Modeling the process of stochastic cooling using the Fokker-Planck equation. Designing of a stochastic cooling system for the Nuclotron

The mathematical model of the algorithm for calculating the evolution of the particle distribution function in transverse phase space and function of the energy spread for the synchrotron with a stochastic cooling system using a notch filter technique is described. Simulation results for the distribution function and momentum spread of the proton and carbon beams in accelerator Nuclotron are presented. The description and working principle of the proposed construction of a stochastic cooling system based on assembly of the ring slot-coupler pickups are also described and a notch filter design and assembly of the entire cryo-vacuum system for installation at Nuclotron are given.