A nonextensive thermostatistical approach to the Haïssinski theory of accelerator beams

We show that bunch-particle interactions in accelerator beams via wakefields as predicted by the Haïssinski theory can be described by the nonextensive entropy proposed by Tsallis for the nonextensivity parameter ν=2. A new method to analyze the Haïssinski problem is proposed that yields explicit expressions for Haïssinski distributions, the length of particle bunches, and the Tsallis entropy. Using this approach we generalize the Haïssinski case ν=2 to ν≠2. In doing so, we develop a Haïssinski theory that can address a more general class of bunch-particle interactions. We derive a new class of Haïssinski distributions and we show that bunch lengthening and shortening may be due to variations in the degree of nonextensivity involved in bunch-particle interactions.