The avalanche occurs in a gaseous medium that can be ionised (such as air).  The electric field and the mean free path of the electron must allow free electrons to acquire an energy level (velocity) that can cause impact ionisation.  If the electric field is too small, then the electrons do not acquire enough energy.  If the mean free path is too short, the electron gives up its acquired energy in a series of non-ionising collisions.  If the mean free path is too long, then the electron reaches the anode before colliding with another molecule.
The avalanche mechanism is shown in the accompanying diagram.  The electric field is applied across a gaseous medium; initial ions are created with ionising radiation (for example, cosmic rays). An original ionisation event produces an ion pair; the positive ion accelerates towards the cathode while the free electron accelerates towards the anode. If the electric field is strong enough, the free electron can gain sufficient velocity (energy) to liberate another electron when it next collides with a molecule. The two free electrons then travel towards the anode and gain sufficient energy from the electric field to cause further impact ionisations, and so on. This process is effectively a chain reaction that generates free electrons. Initially, the number of collisions grows exponentially.  The total number of electrons reaching the anode is equal to 2 with n the number of collisions, plus the single initiating free electron.  Eventually, this relationship will break down - the limit to the multiplication in an electron avalanche is known as the Raether limit.  
The Townsend avalanche can have a large range of current densities. In common gas-filled tubes, such as those used as gaseous ionisation detectors, magnitudes of currents flowing during this process can range from about 10 amperes to about 10 amperes.