  Coulombian diffusion determines a dilution of bunching coefficients in Free
Electron Laser seeded devices. From the mathematical point of view the effect
can be modeled through a heat type equation, which can be merged with the
ordinary Liouville equation, ruling the evolution of the longitudinal phase
space beam distribution. We will show that the use of analytical tools like the
Generalized Bessel Functions and algebraic techniques for the solution of
evolution problems may provide a useful method of analysis and shine further
light on the physical aspects of the underlying mechanisms.
