Why is a spatial grid necessary in plasma simulations? I am new to the topic and I am reading Plasma Physics via Computer Simulations by Birdsall and Langdon. The authors claim that working with a spatial grid is more efficient opposed to considering the $10^{25}$ particle interactions. Additionally the problem of $10^{25}$ singularities ar $r \to 0$ also vanishes.
I understand how the use of a charge density across a grid is more efficient than considering all the 1-1 interactions, nevertheless I don't understand why do we need a spatial grid for this. Why can't the actual charge distribution be used? Why is it better to perform a weighting to the charges and approximate it to a distribution on the grid?
Additionally what is the problem with the singularities at $r \to 0$? Charges simply ignore their own electric fields.
Edit:
I understand how dealing with $10^{25}$ items is not computational possible, nevertheless these simulations work with 1D-2D approximations that reduces the number of particles, say to $10^6$.
What is my problem? If we are working with a grid we still have to go through the $10^6$ particles and distribute their charge along the grid appropriately. We still have to go through all the particles, we just lose accuracy by dividing the charges along a grid.
Why don't we just use the actual particles positions? Does it make easier to numerically solve the fields for the grid opposed to non-uniform positions distribution?
 A: Ok, let us entertain the idea that you can take $10^{25}$ particles and evolve them numerically. Storing each position and velocity is 6 doubles, which gives a whopping 80 yottabytes or $10^{12}$ terrabytes for all the particles. Now you want to evolve these by one time-step. This requires computing the force on each individual particle by each individual particle three times (because of dimension). So that gives you $3\cdot10^{50}$ double operations or $\sim 10^{41}$ corehours or $\sim 10^{28}$ years ($10^{11}$ ages of the Universe) on the most powerful supercomputers to date. You could argue that you do not need to evaluate the force between every two particles, but even then it would require at least thousands of years to evaluate even a single time step on the most powerful supercomputers.
Obviously you need to simplify this model, and passing to an effective continuum description is one of the ways to do it. In that case you actually do not track each particle, you track, for instance, the average number and velocity of particles within a given spatial cell. Other approaches exist, where you track the distribution function of the particles in phase space (averaged over a phase-space cell), or approaches where you do the mentioned in parallel to sampling the behaviour of individual "representative" particles to inform the evolution. All of these make the problems much more tractable while keeping the macroscopic description of the plasma highly accurate (at least most of the time). 
