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Wed Mar 25 01:37:35 2009, rana, yoichi, Summary, IOO, No Reference Cavity Required
Wed Apr 1 23:18:07 2009, rana, koji, Summary, IOO, No Reference Cavity Required
Wed Apr 1 23:18:07 2009
In reply to:
No Reference Cavity Required
Koji sent us a note about our "No Reference Cavity Required" entry. I thought that it nicely summarizes the
whole shebang and so I post it here for its pedagogical value.
Generally, frequency stabilization is a comparison of the two
1. In the conventional case you are comparing the NPRO stability with
the RC stability. The NPRO cavity is short and probably placed in a
less stable environment than that of the RC. Therefore, the PDH
signal only feels the frequency fluctuation of the NPRO, resulting
in the laser PZT fast feedback dominated by the NPRO stability. As
the MC length at low frequency is controlled by the mass feedback,
the resulting laser stability through the MC is virtually limited
by the RC stability.
2. On the other hand, you are comparing the stabilities of the NPRO
crystal and the MC cavity in the direct control configuration. The
stability of the MC at high frequency is better than that of the
NPRO. It is opposite at low frequency, of course, because of the
pendulum motion. The resulting laser stability through the MC is
limited by the MC stability.
3. In the CM servo, the length of the MC is stabilized such that the
arm stability is duplicated to the MC. As a result, your MC servo
compares the stability between the NPRO and the arm cavity. Again
at around 1Hz, the arm cavity is noisier than the NPRO. (This is
true at least TAMA case. I am quite unsure about it in the LIGO
long arm cases.)
One useful consequence is that in those configurations, the laser PZT
feedback at around 1Hz represents the stability of the NPRO, the MC,
and (possibly) the arm cavity, respectively. It was clearly seen
Yoichi's e-log entry 1432. At TAMA we call this signal as "MCPZTfb"
and use this for the diagnostic purposes of the suspended cavities. As
the laser fast PZT is rarely replaced and considered as a stable
actuator, this signal is considered as a good reference at low
frequency which is consistent across various configurations
(e.g. before/after replacement of the suspensions etc). Once the
response and the coefficient are calibrated you can easily convert
this signal to the length displacement.
Another remark: In the direct configuration, the frequency stability
of the beam goes through the MC is determined by the MC stablity. It
means that the beam to the arm has essentially worse stability than
the arm stability by factor of L_arm/L_MC. In the 40m case this factor
is just 3 or so. This is ok. However, for the LIGO 4km arm, the factor
becomes something like 300. This means that if you have 1um_rms of the
MC length fluctuation, the arm PDH feels 300um_rms. (Maybe some extent
less because of the common mode rejection of the MC suspensions.)
Yes, the actuator to the MC length is very strong this time, and
should be able to stop this amount of fluctuation easily... if the
things are all linear. I am not certain whether you can acquire the
lock even by this strong actuator when the arm is crazily swinging,
the PDH signals are ringing all the way, etc, etc...Particularly in
the recycling case!
One possible remedy is a technique developed by the German
necromancers, as always. They used the NPRO cavity as a reference
cavity. They actuate the MC length at low frequency. But I don't know
the exact configuration and how they accomplished the CM hand-off. We
have to ask Hartmut.
The other possibility is your adaptive stabilization of the MC by the
FIR technique. So far I don't know how much stability you can improve
in the LIGO 4km case.
There would be many possibilities like feedforward injection from the
green arm locking signal to the MC length, etc, etc.