Koscielniak, S.R.
Electromagnetic Impulse of Beam Density F(x, y)G(z)
JACoW Publishing
Geneva, Switzerland
978-3-95450-208-0
10.18429/JACoW-IPAC2019-MOPGW007
English
75-77
MOPGW007
factory
site
storage-ring
lattice
interaction-region
Contribution to a conference proceedings
2019
2019-06
https://doi.org/10.18429/JACoW-IPAC2019-MOPGW007
http://jacow.org/ipac2019/papers/mopgw007.pdf
We calculate the transverse impulse on a test particle as a bunch of charged particles beam passes by. It is often assumed, but seldom proven, that the EM field from a beam density distribution factored into transverse and longitudinal parts, F and G respectively, has also a factored form P(x, y)Q(z). This factorization is not possible for stationary charges. Contrastingly, it becomes increasingly accurate for ultra-relativistic particle beams. We give a general analysis, show how to develop the corrections in terms of integrals of F and derivatives of G. What is significant is that if we integrate over longitudinal coordinate z to find the transverse impulse on a witness charge, the correction terms integrate to zero leading to the impulse P(x, y)Integral[Q(z)] independent of bunch shape. If this result is already known, this paper serves as a reminder.