IIMAS - FENOMEC
UNAM
A Backward Monte Carlo method for the solution of the adjoint Fokker-Planck equation
por el Resumen:
The forward Fokker-Planck equation (FFP) describes the time evolution of an initial
probability distribution function f(t=0) for given drift and diffusion transport coefficients.
On the other hand, the backward Fokker-Planck equation (BFP) describes the final value
problem, i.e. the solution of f for t < T given f at the final time T. Formally the BFP is the
adjoint of the FFP. Although the FFP might be more intuitive to understand, the BFP is
valuable in the study of transport problems involving the computation of the probability
for a particle to transition to a prescribe region in the space at, or before, a given time T.
Because of this, it is important to develop efficient methods for the solution of the BFP.
The Backward Monte Carlo method (BMC) is one of these methods based on the direct
solution of the Feynman-Kac formula that links the BFP to the stochastic differential
equation (SDE) associated to the FFP. In this talk, following a tutorial discussion of the
FFP, BFP, BMC, SDE and the Feynman-Kac formula, we present a recent novel
application of these powerful techniques to the dynamics of relativistic electrons in
magnetically confined fusion plasmas [1].
[1] G. Zhang and D. del-Castillo-Negrete, “A backward Monte-Carlo method for time-
dependent runaway electron simulations” Phys. of Plasmas 24, 092511 (2017).
Informes: coloquiomym@gmail.com, o al 5622-3564.