When can I assume that plasma is collisionless? How is the presumption of a plasma being "collisionless" depend on other parameters such as ion density and ion and electron temperature?
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This is problem dependent, and boils down to the question whether collisions have an important effect on the answer or not. For plasma to be considered collisionless, one condition is $\lambda \gg L$ where $\lambda$ is the collisional mean-free path of plasma particles, and $L$ is the spatial scale of interest (typically the spatial scale of plasma parameters such as density or pressure). If plasma is nearly uniform, and all gradient lengths are very large then a more useful criterion is $\nu \ll 1/\tau$ where $\nu$ is the collision frequency and $\tau$ is the temporal scale of interest. An intuitive way to understand this is to imagine a full differential equation governing the time evolution of plasma (say, the Fokker-Planck kinetic equation); it includes time derivatives of the distribution function $\partial{}_{t} f$ and collisional terms that scale as $\nu f$ (just because of dimensionality), so the collisional terms can be dropped when $\nu$ is much smaller than $1/\tau$.
Maxim Umansky
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An easy example is a collisionless shock in the solar wind, where the shock ramp thickness tends to be between the electron and ion inertial lengths (e.g., ~1-150 km near Earth) while the collisional mean free path can exceed 1 AU ~ $10^{8}$ km. – honeste_vivere Aug 11 '19 at 19:30