is calculated assuming Δ ​ ν / ν = 30 % Δ 𝜈 𝜈 percent 30 \Delta\nu/\nu=30\% bandwidth, 60% optical efficiency, total noise of twice the expected photon noise from the sky and the optics of the instrument at 40   K times 40 K 40\text{\,}\mathrm{K} . This configuration has 2100 detectors, about 45% of which are located in CMB channels between 130 and 220   GHz times 220 GHz 220\text{\,}\mathrm{G}\mathrm{H}\mathrm{z} . Those six CMB channels yield an aggregated CMB polarization sensitivity of 2   µ ​ K times 2 microkelvin 2\text{\,}\mathrm{\SIUnitSymbolMicro K} ⋅ ⋅ \cdot arcmin ( 1.7   µ ​ K times 1.7 microkelvin 1.7\text{\,}\mathrm{\SIUnitSymbolMicro K} ⋅ ⋅ \cdot arcmin for the full array).

channel	beam	$N_{\det }$	$\Delta T$	$\Delta P$	$\Delta I$	$\Delta I$	$\Delta y\times {10}^6$	PS ($5\sigma$)
GHz	arcmin		$\mu K$$\cdot$arcmin	$\mu K$$\cdot$arcmin	$\mu K_{RJ}$$\cdot$arcmin	$\mathrm{kJy}/\mathrm{sr}$$\cdot$arcmin	$y_{\mathrm{SZ}}\cdot$arcmin	mJy
60	17.87	48	7.5	10.6	6.81	0.75	-1.5	5.0
70	15.39	48	7.1	10	6.23	0.94	-1.5	5.4
80	13.52	48	6.8	9.6	5.76	1.13	-1.5	5.7
90	12.08	78	5.1	7.3	4.19	1.04	-1.2	4.7
100	10.92	78	5.0	7.1	3.90	1.2	-1.2	4.9
115	9.56	76	5.0	7.0	3.58	1.45	-1.3	5.2
130	8.51	124	3.9	5.5	2.55	1.32	-1.2	4.2
145	7.68	144	3.6	5.1	2.16	1.39	-1.3	4.0
160	7.01	144	3.7	5.2	1.98	1.55	-1.6	4.1
175	6.45	160	3.6	5.1	1.72	1.62	-2.1	3.9
195	5.84	192	3.5	4.9	1.41	1.65	-3.8	3.6
220	5.23	192	3.8	5.4	1.24	1.85	-	3.6
255	4.57	128	5.6	7.9	1.30	2.59	3.5	4.4
295	3.99	128	7.4	10.5	1.12	3.01	2.2	4.5
340	3.49	128	11.1	15.7	1.01	3.57	2.0	4.7
390	3.06	96	22.0	31.1	1.08	5.05	2.8	5.8
450	2.65	96	45.9	64.9	1.04	6.48	4.3	6.5
520	2.29	96	116.6	164.8	1.03	8.56	8.3	7.4
600	1.98	96	358.3	506.7	1.03	11.4	20.0	8.5
Array		2100	1.2	1.7			0.41

Table 2. Table 2 : Parameters for the \coremfive  Gregorian design. Surface parameters refer to Equation  2.1 ; parameters determining the overall telescope geometry are defined in Granet 2002 [ 16 ] . The parameters describing the focal plane dimensions are given at 160 GHz in degrees and in units of F λ 𝜆 \lambda ( λ = 1.875   mm 𝜆 times 1.875 mm \lambda=$1.875\text{\,}\mathrm{m}\mathrm{m}$ ) to facilitate comparison between different telescope configurations. The variation in the focal ratio F 𝐹 F across the focal surface gives a 160   GHz times 160 GHz 160\text{\,}\mathrm{G}\mathrm{H}\mathrm{z} DLFOV that is larger in degrees in the elevation direction, but smaller in F λ 𝜆 \lambda .

Primary mirror		Secondary mirror	Telescope geometry
	$136\mathrm{cm}$ $\times$ $120\mathrm{cm}$	$97\mathrm{cm}$ $\times$ $67\mathrm{cm}$	$D_m$	$120\mathrm{cm}$
$c$	-$5.94\times {10}^{-3}$	0.0127	$L_m$	$165\mathrm{cm}$
$k$	-0.981	-0.319	$L_s$	$148\mathrm{cm}$
$a_2$	$2.45\times {10}^{-9}$	$1.06\times {10}^{-9}$	$h$	$80.3\mathrm{cm}$
$a_3$	$3.67\times {10}^{-13}$	-$7.06\times {10}^{-13}$	$\alpha$	$11.7°$
$a_4$	-$3.35\times {10}^{-17}$	$1.20\times {10}^{-15}$	$\beta$	$3°$
$a_5$	$1.40\times {10}^{-21}$	-$2.72\times {10}^{-19}$	${\theta }_0$	$51.2°$
$a_6$	-$2.25\times {10}^{-26}$	$2.36\times {10}^{-23}$
Focal ratio, F		1.6 at center, increases by 7 % at focal plane edges
$160\mathrm{GHz}$ DLFOV		Az $\times$ El = $7.6°$ $\times$ $7.8°$, 85 F$\lambda \times 73\text{ F}\lambda$

Table 3. Table 3 : Same as table  2 but for the Gregorian design with an alumina lens.

	Primary mirror	Secondary mirror	Alumina Lens		Telescope geometry
	$150\mathrm{cm}$ $\times$ $130\mathrm{cm}$	$100\mathrm{cm}$ $\times$ $70\mathrm{cm}$	$44\mathrm{cm}$	$D_m$	$120\mathrm{cm}$
$c$	-$6.47\times {10}^{-3}$	0.0154	-$2.67\times {10}^{-3}$	$L_m$	$145\mathrm{cm}$
$k$	-0.974	-0.333	0	$L_s$	$140\mathrm{cm}$
$a_2$	-$1.02\times {10}^{-9}$	$6.08\times {10}^{-10}$	$1.76\times {10}^{-6}$	$h$	$76.3\mathrm{cm}$
$a_3$	$2.35\times {10}^{-14}$	-$1.91\times {10}^{-12}$	-$2.69\times {10}^{-8}$	$\alpha$	$23.6°$
$a_4$	$5.73\times {10}^{-19}$	$1.27\times {10}^{-16}$	$2.90\times {10}^{-11}$	$\beta$	$4°$
$a_5$	-$3.50\times {10}^{-23}$	$5.34\times {10}^{-20}$	$4.64\times {10}^{-14}$	${\theta }_0$	$55.9°$
$a_6$	$5.65\times {10}^{-28}$	-$1.35\times {10}^{-23}$	-$7.98\times {10}^{-17}$
Focal ratio, F		1.88 at centre, varies by 17 % across focal plane
$160\mathrm{GHz}$ DLFOV		Az $\times$ El = $6.4°$ $\times$ $7.2°$, 68 F$\lambda \times 75\text{ F}\lambda$

Table 4. Table 4 : Parameters for the \coremfive  Crossed Dragone design. Surface parameters refer to Equation  2.2 ; parameters determining the overall telescope geometry are defined in Granet 2001 [ 25 ] .

	Primary mirror	Secondary mirror		Telescope geometry
	$131\mathrm{cm}$ $\times$ $152\mathrm{cm}$	$125\mathrm{cm}$ $\times$ $146\mathrm{cm}$	$D_m$	$120\mathrm{cm}$
$R_x$	-$1.15\times {10}^3$	$8.29\times {10}^2$	$L_m$	$112\mathrm{cm}$
$R_y$	-$7.14\times {10}^2$	$8.33\times {10}^2$	$L_s$	$264\mathrm{cm}$
$k_x$	2.97	-0.574	$h$	$765\mathrm{cm}$
$k_y$	-3.55	-7.31	$\alpha$	$13.8°$
$A_{2,r}$	$3.02\times {10}^{-10}$	$1.31\times {10}^{-9}$	$\beta$	$90.2°$
$A_{3,r}$	$9.54\times {10}^{-18}$	$3.05\times {10}^{-14}$	${\theta }_0$	$104°$
$A_{4,r}$	-$1.63\times {10}^{-22}$	-$8.17\times {10}^{-19}$
$A_{5,r}$	-$3.49\times {10}^{-34}$	$2.36\times {10}^{-24}$
$A_{2,p}$	-$1.027$	$0.183$
$A_{3,p}$	-$0.255$	$0.0671$
$A_{4,p}$	-$0.281$	$0.259$
$A_{5,p}$	-$0.914$	$0.669$
Tertiary mirror		$104\mathrm{cm}$ $\times$ $74\mathrm{cm}$
Focal ratio, F		2.54 at centre, varies by 5 % across focal plane
$160\mathrm{GHz}$ DLFOV		Az $\times$ El =$14.0°$ $\times$ $12.9°$, 159 F$\lambda \times 140\text{ F}\lambda$

Table 5. Table 5 : Far field beam parameters for two orthogonal polarizations of Gaussian beam inputs located at off-axis angles of ± 3   ° plus-or-minus times 3 degree \pm$3\text{\,}\mathrm{\SIUnitSymbolDegree}$ and ± 4   ° plus-or-minus times 4 degree \pm$4\text{\,}\mathrm{\SIUnitSymbolDegree}$ along the x 𝑥 x direction of the telescope (as illustrated in figure  3 ), at 145   GHz times 145 GHz 145\text{\,}\mathrm{G}\mathrm{H}\mathrm{z} . The coordinates θ 0 subscript 𝜃 0 \theta_{0} and ϕ 0 subscript italic-ϕ 0 \phi_{0} give the offsets of the beam centroids relative to a ray traced along the center of the input Gaussian.

Beam	FWHMθ	FWHMϕ	${\theta }_0$	${\varphi }_0$	Ellipticity
	(arcmin)	(arcmin)
Y $=3^{\circ }$ - X-Polarization	7.16	7.80	0.0001	0.0195	0.082
Y $=3^{\circ }$ - Y-Polarization	7.16	7.80	0.0001	0.0195	0.082
Y $=-3^{\circ }$ - X-Polarization	7.24	7.73	0	-0.022	0.063
Y $=-3^{\circ }$ - Y-Polarization	7.24	7.73	0	-0.022	0.063
Y $=4^{\circ }$ - X-Polarization	7.14	8.10	0.0002	0.0252	0.118
Y $=4^{\circ }$ - Y-Polarization	7.14	8.10	0.0002	0.0252	0.118
Y $=-4^{\circ }$ - X-Polarization	7.26	7.92	0.0001	-0.0285	0.083
Y $=-4^{\circ }$ - Y-Polarization	7.26	7.92	0.0001	-0.0285	0.083

Table 6. Table 6 : Advantages (Pros) and disadvantages (Cons) of the optical systems considered for \coremfive .

	Gregorian	Crossed Dragone
Pros	Small reflectors	Large, flat, telecentric DLFOV
	No lens: high TRL	Low instrumental and low
	Easy to baffle	polarization rotation
Cons	No lens : Smaller, non-flat DLFOV	Larger reflectors
	With lens: low TRL; insufficient DLFOV	Baffling more challenging

Table 7. Table 7 : Summary of the main requirements in terms of performance for the \coremfive  detectors.

	Detector noise	Absorption efficiency	Yield	CR induced data loss
\coremfive goal	5-$30\mathrm{aW}$/$\sqrt{\mathrm{Hz}}$	$>$50$\%$	$>$90$\%$	10$\%$

Table 8. Table 8 : Mass, Power and Heat budgets for the \coremfive  cryogenic system.

CORE Cryogenics: Engineering Budget
				Type of Cooler		PTC	JT $4K$	JT $2K$	CCDR
				Number of coolers		3	2	2	1						STAGES MASS
				Nb of ON coolers		2	1	1	1
			Planck							OFF	Detec	TOTAL		Resulting	Per
Reference	Component	T (K)	Cond.	Cond.	Rad. In.					Cooler	tors	Loss		Margins	Item	Cumulated
	VG 1	208		32.8	40.7								W
Passive	VG 2	124		4.2	12.4								W		29.9	119 kg
Cooling	VG 3	77		1.4	1.4								W		29.4
	VG 4 + Baffle	40,1		0.6	0.6								W		59.3
$80K$ Stage	5 Shells	82		120	475	4059	276	200	0	2052	0	3123	mW	30%	+20%	+20%
PTC						M=10%	M=20%	M=100%		1 PT + 2 JT					Margin	Margin
$15K$ Stage	PTC	15	$39.2\mathrm{mW}$	12	60	783	114	90	9	188	30	503	mW	56%	10.4	$29.9\mathrm{kg}$
PTC	+ R1 Shield		$97.5\mathrm{kg}$	Mass x 0.31	From $50K$	M=10%	M=20%	M=100%	M=50%	1 PT + 2 JT
$4K$ Stage	$4K$ JTC	4.5	$5.7\mathrm{mW}$	14.5	2.30		24		2.25	0.02	0.19	19.22	mW	25%	6.9	$19.5\mathrm{kg}$
JT	+ R2 Shield		7.63 kg	Mass x 2.5	From $20K$		M=20%		M=50%
$1.7K$ Stage	$1.7K$ JTC	1.65	$0.3\mathrm{mW}$	1.26	0.13			10	5.25	0.02	0.08	6.72	mW	49%	4.6	$12.6\mathrm{kg}$
JT	+ R3 Shield		$3.01\mathrm{kg}$	Mass x 4.2	From R2			M=33%	M=50%
$0.1K$ Stage	CCDR	0.1	NA	$\sim$0.0	$\sim$0.0				2.3		1.1	1.1	$\mu W$	112%	6.7	$8\mathrm{kg}$
CCDR				Intercepted	From R3				M=33%
Electrical Power incl. CDE (W)						900	120	120	50	TOTAL POWER (Coolers)+$100W$ Thermal Control						$1290W$
Cooler Mass incl. CDE						84	40	54	31	TOTAL MASS (Coolers)						$209\mathrm{kg}$
Cooler Mass with V-Grooves and Baffle										TOTAL MASS WITH V-GROOVES						$328\mathrm{kg}$

Table 9. Table 9 : CFHX section input data for the calculation of the CFHX temperature profiles shown in Figure  21 . The data consists of the section number, the length L cfhx subscript 𝐿 cfhx L_{\text{cfhx}} of the section, the diameter of the incoming liquid 3 He stream D i subscript 𝐷 i D_{\text{i}} , the diameter of the outgoing liquid 3 He- 4 He mixture stream D o subscript 𝐷 o D_{\text{o}} , an externally applied heat load Q ˙ load subscript ˙ 𝑄 load \dot{Q}_{\text{load}} to a thermal anchoring point at the cold end of the heat exchanger section with the exception of the last section where Q ˙ load = Q ˙ detector subscript ˙ 𝑄 load subscript ˙ 𝑄 detector \dot{Q}_{\text{load}}=\dot{Q}_{\text{detector}} , the distance L cfrp subscript 𝐿 cfrp L_{\text{cfrp}} between two thermal anchoring points, and the ratio A cfrp subscript 𝐴 cfrp A_{\text{cfrp}} / L cfrp subscript 𝐿 cfrp L_{\text{cfrp}} where A cfrp subscript 𝐴 cfrp A_{\text{cfrp}} is the cross section area of the 24 CRFP struts in parallel. The total length of the CFRP struts is 200   mm times 200 millimeter 200\text{\,}\mathrm{mm} , the distance between the thermal anchoring points on thermal screen at 1.7   K times 1.7 kelvin 1.7\text{\,}\mathrm{K} and the cold end of section 1 equals 80   mm times 80 millimeter 80\text{\,}\mathrm{mm} , and L cfrp subscript 𝐿 cfrp L_{\text{cfrp}} in section 4 is the distance between the thermal anchoring point at the cold end of section 3 and the focal plane. The CFRP struts are tubes with an outer diameter of 5   mm times 5 millimeter 5\text{\,}\mathrm{mm} and an inner diameter of 3   mm times 3 millimeter 3\text{\,}\mathrm{mm} .

Section	$L_{\text{cfhx}}$	$D_{\text{i}}$	$D_{\text{o}}$	${\dot{Q}}_{\text{load}}$	$L_{\text{cfrp}}$	$A_{\text{cfrp}}$/$L_{\text{cfrp}}$
	$m$	$\mathrm{mm}$	$\mathrm{mm}$	$\mu W$	$\mathrm{mm}$	$\mathrm{mm}$
0	0.1	0.2	0.2	0.0
1	1.9	0.2	0.2	0.0	80.0	3.77
2	3.0	0.4	0.4	0.0	40.0	7.54
3	3.0	0.4	0.4	0.0	40.0	7.54
4	3.0	0.4	0.4	7.0	40.0	7.54

Table 10. Table 10 : CFHX calculation output data for the input data shown in Table  9 . The data consists of the section number, the heat current Q ˙ cfrp,cold subscript ˙ 𝑄 cfrp,cold \dot{Q}_{\text{cfrp,cold}} through the CRFP struts and intercepted by a thermal anchor at the cold end of the heat exchanger section (for the last section it is the heat current to the focal plane), the externally applied heat load T load,cold subscript 𝑇 load,cold T_{\text{load,cold}} to a thermal anchoring point at the cold end of the heat exchanger section with the exception of the last section where Q ˙ load = Q ˙ detector subscript ˙ 𝑄 load subscript ˙ 𝑄 detector \dot{Q}_{\text{load}}=\dot{Q}_{\text{detector}} , the temperature T i,warm subscript 𝑇 i,warm T_{\text{i,warm}} of the incoming liquid 3 He stream at the warm end of the heat exchanger section, the temperature T i,cold subscript 𝑇 i,cold T_{\text{i,cold}} of the incoming liquid 3 He stream at the cold end of the heat exchanger section, the temperature T o,warm subscript 𝑇 o,warm T_{\text{o,warm}} of the outgoing liquid 3 He- 4 He mixture stream at the warm end of the heat exchanger section, and the temperature T o,cold subscript 𝑇 o,cold T_{\text{o,cold}} of the outgoing liquid 3 He- 4 He mixture stream at the cold end of the heat exchanger section.

Section	${\dot{Q}}_{\text{cfrp,cold}}$	${\dot{Q}}_{\text{load,cold}}$	$T_{\text{i,warm}}$	$T_{\text{i,cold}}$	$T_{\text{o,warm}}$	$T_{\text{o,cold}}$
	$\mu W$	$\mu W$	$K$	$K$	$K$	$K$
0		0.000	1.200	0.413	0.644	0.347
1	43.303	0.000	0.413	0.301	0.347	0.300
2	1.410	0.000	0.301	0.139	0.197	0.137
3	0.071	0.000	0.139	0.119	0.131	0.116
4	0.041	7.000	0.119	0.105	0.115	0.099

Table 11. Table 11 : Proposed MiniCORE  frequency channels. The sensitivity is calculated assuming Δ ​ ν / ν = 30 % Δ 𝜈 𝜈 percent 30 \Delta\nu/\nu=30\% bandwidth, 60% optical efficiency, total noise of twice the expected photon noise from the sky and the optics of the instrument at 85   K times 85 K 85\text{\,}\mathrm{K} . This configuration has 900 detectors.

Channel	Beam	$N_{\det }$	$\Delta P$	$\Delta I$
GHz	arcmin		$\mu K$$\cdot$arcmin	$\mu K_{\mathrm{RJ}}$$\cdot$arcmin
100	16.9	40	11.8	2
115	14.8	40	11.7	2.41
130	13.2	40	11.7	2.82
145	11.9	90	7.9	2.16
160	10.8	90	8.1	2.43
175	10.0	90	8.5	2.71
195	9.0	90	9.2	3.07
220	8.0	90	10.4	3.55
255	7.0	90	13.1	4.29
295	6.1	40	27.6	7.91
340	5.3	40	43.9	9.98
390	4.6	40	79	12.85
450	4.0	40	171	17.11
520	3.5	40	445.8	23.18
600	3.0	40	1397.1	31.47

Table 12. Table 12 : TRLs for the scientific instrument and main SVM systems

Component	Current	Heritage	TRL @ end
	TRL		of phase-A
telescope frame	9	Planck + Herschel heritage	9
telescope mirrors	9	SiC, D1.2m, Herschel heritage	9
thermal filters	4	used in current suborbital CMB exp.	6
plastic-embedded metal-mesh flat lenses	4	demonstrated in the lab	6
plastic-embedded metal-grid polarizers	4	used in current balloon CMB exp.	6
band-defining filters	9	Planck HFI heritage	9
waveguides	9	Planck HFI heritage	9
KIDs ()	3-4	demonstrated in the lab	6
KIDs ($\nu >110\mathrm{GHz}$)	5	used at mm-wave telescopes	6
		(IRAM / APEX)
cryogenic LNA	9	Herschel-HIFI heritage	9
readout electronics	5	used at the telescope with	6
		space qualified components
CCDR	3-4		6
$1.7K$ JT cooler	4		6
$4K$ JT cooler	4		6

Equations

$$z=\frac{c{r}^2}{1+\sqrt{1-\left(1+k\right)c^2{r}^2}}+\sum _{i=1}^n{a}_i{r}^{2i},$$

$$z=\frac{\frac{x^2}{R_x^2}+\frac{y^2}{R_y^2}}{1+\sqrt{1-(1+k_x)\frac{x^2}{R_x^2}-(1+k_y)\frac{y^2}{R_y^2}}}+A_{n,r}((1-A_{n,p})x^2+(1+A_{n,p})y^2{)}^n,$$

Full text

1 Introduction

The measurement of the polarization state of the CMB promises to shed light on the earliest phases of the evolution of the Universe, testing the cosmic inflation scenario, but poses difficult experimental challenges, requiring a polarimeter with very high sensitivity, exquisite control of systematic effects, and the ability to extract the tiny inflation-related signal from overwhelming polarized foregrounds.

In this paper we describe a space-based instrument, optimized to represent the ultimate experiment for probing cosmic inflation measuring CMB polarization (an objective which cannot be achieved by ground-based experiments alone, nor by simpler space-missions), while fulfilling the stringent requirements of a medium-class mission of the European Space Agency. We underline that also the lack of detection of primordial B-modes by CORE would have an impact on the current cosmological paradigm, since a large part of inflation scenarios would be ruled out.

This paper is part of a series describing the \coremfive (Cosmic ORigins Explorer) mission and its scientific context. Here we aim at an instrument baseline description with a level of detail adequate for starting a Phase-A study.

The \coremfive instrument inherits the legacy of Planck, as well as our previous proposals COrE and COrE+.

The goal of \coremfive is to detect unambiguously a tensor to scalar ratio $r$ as small as 1$\times$10*-3* (3$\sigma$ CL), even in the presence of complex polarized foregrounds. In fact, the Starobinsky model, R2 (Higgs) inflation, foresees $r>2\times 10^{-3}$. With this level of sensitivity, a null result would basically disfavour most of the large-field inflation models allowed by Planck (see the companion paper on inflation [1]).

This ultimate measurement is possible only from space and requires a mission that will map the CMB B-modes polarization over most of the sky, with an angular resolution of a few arcminutes and with a polarization survey sensitivity better than $2.5\text{\,}\mathrm{\SIUnitSymbolMicro K}$ per square arcminute pixel, after foreground removal (20 times better than the aggregated CMB polarization sensitivity of the entire set of Planck polarized detectors). This mission will collect virtually all the information about the Early Universe encoded in the CMB polarization.

The \coremfive instrument builds on the success of Planck and Herschel, re-using many of the subsystems and methods developed by the mm/submm community. The sensitivity requirements described above, combined with the requirement of internal control of polarized foregrounds, drives the dimension of the focal plane of the instrument. The proposed \coremfive baseline instrument is based on an array of 2100 cryogenically cooled, linearly polarized detectors at the focus of a 1.2 meter aperture telescope. The entire sky will be surveyed with 19 frequency bands, spanning the range 60 to 600 GHz. The spacecraft will be located in a large Lissajous orbit around the Sun-Earth L2 Lagrange point to keep the Sun, Earth and Moon well away from the line of sight at all times, and thus avoid that they pollute the scientific signal with unwanted far sidelobe contamination. The combination of three rotations of the spacecraft at different timescales provides an observation pattern such that each sky pixel is crossed frequently, and from many different directions. This scan strategy provides for a strong mitigation of systematic effects and would thus ensure optimal use of the high inherent sensitivity, especially for extracting the large angular scale signals.

With this implementation, \coremfive also addresses a broad range of other questions of prime scientific importance that cannot be answered by any other means than very accurate observation of the CMB polarization on all angular scales and over the near full sky. It will probe the distribution of clustered mass in the Universe through the observation of the lensing of CMB polarization due to dark matter structures between our telescopes and the last scattering surface. The reconstruction of the CMB lensing potential will provide high signal-to-noise-ratio maps of the distribution of dark matter at redshifts $z=1-3$ without recourse to biased baryonic tracers. In addition to providing a map of the dark matter integrated along the line of sight up to high redshift, this measurement, combined with cosmological constraints from Euclid, will constrain the sum of the 3 light neutrino masses with a statistical error of 3 meV, 5 times better than any single cosmological probe alone and sufficient to distinguish unambiguously between a normal neutrino hierarchy ($m_{1},m_{2}\ll m_{3}$) with a mass sum of approximately at least 60 meV, and an inverted hierarchy ($m_{3}\ll m_{1},m_{2}$) with a minimal mass sum of about 100 meV (see the companion paper on cosmological parameters [2]).

\coremfive

will also probe the distribution of hot gas up to redshifts $z=2-3$ by measuring the thermal Sunyaev-Zel’dovich effect, the inverse Compton scattering of CMB photons by energetic electrons. It will detect $\sim 50,000$ galaxy clusters extending to high redshift, more than 300000 clusters in combination with high-resolution ground-based surveys, and part of the hot baryons in the cosmic web. Combined with high resolution (2-3′) ground-based CMB data in atmospheric windows between 90 and $250\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ \coremfive will also detect the individual peculiar motions of $\sim 30,000$ galaxy clusters, thus directly measuring the cosmic velocity field at large redshift, a measurement that cannot be performed by any other means (see the companion paper on clusters science [3]).

At frequencies above 350 GHz, where sky signals are dominated by emission from thermal dust and point sources, \coremfive will for the first time provide full sky, high quality polarization maps. These maps will provide astrophysicists with the most detailed view yet at the Galactic magnetic field, unveiling its role in creating the filamentary, web-like, structures where stars form. Magneto-hydrodynamical turbulence will be revealed with unprecedented statistical information characterizing the energy injection and energy transfer down to dissipation scales. The spectral dependence of the polarized signal from dust will be measured with high accuracy across the sky, furthering our understanding of the nature of interstellar dust. Moreover, together with the corresponding high sensitivity intensity maps, these observations will discover and characterize a large number of new galactic and extragalactic point sources and also measure their polarization properties.

Achieving the \coremfive cosmological science programme will require accurate separation of the many astrophysical foregrounds as well as exquisite control and assessment of systematic errors. The \coremfive instrument configuration and calibration procedure are designed to generate all the data needed for this assessment. In particular, the \coremfive array will include a large number of closely packed spectral bands for optimal monitornig of polarized foreground components. Simulations based on the full presently available information, as summarized in the Planck Sky Model [4], and analyzed using state-of-the-art component separation algorithms show that \coremfive will achieve its science objectives and that the design includes redundancy and margin for error. This is described in detail in the “mission” paper of this series [5].

The \coremfive ultra-high sensitivity maps of the three Stokes parameters I, Q, and U in 19 frequency bands will serve as a long standing legacy and a reference dataset for the microwave and submillimeter emission in both intensity and polarization over the full sky. Astrophysicists will mine these maps for decades. In addition to the compelling science deliverables we know about today, even more exciting are all the discoveries buried in these maps, and that we can not yet imagine, nor describe.

Other missions with similar targets have been proposed in the past. Apart from our previous proposals COrE [6] and PRISM [7], a set of CMB polarization mission have been proposed in the USA (see e.g. [8], [9]). In Japan, the LiteBIRD proposal is currently in phase-A [10]. This reflects the awareness of the scientific community that an unambiguous detection and characterizaiton of B-mode polarization from inflation cannot be achieved from ground-based measurements alone. There are two main problems: the need for a large sky coverage (the primordial B-mode signature in the Reionization peak is at the largest angular scales) and the need for a wide frequency coverage (to monitor overwhelming Galactic polarized foregrounds). Ground-based measurements suffer in both cases. Atmospheric noise, following a Kolmogorov statistics, is severe at large angular scales, and anisotropic ground pickup may seriously contaminate the detected signal at these scales. Atmospheric transmission and stability rapidly become a serious limitation at frequencies higher than 250 GHz, even in the best observing sites on Earth. Coordinated ground-based efforts can do extremely well in the well-known 40, 90, 140 GHz atmospheric windows and at intermediate and small angular scales [11], but they have very serious limitations at higher frequencies (where the polarized dust foreground must be monitored) and at large angular scales.

The \coremfive instrument concept described in this paper has been conceived to minimize complexity and single-point criticalities, maximizing reliability in development, test, commissioning and operation. It uses a well developed, mirrors-only cross-Dragone telescope, with mirrors smaller than the mirrors used in Planck. It uses, as a baseline, simple single-frequency single-polarization detectors (dual-polarization is considered only for the lowest frequencies, as explained further on). It does not use a polarization modulator, avoiding critical cryogenic mechanisms. Exploiting the good angular resolution provided by the telescope, it is possible to synthesize in the analysis perfectly circular observation beams, so that the polarization of the sky can be measured simply by rotating the entire instrument. With a smaller aperture, this would not be possible, and the added complexity of a polarization modulator would be required to separate real sky polarization and signal produced by the rotation of an elliptical beam. In addition, the angular resolution provided by the 1.2m reflector allows for internal delensing of the data, a real plus when looking for such a low level of B-mode polarization [12].

In Table 1 we anticipate the baseline configuration for the multi-band polarimeter, and its performance.

The rest of the paper is organized as follows: in the second section we describe the different telescope options which have been considered, taking into account the size constraints coming from the launcher, the need for sufficient angular resolution, the need for a wide, high Strehl ratio, and possibly planar and telecentric focal plane. In the third section we discuss advantages and disadvantages of a mechanical polarization modulator, our baseline choice of avoiding its use, and our approach in case it is found to be required in the phase-A study. In the fourth section we describe the general design of the focal plane array and its optimization in terms of size, number of detectors, weight of the different bands. In the fifth section we describe the selected detectors technology (Kinetic Inductance Detectors) and its implementation in the different frequency bands; the optical coupling and the readout electronics. In the sixth section we describe the cryogenic system. In the seventh section we describe the plan to calibrate the instrument. In section eight we describe a downscoped configuration of the instrument, with reduced aperture of the telescope (0.8m), reduced number of detectors (900), covering a reduced frequency range (100 to $600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$). We conclude comparing our baseline instrument to other proposals, in terms of figure of merit for the measurement of CMB B-modes.

2 Telescope

A combination of science requirements and practical constraints drive the choice of the telescope. The science requirements are (i) a focal surface with sufficiently large diffraction limited field of view (DLFOV) to accommodate the 2100 detectors, (ii) entrance aperture size of $1.2\text{\,}\mathrm{m}$ to give a resolution between 7’ and 8’ at $145\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, and (iii) low instrumental polarization. Cost, the space mission implementation, and experience with previous mm-wave telescopes suggest a compact, low mass telescope, and reflectors that are sufficiently small to be manufactured as a single segment of silicon carbide (silicon carbide has been space proven with the Herschel and Aladin missions). A quantification of the level of instrumental polarization tolerable with \coremfive is awaiting a more comprehensive study of systematic uncertainties.

The baseline detector technology for \coremfive also imposes constraints on the optical design. \coremfive will implement arrays of lens-coupled kinetic inductance detectors fabricated on flat wafers. Therefore, the focal surface should be locally flat and telecentric. The optical design needs to provide a focal surface that is either planar, or can be tiled with flat detector wafers.

We investigated two designs: a two-mirror Gregorian, and a crossed-Dragone. Both designs have rich heritage with CMB experiments [13]. Most recently, WMAP and Planck used off-axis Gregorian telescopes. Tran et al. [14] showed that with equal aperture sizes a crossed-Dragone system can provide larger DLFOV compared to a Gregorian. (We follow standard convention designating an area in the focal surface ‘diffraction limited’ when the Strehl ratio is larger than 0.8.)

2.1 Gregorian Design

2.1.1 All Reflective Design

The basic two-mirror Gregorian design has a parabolic primary and an ellipsoidal secondary. In Gregorian-Dragone designs, astigmatism or both astigmatism and coma are canceled to first order [13]. We began our analysis with a Gregorian-Dragone design in which astigmatism is canceled to first order [15] and used the optimization features available with a commercial ray tracing program111CodeV by Synopsys Inc. to increase the DLFOV over the frequency range between 60 and $600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$. Each of the reflector surfaces was described as a figure of revolution $z(r)$ by

[TABLE]

where $k$ is the conic constant and $c$ is the radius of curvature. Surfaces for which $a_{i}=0$ for all $i$ are conics of revolution. During the numerical optimization we let all the parameters in Equation 2.1 vary, as well as the parameters defining the relative orientations of the surfaces. The parameters of a system that gave a sufficiently large DLFOV are given in table 2. The system is shown in figure 1. We note that the focal surface is not flat. It is a shallow cone. We could not find a solution with a sufficiently large DLFOV and flat focal surface.

This design has a $12\text{\,}\mathrm{\SIUnitSymbolDegree}$, $40\text{\,}\mathrm{c}\mathrm{m}$ field of view at $60\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$. The configuration is compact, and the system is conducive to strong baffling. The instrumental polarization across the entire focal plane, calculated at $145\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ by assuming $n,k=1445,1455$ for aluminum [17], are below 0.05 %, but polarization rotation exceeds $6\text{\,}\mathrm{\SIUnitSymbolDegree}$ at the azimuth edge of the focal surface. There is no polarization rotation along the symmetry plane of the system; see table 2. A significant drawback for this design is the non-flat, non-telecentric focal surface. We concluded that if a Gregorian design is to be used, it requires additional image correction.

2.1.2 Reflective/Refractive Design

Figure 2 shows a Gregorian system with one additional alumina lens ($n=3.1$). Table 3 gives the parameter of the system. It has been optimized in a similar fashion to the one described in Section 2.1.1. The focal surface is flat and nearly telecentric; the largest deviation from telecentricity is at the negative elevation edge (the lower part) of the FOV at a level of 4.1 degrees. This design provides a $9.2\text{\,}\mathrm{\SIUnitSymbolDegree}$ $\times$ $9.5\text{\,}\mathrm{\SIUnitSymbolDegree}$, $36\text{\,}\mathrm{c}\mathrm{m}$ $\times$ $36\text{\,}\mathrm{c}\mathrm{m}$, DLFOV at $60\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$. These values are smaller than those for the all-reflective system. A more robust comparison that takes the focal ratios into account also shows that this system’s performance falls short of the all-reflective one; see the lines giving the number of $F\lambda$ at $160\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ in tables 2 and 3. We could not fit all 2100 of CORE’s detectors in the focal plane.

The lens is $44\text{\,}\mathrm{c}\mathrm{m}$ in diameter with an optical aperture diameter of $42\text{\,}\mathrm{c}\mathrm{m}$ in diameter, and a mass of $6\text{\,}\mathrm{k}\mathrm{g}$. The system is compact and the aperture of the lens causes vignetting for fields near the edge of the focal plane, as can be seen in figure 2. Assuming tophat illumination of the primary, the throughput for this edge of the focal plane is reduced by 7 %. Vignetting reduces the throughput for the fields at both azimuth edges of the focal plane by 6 %.

The anti-reflection coating (ARC) of the lens presents a challenge. Broad, $\Delta\nu/\nu=160$ % ARC are required with differential reflection sufficiently small to give low instrumental polarization. Although the development of broad-band ARC is an active area of research [18, 19, 20], the development of this bandwidth ARC on alumina has not been demonstrated, let alone with low instrumental polarization. In table 3 we give expected levels of instrumental polarization assuming an uncoated alumina lenses. The levels are substantial but are likely over-estimates. The magnitude of polarization rotation in this system is similar to that in the all-reflective system.

In summary, the optical performance of the reflective/refractive system falls short of the requirements and the ARC presents a technical risk.

2.2 Crossed Dragone

The crossed-Dragone configuration more naturally provides a flat, telecentric focal plane and therefore it is a good match to focal planes with arrays of detectors that are micro-fabricated on flat silicon wafers [14]. The configuration has heritage with the QUIET and ABS CMB polarization instruments [21, 22], and is currently the baseline for the JAXA-led LiteBIRD mission [23]. It is being considered for the CMB-S4 project [24].

For \coremfive we started with the $40\text{\,}\mathrm{c}\mathrm{m}$ LiteBIRD telescope, scaled it up to $1.2\text{\,}\mathrm{m}$ aperture, and re-optimized in a process similar to that described in Section 2.1.1. The design included anamorphic surfaces, that is, surfaces with different radii of curvature in two orthogonal directions. The equation describing the surface $z(r)$ is

[TABLE]

where $R_{x}$ and $R_{y}$ are the radii of curvature, $k_{x}$ and $k_{y}$ are the conic coefficients, and $A_{n,r}$, $A_{n,p}$ define the higher order deformation coefficients with $n=2,3,4,5$. When the higher order coefficients are zero this type of surface is called biconic. Figure 3 shows the system and Table 4 gives its parameters.

We found that with only two mirrors the system was too big to fit within the satellite envelope. Therefore we added a flat tertiary fold mirror to make the system more compact. This flat mirror could be replaced by a reflective polarization modulator, if polarization modulation is deemed necessary. Figure 4 gives solid model views of the telescope integrated within the payload module and sunshields. The telescope was rotated about the boresight to put the focal plane close to the main satellite body, reducing the need for additional supports. This was also the only orientation in which the telescope was completely shadowed by the sun-shields.

The focal plane is flat with a DLFOV greater than 12 degrees across at $160\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$. It gives approximately 4 times the number of $F\lambda$ units at $160\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ compared to the all reflective Gregorian system, and a larger factor when compared to the partially refractive Gregorian. It is telecentric to within $3.5\text{\,}\mathrm{\SIUnitSymbolDegree}$ over the entire FOV, and within $2\text{\,}\mathrm{\SIUnitSymbolDegree}$, which is 10 % of the beam divergence angle at the focal plane, at field angles of less than $2.8\text{\,}\mathrm{\SIUnitSymbolDegree}$ . Experience indicates that the system can be further optimized for even stronger telecentricity at the expense of DLFOV area at the edges of the focal plane that are currently not used. The instrumental polarization induced by the reflectors is a factor of 2-3 larger than the reflective Gregorian design, but still below 0.1%. There is significantly lower polarization rotation, a consequence of the flatter reflecting surfaces.

An initial challenge with the crossed Dragone system was baffling of the focal plane to reject stray light. To improve baffling we embedded the portion of the DLFOV that is used for detectors inside a ‘bucket’, and a collar was added around the entrance aperture of the system; the bucket and collar are shown in grey figure 4. The default is all the paylod, including the collar, at $40\text{\,}\mathrm{K}$.

With these additions there is no direct view from the focal plane to the sky. The focal plane area populated by detectors is bounded by the blue dash-dot line in Figure 3 and is smaller than the total available DLFOV.

We analyzed the crossed-Dragone design using physical optics to determine the far field beam shape at $145\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ for various positions on the focal plane. We assumed a Gaussian beam propagating from the focal plane outward. The Gaussian beam had a waist $w_{0}=0.216\sqrt{T_{e}\left(dB\right)}\text{F}\lambda=$5.14\text{,}\mathrm{m}\mathrm{m}$$ with an edge taper of $-20.5\text{\,}\mathrm{d}\mathrm{B}$ on the primary mirror and $\text{F}=2.54$. For this first round of analysis we did not include the baffling structures.

Figure 5 shows representative orthogonal cuts of the far-field beams at $\pm 3^{\circ}$ off-axis along the $x$ axis of the telescope (see figure 3). These field positions correspond to locations that are $15\text{\,}\mathrm{c}\mathrm{m}$ from the center of the focal plane in the horizontal directions in the right panel of figure 3. We present results for only one polarization. The orthogonal polarization, which was also propagated to the sky, is co-located and the differential gain between the two polarizations is $-41\text{\,}\mathrm{d}\mathrm{B}$ over the main beam.

We fit two-dimensional Gaussian to the far-field beam patterns to extract full-width at half-maxima (FWHM) from which we calculate beam ellipticities. Ellipticity is defined as $1-b/a$, where $a$ and $b$ represent the larger and smaller FWHM, respectively. Cross-polarization levels are low, $-48\text{\,}\mathrm{d}\mathrm{B}$ at a maximum for the beams at $\pm 3^{\circ}$, but the co-polar components of the orthogonal polarizations show some aberration and have ellipticities of 6 and 8 % for the -3*∘* and +3*∘* directions, respectively. A summary of the characteristics of the beams at several field locations is given in table 5.

The physical optics study of the telescope performance for a variety of focal plane positions and frequencies is ongoing. There is also initial work currently underway to simulate the far sidelobes and examine the impact of the shielding on the optical performance.

2.3 Telescope Summary

WMAP and Planck used off-axis Gregorian telescopes. However, their useable DLFOV was smaller than that of \coremfive and their detector technology is no longer suitable for modern instruments that use thousands of focal plane elements. Such instruments require a large, flat, and telecentric focal plane. The two mirror Gregorian falls short off the requirements. We attempted to populate this design with $10\text{\,}\mathrm{c}\mathrm{m}$ edge-to-edge flat tiles that were locally telecentric at the center of the tile. However, the optical performance at the edge of these tiles failed to be diffraction limited.

The two-mirror Gregorian with the alumina lens gives an optical performance that is close to the requirements but the anti-reflection coating introduces a technology risk, and a spurious polarization risk. We selected the crossed-Dragone as the baseline because it gives a large, flat, telecentric DLFOV, and it fits within the satellite envelope. A full analysis of the system is ongoing. Table 6 summarizes the advantages and disadvantages of the systems we analyzed.

3 Polarization Modulator

In \coremfive polarization modulation is achieved by means of an optimized telescope pointing strategy, leading to frequent scans of the same sky pixel with different orientations of the polarization sensitive detectors, as described in the Mission paper of this series [5]. This approach has the overwhelming advantage of simplicity and reliability, due to the absence of moving parts in the instrument.

However, the technology of active CMB polarization modulators has significantly advanced in recent years, thanks to an ESA funded project (Large radii Half-Wave Plate (HWP) development, ESA Ref. T207-035EE) focusing on developments for future CMB satellite missions. A novel type of Reflective Half Wave Plate (R-HWP) was successfully manufactured and tested. It has high polarization modulation efficiency across a 150 % bandwidth at incidence angles up to $45\text{\,}\mathrm{\SIUnitSymbolDegree}$ [26, 27]. The design can be further improved to achieve the 164 % bandwidth required for \coremfive. The R-HWP should be inserted in the beam path of polarization-sensitive detectors and rotated around an axis orthogonal to its plane to provide polarization modulation. The position of the flat tertiary mirror in the \coremfive optical design is a natural place to locate a rotating R-HWP, should it be deemed necessary to include polarization modulation. The target of the aforementioned ESA project is develop facilities capable of manufacturing metre-sized devices. This will allow the manufacturing of a R-HWP fitting the size of the \coremfive tertiary mirror ($1.0\text{\,}\mathrm{m}$ $\times$ $0.7\text{\,}\mathrm{m}$).

A cryogenic rotation mechanism is required to operate such a modulator. Two broad classes of devices have been developed: steppers and spinners. In the former, the HWP is stepped across a set of angular positions. Each angular position is held for some integration time (e.g. for one full spin of the instrument) before stepping to the next one. In the latter, the HWP is continuously spun, encoding the polarization information at high frequency (4$\times$ the mechanical rotation frequency).

A rotator of the first type was described in [28] and was flown on the PILOT balloon-borne experiment [29]. The average dissipation of the device, due to friction in the cryogenic bearings, is a few mW. A rotator of the second type, based on magnetic levitation of the HWP, was described in [30], has been flown on the EBEX balloon-borne experiment [31], on the SPIDER experiment [32], and a similar system represents the baseline for the LiteBIRD satellite [33].

The advantage of a continuously spun HWP is the high modulation frequency (order of $10\text{\,}\mathrm{H}\mathrm{z}$) of the polarization information, far from the frequency region affected by 1/f noise. The disadvantage is that eddy currents can heat-up the HWP: this heat can only be radiated away, quite inefficiently at low temperatures. In the case of the stepped HWP the modulation frequency is much lower (order of 0.01-$0.1\text{\,}\mathrm{H}\mathrm{z}$), but the HWP can be thermally connected to the cold reference temperature by means of flexible copper straps.

Simplicity and reliability considerations drove the decision of not using a polarization modulator in \coremfive. However, end-to-end simulations including systematic effects from the HWP on one side, and from the spin/precession scan strategy on the other, will be performed anyway during phase-A, to confirm quantitatively this choice.

4 Focal Plane

4.1 Mission Constraints

The \coremfive instrument is optimized to maximize its mapping speed by means of the widest possible Focal Plane Array (FPA) of diffraction-limited detectors. The total number of detectors is limited by several heterogeneous factors:

$\vskip 3.0pt plus 1.0pt minus 1.0pt\noindent\bullet$ the diffraction limited field of view of the telescope (which in turn depends on the size and configuration of the telescope, as described in Section 2);

$\vskip 3.0pt plus 1.0pt minus 1.0pt\noindent\bullet$ the heat load on the cryogenic system (the larger/heavier the FPA, the stronger and conductive the supports connecting it to the higher temperature stage of the cryogenic system, and the larger the integrated radiative load);

$\vskip 3.0pt plus 1.0pt minus 1.0pt\noindent\bullet$ the maximum allowed data rate;

$\vskip 3.0pt plus 1.0pt minus 1.0pt\noindent\bullet$ the electrical power dissipated on the readout electronics, both at room temperature (impacting on the power budget) and in the cryogenic section (impacting on the power lift budget of the cryo system).

For these reasons, optimization of the FPA is a nontrivial procedure. Starting from the available bay size in the space carrier for a medium-size mission, we have targeted the optimization to a diameter of the FPA of $\sim$ $0.5\text{\,}\mathrm{m}$ at $0.1\text{\,}\mathrm{K}$, and verified that we are at the edge of what can be obtained in terms of telescope and cryogenic system (cfr Section 2 and 6).

The next step of the optimization is the division of the available FPA area into the different frequency bands of observation. Covering a wide frequency range is the key to separate CMB polarization from a number of polarized foregrounds. The range $60\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ to $600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ covers both low frequencies where diffuse synchrotron radiation from our Galaxy is dominant, CMB frequencies where the CMB signal is maximum, and high frequencies, where diffuse emission from interstellar dust is dominant. The \coremfive FPA covers this range with 19 frequency bands. The number of bands was selected to have a number of independent channels larger that the number of parameters required in a first-order description of all the relevant foregrounds. The optimization of the fractions of the FPA area assigned to the different channels has been carried out under the assumption that the detectors of a given frequency channel are sensitive to a wide band ($\Delta\nu/\nu\sim 30\%$, see Figure 6), and are limited by the photon noise associated with the incoming background power. This corresponds to a few to tens of aW/$\sqrt{\rm Hz}$, depending on the channel considered. The figure of merit of the optimization is the survey sentivity for CMB polarization signals, in $$\text{,}\mathrm{\SIUnitSymbolMicro K}$\times$ arcmin, once the foreground removal procedure has been carried out.

The outcome of these optimizations is that the \coremfive instrument will be equipped with a total of 2100 detectors (cfr Table 1), whose noise will not exceed the photon noise associated with the incoming background power. In the baseline configuration high-TRL single-band single-polarization pixels will be adopted, for all but the lowest frequencies ($\nu\leq$ $115\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$), where the use of dual-polarization sensitive pixels is envisaged. The coupling optics and the detectors for all of the pixels occupy a cylindrical volume, $50\text{\,}\mathrm{c}\mathrm{m}$ in diameter and $5\text{\,}\mathrm{c}\mathrm{m}$ tall, which is cooled at $0.1\text{\,}\mathrm{K}$ for optimal operation of the detectors (see Figure 7). Detectors in the focal plane are arranged in tiles, each one including sensors operating in the same frequency band, and placing the highest frequency band tile in the center of the focal plane, where the optical quality is best. The general arrangement is shown in Figure 8.

4.2 Radiation Coupling

Techniques to achieve the desired radiation coupling while respecting the mass and volume constraints imposed by the mission framework described in Section 4.1 are currently available and well developed within the \coremfiveConsortium.

One of the fundamental constraints driving the dimensioning of the focal plane is the acceptable spillover fraction, which in turn might have a different impact depending on the temperature of the telescope enclosure. This quantity must be small enough in such a way that the photon noise from the black payload alone is less than half of the contribution coming from the sky and from Planck-type mirrors together. The sky brightness is a superposition of CMB, Galactic Dust (a greybody at $18\text{\,}\mathrm{K}$, with $\beta=1.7$, corresponding to the cleanest 90$\%$ of the $857\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ Planck sky map), Far-Infrared Background (a greybody at $17\text{\,}\mathrm{K}$, with $\beta=0.96$ and amplitude $0.8\text{\,}\mathrm{M}\mathrm{J}\mathrm{/}\mathrm{s}\mathrm{r}$ at the pivot frequency of $1.87\text{\,}\mathrm{T}\mathrm{H}\mathrm{z}$) and Zodiacal light (a greybody at $200\text{\,}\mathrm{K}$, with $\beta=0.43$ and amplitude $23.4\text{\,}\mathrm{M}\mathrm{J}\mathrm{/}\mathrm{s}\mathrm{r}$ at the pivot frequency of $5\text{\,}\mathrm{T}\mathrm{H}\mathrm{z}$) contributions. The telescope, at a temperature of $40\text{\,}\mathrm{K}$, is assumed to have a frequency dependent emissivity scaling as $\sqrt{\nu}$. For a $40\text{\,}\mathrm{K}$ black payload, the optimised edge taper ranges from about $17\text{\,}\mathrm{d}\mathrm{B}$ at $60\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ to about $27\text{\,}\mathrm{d}\mathrm{B}$ at $600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ (assuming a Gaussian telescope illumination), and its values for the different channels are plotted in Figure 9, together with the corresponding overall photon noise. The illumination beam waist, for a given edge taper level $T_{e}({\rm dB})$ and telescope focal number ($F$), is given by $\omega_{0}=0.216\sqrt{T_{e}({\rm dB})}F\lambda$ [34]. For our optimised $T_{e}$ values, the diameter of the diffractive spot is in the range $1.8-2.2F\lambda$.

The beam-forming elements we will use to illuminate the telescope according to the above criteria are of two different kinds, depending on the frequency:

• •

At frequencies $\leq$ $220\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, planar lenslets based on a metamaterial concept (see Figure 10) are a promising solution in terms of optical performance, and being based on the successful metal-mesh technology well consolidated for filter production, they rely on a solid know-how [35]. Since their thickness is comparable to $\lambda$ and their density is the one of polypropylene, their mass is slightly lower than 1 kg to cover all these bands. These planar lenslets are illuminated by a waveguide section which feeds a planar OMT for the Low Frequencies.

• •

The higher-frequencies ($255\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ and above) are based on antenna-coupled MKIDs, where the beam forming is achieved by means of a slot antenna endowed with a lenslet. These devices are fabricated on a monolithic Si substrate to which we mount, using a proven wafer bonding technique, a commercially available Si lens array fabricated using laser ablation. A parylene-C coating is to be applied to minimize reflection losses. Note that the lens-antenna coupling, including the AR coating, used for these MKIDs was used as well for the Herschel-HIFI band 5 and 6 mixers [36].

5 Detectors

In order to minimize the complexity of the system, one single detector technology will be chosen to cover the full 60-$600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ frequency range. Microwave Kinetic Inductance Detectors (MKIDs) are currently the most advanced solution at the European level in terms of TRL. They also have distinct advantages that make them stand out from other concurrent technologies. These include their intrinsic frequency domanin multiplexing (FDM) and the fast response time, not limited by thermal constraints. Furthermore, different tiles of MKIDs, for example containing the detectors of different sub-bands, can be fabricated separately and easily interconnected during the assembly of the FPA. This represents an additional advantage of the chosen technology, as it makes it possible to share the development and fabrication effort among different institutions. MKIDs have therefore been adopted as the baseline detectors for \coremfive. To limit the radiative background on the resonators, from the telescope and its environment, high performance feed optics are used.

5.1 Detection Technology

Over the last years, these detectors have been successfully used in many ground-based EU-lead experiments. The NIKA camera ([37] [38]), installed at the IRAM $30\text{\,}\mathrm{m}$ telescope in Spain, has been the first KID-based instrument to conduct on-the-sky observations. NIKA showed state-of-the-art performances using Aluminum (Al) Lumped Element KIDs (LEKIDs). Its follow-up instrument, NIKA2 ([39] [40]), has a total of more than 3,000 detectors over two bands, covering the range 100-$300\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, and is currently undergoing the final commissioning phases. Polarization sensitivity in the band centered at $240\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ is achieved using a wire-grid polarizer and two separate arrays, one for each polarization. At higher frequencies, the A-MKID222http://www3.mpifr-bonn.mpg.de/div/submmtech/bolometer/A-MKID/a-mkidmain.html project is being commissioned at the focal plane of the APEX telescope, in Chile. This camera has a total of 25,000 KIDs split between two bands, centered at 350 and $850\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$. In parallel to these ground-based missions, the FP7 project SPACEKIDS has been carried out, with the aim of optimizing KIDs for space applications. The results of this project, and of various laboratory measurements, confirm that MKIDs can meet the requirements of the \coremfive mission, resumed in Table 7. In particular, photon noise limited performance has been shown under optical loads representative of the mission [41] [42]. Furthermore, the tests conducted irradiating MKIDs with ionizing particles have demonstrated their very low susceptibility to Cosmic Rays hits [43].

An overview of the current maturity level of MKIDs in the three main frequency ranges composing the FPA (Low Frequencies, CMB Frequencies, and High Frequencies) is given in the dedicated sections. The details of the design and materials to be adopted in each case will be determined by trade-off studies to be carried out during Phase A.

5.2 Low Frequencies (channels: 60 GHz - 115 GHz):

In MKIDs, the lowest energy that can be detected is determined by the superconducting gap of the material used for realizing the resonator. Thin Al films have proven to be the best choice for the frequency band between 110 and $850\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ (see NIKA2 on the IRAM $30\text{\,}\mathrm{m}$ and AMKID camera on APEX), and have been undergoing intense developments over the last years. However, the use of Al results in a superconducting cut-off at around $110\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ and therefore is not suitable for the \coremfive bands covering the 60 to $110\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ frequency band.

As a consequence, these bands are at present the less mature ones, and will need the strongest development effort during the phase A. In particular, new materials or configurations have to be adopted. The main route for achieving sensitivity in the low frequency bands will be the use of LEKIDs made of superconducting multilayers: the proximity effect[44] allows in this case to tune the critical temperature, and thus the cut-off frequency, by appropriately choosing the materials composing the multilayer and their thickness. The limited number of pixels available for the LF bands also poses a challenge, as on-chip polarization sensitivity must be achieved, implying a further development effort.

As far as the band coverage is concerned, the first measurements conducted on a Ti/Al bilayer have given promising results  [45][46]. As shown in the left panel of figure 11, a simple $10\text{\,}\mathrm{n}\mathrm{m}$ Ti/$25\text{\,}\mathrm{n}\mathrm{m}$ Al bilayer already shows an absorption well adapted to the 80-$120\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ range [45] [47]. In the measured array the mean pixel noise under a $300\text{\,}\mathrm{f}\mathrm{W}$ optical load was around $20\text{\,}\mathrm{a}\mathrm{W}$/$\sqrt{\mathrm{Hz}}$, which is already within a factor 4 of the photon noise level expected at these frequencies. The end-to-end optical efficiency of the system, including the pixel absorption efficiency, was estimated to be above 30$\%$.

Different paths are open in order to meet the \coremfive requirements and will be investigated during phase A:

• •

Band Coverage: to obtain lower cut-off frequencies and thus be able to cover the full \coremfive LF bands, different Ti/Al thicknesses, as well as trilayers such as Ti/Au/Al, will be explored. The latter has already demonstrated a cut-off at around $60\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, as required by \coremfive (right panel of Figure 11). We note here that the decrease in the Tc of the LEKID is associated with a decrease of their working temperature, and these detectors will most probably need to be operated at around $120\text{\,}\mathrm{m}\mathrm{K}$ or below. However, it is worth noting that lower Tc will also result in an increase in responsivity.

• •

Detector Noise: the values reported in [45] have been obtained using pixels that had not been conceived for low optical backgrounds. Furthermore, also the optical configuration was sub-optimal. Thus, an optimization of the pixel design (for example in terms of film thickness and coupling to the readout line) and the maximization of the optical coupling should easily allow to fill the gap between the current performance and the desired goal.

• •

Polarization Sensitivity: To obtain on-chip polarization sensitivity, different solutions will be tested. These include: a) a bi-array structure, in which two arrays are superpoposed and separated by a polarizing grid. The first array will be sensitive to one polarization and the second to the orthogonal one (figure 12, left). b) On-wafer planar Ortho-Mode Transducer (OMT) designs coupled to LEKIDs, to benefit from their very low expected cross polarization level (Figure 12, right). c) Optical separation of the two polarizations thanks to the development of dedicated multi-mesh flat lenses, capable of focalizing the two orthogonal polarization on different spots of the focal plane.

5.3 CMB Frequencies (channels: 130 GHz - 220 GHz):

The frequencies near the peak of the CMB polarization can be detected exploiting Aluminum LEKIDs, a technology consolidated by the developments carried out in several laboratories in Europe and already demonstrated on the field thanks to the the NIKA and NIKA2 instruments, installed at the IRAM 30-m telescope [37][39]. The pixel design adopted for NIKA2  [49] is based on a particular implementation of the LEKID, in which the meandering inductor has an Hilbert fractal shape  [50]. This solution is ideally suited for full-power measurements, as the Hilbert antenna efficiently absorbs both polarizations.

The NIKA2 pixels have shown excellent performance for the typical conditions of a ground-based experiment, and are already photon-noise limited under medium optical backgrounds [42]. The very same pixels, operated under optical loads representative of a CMB mission ($\sim$500 fW/pixel), have shown a mean noise level of 30 aW/$\sqrt{\mathrm{Hz}}$ and an end-to-end optical efficiency of 30$\%$  [46]. As in the case of the low frequency bands, the noise level is already within a factor $\sim$4 of the \coremfive requirements, and an important margin for improvement is granted by the different design parameters that can be optimized to account for the lower optical load.

In the implementation foreseen for the \coremfive mission, the resonators are coupled to incoming radiation through a combination of a plastic-embedded-mesh flat lenses (in the focal plane) and a short section of a waveguide, opening in a cavity surrounding the resonator (see Figure 13). This arrangement allows for efficient coupling with a lighter optical system with respect to horn-coupled LEKIDs. A polarization sensitivity upgrade can be envisaged by means of a layer of plastic-embedded metal-wire grids located in the focal plane, stacked on the band-defining embedded-mesh filters layer and on the flat lenses layer.

5.4 High Frequencies (channels: 255 GHz - 600 GHz):

The high frequency detectors for \coremfive are envisioned to be made from lens-antenna coupled hybrid MKIDs. The device consists of a meandering coplanar waveguide (CPW) $\lambda/4$ resonator made of NbTiN on a high resistivity Si substrate. The resonator has a wide section coupled weakly to a common readout line and a narrow section in which the central line is made of aluminum, which is shorted to ground at the resonator end. The length of the resonator sets the readout frequency of the MKID, the radiation coupled to the device is determined by the antenna located at the shorted end of the resonator. Radiation coupled to the antenna is injected in the Al-NbTiN narrow line, where it is absorbed in the aluminum at frequencies exceeding its gap frequency (\nu>$$90\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}). There are no losses in the NbTiN ground plane since NbTiN has a gap frequency of $1\text{\,}\mathrm{T}\mathrm{H}\mathrm{z}$, the use of NbTiN and Al therefore makes for an excellent, loss-free device at frequencies between $90\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ and $1\text{\,}\mathrm{T}\mathrm{H}\mathrm{z}$. An image of a single hybrid MKID, with an antenna optimized for single polarization radiation coupling around $350\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, is shown in Figure 14(a). For CORE we envisage to use a monolithic array for each frequency band, shown schematically in Figure 15(a). To allow efficient radiation coupling the detector array is coupled to a Si lens array using a well-tested bonding process. The cross section of this assembly is schematically shown in Figure 14(b). Alignment is done using alignment marks etched in the SiN as shown in panel (c). Note that we use at the wafer frontside, i.e. in between the lens array and the detectors, a mesh layer of Beta-phase Ta, with a gap frequency of \sim$$50\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}. This layer has two important functions: it reduces cosmic ray effects and absorbs stray radiation in the detector wafer. A 880 pixel assembly is shown in Figure 15(b). These devices have shown background limited performance in combination with a high radiation coupling efficiency using a single-polarized, narrow-band twin slot antenna at $350\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, see [51], and at $850\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, see [52]. We reproduce in Figure 15(c) the result from [51], making clear that we are comfortably background limited at $350\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ at the power levels expected for the instrument.

To adapt the current technology for the high frequency bands of \coremfive only very limited engineering effort is required. i) We need to make detectors for each frequency band, which requires a limited extrapolation to $255\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ from the demonstrated systems (operating at $350\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ and $850\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$) and interpolation for all other bands. ii) We need to optimize the lens-antenna design for minium spillover and maximum coupling, similar as done for the band 6 of Herschel-HIFI, which has used the same lens-antenna design principle as we will do. iii) We need to make lens arrays with larger lenses. Options here are laser machining, as we currently do, by an external commercial partner (Veldlaser) or mechanical machining using high speed diamond machining. It is to be noted that all frequency bands of \coremfive require significantly less pixels than demonstrated. In Ref. [52] we show that it is possible to multiplex up to 960 pixels using a single readout circuit using only a single cryogenic HEMT amplifier, which is Herschel-HIFI heritage, operated at $4\text{\,}\mathrm{K}$ [53]. On top of that we demonstrated that many relevant issues for space operation, such as yield, sensitivity, dynamic range and susceptibility to ionizing radiation, are very well under control.

5.5 KID Susceptibility to Cosmic Rays

Kinetic Inductance Detectors are pair-braking detectors, and are therefore insensitive to quanta of energy smaller than the superconducting gap 2$\Delta=3.5k_{b}T_{c}$. Thus, only photons or particles of energy larger than 2$\Delta$ can generate a measurable signal in the KID. This represents a key advantage with respect to bolometric detectors when it comes to the data loss induced by Cosmic Rays impacts. When a high energy particle hits a dielectric wafer, it generates a shower of high energy phonons, which then rapidly thermalize in the wafer. The KID are sensitive only to the first, non-thermal part of the event, while it is not effected by the final, thermal tail of the event during which the energy of the impact is released to the cold bath. Thus, the temporal evolution of a CR induced glitch in a KID is sensibly faster than the corresponding glitch in a bolometer. The recovery time of a KID is in fact of order of $1\text{\,}\mathrm{m}\mathrm{s}$ or less, depending on the details of the pixel and the material used. In a bolometer, the typical values are of hundreds of ms or longer, as outlined by the Planck experiment.

To further mitigate the data loss due to CR impacts, a solution has already been proposed [43]. This is based on the deposition, on the same wafer where the KID arrays are fabricated, of layers of a superconducting material having a critical temperature lower than the one of the material used for the detectors themselves. This additional superconducting layer efficiently absorbs the energetic non-thermal phonons. The phonons that are then re-emitted have an energy just above the gap of this superconductor, and are therefore unable to induce a signal in the KIDs. This phonon mopping technique is very effective at limiting the area of the KID array that is affected by each event, and at shortening the timescale of each glitch. The typical CR induced data loss in KID arrays hardened this way has been estimated to be of only a few $\%$  [46][52], and thus fully compatible with the requirements of the \coremfive mission.

5.6 Readout Electronics

The readout system on board \coremfive will be based upon a space-qualified version of the existing readout systems in use for: a) the NIKA2 instrument by Grenoble [54]; b) the system developed by SRON for the SpaceKIDs project [55]; and c) the readout for the A-MKID instrument by the Max Planck Institute for Radio Astronomy in Bonn. A multiplexing factor of 1000 has already been achieved in the latter two systems, and the former (based on the NIKEL readout using the DDC algorithm) allows for around 600. Any proposed readout is independent of the exact KID architecture (absorber or antenna coupled), and thus the particular KID architecture adopted will not influence the readout electronics scheme.

The baseline system architecture consists of the following components (see figure 16): A digital carrier board, which can be loaded with the complex waveforms to read-out up to 1000 MKIDs at the baseband frequency of 0-1 GHz. The complex waveform is converted to the analog world by two DAC’s. The signal is upconverted from the baseband to MKID frequencies in the analog board using IQ upconversion and a separate LO, and the result is a readout band of $2\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ around the LO frequency. The signal is subsequently attenuated/amplified to the correct power level for the MKID array. After being altered by the array, the signal is amplified by a single LNA at $15\text{\,}\mathrm{K}$ [56] and down-converted back to the baseband. We propose the Herchel-HIFI heritage TRL 9 Yebes 2-$4\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ LNA, requiring $5.5\text{\,}\mathrm{m}\mathrm{W}$ per amplifier. The demodulation board demodulates the complex sampled signal using a FFT and bin-selection algorithm. Depending on the exact system design, QDR2 memory is needed in this board. Control of the system is done using a dedicated Leon3 control processor, which controls the digital boards, the clocks, and the RF attenuator. The clocks for both the converters and the mixers are generated on a dedicated clocking board, both of which are locked to the same reference source.

The estimated power consumption and mass per readout chain are $52\text{\,}\mathrm{W}$ and $4.5\text{\,}\mathrm{k}\mathrm{g}$, respectively. Each chain can readout up to 1000 MKIDs. With a margin we will need 3 readout chains, and thus the required total power and mass are $156\text{\,}\mathrm{W}$ and $13.5\text{\,}\mathrm{k}\mathrm{g}$, respectively. In this design, there is a margin but no redundancy. The best option would be to make the system fully redundant, which would require a doubling in mass and volume to be able to have a full readout system as backup. On top of this it might be considered to make also the detector system redundant, which would double the cold power dissipation by the LNAs.

The entire readout system proposed here can be made from space-qualified components, most importantly the VIRTEX-5 FPGA. A qualification program is not needed on the component level, but only for the integrated system.

6 Cryogenic System

The sensitivity of \coremfive detectors should be limited by the intrinsic photon noise of the sky emission for diffraction-limited detectors observing in broad bands of $\Delta\nu/\nu\sim 0.3$. In the 60-$600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ frequency range this corresponds to minimum background loads in the range of 100-$200\text{\,}\mathrm{f}\mathrm{W}$. Achieving this sensitivity requires continuously cooling the detector array to $\sim$ $100\text{\,}\mathrm{m}\mathrm{K}$, and the mirrors down to $40\text{\,}\mathrm{K}$-$100\text{\,}\mathrm{K}$. The CORE cryogenic chain leverages on the ultra-low temperature space missions heritage (Planck [57], Hitomi) and ongoing developments (MIRI/JWST, XIFU/Athena) to succeed.

The \coremfive cryogenic architecture minimizes the development risk for a continuous low temperature cooling chain, and is open to potential evolutions of the instrument needs or configurations during the phase-A study.

The cooling system implementation is based on the following assumptions:

• •

The system should work continuously for at least 5 years in space, and cool the focal plane at 100mK and the telescope at 40-100K.

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All active coolers shall be redundant, except for the $100\text{\,}\mathrm{m}\mathrm{K}$ stage.

• •

For the cooling power, a margin of more than 25% at all temperature stages is required, except for the $100\text{\,}\mathrm{m}\mathrm{K}$ stage, where we require 100% margin.

• •

Coolers from Europe shall be baselined.

The cryo-system is basically divided into 3 sub-systems, as visible in Figure 17 ([58]).

• •

The first sub-system is located in the service module (SVM) and includes all the compressors for the active coolers (described below) in order to limit micro-vibrations and EMI issues at payload module (PLM) level. It also includes a small cryostat thermally anchored to the pulse tube coolers (PTC).

• •

The second sub-system is the SVM to PLM connection. It consists in a set of V-Grooves and insulated lines to transfer 4He and 3He of the coolers from the SVM, where they are pre-cooled, to the PLM. This passive cooling system is made possible by the large surface area of the instrument baffle. With our telescope configuration, V-Grooves similar to the ones proposed for the Planck mission [57], or the SPICA [59] and Ariel studies, can be re-proposed. Given the impact of the scan strategy on the requirements for these V-grooves, their optimization is discussed in detail in the mission companion paper [5]. Here we assume that a baseline temperature of 40-100 K is produced by this subsystem.

• •

The last sub-system consists of a series of concentric shells, going from $\sim$ 18K down to $\sim$ 1.7K, in order to limit the thermal loads on the lower temperature stages. It also includes the 0.1K focal plane unit cooled by the low temperature stages of the closed-cycle dilution refrigerator. The cool-down to around 18K of the PLM external envelope (R1) is achieved by using remote cooling from the SVM, with a concept similar to the one developed for MIRI in JWST.

With this configuration, the baseline system provides $2.3\text{\,}\mathrm{\SIUnitSymbolMicro W}$ continuous at $100\text{\,}\mathrm{m}\mathrm{K}$ (for a requirement of $1.1\text{\,}\mathrm{\SIUnitSymbolMicro W}$). The total mass is \sim$$210\text{\,}\mathrm{k}\mathrm{g} (excluding V-Grooves) with a total electrical power required \sim$$1300\text{\,}\mathrm{W}, including thermal control. The expected lifetime is 5 years, potentially extendable to 10 years. The budgets for this cryogenic system are summarized in Table 8 below.

[FIGURE:]

In the following we give additional information on key sub-systems of the cryogenic system of \coremfive.

6.1 Coolers

In addition to the V-Grooves, the cryo chain is composed of:

• •

3 Pulse Tube Coolers (PTC): two systems ON running below their maximum power and one PTC kept OFF for the purpose of redundancy. The $15\text{\,}\mathrm{K}$ PTC developed by ALAT/CEA/TCBV is baselined [60]. A prototype has recently been tested and has demonstrated $435\text{\,}\mathrm{m}\mathrm{W}$ at $15\text{\,}\mathrm{K}$ on the lower end together with $2\text{\,}\mathrm{W}$ at $80\text{\,}\mathrm{K}$ on the first stage. The system is compact and weighs about $18\text{\,}\mathrm{k}\mathrm{g}$ without its drive electronics (CDE). It uses a maximum of $300\text{\,}\mathrm{W}$ of electrical input at compressor level, i.e. $\sim$ $450\text{\,}\mathrm{W}$ including the CDE. A development phase has recently brought this cooler to TRL 5.

• •

2 Joule Thomson (JT) Coolers operating at $4.5\text{\,}\mathrm{K}$ (one cooler is ON and one is OFF for redundancy) [61]. The compressor will benefit from the ongoing $2\text{\,}\mathrm{K}$ JT cooler development, but will use just 2 compression stages instead of 4. The cold piping and ancillary panels are similar to the $4\text{\,}\mathrm{K}$ JT Planck cooler and do not need additional development. A higher cooling power ($30\text{\,}\mathrm{m}\mathrm{W}$ at $4.5\text{\,}\mathrm{K}$) than for Planck ($20\text{\,}\mathrm{m}\mathrm{W}$ at $4\text{\,}\mathrm{K}$) can be supplied by taking advantage of the lower $15\text{\,}\mathrm{K}$ pre-cooling temperature available from the PTC, and by using an increased ($\sim$ 10 %) mass-flow.

• •

1 Closed Cycle Dilution Refrigerator (CCDR). This cooling technology is based on the Planck heritage, but includes some major evolutions such as the distillation and recirculation of 3He and 4He. It requires precooling at $1.7\text{\,}\mathrm{K}$ ($5.25\text{\,}\mathrm{m}\mathrm{W}$ with 50% margin). It is baselined because the \coremfive mission calls for continuous observation but also because the focal plane is heavy. Mechanical modeling studies show that to avoid a complex mechanical release mechanism as on Planck, 24 Carbon Fiber Reinforced Plastic tubes OD/ID $5\text{/}3\text{\,}\mathrm{m}\mathrm{m}$ are needed to support a $500\text{\,}\mathrm{m}\mathrm{m}$ diameter $8\text{\,}\mathrm{k}\mathrm{g}$ detector plate under $120\text{\,}\mathrm{g}$ static acceleration and with a resonant frequency above $200\text{\,}\mathrm{H}\mathrm{z}$. The price to pay is a conduction load as high as $20\text{\,}\mathrm{\SIUnitSymbolMicro W}$ from $1.7\text{\,}\mathrm{K}$ to $0.1\text{\,}\mathrm{K}$. This subsystem is described in detail below.

6.2 Closed Cycle Dilution Refrigerator

Gravity plays an important role in the operation of 3He-4He dilution refrigerators on Earth since it localizes the interfaces among a relatively dense 3He-poor liquid phase, a less dense 3He-rich liquid phase, and an even less dense 3He-rich vapor phase in convenient positions.

The dilution refrigerator on the Planck satellite has a different design where capillary forces play the role of gravity. This dilution refrigerator consists of three capillaries soldered in parallel to form a heat exchanger. The capillaries form an Y-junction at the cold end of the dilution refrigerator. Liquid 3He and liquid 4He flow separately through two of those capillaries to the Y-junction, where mixing produces cooling. The mixture returns through the third capillary and expands in a $1.6\text{\,}\mathrm{K}$ Joule-Thompson cooler $1.5\text{\,}\mathrm{K}$ before being pumped by space. Therefore, the Planck dilution refrigerator is called an Open Cycle Dilution Refrigerator (OCDR).

The cooling power and the life time of this refrigerator are limited by the amounts of 3He and 4He stocked on the spacecraft. In order to increase the cooling power, the Néel Institute (in collaboration with Air Liquide) has developed an 3He-4He isotope separator working at $0.61.2\text{\,}\mathrm{K}$ to close the cycle.

The Closed Cycle Dilution Refrigerator (CCDR) has three disadvantages with respect to the OCDR:

It requires a $1.7\text{\,}\mathrm{K}$ cooler, because the isotope separator in the CCDR takes the place of the Joule-Thompson cooler in the Planck refrigerator. 2. 2.

It requires to localize a liquid-vapor interface in zero gravity, because the extraction of 3He uses the difference in vapor pressures of 3He and 4He in the phase separator. 3. 3.

It requires a 3He circulation pump.

We discuss the current state of the art by showing some results obtained with an upside-down CCDR in combination with a 3-stage reciprocal compressor developed by JAXA by modifying their 2-stage $1.7\text{\,}\mathrm{K}$ 3He Joule-Thompson compressor. We have built the upside-down CCDR shown in Figure 18 to demonstrate that liquid 3He-4He can be retained by capillary forces in a sponge under the conditions of negative gravity instead of zero gravity. The CCDR consists of 3 subsystems:

A Counter Flow Heat eXchanger (divided in sections CFHX-1 and CFHX-2 in Figure 18) and a Mixing Part (MP). We have scaled up the diameters of the capillaries in this subsystem with respect to Planck’s OCDR to provide more cooling power at lower temperatures. The CCDR will cool the focal plane through the 3He-4He mixture return capillary indicated by the heater $\dot{Q}_{\text{detector}}$. 2. 2.

An isotope separator (still) allowing to pump 3He-rich vapor ( $90\text{\,}\mathrm{\char 37\relax}$) from the liquid 3He-4He mixture confined in a sponge in the still by means of a 3He pump as well as superfluid 4He by means of a fountain pump (FP). Heat exchangers (HX-still-3 and HX-still-4) cool the 3He and 4He streams before they enter into the CFHX. 3. 3.

A $1.7\text{\,}\mathrm{K}$ pot (future 3He Joule-Thompson expansion provided by RAL) to liquefy the 3He gas returning from the 3He pump and to cool the 4He liquid coming from the fountain pump.

We have designed the heat exchanger above the sponge in the still to make the capillary confinement harder because of the hydrostatic pressure exercised by the liquid in heat exchanger. In fact, the MP is sitting $150\text{\,}\mathrm{mm}$ above the still while we estimate the capillary height in the Procelit P160 sponge to be $3040\text{\,}\mathrm{m}\mathrm{m}$. Indeed, the sponge leaks in case of zero 3He and 4He flow rates. Nevertheless, the CCDR works well without any liquid leaking from the sponge as monitored by the capacitance liquid level gauge $C_{\text{level}}$. We explain the successful confinement by the viscous pressure drops in the capillaries of the CFHX when the CCDR is circulating.

Figure 19 shows cooling power data obtained by applying heat to $\dot{Q}_{\text{detector}}$ and measuring the temperature $T_{\text{liquid}}$ which is the temperature of the liquid 3He-4He mixture downstream of $\dot{Q}_{\text{detector}}$ and upstream of the CFHX (see Figure 18). We have fitted the data by the approximate relation $\dot{Q}_{\text{detector}}=A\dot{n}_{\text{4}}T_{\text{liquid}}^{2}-\dot{Q}_{\text{leak}}$, where $\dot{n}_{\text{4}}=$235\text{,}\mathrm{\SIUnitSymbolMicro mol}\text{,}{\mathrm{s}}^{-1} obtained from the relation $\dot{Q}_{\text{fp}}=\dot{n}_{\text{4}}T_{\text{fp}}s_{\text{40}}(T_{\text{fp}})$ which is based on the second law of thermodynamics and the molar entropy ($s_{\text{40}}$) data of liquid *4*He, $A=$2.9\text{\,}\mathrm{J}\text{\,}{\mathrm{mol}}^{-1}\text{\,}{\mathrm{K}}^{2} which is in very good agreement with thermodynamic data of 3He-4He mixtures, and $\dot{Q}_{\text{leak}}=$3.3\text{,}\mathrm{\SIUnitSymbolMicro W}. Note that $\dot{Q}_{\text{detector}}=$3.5\text{\,}\mathrm{\SIUnitSymbolMicro W} at $T_{\text{liquid}}=$0.1\text{,}\mathrm{K}$$ even in the presence of a heat leak of $3.3\text{\,}\mathrm{\SIUnitSymbolMicro W}$.

6.3 Focal Plane Suspension with Thermal Intercepts

Figure 20 shows a simplified model of the focal plane suspension with thermal intercepts to check the feasibility of a suspension system meeting the mechanical requirements of a satellite launch as well as the thermal requirements imposed by the operation of the focal plane at $0.1\text{\,}\mathrm{K}$. We have choosen Carbon Fiber Reinforced ePoxy (CFRP) rods because of its high Young’s modulus, its high yield strength, and its low thermal conductivity. The low thermal contraction of CFRP with respect to metals may be a disadvantage, since the cooling of the struts may impose addition strain. However, in case the satellite is being launched with the focal plain at $300\text{\,}\mathrm{K}$ this disadvantage plays no role. The geometry of the suspension system in Figure 20 is an advantage, since it has the optimal position of the center of mass of the focal plane.

The results of the mechanical study are still preliminary but look promising. We summarize here the results of calculations done to find the optimal angles for 24 CFRP tubes with a fixed length of $195\text{\,}\mathrm{mm}$, a fixed inner diameter of $3\text{\,}\mathrm{mm}$ and a fixed outer diameter of $5\text{\,}\mathrm{mm}$. The effect of varying the angles is that (1) the vertical distance between the strut fixations on the $1.7\text{\,}\mathrm{K}$ envelope below and above the focal plane can change and that (2) the diameter of the $1.7\text{\,}\mathrm{K}$ envelope can change. The vertical distance has been varied from $120\text{\,}\mathrm{mm}$ to $220\text{\,}\mathrm{mm}$ and the diameter of the $1.7\text{\,}\mathrm{K}$ envelope has been varied from $680\text{\,}\mathrm{mm}$ to $740\text{\,}\mathrm{mm}$. The lowest resonant frequencies vary from $182\text{\,}\mathrm{Hz}$ to $265\text{\,}\mathrm{Hz}$ for those configurations while the struts do not buckle for accelerations of 120 times gravity on earth. In order to reduce the diameter of the $1.7\text{\,}\mathrm{K}$ to $580\text{\,}\mathrm{mm}$, the length and the cross-section area of the tubes have to be reduced by the same factor to keep the same resonance frequencies. In this case, we expect the buckling threshold to increase. Those results are very promising, but we point out that the vibration modes of the focal plane should be handled together with its suspension structure.

In order to have a design aid for the focal plane suspension system, we have written a program to solve differential equations for the enthalpy balance in the CFHX using a collocation method for boundary value problems. The differential equations take into account (1) the flows of enthalpy due the incoming 3He stream and the outgoing 3He-4He mixture stream, (2) the heat transfer from the incoming 3He stream to the outgoing 3He-4He mixture stream through the walls the CFHX (the dominant thermal resistance is the boundary resistance between the helium and the CuNi capillaries forming the CFHX), and (3) viscous dissipation due to Poiseuille flow. The program is flexible enough to handle a CFHX consisting of an arbitrary number of sections with different lengths and diameters as shown in Table 9. Table 9 also shows that is possible (1) to short-circuit the CFHX sections with sections of CRFP struts and (2) to apply heat loads to the outgoing 3He-4He mixture between the CFHX. Other parameters are for instance the 3He circulation rate $\dot{n}_{\text{3}}$, the 4He circulation rate $\dot{n}_{\text{4}}$, the still temperature $T_{\text{still}}$, and the diameter $D_{\text{mo}}$ and the length $L_{\text{mo}}$ of the 3He-4He mixing part capillary (the yellow capillary inside the dashed MP box in Figure 18).

We have compared solutions of the differential equations with the performance of the upside-down CCDR and our best upside-up CCDR with $T_{\text{detector}}=$51.4\text{,}\mathrm{mK} and $T_{\text{liquid}}=$44.0\text{\,}\mathrm{mK} for $\dot{Q}_{\text{detector}}=$1\text{,}\mathrm{\SIUnitSymbolMicro W}$$. We have seen that the temperature $T_{\text{liquid}}$ of the solutions agrees within $5\text{\,}\mathrm{\char 37\relax}$ with the experimental data.

Table 10 and Figure 21 show the solution of the differential equations for the input data shown in Figure 9. Some of the other parameters are $\dot{n}_{\text{3}}$=$35\text{\,}\mathrm{\SIUnitSymbolMicro mol}\text{\,}{\mathrm{s}}^{-1}$, $\dot{n}_{\text{4}}$=$205\text{\,}\mathrm{\SIUnitSymbolMicro mol}\text{\,}{\mathrm{s}}^{-1}$, $T_{\text{still}}$=$1.2\text{\,}\mathrm{K}$, $D_{\text{mo}}$=$0.6\text{\,}\mathrm{mm}$, and $L_{\text{mo}}$=$1.5\text{\,}\mathrm{m}$. The flow rates $\dot{n}_{\text{3}}$ and $\dot{n}_{\text{4}}$ are representative of the values during the tests of the upside-down CCDR in combination with the space qualified JAXA 3He circulation pump.

The results show that the thermal intercept at the cold end of CFHX section 1 evacuates $43.3\text{\,}\mathrm{\SIUnitSymbolMicro W}$ in total at $0.3\text{\,}\mathrm{K}$ or $1.8\text{\,}\mathrm{\SIUnitSymbolMicro W}$ per strut. Vertical thermal links between the heat intercepts on the struts below the focal plane and the struts above the focal plane have to intercept the heat current through those struts. The thermal conductivity of high-quality copper or silver is $1000T\;$\mathrm{W}\text{,}{\mathrm{K}}^{-1}\text{,}{\mathrm{m}}^{-1}$$.

In this case, a thermal link for a heat current of $1.8\text{\,}\mathrm{\SIUnitSymbolMicro W}$ with a cross-section of $0.1\text{\,}{\mathrm{mm}}^{2}$ and a length of $0.1\text{\,}\mathrm{m}$ will have a temperature difference of $6\text{\,}\mathrm{mK}$ over the length of the link.

The thermal intercept at the cold end of section 3 is only $1.4\text{\,}\mathrm{\SIUnitSymbolMicro W}$ at $0.14\text{\,}\mathrm{K}$ and is easier to handle and the intercept at the cold end of section 3 is not very useful, since it evacuates only $1\text{\,}\mathrm{\char 37\relax}$ of the heat load on the mixer part.

We point out that the total length of the heat exchanger should be at least $15\text{\,}\mathrm{m}$ in order to intercept heat on the struts at three different temperatures. However, prolonging the heat exchanger to for instance $20\text{\,}\mathrm{m}$ not affect the equivalent of $T_{\text{liquid}}$ in Figure 18, since it is entirely controlled by $\dot{Q}_{\text{detector}}$.

Finally, we point out that we did not discuss the mechanical suspension of the still, but we think it should be treated separately from the CFHX and focal plane assembly and we expect it to be straightforward because the still is much lighter and smaller than the focal plane assembly.

6.4 $1.7\text{\,}\mathrm{K}$ 3He Joule-Thompson expansion cooler requirements

The 3He Joule-Thompson expansion cooler serves (1) to cool the liquid 4He coming from the fountain pump to $1.7\text{\,}\mathrm{K}$ and to cool and liquefy the 3He gas coming from the 3He pump. Therefore, we may write the heat load on the 3He Joule-Thompson expansion as the sum of two contributions \dot{Q}_{\text{JT}}(\dot{n}_{\text{3}})=\dot{n}_{\text{3}}\left(L_{\text{30}}(T=1.7\text{,}\mathrm{K}$)+2.5R(T_{\text{gas}}-$1.7\text{,}\mathrm{K})\right) and \dot{Q}_{\text{JT}}(\dot{n}_{\text{4}})=\dot{n}_{\text{4}}\left(H_{\text{40}}(T_{\text{fp}})-H_{\text{40}}(1.7\text{,}\mathrm{K})\right), where $L_{\text{30}}$ is the latent heat of liquefaction of 3He, $H_{\text{40}}$ the enthalpy of liquid 4He, and $T_{\text{gas}}$ the temperature of the 3He gas before liquefaction. In all our experiments up to now $T_{\text{gas}}=$4.2\text{,}\mathrm{K}, but we plan to reduce it to below $2.0\text{\,}\mathrm{b}$y means of a heat exchanger between the incoming and outgoing *3*He gas. In this case the value $\dot{Q}_{\text{JT}}$($\dot{n}_{\text{3}}$=$35\text{\,}\mathrm{\SIUnitSymbolMicro mol}\text{\,}{\mathrm{s}}^{-1}$) will decrease from $3.4\text{\,}\mathrm{mW}$ to below $1.8\text{\,}\mathrm{mW}$. In case of $T_{\text{fp}}$=$2.15\text{\,}\mathrm{K}$, $\dot{Q}_{\text{JT}}(\dot{n}_{\text{4}}=$205\text{\,}\mathrm{\SIUnitSymbolMicro mol}\text{\,}{\mathrm{s}}^{-1}$)=$1.7\text{\,}\mathrm{mW}. Since $H_{\text{40}}(T_{\text{}})$ is a steep function of $T_{\text{}}$, ($H_{\text{40}}$ decreases by about $20\text{\,}\mathrm{\char 37\relax}$ when $T_{\text{}}$ decreases from $2.15\text{\,}\mathrm{K}$ to $2.1\text{\,}\mathrm{K}$), the design of the fountain pump has to make it work at the lowest temperature possible. In summary, in case $\dot{n}_{\text{3}}$=$35\text{\,}\mathrm{\SIUnitSymbolMicro mol}\text{\,}{\mathrm{s}}^{-1}$ and $\dot{n}_{\text{4}}$=$205\text{\,}\mathrm{\SIUnitSymbolMicro mol}\text{\,}{\mathrm{s}}^{-1}$, the current configuration requires a heat lift of $5.1\text{\,}\mathrm{mW}$ from the 3He Joule-Thompson expansion cooler, but the requirement will decrease to below $3.5\text{\,}\mathrm{mW}$ with a heat exchanger between the incoming and outgoing 3He gas.

7 Instrument Calibration

By instrument calibration we intend the measurement of all instrument characteristics which impact the data analysis and hence the science products of the mission. The experience of Planck shows that the ultimate data quality of extreme sensitivity measurements is likely to be limited not by white noise but by residual systematic effects, which mainly reflect the level of accuracy achieved in the calibration of the instrument. This experience also shows that non-idealities can be corrected for in the data processing as long as they are known with sufficient precision. A broad requirement for calibration accuracy is that uncertainties in the measurements of all the instrument parameters give rise to a level of systematics which is significantly less than the statistical noise. By statistical noise we mean the white noise in the final product maps arising from detector sensitivity averaged over the entire range of angular scales of interest. However, the way in which systematic effects impact the science products of the mission is far from trivial (e.g. [62]). In general it is necessary to simulate systematic effects and propagate them through the data analysis pipeline up to the cosmological results, with an accuracy and a level of detail that depends on the significance of the specific effect being evaluated.

Defining requirements is essential in the calibration plan and requires close interaction with instrument design and mission strategy (see [5]). We propose here two main stages in the calibration plan: 1) ground-based system level characterization and 2) in-flight measurements using astronomical sources. The \coremfive calibration plan will include a combination of tests on ground and in flight for each of the calibration parameters to be measured. The main classes of instrumental parameters to be characterized are:

Photometric (or absolute) calibration: conversion of the product maps from generic telemetry units to physical units ($\text{\,}\mathrm{\SIUnitSymbolMicro}\mathrm{K}_{\rm CMB}$). Gain factors for each radiometer will be measured on the ground at several stages. The final calibration will be performed in-flight. 2. 2.

Relative calibration (signal stability): stability of the gain and zero-level. This will be simplified by the redundancy of the scanning strategy. 3. 3.

Thermal effects: systematics induced by thermal fluctuations in the $0.1\text{\,}\mathrm{K}$, $1.7\text{\,}\mathrm{K}$, $4\text{\,}\mathrm{K}$, $20\text{\,}\mathrm{K}$ and $300\text{\,}\mathrm{K}$ stages; cooler induced microphonics. A set of temperature sensors will monitor the thermal configuration of the instrument and stability. The necessary accuracy and resolution of thermal calibration will be based on simulations requiring a detailed thermal model of the focal plane. 4. 4.

Detector chain non-idealities: detector time-response; non-linearity of the detector response; non-linearity of ADC converters; impact of cosmic rays; sensitivity to microphonics. 5. 5.

Spectral calibration: detailed bandpass measurements on the ground. In-flight verification of the measured bandpasses will be possible through observation of diffuse and point sources with steep spectra. 6. 6.

Optical calibration: main beam determination, near sidelobes, far sidelobes (both total intensity and polarization). Direct measurements of the main beams and near lobes down to -35 $/$ -$40\text{\,}\mathrm{d}\mathrm{B}$ will be possible in-flight exploiting signals from planets and strong polarized sources. Detailed models of the far sidelobes will be constructed with state-of-the-art physical optics codes (GRASP333www.ticra.com) and convolved to models of the full sky emission to propagate signatures from straylight. The optical model will be validated by comparing simulation with direct measurements of main beams and near lobes. 7. 7.

Polarization-specific calibration: polarization efficiency and polarization angle of each detector; and in the case of using a half-wave plate the systematics that it may induce. These will be measured both on the ground and, possiblty, in-flight. 8. 8.

Intrinsic noise characterization: detailed measurements of the noise properties (noise power spectrum, $1/f$ noise, possible non-gaussianity) and their time evolution are needed. These will be standard measurements in ground testing and in-flight operation

7.1 Ground Calibration

The experience gained from the Planck-HFI has shown that while a great deal of effort was put in instrument ground calibration [63], some effects were not anticipated at the level observed (cosmic ray hits for instance) while some other parameters could have benefited from a better characterization. Therefore we will follow a similar but more complete instrument ground calibration and with higher accuracy in the determination of parameters that are crucial for polarization measurements. However, the difficulty will be to adapt this calibration strategy from tens of pixels for Planck to thousands of pixels for \coremfive. It is likley that full characterization of each individual pixel with extremely high accuracy would be too costly and time consuming. It that case, the \coremfive strategy will include general tests conducted on all components and pixels to check for anomalies, failures, and performance inhomogeneity, complemented with thorough testing on a subset of pixels across the frequency bands.

The Planck data analysis has also highlighted the criticality of a detailed knowledge of beams and far-sidelobes, particularly for polarization. Clearly, even the extensive optical testing carried out for Planck [64] would be significantly inadequate for \coremfive  which requires RF calibration to be more accurate by an order of magnitude. The \coremfive optical ground testing will include a highly representative focal plane system, comparable with the final flight model, and multiple in-band pattern measurements.

7.2 In-flight calibration

Following the Planck strategy, photometric and relative calibration will be based on the solar and orbital dipoles as primary calibrators and cross-checked on planets. Using orbital modulation Planck has reached absolute calibration at few $\times 10^{-4}$ level, which can be exploited by \coremfive in its first phase of data analysis. However, \coremfive will be able to far improve over long time intervals by at least one order of magnitude. The Planck experience has shown the extreme importance of direct monitoring of the instruments (subsystem temperatures, electrical bias parameters, thermal stability, cooler performance) and regular processing of the time-ordered data. Indeed, the cross-correlation between monitored parameters and data processing have proved essential for improving systematic effect removal algorithms. Similarly, noise characteristics will be regularly measured in terms of power spectrum, $1/f$ and other non-gaussian components. Noise characteristics will be affected by cosmic rays, that show up as glitches in the data. We will exploit the considerable experience, gained in Planck, of measurements of the time evolution and amplitude of glitch signatures. Detector time response and main beam characterization will be simultaneously performed on planets as they are strongly degenerate. This high level of accuracy will make use of multiple crossing observations (multiple scanning directions and angles) of various planets to achieve a high signal-to-noise well outside the main beam. As \coremfive will map about half sky with all of its detector every 4 days, planets will be scanned repeatedly over the full duration of the mission, allowing very precise sampling of the beams and continuos cross-check of the gain stability. These observations will be also used to measure instrumental polarization and scanning strategy-induced systematic effects (in-scan and cross-scan differences). Polarization efficiency and polarization angles can be measured on well-known polarized astronomical sources, such as the Crab Nebula. \coremfive may benefit from future, high-precision, dedicated ground observation campaigns of these polarized calibration sources.

8 Downscoping Options

The instrument configuration described above is robust enough to allow for downscoping, would cost/programmatic issues require it. The downscoping strategy would be to aim at maintaining extreme CMB polarization sensitivity and accuracy, while reducing the performance for measurements of: the polarized interstellar medium of our galaxy and the study of the galactic magnetic field; Cosmology with galaxy clusters; Extragalactic sources and cosmic infrared background. In practice, a MiniCORE mission would be aimed at:

• •

Constraining inflationary B-modes at the level required to reach $\sigma(r)=0.001$ with MiniCORE alone, and $\sigma(r)=0.0003$ in combination with future ground-based measurements;

• •

Observing dark matter structures by measuring lensing B-modes at S/N$>$3 per individual mode, with angular resolution <$$\sim 3’, in combination with future ground-based measurements;

• •

Measuring polarisation E-modes with cosmic-variance dominated errors over $>30\%$ of the sky, in combination with future ground-based observatories.

The reduction of the requirement on $\sigma(r)$ by a factor of 3 (MiniCORE alone vs \coremfive alone) translates in a reduction of the requirement on the sensitivity by a factor of $\sqrt{3}$, or $\Delta P=$3\text{,}\mathrm{\SIUnitSymbolMicro K}$\cdot$arcmin (similar to LiteCORE-80 in the companion papers of this series). As foreground emission dominates over lensing B-modes for $\ell<1000$, we require the CMB to be mapped from space up to $\ell=1000$, i.e. with an angular resolution of about 12 arcmin FWHM. To reach its goals in combination with future ground-based observatories, MiniCORE should provide the capability to monitor high-frequency foreground emission at a level compatible with $\sigma(r)=0.0003$.

The first change with respect to \coremfive is the reduction of the diameter of the telescope aperture to $80\text{\,}\mathrm{c}\mathrm{m}$. This results in a number of savings, as detailed below. The second important change is the reduction of the number of detectors and the removal of all channels with frequency below $100\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$ (15 frequency bands in place of 19). This will require teaming with ground-based surveys, which are possible and effective at low frequency. Angular scales to a few arcmin will be mapped from the ground with several-meters-aperture telescopes, up to 150 GHz: MiniCORE will add the essential coverage of the same angular scales at frequencies up to $600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$, where polarized dust emission becomes very strong. The proposed frequency channels of MiniCORE are outlined in Table 11. The aggregated CMB polarisation sensitivity is 3.2\text{\,}\mathrm{\SIUnitSymbolMicro K}$$\cdotarcmin for a temperature of $85\text{\,}\mathrm{K}$ of the telescope and its surroundings.

Assuming a filling factor of 70%, the focal plane radius is $15.6\text{\,}\mathrm{c}\mathrm{m}$ instead of $25\text{\,}\mathrm{c}\mathrm{m}$. The area and mass of the sub-Kelvin focal plane are reduced by a factor 2.5, with 900 detectors in place of 2100. The MiniCORE payload is passively cooled to $85\text{\,}\mathrm{K}$ instead of $40\text{\,}\mathrm{K}$. This can be achieved with only two V-groove plates instead of three, or with MLI insulation between the SVM and the PLM. The mass of the telescope is reduced from \sim$$100\text{\,}\mathrm{k}\mathrm{g} to \sim$$40\text{\,}\mathrm{k}\mathrm{g}. The mass of the optical bench from \sim$$50\text{\,}\mathrm{k}\mathrm{g} to \sim$$20\text{\,}\mathrm{k}\mathrm{g}; the mass of the telescope structure from \sim$$20\text{\,}\mathrm{k}\mathrm{g} to \sim$$5\text{\,}\mathrm{k}\mathrm{g}. The total mass of the payload reduces from \sim$$200\text{\,}\mathrm{k}\mathrm{g} to \sim$$80\text{\,}\mathrm{k}\mathrm{g}. The combination of reduced number of detectors and reduced angular resolution results in reduced sampling requirements, reducing the continuous data rate from $1.15\text{\,}\mathrm{M}\mathrm{b}\mathrm{i}\mathrm{t}\mathrm{/}\mathrm{s}$ to $330\text{\,}\mathrm{k}\mathrm{b}\mathrm{i}\mathrm{t}\mathrm{/}\mathrm{s}$. The size and mass reduction of the payload allows for the use of only one pulse-tube instead of two; moreover with 900 detectors instead of 2100 the readout electronics is also reduced, so that the on-board power required is reduced from \sim$$2100\text{\,}\mathrm{W} to \sim$$1500\text{\,}\mathrm{W}.

All these changes result in a very significant reduction of the cost of the instrument and of the mission, maintaining basically untouched its main scientific goals, provided that ground-based observatories can indeed meet their ambitious objectives and complement the space mission observations, in particular with noise-dominated small scale CMB maps over a large fraction of sky.

9 Conclusions

We have described a space-borne polarimeter optimized for a medium-size space mission within the Cosmic Vision Programme of the European Space Agency. The instrument uses the legacy of the successful Planck mission, and the most recent advances in the technology of panoramic detectors for mm-waves. The Technology Readiness Level (TRL) for the different parts of the instrument is summarized in Table 12, and is perfectly compatible with the requirements for the M5 call of ESA. With its wide frequency coverage (60-$600\text{\,}\mathrm{G}\mathrm{H}\mathrm{z}$), and large throughput this instrument will map CMB polarization with unprecedented sensitiviy and accuracy. The outstanding scientific performance of \coremfive is thoroughly discussed in companion papers of this series ([1], [2], [3], [5]).

10 Acknowledgements

PdB acknowledges support from University of Rome La Sapienza (project “Cosmologia di Precisione 2015”) and from the Italian Space Agency (Agreement 2016-019-H.0 “Kinetic Inductance Detectors for Space”). CJM is supported by an FCT Research Professorship, contract reference IF/00064/2012, funded by FCT/MCTES (Portugal) and POPH/FSE (EC). C.H.-M. acknowledges the financial support of the Spanish Ministry of Economy and Competitiveness via I+D project AYA-2015-66211-C2-2-P. GDZ acknowledges the financial support of ASI/INAF agreement n. 2014-024-R.1. J.G.N. acknowledges financial support from the Spanish MINECO for a “Ramon y Cajal” fellowship (RYC-2013-13256) and the I+D 2015 project AYA2015-65887-P (MINECO/FEDER). F.J.C., E.M.-G. and P.V. acknowledge support from the Spanish Ministerio de Economía y Competitividad project ESP2015-70646-C2-1-R co-financed with EU FEDER funds.