  The present paper studies two particle management strategies for dynamically
adaptive Cartesian grids at hands of a particle-in-cell code. One holds the
particles within the grid cells, the other within the grid vertices. The
fundamental challenge for the algorithmic strategies results from the fact that
particles may run through the grid without velocity constraints. To facilitate
this, we rely on multiscale grid representations. They allow us to lift and
drop particles between different spatial resolutions. We call this cell-based
strategy particle in tree (PIT). Our second approach assigns particles to
vertices describing a dual grid (PIDT) and augments the lifts and drops with
multiscale linked cells.
  Our experiments validate the two schemes at hands of an electrostatic
particle-in-cell code by retrieving the dispersion relation of Langmuir waves
in a thermal plasma. They reveal that different particle and grid
characteristics favour different realisations. The possibility that particles
can tunnel through an arbitrary number of grid cells implies that most data is
exchanged between neighbouring ranks, while very few data is transferred
non-locally. This constraints the scalability as the code potentially has to
realise global communication. We show that the merger of an analysed tree
grammar with PIDT allows us to predict particle movements among several levels
and to skip parts of this global communication a priori. It is capable to
outperform several established implementations based upon trees and/or
space-filling curves.
