   Next: Solution of Poisson's equation Up: Particle-in-cell codes Previous: Solution of electron equations

## Evaluation of electron number density

In order to obtain the electron number density from the electron coordinates we adopt a so-called particle-in-cell (PIC) approach. Let us define a set of equally spaced spatial grid-points located at coordinates (300)

for , where . Let . Suppose that the th electron lies between the th and th grid-points: i.e., . We let (301)

and (302)

Thus, increases by 1 if the electron is at the th grid-point, increases by 1 if the electron is at the th grid-point, and and both increase by if the electron is halfway between the two grid-points, etc. Performing a similar assignment for each electron in turn allows us to build up the from the electron coordinates (assuming that all the are initialized to zero at the start of this process).   Next: Solution of Poisson's equation Up: Particle-in-cell codes Previous: Solution of electron equations
Richard Fitzpatrick 2006-03-29