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<H2><A NAME="SECTION00032000000000000000">
Dielectric wakefields</A>
</H2>
<P>
Investigated as new collective acceleration methods (Park,
Hirshfield (2000))
<P>
Usual approach is similar to resistive wakes - field matching
technique on boundaries
<P>
The difference is that we don't need to count energy loss in the
walls but have waves with different speed in different media.
<P>
<BR><P></P>
<DIV ALIGN="CENTER">
<!-- MATH
\begin{displaymath}
\begin{array}{l}
\left( {\begin{array}{*{20}c}
{E_z (r,s)} \\
{E_r (r,s)} \\
{E_\theta (r,s)} \\
\end{array}} \right) = - 2q\sum\limits_{l = 0}^\infty {\sum\limits_{n = 1}^\infty {\frac{1}{{C_n }}} } \left( {\frac{{r_0 }}{{R_1 }}} \right)^l \times \left( {\begin{array}{*{20}c}
{\left( {\frac{r}{{R_1 }}} \right)^l g_{z,n}^0 (s)\cos l\theta } \\
{l\left( {\frac{r}{{R_1 }}} \right)^{l - 1} g_{t,n}^0 (s)\cos l\theta } \\
{ - l\left( {\frac{{r_0 }}{{R_1 }}} \right)^l g_{t,n}^0 (s)\sin l\theta } \\
\end{array}} \right) \\
\left( {\begin{array}{*{20}c}
{g_{z,n}^0 (s)} \\
{g_{t,n}^0 (s)} \\
\end{array}} \right) = \left( {\begin{array}{*{20}c}
{\cos k_n^{} s} \\
{\sin k_n^{} s} \\
\end{array}} \right)\Theta ( - s) \\
\end{array}
\end{displaymath}
-->
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WIDTH="500" HEIGHT="152" BORDER="0"
SRC="img34.gif"
ALT="\begin{displaymath}
\begin{array}{l}
\left( {\begin{array}{*{20}c}
{E_z (r,s)}...
..._n^{} s} \\
\end{array}} \right)\Theta ( - s) \\
\end{array}\end{displaymath}">
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<BR CLEAR="ALL">
<P></P>
<P>
Cn-normalization constant that can be received by orthonormality
relation and from the source currents.
<P>
<BR><HR>
<ADDRESS>
german_kourevlev
2006-01-19
</ADDRESS>
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