PP/JAI Web>RFLab>BeamPosition>ClicBpm>Ctf3Sensitivity (11 Feb 2014, FrankieCullinan)

Cavity Sensitivity Estimates

Position Cavity

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
GdfidL	0.85	8.7
Ace3p	0.77	8.3
CST	0.77	8.3

Reference Cavity

The measured external quality factor of the reference cavity is 203.

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

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

Position scale factor: 1.25 mm

Correction, June 2013

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	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
GdfidL	50.3	117
Ace3p	50.7	118

	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

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time, the assumption that the root mean square voltage over one period is the peak voltage divided by $\sqrt{2}$ is no longer valid.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

$\left(\frac{V_{rms}(\tau)}{\hat{V}}\right)^2=\frac{1}{T} \int_0^T e^{-\frac{2t}{\tau}}\sin^2 (2 \pi f t) dt = \frac{1}{2T}\int_0^T e^{-\frac{2t}{\tau}}(1-\cos (4 \pi f t)) dt$

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

$\begin{displaymath} \left(\frac{V_{rms}(\tau)}{\hat{V}}\right)^2=\frac{\tau}{4T}\left(1-\frac{1}{1+(2 \pi f \tau)^2}\right)\left(1-e^{-\frac{2 T}{\tau}}\right) \end{displaymath}$

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

peak.pdf: peak.pdf
power.pdf: power.pdf

Physics Webpages • RHUL Webpages • Campus Connect • Royal Holloway, University of London, Egham, Surrey TW20 0EX; Tel/Fax +44 (0)1784 434455/437520

Topic revision: r16 - 11 Feb 2014 - FrankieCullinan

Copyright © 2008-2024 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding RHUL Physics Department TWiki? Send feedback