Changeset 753 in ETALON for papers/2016_HDR_ND/Compton/synchro.tex

Timestamp:

Dec 4, 2017, 12:10:19 AM (7 years ago)

Author:

delerue

Message:

HDR finished

File:

• papers/2016_HDR_ND/Compton/synchro.tex (modified) (4 diffs)

papers/2016_HDR_ND/Compton/synchro.tex

@@ -2 +2 @@
 \input{./header}
 
-\chapter{Laser accelerator synchronisation}
+\chapter{Laser and  accelerator synchronisation}
 
-Several of the projects on which I worked involved both lasers and accelerators and each time were faced with the problem of synchronizing them. Here I describe how this was achieved.
+Several of the projects on which I worked involved both lasers and accelerators and each time we were faced with the problem of synchronizing them. Here I describe how this was achieved.
 
 \section{Time reference in accelerators and in lasers}
@@ -10 +10 @@
 Lasers and accelerators both require to have their own internal clocks. 
 
-In the case of lasers the internal clock is the laser cavity which will determine the frequency at which the pulses are produced. The length of this cavity is determined by the optical path between the mirrors (and the frequency is this length divided by the speed of light). This length (frequency) can be adjusted by having a mirror on a translation stage (long adjustment at slow rate) or a piezoactuator (short adjustments at fast rate).
+In the case of lasers the internal clock is the laser cavity which will determine the frequency (repetition rate) at which the pulses are produced. The length of this cavity is determined by the optical path between the mirrors (and the frequency is this length divided by the speed of light). This length (frequency) can be adjusted by having a mirror on a translation stage (long adjustment at slow rate) or a piezoactuator (short adjustments at fast rate).
 
 In the case of accelerators the internal clock is the RF frequency of the accelerating sections or that of the ring cavity (in the case of a circular accelerator). In a ring this frequency may change due to environmental conditions such as minute changes in the temperature of the cooling water.
@@ -20 +20 @@
 For the ATF laser-wire we had the opportunity to specify the laser we wanted to purchase. Hence we did specify that the laser had to have an adjustable length cavity with a range compatible with the ATF frequency changes, both slow and fast. One of the mirrors had to be mounted on a piezoactuator to follow very accurately the ATF frequency and another had to be adjustable over several millimeters to allow compensation of large frequency changes.
 
-The noise of one electronic device with respect to another is called phase noise. Phase is often given as a power spectrum giving the XXXX
+The noise of one electronic device with respect to another is called phase noise. Phase is often given as a power spectrum giving the ``Single Side Band phase noise (SSB)'' in decibels below the carrier per Hertz (\si{dBc/Hz}). The SSB must be integrated in the relevant range of frequencies to estimate its effect. Noise that occurs at too high frequencies will be smoothed out: for example a 1-GHz noise will not appear on a 75-MHz oscillator and similarly noise that is slow compared to the repetition rate of the device can also be ignored as its effect is not visible on a given shot (but it can appear when shots are compared with each others). The low frequency noise often dominates the integral, so a correct determination of the low frequency bound is more important. In the case of ThomX, the linac frequency will be \SI{3}{GHz} and the repetition rate will be \SI{50}{Hz} so the noise must be integrated between these two bounds.
+
+This integrated phase noise is expressed as a power (with respect to the carrier signal). It is usual to convert this phase noise into a jitter by looking at the jitter induced by such power fluctuation on the nominal signal. Such conversion is obviously dependent on the carrier signal frequency.
+
+The achieve the luminosity required for the ILC we estimated that the litter had to be lower than \SI{1}{ps}. This was challenging but within the reach of lasers at that time.
 
 
 
 
-XXX
+%\section{The accelerator is the reference clock, but the laser has two clocks: MightyLaser}
+
+%The MightyLaser experiment is in a different situation because the laser pulses do not directly interact with the electron beam, they are first stacked in a Fabry-Perot cavity. I did not directly work on the MightyLaser synchronisation scheme but I report it here for completeness.
 
 
-Let's assume that the laser and the accelerator both deliver perfect gaussian pulses with a sigma of \SI{1}{ps}. If the integrated phase noise between the two pulses is also \SI{1}{ps} then the intensity of the Compton signal for this deviation will be XXX and it will be XXX for XXX.
-
-XXX
-
-Simulations taking into account the more complex electron pulse shapes in the ThomX ring have been reported in~\cite{drebot:tel-00920424}.
-
-\section{The accelerator is the reference clock, but the laser has two clocks: MightyLaser}
-
-The MightyLaser experiment is in a different situation because the laser pulses do not directly interact with the electron beam, they are first stacked in a Fabry-Perot cavity. I did not directly work on the MightyLaser synchronisation scheme but I report it here for completeness.
-
-
-\section{The accelerator has two independent clocks: ThomX and ESCULAP}
+\section{The accelerator and the laser have independent clocks: ThomX and ESCULAP}
+\sectionmark{Two independent clocks }
 \label{sec:thomx_synchro}
 
@@ -45 +41 @@
 
 
+%Let's assume that the laser and the accelerator both deliver perfect gaussian pulses with a sigma of $\sigma_p = $ \SI{1}{ps}. If the integrated phase noise between the two pulses is also $\sigma_N = $ \SI{1}{ps} then the intensity of the Compton signal for this deviation will be the convolution of the two gaussians.
+
+%Assuming that the normalisation for the signal is ${\cal I}_{\mbox{signal}} = \frac{1}{\sqrt{2\pi} \sigma_p}$ and that of the noise is $\frac{1}{\sqrt{2\pi} \sigma_N}$. Then the signal remaining $R$ once the noise is taken into account is:
+
+%\begin{eqnarray}
+%{\cal I}_{\mbox{signal with noise}} & = & \frac{1}{\sqrt{2\pi \frac{\sigma_N^2 \sigma_p^2}{\sigma_{Np}^2}}} \\
+%\mbox{with: } \frac{1}{\sigma_{Np}^2} & = & \frac{1}{\sigma_{N}^2} +  \frac{1}{\sigma_{p}^2} \\
+%\mbox{then } R = \frac{{\cal I}_{\mbox{signal with noise}}}{{\cal I}_{\mbox{signal}}} & = & \frac{ \frac{1}{\sqrt{2\pi} \sigma_p}}{\frac{1}{\sqrt{2\pi\frac{\sigma_N^2 \sigma_p^2}{\sigma_{Np}^2}}}} \\
+%R & = &  \frac{ \sqrt{ \frac{\sigma_N^2 \sigma_p^2}{\sigma_{Np}^2}}}{ \sigma_p} \\
+%R & = &  \sqrt{ \frac{\sigma_N^2 }{\sigma_{Np}^2}}\\
+%R & = &   \sigma_N \times \sqrt{   \frac{1}{\sigma_{N}^2} +  \frac{1}{\sigma_{p}^2} } \\
+%R & = &   \sqrt{ 1 +  \frac{\sigma_{N}^2}{\sigma_{p}^2} } \\
+%\end{eqnarray}
+
+Simulations taking into account the effect of the beam jitter with complex electron pulse shapes in the ThomX ring have been reported in~\cite{drebot:tel-00920424}.