  We propose ParaPIF, a parareal based time parallelization scheme for the
particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in
kinetic plasma simulations. Our coarse propagators are based on the coarsening
of the numerical discretization scheme combined with, if possible, temporal
coarsening rather than coarsening of particles and/or Fourier modes, which are
not possible or effective for PIF schemes. Specifically, we use PIF with a
coarse tolerance for nonuniform FFTs or even the standard particle-in-cell
schemes as coarse propagators for the ParaPIF algorithm. We state and prove the
convergence of the algorithm and verify the results numerically with Landau
damping, two-stream instability, and Penning trap test cases in 3D-3V. We also
implement the space-time parallelization of the PIF schemes in the open-source,
performance-portable library IPPL and conduct scaling studies up to 1536 A100
GPUs on the JUWELS booster supercomputer. The space-time parallelization
utilizing the ParaPIF algorithm for the time parallelization provides up to
$4-6$ times speedup compared to spatial parallelization alone and achieves a
push rate of around 1 billion particles per second for the benchmark plasma
mini-apps considered.
