on last tuesday, I did a long-term measurement of the frequency drift when the heating cable is powered ON at 20V (2x 10V) @ t=0mn.

the freqeuncy drift (between the laser, locked in open loop on the FP-cavity, and the RF reference oscillator) acquisition was made by the National Instrument software.
the sampling rate of this acquisition is not set by the user but depends on several parameters of the acquisition... and then can be subject to change.

on can see on the data, in blue, a possible sampling rate change @ t~30mn.
@ t~100mn : the frequency sign changes but the measurement gives always the absolute value.

in orange, the fit is not very good... possibly due to the sampling rate change.

the conclusion we can have is only this frequency drift action has a very long time constant ~ 2h
and could be used to compensate, as soon as the power is in the FPcavity, the frequency drift coming from this power.
 

the 2 files describe the specfications for the16  mirrors ordered (4 for ThomX + spare, 4 for SBOX + spare) and the measurements made by the LMA.

last friday, I locked the cavity and then, switched ON the heating cable after waiting the cavity reaches a steady state in frequency drift : see the figure.
blue : temperature of the probe on the heating cable
red : freqeuncy drift between FP-cavity (laser locked on it) and RF reference oscillator.

@ 10min : filling the FP-cavity with 50kW
@ 50min : "long" lock loss of about 1min => jumb in frequency => it is strange to see the cavity does not reach the same frequency steady state after the lock loss than before the lock loss.
(just before the small frequency jump, the frequency is increasing a bit because of the lock has been lost and the laser is drifting by itself in open loop. the jump, after that, corresponds to the moment where the laser is locked back to the FP-cavity)
​@ 55min : switch ON the heating cable with 20V on the voltage supply => the probe stuck on the cable shows the temperature increases => and a bit later, one can see the frequency decreasing.

surprisingly, we don't reach a steady state ...
I suspect that filling the FP-cavity with power (without switching ON the heating cable) could first inscrease the frequency and later could decrease it if several parts of the mechanics are involved and if the thermal conduction is slow because of some isolation embbedded in the mechanics (for example ceramics balls).

it is possible to make the frequency drifting sensitivity test of the heating cable without locking the cavity at 50kW.
one can work in open loop, without power in the FP-cavity, and follow the frequency drift by keeping the main resonance at the same relative position to the laser PZT.
 

this afternoon, I started the heating cable after the warm-up of the FP-cavity :

14h20 : start to fill 50kW in the cavity
15h : start of the heating cable @10V (2x 5V) (iteration 2300)
15h16 : start of the heating cable @60V (2x 30V) (iteration 3400)
15h20 : start of the heating cable @20V (2x 10V) (iteration 3600)

the offset frequency, for 20V of voltage on the DC voltage supply, is 175Hz @500MHz (equivalent to 3.5µm)
 

this morning I monitored the frequency shift between the FP-cavity frequency (the laser is locked on it) and the RF reference frequency @ 500MHz,
during the warm-up time, for 50kW stored in the cavity (the recording started ~ 9h20).

one observes on fig.1 a simple exponential behavior with 500Hz frequency shift @500MHz (equivalent to ~ 10µm) for 50kW stored. 
the time constant T of the exponential curve is 12.5 minutes and the stable region starts at 5T ~ 1h.

the small drop at the end of the curve ( ~ @10h30) could come from the external temperature which started to drift before (see fig.2)

this afternoon, we did a new long-term "double lock" run w/o any single lock loss during 1/2h.

we did 2 acquisitions :

fig 1 : phase measurement between the 33MHz signal coming from the laser and the 500MHz RF.
this plot doesn't last 1/2h.
the measured jitter is ~45ps, at the limit of the scope resolution.

fig 2 : same phase measurement between the two 500MHz signals (laser and RF)
the lock is lost at the end of the plot.
the measured voltage noise is Vrms ~ 2.5mV rms => jitter ~  2.8ps rms

the conversion factor between jitter and voltage is 1,1 ps / mV

!!! CAREFUL !!! heating the FP-cavity with the heating cable works in the opposite direction of the heating due to power in the cavity !

today, I did a 20 minutes "double lock" run w/o any single lock loss.

the attached file shows the recorded RMS beating voltage between 500MHz signals (laser harmonic and RF reference).
the end of the plot after iteration ~1.8k shows the lock loss to the RF reference.

when the lock is not working, one gets a sine signal V=V0*sin(phi(t)) with V0=288mV => Vrms = 288/sqrt(2)) = 204mV rms
(this signal is not on the figure)

for low phase values : V=V0*dphi
when the locking is good, this voltage is about V = 3.5mV rms => dphi = 12mrad rms
a full beating signal period (500MHz => 2ns) corresponds to 2pi, so dphi = 12mrad rms => jitter dt = 4ps rms

today, I removed one of the DC voltage supply (as with 30V, we are already able to 30°C on the heating cable).

the remaining DC voltage supply is configured in series (2x30V = 60V max) and is at the IP address : 192.168.1.101

long-term correlation, over 5-6 days, between the temperature measured in the bunker, outside of the housing (blue curve) and the temperature measured with a probe stuck on the laser housing, inside of the FP-cavity housing (green).

it's a perfect correlation with almost the same temperature scale : 1°C outisde the housing => 1°C of laser housing

thus, a stabilization of the temperature, inside of the housing, could help to reduce the frequency drifts of the laser.

today for the first time, we were able to make a long term lock of all the elements (Laser on FP cavity and FP-cavity on RF reference) during 20 minutes @50kW without any single loss of lock.

the success of this long term lock was coming from the possibility to drive the Smaract motor in piezo-scan mode and to apply a heating on one vessel of the FP-cavity to let its frequency slowly drift always in the same direction.
then, the FP-cavity motor can follow this drift without any loss of the lock.

even when we lost the lock, it was quite easy to get it back because of the frequency drift, always in the same direction due to the FP-cavity heating with the heating cable.

a good strategy to make this double lock :
1) adjust the laser frequency to the RF reference frequency in using the Smaract motor in "closed loop" mode until reaching a beating < 10Hz.
2) search for FP-cavity resonance in using the ISP motor of the FP-cavity
3) once the laser is locked on the FP-cavity, the FP-cavity length changes => work on the FP-cavity motor to follow the drift until one reachs a thermal equilibrium.
4) once the thermal equilibrium is reached, one can switch on the heating of the heating cable to continue the slow "thermal" drift in the same direction 5V of total voltage should be enough for 1h of work.
5) in the same time, one need to cancel the frequency offset between the RF reference and the FP-cavity using the FP-cavity motor and one need to follow the laser cavity fluctuations using the Smaract motor in "closed loop" mode.
6) once the FP-cavity is at the same length than the RF-reference, one can close the second loop (when both PZT are in the middle of their range).
7) at that point, one need to swap the Smaract motor control to "piezo scan" mode => one follows only the laser fluctuations ~ 1µm peak-peak
8) one always follows the FP-cavity drift using the IcePap controller on the FP-cavity motor, 10 steps by 10 steps => it should work during 1h.
9) when one reachs the thermal equilibrium again, one can add 5V to the heating cable voltage.
 

several days ago, we installed a heating cable around the output flange (close to the X-hutch) of the FP-cavity vessel.
we are able to heat this cable by applying a DC voltage coming from 2 DC voltage supplies in serie (2 devices with 2x 0-30V / 3A => 0-120V / 3A).
currently, we apply at maximum 7V DC on each channel => 28V DC on the cable. its temperature reach ~ 30°C after 1/2h or more.

this temperature increase on one vessel of the FP-cavity, changes very slowly the length of the FP-cavity.
see this post (red curve on fig. 2) for a typical temperature curve measured (exponential-like curve) on the heating cable itself : https://elog.lal.in2p3.fr/FPC/THOMX+commissioning/290

the length change rate of the FP-cavity, due to this heating, is difficult to estimate because it depends on the part of this exponential curve you make the measurement.
but globally the drift is about 50nm every 5 minutes, which is roughly equivalent to 10 steps of the FP-cavity motor every 5 minutes.

current Smaract motors parameters : 
- Closed loop Max frequency : 5000
- Signal Amplitude threshold : 2047
- High voltage threshold : 511

when one drives the Smaract motors in "closed loop" mode, one can get a displacement as small as 50nm... but at the price of a delock of the laser/FP-cavity.

when one drives the motor in "open loop" mode, 1 step is equivalent to 4µm !!! it is much larger than the laser PZT range.

when one drives the motor in "Piezo Scan" mode with a speed of 1V/s, one can move the motor without losing the laser/Fp-cavity lock.
the PZT voltage range of 100V (max value) is roughly equivalent to 2-3µm of round trip length, which is enough to manage several "fast" (10-20 minutes) oscillations of the laser frequency :
see these posts to get some info on the laser frequency oscillations : https://elog.lal.in2p3.fr/FPC/THOMX+commissioning/289

today, I swapped the 500MHz RF reference oscillator for a Siglent 500MHz DDS oscillator.

see the attached plot : the beating frequency with the 500MHz laser harmonics produces the same behavior as before.
so, the oscillations should come from the laser temperature regulation.

the last thing we did with Daniele, is to start/stop the airflow on top of the housing (closed) to see a possible pressure effect on the laser frequency drift.

fig 1 : in green, the temperature measured with the probe stuck on the laser housing.
one can clearly see the 2 "start - wait ~10mins - stop" we did at 16h50 then at 17h30.
the air temperature blowed by the airflow is cooler than the housing temperature and we see the effect on the probe.

fig 2 : this is the laser frequency drift during the 1st airflow start/stop
the airflow has been turned on at 100 iterations and stopped at 500 iterations (~5 mins)
we don't see any correlation

fig 3 : this is again the laser frequency drift during the 2nd airflow start/stop
the airflow has been turned on at 1850 iterations and stopped at 2550 iterations (~10 mins)
we don't see any correlation

CONCLUSION : neither external temperature change or pressure variations can explain the 10-20min period oscillations observed on the laser frequency variations.
it can be either the laser temperature regulation or the RF reference oscillator temperature regulation (due to the oven of the quartz)

Now, I placed a temperature probe stuck on the laser housing itself.

fig. 1

one can compare the temperature measured at the surface of the laser housing and the beating frequency with the 500MHz reference oscillator
one sees a possible very long term correlation but there is no correlation at the minute level when we see the frequency oscillation after t=2000s.

the laser housing temperature seems not to induce directly a frequency variation.

fig 2 / 3

we applied 15W on the heating wire rolled around the FP-cavity flange.
in red, we see the temperature increasing on the probe rolled around the wire, reaching almost 30°C.
we heat the inside of the housing (airflow stopped) during more than 30 minutes
in green, we don't see any variation (even if one makes a zoom) of the temperature of the probe stuck on the laser housing.

in same time, on fig 3, one can see the frequency drift.
there is no correlation between the oscillations and the temperature.

CONCLUSION :
the laser frequency fluctuations does not seem to come from the outside temperature.
 

laser cavity :

when one decreases the laser motor position, the laser repetition rate increases (laser cavity length decreases).
=> +/- laser motor step  =>  +/- laser cavity roundtrip length => -/+ laser repetition rate => -/+ laser harmonic @500MHz 
=> +/- 100nm => +/- 200nm => -/+ 0.7Hz @33.33MHz => -/+ 10Hz @500MHz

here is the natural variation of the laser cavity frequency beating with RF @500MHz over 1h (~1.6s / iteration)
one can see some oscillations equivalent to ~1µm of roundtrip length with ~10 minutes period and maybe a slower drift or oscillation with ~2µm of roundtrip range over the hour.
I mention that I moved the laser "PZT" motor before taking the data : could it be the reason of the 10-20min oscillations ?

during the same time, here is a probe temperature curve (the probe in stuck on the end flange, close to X-hutch, of the FP-cavity, inside the housing... not close to the laser position).
the temperature variation range is ~2.5/100 °C which induces on inox (relative length thermal effect : 17e-6 /K) a length variation of 4µm of roundtrip (10m) which could be compatible to the laser cavity length variation measured.

bunker temperature @ 22.5°C

today, Sebastien Pitrel improved its python software to manually control the laser peltier.
we were able to make to some test. unfortunately, doing only one step change the 500MHz relative frequency by ~400Hz (see the attached plot from 480Hz to 100Hz which is the laser harmonic @500MHz compared to the RF reference @500MHz), which is equivalent to a round trip length variation of 8µm !!!
the present PZT's ranges are equivalent to 400nm of the round trip length. the laser PZT range could be extended by a factor 10 if one drives it using 100V instead of 10V actually, but it would not be enough to be able to use the Peltier ! :-(

if the Peltier changes the inox baseplate of the laser, the relative length change is 1e-5 /K which is equivalent to 100µm/K of the round trip length.
it means the internal temperature steps, done by the peltier, are around 0.08K.
maybe we could try to have smaller steps by using an external thermal setup ?

as the CFP motors displacements induce a cavity unlock, we try to change the cavity length by changing the temperature of elment of the cavity.

yesterday, we tried to put a "heating cable" borrowed to the vacuum group to change the temperature of one bellows between the FP-cavity and the electron ring.
we chose a below because it is flexible and should not apply a too strong force on the cavity vessels.
we heated the cable at ~30°C but we didn't see a clear effect on the FP-cavity frequency measurement.

then, we put a heating cable around the X-ray output flange of the FP-cavity vessel and we saw a clear effect : a relatively fast (at a "second" level) frequency change.
the problem is the heating system is not remotely driven.

the cable is R=55ohms impedance and can reach 450°C for 1kW dissipated.
so today, we will try to use 2 remotely controlled Siglent SPD3303X power supplies.
they can reach V=120V DC => P=V²/R=260W => we could reach more than 100°C

temperature @ 21.9°C

48.5kW inside CFP for 30% amplifier ratio

Frep Laser motor = 123.4µm
CEP motor = -67.8µm

below the image of the relative voltage range between CFP PZT (pink) and laser PZT (green).
the CFP PZT is driven by 10x the voltage range showed by the scope (0-100V HV output and 0-10V monitor on the Laselock)
one can see on the scope that the relative range of both PZT voltage range is roughly the same which means that the real CFP PZT sensitivity is 10x smaller than the Laser PZT sensitivity.
as the CFP PZT is driven by 0-100V and the Laser PZT is driven by 0-10V voltages, they have approximately the same range which is ~200nm (calibrated with the Laser motor in closed loop mode).

in a previous email, the CFP PZT should be given with a sensitivty of about 4nm/V => 400nm/100V of length range => 800nm/100V of CFP roundtrip range => 80e-9/100V of relative sensitivity => 40Hz of frequency peak-peak range for 500MHz carrier frequency.
there is a discrepancy between measurements (~10Hz peak-peak range for 500MHz carrier) and expected value !

temperature @ 22.3°C

today, all the PC applications were closed except the web browser.
I had to restart all of them, then try to relock.
(maybe I let the terminal window open with all the apps and someone tried to unlog by removing them ?)

the cavity height was pretty misaligned.
after a rough alignment, the power inside the cavity was back at 49kW for 30% amplifier ratio.

the CEP motor needs to be adjusted a lot during the cavity heating process