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Charge Density in Particle-in-Cell Simulation

  1. Jun 9, 2014 #1
    I am creating a particle in cell simulation that models an electron plasma in a cylindrical container. Part of this process is assigning charge density to grid points based on the position of each particle. My question is this: for the examples of these simulations that I have seen, the charge density is given by the amount of charge on a grid point divided by the volume of a unit cell, or: [tex]\rho=\frac{q}{d\tau}[/tex]

    which for cylindrical coordinates is: [tex]\rho=\frac{q}{r\bigtriangleup_r \bigtriangleup_z \bigtriangleup_{\theta}}[/tex], where the deltas represent the grid spacing that we have specified. For r and z, these are well defined.

    however, we are taking the system to be symmetric about [itex]\theta[/itex], meaning that this simulation is basically in two dimensions, r and z, and that [itex]\bigtriangleup_{\theta}=0[/itex]. How would I resolve this, because it looks to me like this would blow up?
  2. jcsd
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