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<H2><A NAME="SECTION00021000000000000000">
Definition</A>
</H2>
<P>
When charged particle is moving through linac or any other structure
in accelerator it generates fields in the structure.
<P>
Reasons of the fields can be different: limited resistivity of the
pipes, dielectric layers on the walls, macro obstacles or micro
obstacles due to surface roughness.
<P>
The generated fields will affect any trailing particle following the
leading one. In general the fields depend on both particles
positions so the momentum change is [<A
HREF="node27.html#StupakovJAS2002">1</A>]:
<P>
<BR><P></P>
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<!-- MATH
\begin{displaymath}
\Delta p(\rho ,\rho_1 ,s) = \int {dt[} E(\rho ,\rho_1 ,z,t) + z
\times B(\rho ,\rho_1 ,z,t)]_{z = ct - s}
\end{displaymath}
-->
<IMG
WIDTH="431" HEIGHT="42" BORDER="0"
SRC="img1.gif"
ALT="\begin{displaymath}
\Delta p(\rho ,\rho_1 ,s) = \int {dt[} E(\rho ,\rho_1 ,z,t) + z
\times B(\rho ,\rho_1 ,z,t)]_{z = ct - s}
\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
<P>
And we can define wakes
<P>
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
\begin{array}{l}
w_l (\rho ,\rho_1 ,s) = - \frac{c}{q}\Delta p_z = - \frac{c}{q}\int {dt} \left. {E_z } \right|_{z = ct - s} \\
w_t (\rho ,\rho_1 ,s) = - \frac{c}{q}\Delta p_t = - \frac{c}{q}\int {dt[} E_t + z \times B]_{z = ct - s} \\
\end{array}
\end{displaymath}
-->
<IMG
WIDTH="374" HEIGHT="54" BORDER="0"
SRC="img2.gif"
ALT="\begin{displaymath}
\begin{array}{l}
w_l (\rho ,\rho_1 ,s) = - \frac{c}{q}\Delt...
...c}{q}\int {dt[} E_t + z \times B]_{z = ct - s} \\
\end{array}\end{displaymath}">
</DIV>
<BR CLEAR="ALL">
<P></P>
<P>
We can integrate over the structure fields generated by the bunch to
get total effect of fields on particles from the same or the next
bunch. Total effects are usually expressed in loss and kick factors.
Loss factor is the integrated energy (momentum) loss by the bunch
over passing the structure. Kick factor is usually average
transverse angle gained by the bunch passing the structure.
<P>
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
\Delta y' = \frac{{Nr_e }}{\gamma }ky
\end{displaymath}
-->
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WIDTH="104" HEIGHT="46" BORDER="0"
SRC="img3.gif"
ALT="\begin{displaymath}
\Delta y' = \frac{{Nr_e }}{\gamma }ky
\end{displaymath}">
</DIV>
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<P></P>
<P>
Fields of the leading particle are calculated assuming there are no
transverse displacements of the particle during passing the
structure due to the Wake fields.
<P>
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<ADDRESS>
german_kourevlev
2006-01-19
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