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I'm doing some particle-in-cell (PIC) simulations of propagation of short pulses in plasmas with a widely used code. This code uses Yee's field solver. So, the timestep must be lower than the Courant limit. But the question is: How much? In one published work I read that a value much smaller than the Courant limit can cause numerical errors in PIC simulation.

In my own experience the simulation results for a timestep of ~90% of the Courant limit and for a timestep of ~50% are significantly different. An experienced physicist doing these kinds of simulations told me that I should use a timestep of ~90% of the Courant limit. But then, how can the significant difference that I just mentioned be understood?

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    $\begingroup$ Time steppers coupled with space discretizations have this problem called numerical diffusion, sometimes called dissipation. For finite difference methods you can actually even figure out given time step size how much numerical diffusion there will be using Taylor series expansions. Hence, choosing a time step is a balancing act between satisfying the Courant condition and minimizing the numerical diffusion. For a problem we asked in a numerical analysis course, the optimal step size ended up being exactly the Courant limit. Optimal value may be less, may even be more than the Courant limit. $\endgroup$ – Abdullah Ali Sivas Aug 6 '20 at 20:21

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