• Corpus ID: 54077066

EFFECT OF COULOMB COLLISIONS ON ECHO-ENABLED HARMONIC GENERATION (EEHG) ∗

@inproceedings{Stupakov2012EFFECTOC,
  title={EFFECT OF COULOMB COLLISIONS ON ECHO-ENABLED HARMONIC GENERATION (EEHG) ∗},
  author={Gennady Stupakov},
  year={2012}
}

• G. Stupakov
• Published 2012
• Physics

We calculate the EEHG bunching factor with account of the collisions and derive a simple scaling relation for the strength of the effect. Our estimates show that collisions become a limiting factor in EEGH seeding for large har- monic numbers. Echo-enabled harmonic generation (EEHG) for FEL seeding usestwo undulator-modulatorsand two chicanesto introduce a fine structure into the beam longitudinal phase space which, at the end of the system, transforms into a high harmonic modulation of the beam current (1, 2). As a result of this phase space manipulation the energy distribu- tion function after the first chicane becomes a rapidly mod- ulated function of energy, with the scale of the modulation of the order of the initial energyspread of the beam divided bytheEEHGharmonicnumber. Small-angleCoulombcol- lisions between the particles of the beam (also knownas in- trabeam scattering) tend to smear out this modulation and hence to suppress the beam bunching. In this paper we cal- culate the EEHG bunching factor with account of the col- lisions and derive a simple scaling relation for the strength of the effect. It is well known that the dominant process in Coulomb collisions is a small-angle scattering, which leads to a dif- fusion process in the momentum space. We first derive the diffusion coefficient for this process in the beam frame us- ing an approximation that the longitudinal temperature of the beam is much smaller than the transverse one. We then make a Lorentz transformation into the laboratory frame, and calculate the effect of the Coulomb collisions on the bunching factor in the EEGH seeding.