  We consider a periodic planar Lorentz process with strictly convex obstacles
and finite horizon. This process describes the displacement of a particle
moving in the plane with unit speed and with elastic reflection on the
obstacles. We call number of self-intersections of this Lorentz process the
number V(n) of couples of integers (k,m) smaller than n such that the particle
hits a same obstacle both at the k-th and at the m-th collision times. The aim
of this paper is to prove that the variance of V(n) is equivalent to cn^2 (such
a result has recently been proved for simple planar random walks by
Deligiannidis and Utev).
