implementation of wake potentials generated by a Gaussian bunch
Posted: 06 Mar 2019, 08:36
Dear all,
I want to implement wake potentials which I got from the software ECHO. ECHO uses a Gaussian source bunch to calculate the wake potentials. The results from ECHO for an example pillbox cavity and an example Gaussian bunch with sigma=1 mm are plotted below:
As you can see, the (converted) output from ECHO is longitudinal distance relative to the center of the Gaussian bunch vs. wake potential in V/C (longitudinal, mode 0) and V/C/m (transverse, mode 1) respectively, plotted in blue. As a reference, you can find the Gaussian bunch with sigma=1 mm in the plot (arbitrary y-axis), plotted in red. I am not sure if my wake potentials are the "integrated wakes" one can import via the elegant elements WAKE and TRWAKE (maybe I have to change the sign of the longitudinal one, since in the manual is written "A physical wake function should be positive at t = 0").
My question is: how do I implement these wake potentials correctly, because in the manual is written "The values of the time coordinate should begin at 0", but since I use a Gaussian bunch instead of a point charge, I get a more complicated distribution as you can see from the plots. In particular there are negative time coordinates (with reference to the center of the Gaussian bunch). A comment like "test particle behind the wake-potential-generating particle" is not easy in that case, since the wake is not generated by a single point charge. There is only a comment like "test particle relative to the center of the wake-potential-generating bunch" possible.
Thanks,
Amelie
I want to implement wake potentials which I got from the software ECHO. ECHO uses a Gaussian source bunch to calculate the wake potentials. The results from ECHO for an example pillbox cavity and an example Gaussian bunch with sigma=1 mm are plotted below:
My question is: how do I implement these wake potentials correctly, because in the manual is written "The values of the time coordinate should begin at 0", but since I use a Gaussian bunch instead of a point charge, I get a more complicated distribution as you can see from the plots. In particular there are negative time coordinates (with reference to the center of the Gaussian bunch). A comment like "test particle behind the wake-potential-generating particle" is not easy in that case, since the wake is not generated by a single point charge. There is only a comment like "test particle relative to the center of the wake-potential-generating bunch" possible.
Thanks,
Amelie
I happen to read a reference from Michael for other questions, which shows how to get the Green function from your short beam's wake potential: "the analytic Green function ... can be obtained via Bane's algorithm by folding the wake in the head with respect to the center of the bunch to be added to the wake in the tail."