I was studying Plasma physics, when I came across this statement:
As a consequence of their high electrical conductivity they do not support electrostatic fields except, to a certain extent, in a direction normal to any magnetic field present, which inhibits the flow of charged particles in this direction.
I didn't understand this part. Why can't charges flow in a direction perpendicular to some Magnetic field?
The force on a charge with velocity $\vec{v}$ in a magnetic field $\vec{B}$ is given by the Lorentz force, which is proportional to the cross product $\vec{v}\times\vec{B}$, which means that if $\vec{v}$ is perpendicular to $\vec{B}$, the resultant force is always perpendicular to $\vec{v}$, so no free flow in a given direction is possible. The charge is just moving around in a circle about the magnetic field line. Only parallel to the latter is a free flow possible i.e. do we have a good electrical conductivity. And inside a good conductor any externally applied electric field will be quickly neutralized as charges can easily move around such as to set up a force free state. A field will only be noticeable outside the conductor.
Having said this, the paragraph quoted by the OP is actually not quite correct, at least not out of its context (which I don't know): even without any magnetic field it can support an electric field in case of inhomogeneities of the plasma or border effects. These lead to some degree of charge separation and thus to a so called plasma polarization field even inside the plasma (which however in this case is strictly speaking not locally neutral anymore).
In principle they can, the point is that this is not the primary motion of charged particles in a magnetic field. The movement along magnetic field lines is much faster than any other, perpendicular motion. This is probably why the author used the phrase to some extent.
This is usually summarized under the term guiding center motion. In leading order, the particle will follow magnetic field lines and will gyrate around them. Only if you consider corrections due to the finite width of the gyration radius, you will get higher order effects such as drifts perpendicular to the magnetic field.
