By Vladyslav Syrotenko (student of V. N. Karazin Kharkiv National University,

1. Introductory presentation Application of a Vlasov Solver to investigate The longitudinal beam dynamics in electron linear accelerators By Vladyslav Syrotenko (student of V. N. Karazin Kharkiv National University, School of Physics and Technology) Supervised by P. Piot, T. Sen, F. Ostiguy at Fermi National Accelerator Laboratory Accelerator Physics Centre PARTI Summer Internship Program

2. General overview of ASTA beamline elements pertinent to the longitudinal beam dynamics ASTA = Advanced Superconducting Test Accelerator Linac-based free-electron lasers require very short (<100 fs) high-brightness electron beam with peak currents on the order of kiloamperes. These bunches cannot be produced directly in the electron guns because space charge forces would destroy the beam quality within the short distance. So it’s necessary to start with a low intensity bunch with peak current of a few tens amperes, accelerate it to energies where the space charge forces are weakened sufficiently by 1/gamma^2 scaling and then reduce the bunch length to increase the peak current.

3. PLANS • Consider a beamline to be a four-dipole chicane and inject a bi-Gaussian distribution in the longitudinal phase space (t, E) with variable chirp and verify compression works as it was expected. • A second step will be to include CSR effects. Chirp means differentiation of particles energy relatively to some reference particle four-dipole chicane CSR is an abbreviation of coherent synchrotron radiation The example of how CSR can influence on bunch energy distribution

4. Purpose of this project The idea of this method is not to track each particle, but to observe how distribution function is changing. • The purpose of this project is to carry numerical simulations of the longitudinal beam dynamics of an electron bunch undergoing longitudinal compression using Vlasov solver developed at Fermilab by Francois Ostiguy. We will use a Vlasov solver in the 2D longitudinal phase space suitable for applications in single-pass systems. • We want to investigate how useful existing Vlasov solver is. Do we need variable mesh or not? Vlasov equation written for bunch compressor. Here F(z, s) includes collective forces.

5. Steps • Check bunch compressor model without space charge forces, but including non-linear optics, • Include space charge and investigate how the compression works, • Include CSR into bunch compressor model and investigate microbunching instabilities on their onset.

6. Additional explanation slide. How the compression works Dependently of an energy chirp particles will travel shorter or longer distance. Under certain conditions we can make tail propagating faster than the head of the bunch. That will cause the compression. Initial bunch length After compression

7. Parameters