  It is proved that the radially symmetric solutions of the repulsive
Euler-Poisson equations with a non-zero background, corresponding to cold
plasma oscillations blow up in many spatial dimensions except for $\bd=4$ for
almost all initial data. The initial data, for which the solution may not blow
up, correspond to simple waves. Moreover, if a solution is globally smooth in
time, then it is either affine or tends to affine as $t\to\infty$.
