  We study the influence of the friction term on the radially symmetric
solutions of the repulsive Euler-Poisson equations with a non-zero background,
corresponding to cold plasma oscillations in many spatial dimensions. It is
shown that for any arbitrarily small non-negative constant friction
coefficient, there exists a neighborhood of the zero equilibrium in the $C^1$
norm such that the solution of the Cauchy problem with initial data belonging
to this neighborhood remains globally smooth in time. Moreover, this solution
stabilizes to zero as $t\to\infty$. This result contrasts with the situation of
zero friction, where any small deviation from the zero equilibrium generally
leads to a blow-up. Our method allows us to estimate the lifetime of smooth
solutions. Further, we prove that for any initial data, one can find such
coefficient of friction that the respective solution to the Cauchy problem
keeps smoothness for all $t>0$ and stabilizes to zero. We also present the
results of numerical experiments for physically reasonable situations, which
allows us to estimate the value of the friction coefficient, which makes it
possible to suppress the formation of singularities of solutions.
