Self-Force in 1D Electrostatic Particle-in-Cell Codes for Non-Equidistant Grids

Effects of non-equidistant grids on momentum conservation is studied for simple test cases of an electrostatic 1D PIC code. The aim is to reduce the errors in energy and momentum conservation. Assuming an exact Poisson solver only numerical errors for the particle mover are analysed. For the standard electric field calculation using a central-difference scheme, artificial electric fields at the particle position are generated in the case when the particle is situated next to a cell size change. This is sufficient to destroy momentum conservation. A modified electric field calculation scheme is derived to reduce this error. Independent of the calculation scheme additional fake forces in a two-particle system are found which result in an error in the total kinetic energy of the system. This contribution is shown to be negligible for many particle systems. To test the accuracy of the two electric field calculation schemes numerical tests are done to compare with an equidistant grid set-up. All tests show an improved momentum conservation and total kinetic energy for the modified calculation scheme of the electric field. (C) 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim