Grid heating analysis based on energy conserving and momentum conserving PIC formulations*

To study the instability responsible for grid heating, we start with a

meshfree formulation and then discretize on a grid. We then study the ef-

fects of different discretizations. Direct discretization of the meshfree equa-

tions leads to the well-known momentum conserving (MC) algorithm. A

modification leads to an energy conserving (EC) discretization. For a cold

non-drifting plasma the EC discretization involves a symmetric positive def-

inite (SPD) kernel matrix, showing stability, in agreement with PIC tests.

For this cold plasma case the MC discretization leads to a non-symmetric

kernel matrix, and in some cases this matrix is even non-normal. This matrix

is found to have no eigenvalues with positive real part, implying stability,

also in agreement with PIC tests. Results and analysis of the warm plasma

and the cold beam cases will be presented.