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L_BS_PR2 is the separation between the center of BS chamber and the center of PR2 chamber. The following table shows the the Folding parameters with three different cases of L_BS_PR2. Case 1 is the default plan. Case 2 adds 2m to the BSPR2 separation, and Case 3 adds 3m. Note that the arm cavity gfactor is assumed to be negative (1.5km1.9km), which usually gives slightly smaller beam sizes on the PRM.  L_BS_PR2Folding AngleLp1 Lp2 Lp3 PRM ROCPRM Beam SizePR2 ROCPR2 Beam SizePR3 ROCPR3 Beam Size Case 12.7m0.63deg14.76m12.07m14.76m310.42m4.05mm3.13m4.05mm27.01m35.43mm Case 24.7m0.67deg14.09m11.40m16.10m295.3m3.95mm2.88m3.95mm25.45m35.46mm Case 35.7m0.69deg13.76m11.06m16.76m287.75m3.91mm2.75m3.91mm24.67m35.48mm === Layout files === The optical layout files corresponding to the above cases. [[https://granite.phys.s.utokyo.ac.jp/svn/LCGT/trunk/mif/OptLayout/Layout/bLCGT_OptLayout.dxfCase 1]] [[https://granite.phys.s.utokyo.ac.jp/svn/LCGT/trunk/mif/OptLayout/Layout/bLCGT_OptLayout_add2m.dxfCase 2]] [[https://granite.phys.s.utokyo.ac.jp/svn/LCGT/trunk/mif/OptLayout/Layout/bLCGT_OptLayout_add3m.dxfCase 3]] == iLCGT > bLCGT PRCL/SRCL change due to the substrate change == Because the substrate material will be changed from Silica to Sapphire between iLCGT and bLCGT, the index of refraction change will induce the optical path length change of PRC and SRC. We can cancel this change by simply moving the ITMs. Probably we will do this. However, a question to be answered here is whether it is possible to cancel the change by changing the MC length and consequently changing the f1/f2 frequencies. In short, the answer to the question is "Yes". In general, it is not possible to satisfy the resonant condition of PRC and SRC at the same time, just by changing the MC length. Once the Lprc is given, the RF sideband frequencies are given as follows, f1 = q*c/(4*Lprc)<<BR>> f2 = p*c/(4*Lprc) ,where p, q are integral numbers and c is the speed of light.<<BR>> Now, once the f1 frequency is given, the length of SRC is given in the following form: Lsrc = n*c/(2*f1) Lprc ,where n is an integer. The MC length is given as Lmc = 2*Lprc/a, a = GCD(p,q). <<BR>> If Lprc is changed to Lprc2 = Lprc + dL, then a new f1 frequency f1d has to be chosen to still resonate it in the PRC. Since, f1d = q*c/(4*Lprc2), 1/f1d = 1/f1 + 4*dL/(q*c). Therefore, the new SRC length (Lsrc2) to resonate f1 in the SRC is: Lsrc2 = n*c/(2*f1d)  Lprc2 = Lsrc + 2*n*dL/p. This means, if n = p, Lprc2 = Lsrc + dL, meaning that f1d automatically resonates in the SRC. This is not the case in general. However, if we chose n to make Lprc = Lsrc, then n = p is automatically satisfied. The current length parameters of LCGT falls into this category. Therefore, it is possible to cancel the optical distance change by the substrate change of ITMs just by changing the MC length. 
Layout related issues
Contents
Location of PR2 tank
Is it possible to put the PR2 and SR2 vacuum chambers further away from the BS chamber ? The minimum separation is 2.7m (centertocenter). However, in order to improve the workability around the BS chamber, we want increase the separation.
Comparison Table
L_BS_PR2 is the separation between the center of BS chamber and the center of PR2 chamber. The following table shows the the Folding parameters with three different cases of L_BS_PR2. Case 1 is the default plan. Case 2 adds 2m to the BSPR2 separation, and Case 3 adds 3m.
Note that the arm cavity gfactor is assumed to be negative (1.5km1.9km), which usually gives slightly smaller beam sizes on the PRM.

L_BS_PR2 
Folding Angle 
Lp1 
Lp2 
Lp3 
PRM ROC 
PRM Beam Size 
PR2 ROC 
PR2 Beam Size 
PR3 ROC 
PR3 Beam Size 
Case 1 
2.7m 
0.63deg 
14.76m 
12.07m 
14.76m 
310.42m 
4.05mm 
3.13m 
4.05mm 
27.01m 
35.43mm 
Case 2 
4.7m 
0.67deg 
14.09m 
11.40m 
16.10m 
295.3m 
3.95mm 
2.88m 
3.95mm 
25.45m 
35.46mm 
Case 3 
5.7m 
0.69deg 
13.76m 
11.06m 
16.76m 
287.75m 
3.91mm 
2.75m 
3.91mm 
24.67m 
35.48mm 
Layout files
The optical layout files corresponding to the above cases.
iLCGT > bLCGT PRCL/SRCL change due to the substrate change
Because the substrate material will be changed from Silica to Sapphire between iLCGT and bLCGT, the index of refraction change will induce the optical path length change of PRC and SRC. We can cancel this change by simply moving the ITMs. Probably we will do this. However, a question to be answered here is whether it is possible to cancel the change by changing the MC length and consequently changing the f1/f2 frequencies.
In short, the answer to the question is "Yes".
In general, it is not possible to satisfy the resonant condition of PRC and SRC at the same time, just by changing the MC length. Once the Lprc is given, the RF sideband frequencies are given as follows,
f1 = q*c/(4*Lprc)
f2 = p*c/(4*Lprc)
,where p, q are integral numbers and c is the speed of light.
Now, once the f1 frequency is given, the length of SRC is given in the following form:
Lsrc = n*c/(2*f1) Lprc
,where n is an integer. The MC length is given as Lmc = 2*Lprc/a, a = GCD(p,q).
If Lprc is changed to Lprc2 = Lprc + dL, then a new f1 frequency f1d has to be chosen to still resonate it in the PRC. Since, f1d = q*c/(4*Lprc2), 1/f1d = 1/f1 + 4*dL/(q*c). Therefore, the new SRC length (Lsrc2) to resonate f1 in the SRC is:
Lsrc2 = n*c/(2*f1d)  Lprc2 = Lsrc + 2*n*dL/p.
This means, if n = p, Lprc2 = Lsrc + dL, meaning that f1d automatically resonates in the SRC. This is not the case in general. However, if we chose n to make Lprc = Lsrc, then n = p is automatically satisfied. The current length parameters of LCGT falls into this category. Therefore, it is possible to cancel the optical distance change by the substrate change of ITMs just by changing the MC length.