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Evaluation of electron number density

In order to obtain the electron number density [画像:$n(x)$] from the electron coordinates $r_i$ we adopt a so-called particle-in-cell (PIC) approach. Let us define a set of $J$ equally spaced spatial grid-points located at coordinates
for $j=0,J-1,ドル where [画像:$\delta x = L / J$]. Let [画像:$n_j\equiv n(x_j)$]. Suppose that the $i$th electron lies between the $j$th and [画像:$(j+1)$]th grid-points: i.e., $x_j < r_i < x_{j+1}$. We let
and
Thus, $n_j,円\delta x$ increases by 1 if the electron is at the $j$th grid-point, $n_{j+1},円\delta x$ increases by 1 if the electron is at the [画像:$(j+1)$]th grid-point, and $n_j,円\delta x$ and $n_{j+1},円\delta x$ both increase by 1ドル/2$ 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 $n_j$ from the electron coordinates (assuming that all the $n_j$ are initialized to zero at the start of this process).

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

Richard Fitzpatrick 2006年03月29日