Pros and cons of cryogenics for Einstein Telescope

Pros and cons of cryogenics for Einstein Telescope and Cosmic Explorer Kazuhiro Yamamoto Institute for Cosmic Ray Research, the University of Tokyo 22 May 2014 Gravitational Wave Advanced Detector Workshop @ Alyeska Resort, Girdwood, Alaska, U. S. A. 1

0. Abstract 3 rd generation detectors (Einstein Telescope, Cosmic Explorer) have 10 km scale baselines. Pro and Con of cryogenic for them are summarized here. 2

0. 1. Excuses In official, Cosmic Explorer interferometer is at room temperature. Kazuhiro Yamamoto assumes some values (especially for Cosmic Explorer). His calculation is some kinds of order evaluation. Somebodies who are in charge of it should check. Kazuhiro welcomes comments and discussions. 3

Contents 1. Introduction(Pros) 2. Specifications of mirror and fiber 3. Heat extraction 4. Issues(Cons) 5. Summary 4

1. Introduction(Pros) 3 rd generation interferometer : 10 times better sensitivity than that of 2 nd generation Einstein Telescope (ET) : 10 km baseline in Europe Low Frequency (LF) and High Frequency (HF) Cosmic Explorer (CE) : 40 km baseline in U. S. A. Cryogenic technique is adopted in ET-LF(10 K). (In official, CE interferometer is at room temperature). Pros and cons of cryogenic in ET-LF and CE (if CE adopts !)are summarized here. 5

1. Introduction(Pros) ET-LF Mirror thermal noise : 10 times smaller Pendulum thermal noise : 300 times smaller S. Hild et al. , Classical and Quantum Gravity 28 (2011) 094013. R. Nawrodt et al. , General Relativity and Gravitation 43 (2011) 363. 6

1. Introduction(Pros) CE Mirror thermal noise : 10 times smaller Pendulum thermal noise : 10 times smaller LIGO T 1400316 -v 5 7

1. Introduction(Pros) In principle, at lower temperature, thermal noise is smaller. 　 > 50 K Constant <20 K Enough small Sapphire 8

1. Introduction(Pros) In principle, at lower temperature, thermal noise is smaller. 　But there is an exception. 　 Silicon 120 K Thermoelastic noise vanishes. Silicon 9

1. Introduction(Pros) Coating thermal noise 10 km scale baselines and cryogenics (20 K) are excellent remedies. ET-LF : 10 km baseline 10 K operation, 9 cm beam radius Drastic improvement of coating loss angle is not necessary. CE : 40 km baseline Drastic improvement of coating loss angle and enhancement of beam radius are not necessary. (Beam radius in 40 km arms is about 9 cm at least). 10

1. Introduction(Pros) Coating loss angle Peak around 20 K are reported (f = 10 -3). (G. Cagnoli slides on the last Wednesday) In some papers, there is no peak (f=4*10 -4). (K. Yamamoto et al. , Physical Review D 74 (2006) 022002. E. Hirose et al. , Physical Review D 90 (2014) 102004. ) Even if our coating has loss peak, thermal noise at lower temperature is smaller and this noise is (at least twice time) smaller than goal sensitivity. 11

1. Introduction(Pros) Coating thermal noise CE : 40 km baseline (120 K operation, 12 cm radius beam) Drastic improvement of coating loss is not necessary. (Beam radius in 40 km arms is about 9 cm at least). 12

1. Introduction(Pros) Why the mirrors and suspension in KAGRA are cooled ? (1)Smaller thermal noise Kenji Numata and Kazuhiro Yamamoto, ”Chapter 8. Cryogenics”, in ”Optical Coatings and Thermal Noise in Precision Measurement” Cambridge University Press (2012). (2)Smaller thermal lens T. Tomaru et al. , Classical and Quantum Gravity 19 (2002) 2045. (3)Less serious parametric instability K. Yamamoto et al. , Journal of Physics: Conference Series 122 (2008) 012015. These items are correct in the case of ET-LE. K. Yamamoto GWADW 2011 https: //agenda. infn. it/contribution. Display. py? session. Id=17&contrib. Id=69&conf. Id=3351 13

1. Introduction(Pros) How about CE ? (1)Thermal noise : OK. (2)Thermal lens (probably OK but) must be checked if silicon at 120 K is adopted (temperature coefficient of refractive index is high). (3)Parametric instability is less serious (than that of room temperature interferometer). Gain at 120 K is smaller. 14

2. Specification of mirror and fiber Mirror should be larger in 3 rd generation. (1)Smaller Standard Quantum Limit (Binary coalescence) (2)Larger beam radius due to longer baseline (3)If necessary, beam radius is enhanced to suppress mirror thermal noise. KAGRA mirror : 23 kg (22 cm diameter, 15 cm thickness) ET-LF mirror : 211 kg (>45 cm diameter) CE mirror : 80 kg (silicon) , 120 kg (sapphire) [Kazuhiro assumes that size is the same as current one] 15

2. Specification of mirror and fiber Fibers suspending mirror should be thicker because mirror is heavier. KAGRA mirror : 23 kg, (Tensile strength : 400 MPa, Safety margin : 7) Fiber diameter must be larger than 1. 1 mm. ET-LF mirror : 211 kg, Fiber diameter is 3. 3 mm at least. CE mirror : 80 kg (silicon) , 120 kg (sapphire), Fiber diameter is 2. 5 mm at least. [Kazuhiro assumes that strength is the same as that of sapphire] 16

2. Specification of mirror and fiber Fibers suspending mirror should be longer. At least, fiber length must be comparable with mirror diameter (about 500 mm). ET-LF : Length is 2 m in length to improve sensitivity at low frequency region. CE : If 120 K operation is selected and upper side of fiber is at room temperature as like Voyager, 2 m length is better for thermal insulation. Otherwise, 0. 5 m length fiber is better. 17

3. Heat extraction Heat absorption in mirror is a crucial issue. KAGRA : 400 k. W in arm, 800 W at beam splitter (Optimistic) assumption : 0. 5 ppm and 20 ppm/cm absorption in coating and substrate Absorption in coating and substrate: 0. 2 W and 0. 24 W(15 cm thickness) (total : 0. 44 W) [Kazuhiro assumes same absorption and thickness in the cases of ET and CE. ] ET-LF : 18 k. W in arm, 63 W at beam splitter Total heat absorption in mirror : 9 m. W and 19 m. W (total : 28 m. W) CE : 800 k. W in arm, 125 W input power : 0. 4 W and 0. 38 W (total : 0. 78 W) 18

3. Heat extraction (10 K or 20 K operation) Fibers are bottle neck. Assumption : Fiber thermal conductivity is the same as that of sapphire. ET-LF : 3. 3 mm diameter fibers can transfer 55 m. W (10 K operation). CE : 2. 5 mm diameter fibers can transfer 1. 5 W (20 K operation). When fibers can suspend mirror, they could transfer enough heat. 19

3. Heat extraction (120 K operation; CE? ) Radiation Black body radiation can transfer about 7 W. Black coating on mirror is necessary. [Kazuhiro explained details on the last Tuesday] Conduction in fiber 2. 5 mm diameter fibers can transfer 0. 8 W (Upper end of fiber: 80 K). At least, it does not look impossible. 20

3. Heat extraction Scattered light by mirror is absorbed by radiation shield. KAGRA : Shield at 12 K and 20 K can absorb 2 W and 10 W, respectively. Assumption : Scattered loss is 10 ppm. ET-LF : 18 k. W power in arm. : 0. 18 W. CE : 800 k. W in arm : 8 W. They look acceptable. 21

4. Issues(Cons) Initial cooling KAGRA : 5 weeks, 4 cryocoolers for each cryostat ET-LF and CE Several or tens times heavier payload (1)Short cooling of radiation shield Powerful heat extraction device with small vibration (2)Short cooling of payload below 100 K Large heat path without transmission of external vibration (or with thermal switch). If you select 120 K operation, item (2) is not 22

4. Issues(Cons) Heat extraction Kazuhiro’s calculation shows that heat absorbed in mirror can be extracted. But, (1) assumed absorption is optimistic. (2) safety margin is not large. Heat absorption in large mirror should be checked carefully. “Large” is not a problem but “Large and low absorption” is an issue. Driving force should provided by ourselves ! 23

4. Issues(Cons) Silicon : Size itself is not a issue. Absorption in large bulk is an issue. Silicon bulk 450 mm 300 mm Harald Lueck(ELi. TES meeting 2013) https: //events. egogw. it/indico/conference. Other. Views. py? view= standard&conf. Id=7 Source: http: //www. iisb. fraunhofer. de/content/dam/iisb/de/i mages/geschaeftsfelder/halbleiterfertigungsgeraete _und_methoden/gadest_2011/ J. Degallaix slides on the last Tuesday 24

4. Issues(Cons) Sapphire : Some companies can provide large sapphire bulk (As far as Kazuhiro knows, 60 kg). Optical (and mechanical) quality is unknown. 23 kg, 23 cm diameter, 15 cm thickness J. Degallaix slides on the last Tuesday 25

5. Summary Cryogenics in 3 rd generation (10 km scale). Pros (1)Smaller thermal noise We do not need drastic improvement of coating loss angle and can adopt smaller beam. (2)Smaller thermal lens (3)Less serious parametric instability Even if in the case of 120 K operation, these items are correct but gain is smaller. 26

5. Summary Cryogenics in 3 rd generation (10 km scale). Cons (1)Initial cooling (a)Shorter cooling of radiation shield (b)Shorter cooling of payload below 100 K Item (b) is not necessary in 120 K operation. (2)Heat absorption in mirror Large mirror with low absorption is an issue. We can purchase larger silicon with smaller absorption than sapphire bulk. Driving force must be applied by ourselves. 27

Thank you for your attention ! 28

1. Introduction Heat extraction: Fiber is bottle neck. Assumption : Fiber thermal conductivity is the same as that of sapphire. ET-LF : Fiber diameter must 2. 0 mm at least (10 K operation). CE : Fiber diameter must 2. 2 mm at least (10 K operation). 29

5. Einstein Telescope (a) Thermal noise Mirror thermal noise : 10 times smaller Suspension thermal noise : 300 times smaller S. Hild et al. , Classical and Quantum Gravity 28 (2011) 094013. R. Nawrodt et al. , General Relativity and Gravitation 43 (2011) 363. 30

5. Einstein Telescope (a) Thermal noise Mirror thermal noise : 10 times smaller 3 times longer arm (10 km) 3 times larger beam radius (9 cm) Suspension thermal noise : 300 times smaller 3 times longer arm (10 km) 7 times heavier mirror (200 kg) 5 times longer suspension wire (2 m) 100 times smaller dissipation in wires (Q=109) 31

4. Challenges for cryogenic 1. Issues of cooling : Reduction of heat load (Absorption in mirror) In order to keep mirror temperature … Absorption in mirror : less than 1 W Coating : 0. 4 W (1 ppm) Substrate : 0. 6 W (50 ppm/cm) Our target of substrate : 20 ppm/cm 32

Sensitivity of KAGRA Thermal noise Assumption (1) : Upper ends of fibers are fixed rigidly. Resonant frequencies (except for violin modes) are different from the actual system. However, thermal noise above the resonant frequency is the same. Assumption (2): Number of fiber : 4 Fiber length : 0. 3 m Fiber diameter : 0. 16 mm Q-values of sapphire fibers : 5*106 Horizontal motion along optical axis Pendulum and violin modes Loss dilution by tension (gravity) must be taken into account. 33

1. Introduction 34

Thermal noise (pendulum) ET-LF : 211 kg mirror, 3. 3 mm diameter and 2 m length fiber. Pendulum Q > 109 Fiber Q > 107 CE : 120 kg mirror, 2. 5 mm diameter and 0. 5 m length fiber. 20 K operation : Pendulum Q > 107 Fiber Q > 5*105 120 K operation : Pendulum Q > 2*108 Fiber Q > 3*106 CE : 120 kg mirror, 2. 5 mm diameter and 2 m length fiber. 120 K operation : Pendulum Q > 6*108 Fiber Q > 2*10635