Operational Markov matrix formulation for structures in continuum plasma models

Physical systems supporting stationary-structures allow translation of their mathematical formulations in to stochastic models. This paper presents the application of Markovian nonuniform generation formulation to achieve, for the first time, the analytically inaccessible flow configurations by letting the continuum fluid model to translate into a stochastic model of the Markovian class. The developed procedure achieves solutions in the infinitely large number limit of realizations, however completely free-from any computational realizations of the random variables. Fundamental properties of elements underlying this translation are developed by treating the representative, yet highly application relevant, case of plasma transport equilibria which solve the continuum fluid model of the target-bound plasma flow in the open magnetic field line region of fusion devices. Operational Subcomponent Markov Matrices (SMM), generating stationary structures of plasma flow, are constructed for the first time and quantitatively verified against the properties of SMMs systematically defined under the Markov-Chain Monte-Carlo (MCMC) formulation. The equivalent stochastic solutions simulated by a direct Markovian Monte-Carlo Simulation code MMSIM are validated against the corresponding structures produced by the developed SMMs in a procedure free-from numerical realizations of random variables. Benchmark of standard cases with the analytical solutions is presented followed by more general analytically inaccessible structures relevant to SOL configurations of fusion devices, demonstrating the capacity of SMM-MCMC based formulation to validate the general transport equilibria obtained from the associated stochastic simulations.