exist for only about 11 nanoseconds before being captured. Captured electrons are effectively removed from play — they can no longer contribute to the avalanche process. If electrons are being created at a rate greater than they are being lost to capture, their number rapidly multiplies, a process characterized by exponential growth. The degree of multiplication that this process can provide is huge, up to several million-fold depending on the situation. The multiplication factor M is given by Where X1 and X2 are the positions that the multiplication is being measured between, and α is the ionization constant. In other words, one free electron at position X1 will result in M free electrons at position X2. Substituting the voltage gradients into this equation results in Where V is the applied voltage, VBR is the breakdown voltage and n is an empirically derived value between 2 and 6. As can be seen from this formula, the multiplication factor is very highly dependent on the applied voltage, and as the voltage nears the breakdown voltage of the material, the multiplication factor approaches infinity and the limiting factor becomes the availability of charge carriers. Avalanche sustenance requires a reservoir of charge to sustain the applied voltage, as well as a continual source of triggering events. A number of mechanisms can sustain this process, creating avalanche after avalanche, to create a corona current. A secondary source of plasma electrons is required as the electrons are always accelerated by the field in one direction, meaning that avalanches always proceed linearly toward or away from an electrode. The dominant mechanism for the creation of secondary electrons depends on the polarity of a plasma. In each case, the energy emitted as photons by the initial avalanche is used to ionise a nearby gas molecule creating another accelerable electron. What differs is the source of this electron. When one or more electron avalanches occur between two electrodes of sufficient size, complete avalanche breakdown can occur, culminating in an electrical spark that bridges the gap. See also Townsend discharge Avalanche breakdown Avalanche diode Corona discharge Multipactor Geiger–Müller tube Geiger counter Spark chamber Wire chamber Runaway breakdown Relativistic runaway electron avalanche List of plasma (physics) articles References External links Breakdown effects in semiconductors Electrical breakdown