Planche, T. Jung, P. M. JACoW Publishing Geneva, Switzerland 978-3-95450-200-4 10.18429/JACoW-ICAP2018-SUPAF04 English 42-45 SUPAF04 plasma simulation space-charge betatron resonance Contribution to a conference proceedings 2019 2019-01 https://doi.org/10.18429/JACoW-ICAP2018-SUPAF04 http://jacow.org/icap2018/papers/supaf04.pdf This paper is a review of algorithms, applicable to particle accelerator simulation, which share the following two characteristics: (1) they preserve to machine precision the symplectic geometry of the particle dynamics, and (2) they track the evolution of the self-field consistently with the evolution of the charge distribution. This review includes, but is not limited to, algorithms using a Particle-in-Cell discretization scheme. At the end of this review we discuss to possibility to derived algorithms from an electrostatic Hamiltonian.