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## Temperature study.

• QD10X was tuned at 00:38:30 on 19:10:11 local time.
• Cavities from QD10X to QD19X and REFC1 were tuned between 21:20 to 21:50 on 20/10/2011.

• As only IQ phase is been observed, the phase change observation of any cavity will be affected by frequency change in reference cavity as well. I think, best way to study is to export phase of signal (Before reference phase subtraction) at three sample points during signal. Advantage of this over exporting phase difference is that, the effects of phase wrapping will be visible.

• Thermal expansion coefficient (linear) of copper (at 20 ) is,

• Change in radius of pipe (with both ends free) with temperature is, dr = dT * r * alpha,
where 'r' is radius of pipe, 'dT' is temperature change, 'alpha' is thermal expansion coefficient of the material

• As resonant frequency of the cavity varies linearly with radius, the approximate change in cavity frequency will be, = 109 kHz for C-band Cavity and 49 kHz for S-band cavity.

Where is resonant frequency of the cavity.

### Temperature and phase for start=10/20/2011 21:50:00 to 10/21/2011 08:30:00

Overall temperature variation and IQ-phase

• Maximum temperature difference during specified time.
• IQ-Phase plot for QD10X and other cavities does not show any apparent phase change, but I still need to get some sensible number of of it.
• Red curves -> without reference amplitude cut.
• Green curves -> with reference amplitude >1500 .
• Black partial segments -> data used to calculate d.

• The DDC-Phase (without normalization) dipole and reference cavities show change with time, as well as phase jumps. It is hard to determine if is because of change in beam arrival time or frequency change.

### QD10X- DDC phase change observation

• Average temperature (reference amplitude cut>1500) for cutsample[0:400] = 25.3 (residual=0) and for [cutsample][7800:8200] = 25.809 C, implies dT = 0.5 C

• Average phase (with reference amplitude cut >1500) for cutsample[0:400] = -1.035575 radian, and for [cutsample][7800:8200] = -1.229143 radian,implies dphi/dT = 0.48 rad/C

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Topic revision: r9 - 29 May 2014 - FrankieCullinan

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