OpenPIC3D algorithm description

Staggered grid with regular grid step $\QTR{large}{h}$ is used:

Staggered grid

Components of ions and mean velocity $<\vec{v}>,$ $\vec{v}_{e}$ are stored in the same nodes as $\vec{E}$. The ions density is stored in cell center.

On each time-step the algorithm consists of several stages:

1. Preliminary value of a magnetic field using the equation on time layer $m$:MATH

2. New velocity and coordinates of ions on layer $m+1/2$:MATHMATH

3. Ions charge density $\QTR{Large}{n}$ and ions mean velocity on layer $m+1/2$:

MATHMATHMATH

where $M_{j}$ -- charge of $j$-th particle, $R$ -- particle form factor.

For regular grid with step $h$MATH

4. Coordinates of particles on layer $m+1$:MATH

5. Magnetic field final value on layer$\ m+1/2$:MATH

6. Electron velocity:MATH

Face-centered values of MATHare need at this stage.

Question: What is the best way to interpolate from cell-centered $n^{m+1/2}$ values to face centers?

7. Electric field:MATHMATH

With MATH and neglecting dissipation:MATH

8. Electron temperature (not used in current version of code - MATH):MATHMATH

Grid step $\QTR{large}{h}$ and time step $\QTR{large}{\tau }$ selected according CFL condition:MATH

and required spatial resolution, e. g.MATH.

Additional stability conditions:MATH

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