  Kinetic Particle In Cell (PIC) methods can extend greatly their range of
applicability if implicit time differencing and spatial adaption are used to
address the wide range of time and length scales typical of plasmas. For
implicit differencing, we refer the reader to our recent summary of the
implicit moment PIC method implemented in our CELESTE3D code [G. Lapenta, Phys.
Plasmas, 13, 055904 (2006)]. Instead, the present document deals with the issue
of PIC spatial adaptation. Adapting a kinetic PIC code requires two tasks:
adapting the grid description of the fields and moments and adapting the
particle description of the distribution function. Below we address both
issues. First, we describe how grid adaptation can be guided by appropriate
measures of the local accuracy of the solution. Based on such information, grid
adaptation can be obtained by moving grid points from regions of lesser
interest to regions of higher interest or by adding and removing points. We
discuss both strategies. Second, we describe how to adapt the local number of
particles to reach the required statistical variance in the description of the
particle population. Finally two typical applications of adaptive PIC are
shown: collisionless shocks and charging of small bodies immersed in a plasma.
