Materials used in the teaching of Numerical Methods for the Master 2 students at Sorbonne University during academic year 2023-2024

Based on Kinetic Simulation of Plasmas using Particle-in-cell (PIC) code [by Anna Grassi, Mickael Grech]

• implement the particle pusher using the Boris algorithm [J. P. Boris, Proc. Fourth Conf. Num. Sim. Plasmas 3-67 (1970)]

  • gyro-motion
  • ExB drift
  • magnetic reconnection
  • relativistic regime
  • energy conservation

• Electromagnetic fields propagation via Finite-Difference Time-Domain (FDTD) method [A. Taflove, Computation electrodynamics: The finite-difference time-domain method, 3rd Ed. (2005)]

  • boundary conditions [Mur, Gerrit. "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations." IEEE transactions on Electromagnetic Compatibility 4 (1981): 377-382.]
  • source terms with only E vs. both E and B
  • vectorization the for-loops

• Landau damping of Langmuir waves with SMILEI
• bump-on-tail instability with SMILEI