The simplified stochastic Fermi-Ulam model revisited

TL;DR

This paper revisits the simplified stochastic Fermi-Ulam model, providing a consistent scheme for describing Fermi acceleration that resolves previous contradictions between theoretical transport coefficients and numerical results.

Contribution

It introduces a new, consistent framework for modeling Fermi acceleration in the SFUM, correcting inconsistencies in the standard FPE approach.

Findings

The new scheme aligns theoretical predictions with numerical simulations.

It clarifies the role of transport coefficients in the FPE.

The approach improves understanding of stochastic Fermi acceleration mechanisms.

Abstract

The description of Fermi acceleration developing in the phase-randomized simplified Fermi-Ulam model (SFUM) can be achieved in terms of a random walk taking place in momentum space. Within this framework the evolution of the probability density function of particle velocities is determined by the Fokker-Planck equation (FPE). However, the standard treatment in the literature leads to a result, which even though is in agreement with the numerical results, it is inconsistent with the transport coefficients used for the construction of the FPE. In this work we present a consistent scheme for the description of Fermi acceleration, resolving this contradiction.