Ice made of ultrapure water or water doped with 1 % polymer (polyethylene glycol, "PEG") was irradiated by laser light with fluences between 2 and 80 J/cm(2) in the ultraviolet (UV) regime at 355 nm and in the infrared (IR) regime at 1064 nm in vacuum. In the UV regime there is a threshold for plasma formation at 3.5 J/cm(2), whereas the threshold is at 8.5 J/cm(2) in the IR regime. The ions from the plasma plume were studied by a Langmuir probe. The ion yield was much higher for UV laser irradiation than for IR laser irradiation. The peak of the time-of-flight spectra comprises ions of velocity from 60 to 110 km/s. Generally, the ion yield was slightly larger for ice samples doped with PEG than for pure ones. The threshold behavior was much more pronounced in the IR regime than in the UV regime. These results indicate that the behavior of the plasma current can be understood in terms of ionization breakdown at the ice surface.