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TY - CONF AU - Planche, T. AU - Jung, P. M. AU - Rädel, S.D. ED - Koscielniak, Shane ED - Satogata, Todd ED - Schaa, Volker RW ED - Thomson, Jana TI - Space-Charge Hamiltonian with a Space Coordinate as Independent Variable J2 - Proc. of IPAC2018, Vancouver, BC, Canada, April 29-May 4, 2018 C1 - Vancouver, BC, Canada T2 - International Particle Accelerator Conference T3 - 9 LA - english AB - We present a version of the Low Lagrangian tailored to treat space-charge effects in particle accelerators: the Lagrangian is relativistic and uses a space coordinate as the independent variable. From this Lagrangian we obtain the corresponding Hamiltonian. From the Hamiltonian we obtain equations of motion for the 8 canonical variables, which can be plugged into a symplectic numerical integrator. We will finally discuss the possibility of numerically solving this problem using an explicit symplectic integrator. PB - JACoW Publishing CP - Geneva, Switzerland SP - 3484 EP - 3485 KW - plasma KW - space-charge KW - TRIUMF KW - vacuum KW - synchrotron DA - 2018/06 PY - 2018 SN - 978-3-95450-184-7 DO - 10.18429/JACoW-IPAC2018-THPAK107 UR - http://jacow.org/ipac2018/papers/thpak107.pdf ER -