40m Upgrade parameters Preliminary, 5/16/2002 Alan Weinstein, ajw@ligo.caltech.edu ______________________________________ Readout scheme: - Two pairs of phase-modulated sidebands, applied in series. - Both are resonant in the power recycling cavity (PRC). Neither are resonant in the F-P arms. - Chose one to be as high as possible, limited by practical high-power modulators and photodetectors: 180 MHz. Chose the other to be as low as possible, while still resonant in an ~2m PRC: 36 MHz. The higher sideband must be an integral multiple of the lower; both must pass through the mode cleaner. - The Schnupp asymmetry is chosen to make the 180 MHz bright at the asymmetric port of the BS; the 9 MHz is near the dark fringe, and the carrier is at the dark fringe. - THUS, the 180 MHz mainly senses the signal recycling mirror (SRM), leaving the 9 MHz primarily sensitive to the power recycling mirror (PRM). - Carrier light, beating against the 9 MHz at the symmetric port, senses L+; Carrier light, beating against the 180 MHz at the asymmetric port, senses L-; and the l_PRC, l_SRC, and l_M (Michelson) are sensed by beating the 180 against the 9 MHz at the various ports; carrier light, sensing the large arm phase shifts, is not used for sensing the shorter degrees of freedom. __________________________________________ Cavity lengths, asymmetry, RF frequencies: L_arm = (n1 + 0.5) * c / 2 f1 = 38.55 m for f1 = 33.207e6 Hz, n1 = 8.040 (n1 should not be an integer+0.5, so that f1 is not resonant in the arms. it need not be exactly an integer; f1 need not be exactly antiresonant.) L_arm = (n11 + 0.5) * c / 2 f2 = 38.55 m for f2 = 166.033e6 Hz, n11 = 42.20, not resonant. L_MC = n2 * c / 2 f1 = 13.542 m for n2 = 3 This is the shortest mode cleaner that will pass both f1 and f2 f2 = n3 * f1 = 166.033 MHz for n3 = 5 so that both f1 and f2 are resonant in both the MC and the PRC L_PRC = (n4 + 0.5) * c / 2 f1 = 2.257 m for f1 = 33.207 e6 Hz, n4 = 0. L_M = Michelson asymmetry = c / 4 f2 = 0.451 m for f2 = 166.033 MHz. L_SRC = (n3 - dt / 2) * c / 2 f2 - L_PRC = 2.151 for n3 = 5 and dt = 0.235 where dt is the round-trip carrier tune in the SRC, in units of pi radians. This value of dt places the peak response of the IFO at 4000 Hz, maximizing the S/N for a binary inspiral in the presence of thermal test mass noise. L(PRM to BS) = 0.300 m L(SRM to BS) = L_SRC + L(PRM to BS) - L_PRC = 0.200 L(BS to ITMx) = L_PRC - L(PRM to BS) + L_M/2 = 2.183 L(BS to ITMy) = L_PRC - L(PRM to BS) - L_M/2 = 1.731 These lengths are OPTICAL path lengths; physical path lengths are a bit shorter for L(BS to ITMx) by approximately (n-1)*(sqrt2*Thickness_BS+Thickness_ITM) for L(BS to ITMy) by approximately (n-1)*(Thickness_ITM) for L(BS to SRM) by approximately (n-1)*(sqrt2*Thickness_BS) where n = 1.4496 for FSi. __________________________________________ Mirror transmissivities, DC fields: AdvLIGO was optimized for best S/N for binary inspiral in the presence of test mass thermal noise, by P Fritchel, K Strain, etal, 8/2000, using bench.m. See: http://www.ligo.caltech.edu/~ligo2/scripts/l2refdes.htm 40m uses SAME transmissivities, to acheive SAME cavity finesses (different light storage times, cavity poles). - T_ITM = 0.005 - T_SRM = 0.070 - T_PRM = 0.060, 0.065, 0.070 - T_ETM = 15 ppm - Average power loss per mirror = 37.5 ppm - laser power = 1 W Due to the SRC detuning, the response of the IFO to the +ve and -ve RF sidebands are different (unbalanced). For these numbers (somewhat unrealistic for sapphire loss), - arm pole frequency = 1578 Hz - arm finesse = 1235 - Arm power gain = 775 - PRC finesse = 47 - PRC power gain = 16.5 (carrier) DC fields @ 1 Watt input power, Assuming modulation depth of 0.1 for both pairs of RF sidebands: Input SymPort AsymPort PRC SRC Armx Army SB -2 0.0025 0.0025 0.0000 0.0000 0.0001 0.0000 0.0000 SB -1 0.0025 0.0023 0.0001 0.0577 0.0017 0.0012 0.0018 Carrier 0.9900 0.0062 0.0000 14.067 0.0000 5414.8 5414.8 SB +1 0.0025 0.0021 0.0003 0.1482 0.0039 0.0043 0.0035 SB +2 0.0025 0.0000 0.0024 0.0345 0.0321 0.0001 0.0001 It all depends on what and where you put the losses; your mileage may vary! __________________________________________ Radii of curvature, beam sizes: Choose a half-symmetric arm cavity with g factor = 1/3: R_ETM = 57.375 m R_ITM = flat (> 5625 m) waist = 3.027 mm at ITM (1/e^2 intensity) zr = 27.05 m w_ITM = 3.027 mm w_ETM = 5.242 mm d1ppm_ETM = 28 mm GuoyArm = 0.955 rad R = 21192 m (back of ITM) w = 3.027 mm (back of ITM) R_BS = 412 m w_BS = 3.033 mm R_RM = 348 m w_RM = 3.036 mm R_RM2 238 m (back of RM) w_RM2 = 3.036 mm (back of RM) R_SM = 365 m w_SM = 3.035 mm OK, this was the pre-10/31/01 spec, which was used to order the mirrors. On 10/31/01, some lengths were changed (eg, Larm = 38.25 -> 38.55 m) and in 6/02, the polished mirrors were received. Here's a revised (8/14/02) spec: optic spec toler delivered new-spec ETM 57.375 0.600 57.57,57.68 57.625 PRM 348 20 355,356,343 328+-20 SRM 365 25 367,377,386 343+-25 The ROC as delivered lead to <1% mode mismatch. See also http://www.ligo.caltech.edu/~ajw/40m_optspecs.txt for info about optics as delivered. __________________________________________ Mirror dimensions: ITM (FSi, Heraeus low absorption) and ETM (Fsi, Corning): 125 mm diameter 50 mm thick 30 mm clear aperture 1.3 kg mass BS (FSi, Heraeus low absorption), PRM (Fsi, Corning), and SRM (Fsi, Corning): 75 mm diameter 25 mm thickness 30 mm clear aperture 0.23 kg mass