Question

Vlasov equation: weak and long-range vs weak or long-range?

Answer 1

Suppose V is short-ranged, effectively vanishing for |r−r′|>σ. In the context of neutral gases, σ would represent the effective diameter of the particles. It stands to reason that g2 will also vanish beyond this range. In this case, both the neglected collision term and the mean-field term are of the same order, since they both involve integrals over r′ that vanish except when the two particles are within a distance σ from one another.

However, what if V is the Coulomb interaction, whose range in infinite? In this case, the mean field integral over r′ must extend over all space. On the other hand, g2 will still have a finite extent, since Debye screening will cause pair correlations to die out when |r−r′|>λD, the Debye length. For this reason, the "collision" term with g2 is of smaller order than the mean-field term.

So to answer your question directly now: within the approximation of collisionlessness, the Vlasov equation is valid regardless of the range of the interaction potential. However, the mean-field term must be retained if the interaction is long-ranged and must be dropped if it is short-ranged.

side note: The mean-field term is really the hallmark of the Vlasov equation. It is responsible for many of the interesting kinetic phenomena in plasma that are not present in neutral gases, e.g., Landau damping and Debye screening.

Answer 2

We can recognize the van der waal's forces in class 9 in ncert and in ICSE we can even get it in class 7 or 8. The van der waal's forces means the attraction between the particles of matter. This in characterised by weak or firm forces of the following.