(294) |

which is the length-scale above which the electrons exhibit collective (

Our normalized equations take the form:

whereas our initial distribution function becomes

(299) |

Let us solve the above system of equations in the domain .
Furthermore, for the sake of simplicity, let us adopt *periodic* boundary conditions:
*i.e.*, let us identify the left and right boundaries of our solution domain.
It follows that ,
, and . Moreover, any electron
which crosses the right boundary of the solution domain must reappear at the left boundary with
the same velocity, and
*vice versa*.