The theory of the shot effect. II

Summary of the previous paper

The previous paper dealt first with the shot effect without secondary emission. We considered a stream of electrons arriving at random, with a fixed probable density N, at the anode of the resistance-capacity coupled first valve of a linear amplifier. This does not allow for the effect whereby the arrival of electrons alters the anode potential, and consequently the probability of arrival of succeeding electrons. The valve must be working with what is conventionally called an infinite internal resistance, and without space-charge effects. Each electron arriving at time t_r is supposed to produce at time t an output effect f(t − t_r) from the amplifier. We considered the hypotheses, first, that electrons may, with specific probabilities, have lives of any length on the anode system, during which they add − ε/C to the anode potential, and alternatively that each electron adds to the anode potential of the valve whose anode to earth capacity is C and whose feed resistance is R. These hypotheses determine the form of f(t − t_r) when the behaviour of the main part of the amplifier is known. Since the amplifier is linear, the effects of various electrons are additive, so that the total output is ∂(t) = ∑_rf(t − t_r).