Measured Q of sapphire mirrors at KAGRA site All results are summarized in klog. ETMX : 23.6904 kHz Q=1.1*10^5 80K GTAT ITMX : 23.65325 kHz Q = 6.4*10^4 250K 34.3927 kHz Q = 3.5*10^4 Shikosha ITMY : 23.6476 kHz Q=2.1*10^4 250K 34.3465 kHz Q=1.8*10^5 Shinkosha ETMY : 23.7124 kHz Q=2*10^4 250K 34.4963 kHz Q=2*10^5 GTAT 50.7746kHz Q=1*10^5 51.03675kHz Q= 3*10^4 51.1698 kHz Q=3*10^4 Ref.1 Mirror Q in KAGRA official sensitivity is 10^8. Ref.2 T. Uhiyama Ph.D. Suspended sapphire mirror (100mm in diameter, 60mm in thickness, Crystal systems Hemlite grade) without ears and nail heads and any bonding techniques. 300K 51kHz 3*10^6 68kHz 4*10^6 77K 51kHz 3*10^7 68kHz 4*10^7 20K 51kHz 5*10^7 68kHz 1*10^8 Thermal noise evaluation by K. Komori (K. Yamamoto checked) Mirror thermal noise by sapphire substrate is half order of magnitude smaller than O4a sensitivity. Note 1 : The mirror temperature is assumed to be room temperature. If Q is independent of temperature, the thermal noise at 20K is 4 times smaller than that at 300K. -> 20Mpc ? (25 Mpc, Virgo in O2) Note 2 : Thermal noise strongly depends on loss distribution in mirror. Homogeneous distribution is assumed in above calculation. If loss is inhomogeneous, thermal noise amplitude could be 3 or 10 times smaller (K.Yamamoto Ph.D.) except for coating. Fundamentals (1)Measured Q of mirror is limited by sapphire substrate loss and other parts (bonding and so on). (2)Thermoelastic noise of substrate does not matter for Q (Q limited by thermoelastic noise depends on size and shape. Q of bulk thermoelastic damping is quite small). (3)Here we do not consider coating (According to measurement and calculation at Toyama, Q limited by coating is 10^8). What do old theses tell us ? Q limited by substrate loss has no or weak frequency dependence (K. Numata, master and Ph.D. theses). Q limited by inhomogeneous loss has strong frequency dependence (N. Ohishi, master thesis) because energy density around loss depends on mode. -> If measured (a few or several or even more) Q-values varies, (a)the highest Q indicate the upper limit of substrate loss (b)the lowest Q indicate the upper limit of inhomogeneous loss (bonding and so on). Example 1 ITMY : 23.6476 kHz Q=2.1*10^4 250K 34.3465 kHz Q=1.8*10^5 Shinkosha ETMY : 23.7124 kHz Q=2*10^4 250K 34.4963 kHz Q=2*10^5 GTAT 50.7746kHz Q=1*10^5 51.03675kHz Q= 3*10^4 51.1698 kHz Q=3*10^4 -> Only 34kHz mode Q is high. -> Sapphire substrate Q is 2*10^5 AT LEAST. No vendor dependence. Example 2 ITMX : 23.65325 kHz Q = 6.4*10^4 250K 34.3927 kHz Q=3.5*10^4 Shikosha ITMY : 23.6476 kHz Q=2.1*10^4 250K 34.3465 kHz Q=1.8*10^5 Shinkosha ITMX Q (34kHz) is smaller than ITMY Q (34kHz). Vendor is same. -> by inhomogenous loss ? or individual differences of substrate from same company ?? Example 3 ETMX : 23.6904 kHz Q=1.1*10^5 80K GTAT ITMX : 23.65325 kHz Q = 6.4*10^4 250K Shikosha ITMY : 23.6476 kHz Q=2.1*10^4 250K Shinkosha ETMY : 23.7124 kHz Q=2*10^4 250K GTAT -> Temperature dependence ? Summary (1)Sapphire substrate Q is 2*10^5 AT LEAST. No vendor dependence. Q which is on the order of 10^4 might be limited by inhomogeneous loss. -> First priority ? (2)Q of 24kHz suggests temperature dependence ? No vendor dependence. -> Q measurement after cooling is necessary. Reason why measured Q was so low can NOT be explain easily. (mirror Q limited by inhomogeneous loss) = (Q of loss)*(total energy of mirror)/(energy in loss) can be approximated as (Q of loss)*(total volume of mirror)/(loss region volume) Example Let us assume that sapphire ears has large loss and it limit Q. The ratio of volume of ears to mirror is on the order of 0.01. If sapphire ears Q is 10^2, the mirror Q is 10^4. Loss in smaller parts can not reduce Q as measured. Concern : Young's modulus in bonding is smaller than sapphire. Although D.Chen (Ph.D.thesis) calculated thremal noise with Levin's method, Q was not calculated. Comparison with T.Uchiyama Ph.D. thesis His mirror was smaler than KAGRA mirror -> Size dependence of Q ? His sapphire suspension did NOT have (1)HCB -> It works in LV well. (2)Ears -> If ear Q is 10^2, mirror Q is 10^4. (3)Gallium -> D. Chen (Ph.D.) investigated Indium. Q of sapphire sample with indium bonding was about 10^5 at 300K. Indium Q is about 10^2. Weak temperature dependence (Q at 6K is 10 times smaller than that at 300K) Glasgow measurement shows Ga Q is comparable with In Q. (4)Nail head of fiber ->T. Shishido (master thesis). Q of fiber with nail hear is 10^5 ? (5)Magnet and magnet spacer -> N. Ohishi (master thesis) Q of mirror with magnet 10^4 ~ 10^5. Her mirror is TAMA size (100mm in diameter, 60mm in thickness) which is smaller than KAGRA mirror. Her magnets were larger than KAGRA magnet. Coil induced current -> Viscous damping. If Q (=10^4) of mirror is limited by this damping, the pendulum mode Q must be around unity (Q is proportional to resonant frequency). If we assume structure damping of sapphrie substrate, sapphire substrate loss at 20K (Q=10^7) is comparable with coating thermal noise. The details must be checked. Errors must be checked carefully. Experiment Loss budget must be clear. Mesurement of Q of sapphire substrate or sapphire mirror with ears in order to where the loss is. NAOJ has sapphire bulk with ears. Nodal support system -> Coating damage. It is difficult to treat heavy mass. Steel wire suspension -> Stand off is necessary. However it can be removed. Electro static actuator -> D. Chen used in his Ph.D. thesis. The gap is 1mm. KAGRA mirror is much havier than his sample. Room temperature ? Team to cosider plan and so on is necessary.