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Particle simulation

As any space environment is made up of particles, so particle simulation is the most obvious method to simulate physical processes in space. As long as we know the physical parameters of each particle(such as location, velocity, charge, mass, etc.) we can decide the evolution of the whole system by combining the information of particles with background environment.

The motion of a particle is described by eq.(1)-(2):


\begin{displaymath}m\frac{d\textbf{v}_k}{dt}=q(\textbf{E}+\frac{1}{c}
\textbf{v}_k\times \textbf{B})
\end{displaymath} (1)


\begin{displaymath}\frac{d\textbf{x}_k}{dt}=\textbf{v}_k
\end{displaymath} (2)

From the current velocity and location of each particle, we can get E and B using Maxwell equations:

\begin{displaymath}\nabla\cdot \textbf{E}=\sum_k q_k \delta(\textbf{x}-
\textbf{x}_k)
\end{displaymath} (3)


\begin{displaymath}\nabla\times \textbf{B}=\frac{1}{c}\frac{\partial \textbf{E}}...
...\pi}{c}\sum_k q_k \textbf{v}_k
\delta(\textbf{x}-\textbf{x}_k)
\end{displaymath} (4)

One needs to iterate between eq.(1)-(2) and eq.(3)-(4) to push the evolution of the system. Then we can get all the particle and field information for any time or location in the simulation region, from which we can understand the physical processes of the system.

In particle simulation, single particle movement is considered and this movement is important in the interesting process. Generally, we can use the particle simulation when the time scale of the interesting process is around the order of the proton gyroperiod, while the space scale of interest is around the order of the proton gyroradius. At the same time, particle simulation keeps the information of the particle distribution, so generally, particle simulation is appropriate for simulating such problems as wave particle interactions, particle distribution evolution in space environments, etc. While in other cases, such as global magnetosphere simulations and reconnection processes in space, the time scale and space scale of interest are generally much larger than proton gyroperiod and gyroradius. Then MHD simulation, instead of particle simulation can be used to attack such problems.


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