Monte Carlo vs. Transport Equations' Description of Outflowing Fully-Ionized Ionospheric Plasma

At terrestrial high latitudes, the plasma flows along "open" field lines from the high-pressure ionosphere into the low-pressure magnetosphere. At relatively high altitudes, the plasma is fully ionized and the dominant collision mechanism corresponds to the Coulomb interaction. As the plasma flows upward, it gradually goes from a collision-dominated region into a collisionless region. Over several decades, the (fluid-like) generalized transport equations, and the (particle-based) Monte Carlo approaches evolved as two of the most powerful simulation techniques that address this problem. Each approach has its intrinsic advantages and drawbacks. For example, the transport equations' approach is relatively much more computationally efficient but its validity is questionable in the collisional-to-collisionless transition region where double-peaked velocity distribution functions can form. On the other hand, the Monte Carlo's approach can handle a wide variety of velocity distributions, but it is computationally intensive, especially deep into the collision-dominated regions. In this study, we discuss the inherent strengths and weaknesses of these two approaches as they are applied to the problem of plasma outflow at high latitudes. Special attention is given to the different techniques of improving the performance of each approach. We also discuss how these two approaches can be combined and the corresponding potential pitfalls.