Changeset 397 in ETALON for CLIO/IPAC16/IPAC.tex

Timestamp:

Mar 22, 2016, 3:23:18 PM (9 years ago)

Author:

delerue

Message:

IPAC paper updated

File:

• CLIO/IPAC16/IPAC.tex (modified) (1 diff)

CLIO/IPAC16/IPAC.tex

@@ -56 +56 @@
 
 \section{Intro}
-When a relativistic charged particle crosses the interface between two media of different dielectric properties, then occurs emission of transition radiation (TR). This process was calculated analytically by Ginzburg and Frank \cite{GF}. We use their formula with virtual-quanta method to compute backward TR from finite screen\cite{GFa} This will give single electron yield. To calculate whole spectrum, formula \ref{eq:eq1} is used:
+When a relativistic charged particle crosses the interface between two media of different dielectric properties, transition radiation (TR) is emitted. This process was calculated analytically by Ginzburg and Frank \cite{GF}. We use their formula with virtual-quanta method to compute the backward TR from a finite screen\cite{GFa} This gives the single electron yield (SEY). For the SEY the  whole spectrum can be derived using the following formula:
 \begin{equation}
 \frac{d^2I}{d\omega d\Theta}=\frac{d^2I_1}{d\omega d\Theta}[N+N(N-1)F(\omega)]
 \label{eq:eq1}
 \end{equation}
-Where N -- is number of electrons in bunch and $F(\omega)$ is form factor of time profile of the bunch. Using phase recovery methods, such as Kramers-Kronig or Hilbert, it's possible to recover phase and then time profile of the bunch.\par
-Same formula, but with other single electron yield used for calculation of Smith-Purcell (SP) spectrum. SP radiation occurs when cnarged particle move above matalic periodic structure. Also big difference from TR is that, that emited radiation not concentrate in small observation angle (usually 10mrad), but spread in space. Wavelength of radiation for SP depends from observing angle as:
+Where N is the number of electrons in the bunch and $F(\omega)$ is the form factor of the time profile of the bunch. Using phase recovery methods, such as Kramers-Kronig or Hilbert~\cite{IPAC14}, it is possible to recover  the phase and then the time profile of the bunch.\par
+The same formula, but with a different SEY is used for calculation of Smith-Purcell (SP) spectrum. SP radiation occurs when a charged particle move above a metallic periodic structure. Unlike TR, SP has the advantage  that the emmited radiation is not concentrated in a small observation angle (usually 10mrad), but spread in angle. The wavelength of the radiation for SP depends on the observing angle according to the following:
 \begin{equation}
 \lambda=\frac{l}{n}(\frac{1}{\beta}-cos\Theta)
 \end{equation}
-where l is grating period, n -- order of rediation, $\Theta$ is observation angle and $\beta$ is relativistic velocity.\par
-To calculate single electron yield and total spectrum for SP effect, qfw code was used.\cite{GD} Calculation based on the surface current model. Taking into account that fact, that grating have finite width, energy per solid angle for single electron can be written as:
+where l is the grating period, n is the order of radiation, $\Theta$ is the observation angle and $\beta$ is the relativistic velocity.\par
+To calculate the SEY and the total spectrum for SP effect, the gfw code was used~\cite{GD}. The calculation is based on the surface current model. Taking into account the fact that the grating have a finite width, the energy per solid angle for single electron can be written as:
 \begin{equation}
 \frac{dI}{d\Omega}=2\pi e^2\frac{Z}{l^2}\frac{n^2\beta^3}{(1-\beta cos\Theta)^3}R^2