Difference: Ctf3Sensitivity (1 vs. 16)

Revision 1611 Feb 2014 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Finite Decay Time

Because the signal decays with a finite decay time, the assumption that the root mean square voltage over one period is the peak voltage divided by $\sqrt{2}$ is no longer valid. The corresponding value can be found by

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\[ \left(\frac{V_{rms}(\tau)}{\hat{V}}\right)^2=\frac{1}{T} \int_0^T e^{-\frac{2t}{\tau}}\sin^2 (2 \pi f t) dt = \frac{1}{2T}\int_0^T e^{-\frac{2t}{\tau}}(1-\cos (4 \pi f t)) dt \]
where f is the signal frequency, τ is the decay time and T is the time of one period in time t and is equal to 1/f. Evaluating the definite integral gives
 %BEGINLATEX%
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\begin{equation*} \frac{V_{rms}(\tau)}{\hat{V}}=\int_0^T e^{-\frac{2t}{\tau}}\sin^2 (\omega t) dt = \frac{1}{2}\int_0^T e^{-\frac{2t}{\tau}}(1-\cos (2 \omega t) dt \end{equation*} %ENDLATEX% where ω is the angular frequency, τ is the decay time and T is the time of one period in time t. Evaluating the integral gives
 \begin{equation*} \frac{V_{rms}(\tau)}{\hat{V}}=\frac{\tau}{4T}\left(1-\frac{1}{1+\omega^2\tau^2}\right)\left(1-e^{-\frac{T}{\tau}}\right) \end{equation*}
This is one case where the signal is given by a sine function. In the opposing case, where a cosine function is used instead, the expression evaluates to %BEGINLATEX{}%
Latex rendering error!! dvi file was not created.
 \begin{displaymath}
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\frac{V_{rms}(\tau)}{\hat{V}}=\frac{\tau}{4}\left(1+\frac{1}{1+\omega^2\tau^2}\right)\left(1-e^{-\frac{T}{\tau}}\right)\, .
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\left(\frac{V_{rms}(\tau)}{\hat{V}}\right)^2=\frac{\tau}{4T}\left(1-\frac{1}{1+(2 \pi f \tau)^2}\right)\left(1-e^{-\frac{2 T}{\tau}}\right)
 \end{displaymath} %ENDLATEX%
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This is one case where the signal is given by a sine function. In the opposing case, where a cosine function is used instead, the expression evaluates to
\[ \left(\frac{V_{rms}(\tau)}{\hat{V}}\right)^2=\frac{\tau}{4T}\left(1+\frac{1}{1+(2 \pi f \tau)^2}\right)\left(1-e^{-\frac{2T}{\tau}}\right)\, . \]
The median of these two cases is
\[ \frac{V_{rms}(\tau)}{\hat{V}}=\sqrt{\frac{\tau}{4T}\left(1-e^{-\frac{2T}{\tau}}\right)}\, . \]
 Another effect is the signal decaying before the first peak in the oscillation is seen. The peak time in the case of a

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META FILEATTACHMENT attachment="power.pdf" attr="h" comment="" date="1392113079" name="power.pdf" path="power.pdf" size="21245" user="pvap079" version="1"
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Revision 1511 Feb 2014 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Digitiser in 4.44 26.0 7.11 30.0

  • Position scale factor: 0.62 mm
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Finite Decay Time

Because the signal decays with a finite decay time, the assumption that the root mean square voltage over one period is the peak voltage divided by $\sqrt{2}$ is no longer valid. The corresponding value can be found by

 \begin{equation*} \frac{V_{rms}(\tau)}{\hat{V}}=\int_0^T e^{-\frac{2t}{\tau}}\sin^2 (\omega t) dt = \frac{1}{2}\int_0^T e^{-\frac{2t}{\tau}}(1-\cos (2 \omega t) dt \end{equation*}
where ω is the angular frequency, τ is the decay time and T is the time of one period in time t. Evaluating the integral gives
 \begin{equation*} \frac{V_{rms}(\tau)}{\hat{V}}=\frac{\tau}{4T}\left(1-\frac{1}{1+\omega^2\tau^2}\right)\left(1-e^{-\frac{T}{\tau}}\right) \end{equation*}
This is one case where the signal is given by a sine function. In the opposing case, where a cosine function is used instead, the expression evaluates to
 \begin{displaymath} \frac{V_{rms}(\tau)}{\hat{V}}=\frac{\tau}{4}\left(1+\frac{1}{1+\omega^2\tau^2}\right)\left(1-e^{-\frac{T}{\tau}}\right)\, . \end{displaymath}
Another effect is the signal decaying before the first peak in the oscillation is seen. The peak time in the case of a


Latex rendering error!! dvi file was not created.
 

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META FILEATTACHMENT attachment="possense.png" attr="h" comment="" date="1361106460" name="possense.png" path="possense.png" size="82817" stream="possense.png" user="Public.FrankieCullinan" version="2"
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META FILEATTACHMENT attachment="peak.pdf" attr="h" comment="" date="1392113079" name="peak.pdf" path="peak.pdf" size="14135" user="pvap079" version="1"
META FILEATTACHMENT attachment="power.pdf" attr="h" comment="" date="1392113079" name="power.pdf" path="power.pdf" size="21245" user="pvap079" version="1"

Revision 1408 Aug 2013 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Ace3p 9.8 52
CST 10 52
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possense.png refsense.png
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possense.png refsense.png
 

Electronics Chain Propagation

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 The mode R/Qs were now calculated by integrating over the full geometry instead of just the cavity length:. The results for the position cavity are:

Code R/Q /Ω Sensitivity/V nC-1 mm-1
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GdfidL 3.26 14.73
Ace3p 3.27 14.75
CST 4.55 17.40
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GdfidL 3.26 17.08
Ace3p 3.27 17.11
CST 4.55 20.2
  The results for the reference cavity are:

Code R/Q /Ω Sensitivity/V nC-1
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GdfidL 50.3 118
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GdfidL 50.3 117
 
Ace3p 50.7 118

Position signal (offset=1mm, charge=1nC) Reference signal (Charge=1nC)

Revision 1303 Jul 2013 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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GdfidL 50.3 118
Ace3p 50.7 118
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Position signal (offset=1mm, charge=1nC) Reference signal (Charge=1nC)
Location Volts dBm Volts dBm
Cavity out 14.7 36.4 118 54.4
Electronics in 3.37 23.6 5.39 27.6
Electronics out 5.99 9.60 9.2 32.6
Digitiser in 4.44 26.0 7.11 30.0

  • Position scale factor: 0.62 mm
 

Revision 1203 Jul 2013 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Correction, June 2013

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The mode R/Qs were now calculated by integrating over the full geometry instead of just the cavity length:
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The mode R/Qs were now calculated by integrating over the full geometry instead of just the cavity length:. The results for the position cavity are:
 
Code R/Q /Ω Sensitivity/V nC-1 mm-1
GdfidL 3.26 14.73
Ace3p 3.27 14.75
CST 4.55 17.40
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The results for the reference cavity are:

Code R/Q /Ω Sensitivity/V nC-1
GdfidL 50.3 118
Ace3p 50.7 118
 

Revision 1128 Jun 2013 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Ace3p 9.8 52
CST 10 52
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possense.png refsense.png
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possense.png refsense.png
 

Electronics Chain Propagation

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  • Position scale factor: 1.25 mm
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Correction, June 2013

The mode R/Qs were now calculated by integrating over the full geometry instead of just the cavity length:

Code R/Q /Ω Sensitivity/V nC-1 mm-1
GdfidL 3.26 14.73
Ace3p 3.27 14.75
CST 4.55 17.40
 

Revision 1012 Apr 2013 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Electronics out 7.4 30.4 9.2 32.3
Digitiser in 5.5 27.8 6.9 29.7
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  • Position scale factor: 0.8 mm-1
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  • Position scale factor: 1.25 mm
 

Revision 904 Apr 2013 - FrankieCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Electronics out 7.4 30.4 9.2 32.3
Digitiser in 5.5 27.8 6.9 29.7
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  • Position scale factor: 0.8 mm-1
 

Revision 818 Feb 2013 - webmanip_5foldt2nt_2esh

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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META FILEATTACHMENT attachment="refsense.png" attr="h" comment="" date="1361106346" name="refsense.png" path="refsense.png" size="86511" stream="refsense.png" user="Public.FrancisCullinan" version="1"
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META FILEATTACHMENT attachment="possense.png" attr="h" comment="" date="1361106460" name="possense.png" path="possense.png" size="82817" stream="possense.png" user="Public.FrankieCullinan" version="2"
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Revision 718 Feb 2013 - FrancisCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

Revision 617 Feb 2013 - FrancisCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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Ace3p 9.8 52
CST 10 52
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possense.png refsense.png

Electronics Chain Propagation

Electronics gain/dB 5
Cable loss/dB -2.6
Position cavity attenuation/dB 6
Reference cavity attenuation/dB 20

Position signal (offset=1mm, charge=1nC) Reference signal (Charge=1nC)
Location Volts dBm Volts dBm
Cavity out 8.3 31.4 52.0 47.3
Electronics in 4.2 25.4 5.2 27.3
Electronics out 7.4 30.4 9.2 32.3
Digitiser in 5.5 27.8 6.9 29.7
 

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META FILEATTACHMENT attachment="possense.png" attr="h" comment="" date="1361106460" name="possense.png" path="possense.png" size="82817" stream="possense.png" user="Public.FrancisCullinan" version="2"
META FILEATTACHMENT attachment="refsense.png" attr="h" comment="" date="1361106346" name="refsense.png" path="refsense.png" size="86511" stream="refsense.png" user="Public.FrancisCullinan" version="1"

Revision 526 Nov 2012 - FrancisCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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 The dipole mode sensitivity was estimated from the following formula, the measured external quality factor of 617 and R/Q from simulation in several codes, of which CST and GdfidL use a hexahedral mesh while Ace3p uses a tetrahedral mesh:

Code R/Q /Ω Sensitivity/V nC-1 mm-1
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GdfidL    
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GdfidL 0.85 8.7
 
Ace3p 0.77 8.3
CST 0.77 8.3
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 The measured external quality factor of the reference cavity is 203.

Code R/Q /Ω Sensitivity/V nC-1
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GdfidL 14.1 62
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GdfidL 28.2 87
 
Ace3p 9.8 52
CST 10 52

Revision 426 Nov 2012 - FrancisCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

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  The measured external quality factor of the reference cavity is 203.
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Code R/Q Sensitivity/V nC-1
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Code R/Q /Ω Sensitivity/V nC-1
 
GdfidL 14.1 62
Ace3p 9.8 52
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CST 9.2 51
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CST 10 52
 

Revision 326 Nov 2012 - FrancisCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

Position Cavity

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The dipole mode sensitivity was estimated from the following formula, the measured external quality factor of 830 and R/Q from simulation in several codes:
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The dipole mode sensitivity was estimated from the following formula, the measured external quality factor of 617 and R/Q from simulation in several codes, of which CST and GdfidL use a hexahedral mesh while Ace3p uses a tetrahedral mesh:
 
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Code R/Q Sensitivity/VpC-1mm-1
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Code R/Q/Ω Sensitivity/V nC-1 mm-1
 
GdfidL    
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Ace3p 0.77  
CST 0.77  
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Ace3p 0.77 8.3
CST 0.77 8.3
 

Reference Cavity

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Code R/Q Sensitivity/VpC-1
GdfidL 14.1  
Ace3p 9.8  
CST 9.2  
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The measured external quality factor of the reference cavity is 203.

Code R/Q
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Sorted ascending
Sensitivity/V nC-1
CST 9.2 51
Ace3p 9.8 52
GdfidL 14.1 62
 

Revision 223 Nov 2012 - FrancisCullinan

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Cavity Sensitivity Estimates

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Code R/Q Sensitivity/VpC-1mm-1
GdfidL    
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Ace3p    
CST    
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Ace3p 0.77  
CST 0.77  
 

Reference Cavity

Code R/Q Sensitivity/VpC-1
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GdfidL    
Ace3p    
CST    
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GdfidL 14.1  
Ace3p 9.8  
CST 9.2  
 
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Revision 123 Nov 2012 - FrancisCullinan

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META TOPICPARENT name="ClicBpm"

Cavity Sensitivity Estimates

Position Cavity

The dipole mode sensitivity was estimated from the following formula, the measured external quality factor of 830 and R/Q from simulation in several codes:

Code R/Q Sensitivity/VpC-1mm-1
GdfidL    
Ace3p    
CST    

Reference Cavity

Code R/Q Sensitivity/VpC-1
GdfidL    
Ace3p    
CST    

 
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