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Entry  Sat Sep 24 17:12:54 2011, Koji, Update, LSC, Realignment of REFL / Some 3f PRMI locking / Recycling Gain 
    Reply  Sat Sep 24 20:14:36 2011, Koji, Update, LSC, Rough estimation of the PR gain 
    Reply  Mon Sep 26 15:15:45 2011, Anamaria, Update, LSC, Realignment of REFL / Some 3f PRMI locking / Recycling Gain 
Message ID: 5541     Entry time: Sat Sep 24 20:14:36 2011     In reply to: 5539
Author: Koji 
Type: Update 
Category: LSC 
Subject: Rough estimation of the PR gain 

 

POXDC (i.e. POY DCout)
PRM misaligned: 70cnt
CA resonant PRMI: ~8000cnt (max)

REFLDC

PRMI antiresonant = 5200cnt
PRMI resonant = ~3000cnt
==> Visivility = 0.6

PRM
Transmissivity: TR=0.0575, tR=sqrt(TR)


Rough estimation of the power recycling gain (assuming perfect mode matching)

PPRM_mialign = Pin tR2
PPRM_resonant = Pin [tR/(1-rR rMI)]2

G = tR2 PPRM_resonant / PPRM_mialign = 8000/70*0.0575 = 6.5

This is way too low compared with the design (G>40)
This corresponds to rMI2=0.885 (loss of 10%) in the power recycling cavity.
But this yields visibility of 16%, instead of 60% which we saw. This is inconsistent.


If mode matching is not perfect, effective incident power of PRMI decreases
and this discrepancy may be explained

Pin = Pjunk + (Pin-Pjunk)

PPRM_mialign = Pin tR2
PPRM_resonant = (Pin-Pjunk) [tR/(1-rR rMI)]2

PREFL_antires ~ Pin
PREFL_resonant = Pjunk+(Pin-Pjunk)[-rR+(tR2 rMI)/(1-rR rMI)]2

===>

PPRM_resonant / PPRM_mialign = (1-Rmm) /(1-rR rMI)2=8000/70
PREFL_resonant /PREFL_antires= Rmm+(1-Rmm)[-rR+(tR2 rMI)/(1-rR rMI)]2=0.6

here Rmm= Pjunk/Pin is the mode matching ratio

Solving the last two equations, we obtain

Rmm=0.6,
rMI2= 0.939 (loss of 4-5%)

Can we believe that the mode matching is 60% and the loss is 5%???

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