Kinetic plasma simulations in a 6D phase space is usually difficult for grid-based methods because the six-dimensional phase space seems to be too high for Euler-gird-based methods to handle. As a result, I have not seen any 6D grid-based kinetic simulation code. With the invention of the gyrokinetic model, the dimenionality of the phase space is reduced to five, which makes it possible for Euler-grid-based method to handle. As a result, there appear several widely used gird-based gyrokinetic codes, such as GYRO and GENE.
Another reason why particle methods are (if they are) more popular than the Eulerian-grid-based methods in plasma community is the algorithmic compactness and subsequent ease of coding in comparison with the Eulerian-grid-based methods. The popularity of PIC methods may also be related to that PIC method seems more intuitive at first glance (although this first impression may be only partially correct and even misleading). This is not about accuracy or even science. Historical or psychological reasons can partially account for the popularity of one particular method.
Parallization of the marker pushing part is usually easy in PIC codes. All the markers used in a simulation can be evenly distributed among all the MPI processes used. The loading balance can be good among all the processes in terms of marker pushing. The deposition part of a PIC code can be slow because it involves random access to a large grid array when looping over all the markers in a MPI process. The parallization of the field solving part is the same as Euler based codes.
For gyrokinetic simulation of tokamak plasmas, it is not easy to judge which method, particle-based method or grid-based mthod, is better than the other. When dealing with full Landau collision oprators, some PIC codes, e.g., XGC, uses velocity space grids. This may indicate that velocity grids are generally needed, suggesting that grids-methods may have advantages. On the other hand, hybrid methods that use both velocity grids and markers may be a practical way since “hybrid” provides us freedoms to use whatever methods available that can get work done.