Actually, ionization can be caused by the radioactive background (ionizing) radiation, as for instance in the Geiger-Mueller tube. In a sufficiently strong electric field this can be followed by (Townsend) avalanche multiplication due to sufficient acceleration of this first ionized electron (and possibly the associated positive ion from that atom that's just been ionized) that it is able to ionize other atoms, eventually possibly leading to an electric arc.
The electric field can be 'strong' because the voltage is high over a considerable distance, for instance 500 V over 1/2 meter , but the same electric field strength (E = 500V/0.5m = 1 kV/m) can be obtained by applying only 1 V of potential difference over two contacts which are spaced a mere 1 mm away, as occurs in our relays just before they latch.
It's the strength of the electric field (potential difference over distance with S.I. dimension [V/m]) which determines whether this avalanche occurs after the first ionization due to ionizing radiation already has occurred.
I must admit though that I haven't calculated whether or not that length (e.g. 1 mm) is enough to accelerate the first ions, ionized by the external radiation, enough to ionize the next atom.
If not, I propose a compromise, tunnel ionization, but in order for that to occur with a significant probability the electron first needs to be 'pumped up' a bit through near-infrared strong laser pulses, as I just learned from this interesting article:
But in fact I doubt if it makes any difference which phenomenon caused the original ionization event.
joe