New features in a time dependent magnetic field lens

In this work we study the noise effect in a time dependent magnetic lens. We focus our analysis in a magnetic field, such that, it can be separate in two terms, one a constant and the other a random field. Using the Furutsu-Novikov-Shapiro-Logunov method, for dichotomous colorized noise, we find explicit differential equations for the first and second momenta and the correlation functions. Finally, we show that for some range of parameters is possible to find stable behaviors of these quantities.