  The purpose of this work is simulation of magnetised plasmas in the ITER
project framework. In this context, kinetic Vlasov-Poisson like models are used
to simulate core turbulence in the tokamak in a toroidal geometry. This leads
to heavy simulations because a 6D dimensional problem has to be solved, even if
reduced to a 5D in so called gyrokinetic models. Accurate schemes, parallel
algorithms need to be designed to bear these simulations. This paper describes
the numerical studies to improve robustness of the conservative PSM scheme in
the context of its development in the GYSELA code. In this paper, we only
consider the 4D drift-kinetic model which is the backbone of the 5D gyrokinetic
models and relevant to build a robust and accurate numerical method.
