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TY - CONF AU - Amstutz, Ph. AU - Vogt, M. ED - Schaa, Volker R.W. ED - Decking, Winfried ED - Sinn, Harald ED - Geloni, Gianluca ED - Schreiber, Siegfried ED - Marx, Michaela TI - Arbitrary Order Perturbation Theory for a Time-Discrete Model of Micro-Bunching Driven by Longitudinal Space Charge J2 - Proc. of FEL2019, Hamburg, Germany, 26-30 August 2019 CY - Hamburg, Germany T2 - Free Electron Laser Conference T3 - 39 LA - english AB - A well established model for studying the micro-bunching instability driven by longitudinal space charge in ultra-relativistic bunches in FEL-like beamlines can be identified as a time-discrete Vlasov system with general drift maps and Poisson type collective kick maps. Here we present an arbitrary order perturbative approach for the general system and the complete all-orders solution for a special example. For this example we benchmark our theory against our Perron-Frobenius tree-code. PB - JACoW Publishing CP - Geneva, Switzerland SP - 596 EP - 598 KW - bunching KW - space-charge KW - FEL KW - simulation KW - electron DA - 2019/11 PY - 2019 SN - "" SN - 978-3-95450-210-3 DO - doi:10.18429/JACoW-FEL2019-THP003 UR - http://jacow.org/fel2019/papers/thp003.pdf ER -