A complicated question if conditions are not defined. What is the ionizing agent, what is the energy of the particles and what is their concentration?

In surface potential measurements with radioactive Am electrode, where one ionizes the gas above a Langmuir monolayer, there is no evidence of surfactant destruction. Surfactants with paraffinic tails are generally stable with respect to nucleophilic/electrophilic reactions.

If you increase the load/the energy a lot, you will eventually burst the film due to heating. If the foam is not very stable and is electrolyte-free, you can accumulate ions in the film until they screen the electrostatic repulsion to the point of instability. If there is not much surfactant, a tiny heating will lead to thermal Marangoni effect, which may be actually stabilizing. If you use ions that can change their oxidation state, they can catalyze a radical chain oxidation, but this will require elevated temperature (too slow at 25 deg).

If you expect something similar to the instability of charged droplets, I wouldn't expect that since it is hard to charge a foam film that much. It may be possible the ionization to induce an electro-Marangoni effect, but the outcome is hard to predict.

Radomir, this is an interesting problem with important practical applications. I am designing sensitive neutron detectors based on soap foam. The foam contains neutron capture isotopes that create high energy charged particles on a capture reaction. The situation is similar to the Am electrode over Langmuir monolayer scenario except that in my case we have pressurized Argon that ionises due to interaction with high energy alpha particles (~ 2.5 MeV) . I am expecting a change in the statistics of bubble bursting due to energy deposition on the foam cell walls and the system will work as a neutron detector. The question is how the ionization of the gas is going to alter the bubble statistics. Experimentally it can be understood by varying the argon pressure. I am asking the question why it may alter the foam cell stability. 

Draw a picture of your setup.

As I imagine it, you hit a single foam film with a high-energy particle. It will probably create a hole due to heating. The balance between the kinetic energy of the particle and the heat of evaporation of a portion of the film will tell you if this is possible at all or you should think of another mechanism. The hole must be of radius larger than the critical value above which self-healing is impossible (which is of the order of the film thickness if capillary forces are the only factor, but this will probably be significantly different in the presence of temperature and surfactant concentration gradients - you probably need to consider that). Once a single film is broken, the foam can be destroyed by the usual cascade mechanism.

It is perhaps more probable to create the high energy particle in the menisci, is it? If so, you might have a situation with hot meniscus and cold film, which is a destabilizing effect.

By the way, if you are in BAS, you can check the foam guys in the Physical Chemistry Institute, they are really good and will probably be interested. I remember that in Sofia University they were studying the cascade destruction of foam in the Dept. of Chemical Engineering.