Comptes Rendus
Theoretical and numerical approaches for Vlasov–Maxwell equations
Case studies in space charge and plasma acceleration of charged beams
Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 647-661.

Plasma acceleration with electron or proton driver beams is a challenging opportunity for high-energy physics. An energy doubling experiment with electron drivers was successfully performed at SLAC and a key experiment AWAKE with proton drivers is on schedule at CERN. Simulations play an important role in choosing the best experimental conditions and in interpreting the results. The Vlasov equation is the theoretical tool to describe the interaction of a driver particle beam or a driver laser pulse with a plasma. Collective effects, such as tune shift and mismatch instabilities, appear in high intensity standard accelerators and are described by the Poisson–Vlasov equation. In the paper, we review the Vlasov equation in the electrostatic and fully electromagnetic cases. The general framework of variational principles is used to derive the equation, the local form of the balance equations and related conservation laws. In the electrostatic case, we remind the analytic Kapchinskij–Vladimirskij (K–V) model and we propose an extension of the adiabatic theory for Hamiltonian systems, which ensures stability for perturbation of size ϵ on times of order 1/ϵ. The variational framework is used to derive the Maxwell–Vlasov equations and related conservation laws and to briefly sketch the particle-in-cell (PIC) approximation schemes. Finally, the proton-driven acceleration is examined in the linear and quasi-linear regime. A PIC simulation with the code ALaDyn developed at Bologna University is presented to illustrate the longitudinal and transverse fields evolution which allow a witness electron bunch to be accelerated with a gradient of a few GeV/m. We also present some remarks on future perspectives.

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DOI: 10.1016/j.crme.2014.07.004
Keywords: Plasma acceleration, Vlasov equation, Stationary distributions, PIC simulations

Armando Bazzani 1, 2; Massimo Giovannozzi 3; Pasquale Londrillo 2; Stefano Sinigardi 1, 2, 4; Giorgio Turchetti 1, 2

1 Dipartimento di Fisica e Astronomia, Università di Bologna, Via Irnerio 46, 40126 Bologna (BO), Italy
2 INFN Sezione di Bologna, Via Irnerio 46, 40126 Bologna (BO), Italy
3 BE Department, CERN, CH-1211 Geneva 23, Switzerland
4 Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche (CNR/INO), U.O.S. ‘Adriano Gozzini’, Pisa, Italy
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Armando Bazzani; Massimo Giovannozzi; Pasquale Londrillo; Stefano Sinigardi; Giorgio Turchetti. Case studies in space charge and plasma acceleration of charged beams. Comptes Rendus. Mécanique, Volume 342 (2014) no. 10-11, pp. 647-661. doi : 10.1016/j.crme.2014.07.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.07.004/

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