ELOG - North Cavity Temperature Fluctuations from Slow Voltage Laser Control

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Fri Dec 22 10:54:24 2017, Craig, DailyProgress, TempCtrl, North Cavity Temperature Fluctuations from Slow Voltage Laser Control

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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