  We systematically investigate the formation and stability of snowballs formed
by femtosecond photo-ionization of small alkali clusters bound to helium
nanodroplets. For all studied alkali species Ak=(Na, K, Rb, Cs) we observe the
formation of snowballs (AkHe_N)^+ when multiply doping the droplets.
Fragmentation of clusters Ak_N upon ionization appears to enhance snowball
formation. In the case of Na and Cs we also detect snowballs (Ak_2He_N)^+
formed around Ak dimer ions. While the snowball progression for Na and K is
limited to less than 11 helium atoms, the heavier atoms Rb and Cs feature wide
distributions at least up to (AkHe_41)^+. Characteristic steps in the mass
spectra of Cs-doped helium droplets are found at positions consistent with
predictions on the closure of the 1st shell of helium atoms around the Ak^+ ion
based on variational Monte Carlo simulations.
