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Entry  Fri Dec 22 10:54:24 2017, Craig, DailyProgress, TempCtrl, North Cavity Temperature Fluctuations from Slow Voltage Laser Control 
    Reply  Wed Jan 10 16:04:03 2018, awade, DailyProgress, TempCtrl, North Cavity Temperature Fluctuations from Slow Voltage Laser Control 
Message ID: 2027     Entry time: Fri Dec 22 10:54:24 2017     Reply to this: 2038
Author: Craig 
Type: DailyProgress 
Category: TempCtrl 
Subject: North Cavity Temperature Fluctuations from Slow Voltage Laser Control 

We have a calibration of the north slow voltage control into laser frequency of \dfrac{df}{dV_{\text{slow}}} = 3.481 \,\dfrac{\text{GHz}}{\text{V}_\text{slow}}.

From this number we can estimate how much the cavity temperature is fluctuating based on what laser frequencies lock our cavities:

\dfrac{\Delta L}{L} = -\dfrac{\Delta f}{f}, where L is the cavity length of 3.68 \,\text{cm} and f is the frequency of the resonating laser in the cavity.  

When the temperature of the cavity changes, we change the length of the cavity as well according to

\Delta L = \alpha \,L \,\Delta T, where \alpha is the coefficient of linear expansion of 5.5 \times 10^{-7} \,\text{K}^{-1}, and T is temperature.

Combining the above gives

\dfrac{df}{dT} = -\alpha \,f = -155 \,\dfrac{\text{MHz}}{\text{K}}

Combining with the calibration of the laser slow voltage:

\dfrac{df}{dV_{\text{slow}}} \bigg/ \dfrac{df}{dT} = -22.5 \dfrac{\text{K}}{\text{V}_\text{slow}}

We usually get fluctuations in \text{V}_\text{slow} on the order of 10^{-4} \,\text{V}, which would mean our cavity is fluctuating in temperature by ~2\, \text{mK}.

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