Functional methods applied to plasma theory problems


 Basic path-integral method for the statistical analysis of stochastic processes

The classical statistical analysis of simple random processes, can be formulated in terms of the Martin Siggia Rose functional and re-formulated (Jensen) in terms of path-integral. The Faynman diagrammatic expansion allows to calculate the generating functional and derive the irreducible correlations by functional derivatives. It is a classic approach, it has been used in a large number of problems and is efficient.

Simple Langevin equations

Examples of processes that can be directly analysed using path-integral methods. It also include an application to the Levy process.


 Magnetic stochasticity

Particle trajectories in stochastic magnetic fields

Statistical analysis of ensemble of realizations of particle trajectories in stochastic magnetic field.

Collisional particles in stochastic magnetic field

Collisional diffusion in stochastic magnetic field. The reference case is a Tokamak.


 Diffusion with trapping

There is a wide variety of methods that have been developed for this problem. We restrict here to our path-integral applications.

Diffusion with trapping in 2D fluid or plasmas

  The 2D process that is examined here is more general, but it was isnpired by the trapping of impurities in turbulent eddies in Tokamak

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