... | ... | @@ -213,12 +213,12 @@ latexmath:[\omega / \beta c \approx 10\pi]. We then get |
|
|
= & \int_{0}^{3\cdot s}\sin\left(\omega \left(\frac{z}{\beta c} + t_{0}\right) + \varphi\right) \left(E_z^{(2)} - 26\cdot E_z^{(1)}\right)(z)\,dz\end{aligned}
|
|
|
++++
|
|
|
|
|
|
where we used
|
|
|
where we used latexmath:[(z' = z + s)]
|
|
|
[latexmath]
|
|
|
++++
|
|
|
\begin{aligned}
|
|
|
&\int_{0}^{3\cdot s} \sin\left(\omega \left(\frac{z}{\beta c} + t_{0}\right) + \frac{3\pi}{2} + \varphi\right) E_z^{(1)}((z + s) \text{ mod}(3\,s),r) dz \\
|
|
|
\overset{z' = z + s}{\longrightarrow}& \int_{s}^{4\cdot s} \sin\left(\omega \left(\frac{z'-s}{\beta c} + t_{0} \right) + \frac{3\pi}{2} + \varphi\right)E_z^{(1)}(z' \text{mod}(3\,s),r)dz' \\
|
|
|
= & \int_{s}^{4\cdot s} \sin\left(\omega \left(\frac{z'-s}{\beta c} + t_{0} \right) + \frac{3\pi}{2} + \varphi\right)E_z^{(1)}(z' \text{mod}(3\,s),r)dz' \\
|
|
|
= &\int_{0}^{3\cdot s} \sin\left(\omega \left(\frac{z}{\beta c} + t_{0}\right) + \frac{5\pi}{6} + \varphi\right) E_z^{(1)}(z,r)\,dz.
|
|
|
\end{aligned}
|
|
|
++++
|
... | ... | |