Limitations of particle in cell method for high desnity plasma Are there any limitations of particle in cell (PIC) method for high density plasma? To be more specific, is modelling of a narrow channel of high density plasma possible or are there any limitations connected with PIC approximation?
 A: The main limitation on PiC is not density per se, but rather that the plasma should be collisionless. The frequency of collisions is (as a rough approximation)
$\nu \propto \omega_p \cdot \frac{\ln(\Lambda)}{\Lambda} $
where $\Lambda$ is the number of particles in a Debye sphere $\propto T^{3/2} / n^{1/2}$
So what you want a plasma that has low enough density and more importantly that is warm enough that a negligable number of collision happens for the duration of whatever other process you want to study in the first place. Collisions can be added to PiC via MonteCarlo methods, but then things quickly get tricky.
The number of particles and the limit of RAM are less important than you could assume from the comments to your question as you usually don't treat every single electron individually, but group particles of one species that have similar velocities into a single macro particles, reducing the number of computational particle by $10^5 \dots 10^{15}$. The $10^7 \dots 10^{10}$ macro particles that you can hold in RAM can thus cover a large, high density domain.
A: This is a very complex and broad question.
There are first some technical difficulties:


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*The memory consumption, as noted by others.

*The time it takes to compute.


They can be very high, because a very large number of particles may be required to limit the statistical noise. This noise can create many problems, such as numerical plasma waves, strong numerical heating, etc. These limitations can vary drastically from one specific problem to another. It is difficult to assess without knowing your situation.
Secondly, there are physical difficulties:


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*Collisions, which can be treated but only with approximations that can fail.

*Collisionnal ionization, which can prove difficult when dealing with exponentially growing number of electrons.

*Field ionization (same problem)

*Recombination and other atomic processes

*Radiation due to these atomic processes or due to Bremsstrahlung, and all the physics related to this radiation interacting with ions or electrons

*Nuclear reactions

*Quantum processes (pair creation, quantum Bremsstrahlung, etc.)

*... (an endless list really)


You have to define clearly your problem and identify which of these physical aspects require additionnal computation.
