APPLICATION OF A VLASOV SOLVER TO INVESTIGATE THE

LONGITUDINAL BEAM DYNAMICS IN ELECTRON LINEAR ACCELERATORS

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By Vladyslav Syrotenko (student of V. N. Karazin Kharkiv National University, School of Physics and Technology)

Supervised by P. Piot, T. Sen, F. Ostiguy atFermi National Accelerator Laboratory

Accelerator Physics CentrePARTI Summer Internship Program

Introductory presentation

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GENERAL OVERVIEW OF ASTA BEAMLINE ELEMENTS PERTINENT

TO THE LONGITUDINAL BEAM DYNAMICS

ASTA = Advanced Superconducting Test Accelerator

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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.

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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.

The example of how CSR can influence on bunch energy distribution

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four-dipole chicane

Chirp means differentiation of particles energy relatively to some reference particle

CSR is an abbreviation of coherent synchrotron radiation

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Purpose of this project

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.18/07/2012

The idea of this method is not to track each particle, but to observe how distribution function is changing.

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Steps

1) Check bunch compressor model without space charge forces, but including non-linear optics,

2) Include space charge and investigate how the compression works,

3) Include CSR into bunch compressor model and investigate microbunching instabilities on their onset.

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Additional explanation slide. How the compression works

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𝑧 𝑧

∆𝐸 /𝐸

Initial bunch length

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.

After compression

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Parameters

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