A gauge-compatible Hamiltonian splitting algorithm for particle-in-cell simulations using finite element exterior calculus

A particle-in-cell algorithm is derived with a canonical Poisson structure in the formalism of finite element exterior calculus. The resulting method belongs to class gauge-compatible splitting algorithms, which exactly preserve gauge symmetries and their associated conservation laws via momentum map. We numerically demonstrate this time invariance map its usefulness establishing precise initial conditions desired electric field fixed background charge. restriction canonical, 1X2P $1\frac {1}{2}$ -dimensional phase space also considered simulated numerically.