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C S Chang - One of the best experts on this subject based on the ideXlab platform.

  • a fully non linear multi species fokker planck landau Collision Operator for simulation of fusion plasma
    Journal of Computational Physics, 2016
    Co-Authors: R Hager, Eisung Yoon, E Dazevedo, Patrick H Worley, C S Chang
    Abstract:

    Fusion edge plasmas can be far from thermal equilibrium and require the use of a non-linear Collision Operator for accurate numerical simulations. In this article, the non-linear single-species Fokker-Planck-Landau Collision Operator developed by Yoon and Chang (2014) 9 is generalized to include multiple particle species. The finite volume discretization used in this work naturally yields exact conservation of mass, momentum, and energy. The implementation of this new non-linear Fokker-Planck-Landau Operator in the gyrokinetic particle-in-cell codes XGC1 and XGCa is described and results of a verification study are discussed. Finally, the numerical techniques that make our non-linear Collision Operator viable on high-performance computing systems are described, including specialized load balancing algorithms and nested OpenMP parallelization. The Collision Operator's good weak and strong scaling behavior are shown.

  • a self adjoint form of linearized coulomb Collision Operator for energetic ions
    Physics of Plasmas, 1995
    Co-Authors: Hogun Jhang, C S Chang
    Abstract:

    A self‐adjoint form of linearized Coulomb Collision Operator for energetic ions is obtained. Background electron and ion species are assumed to have Maxwellian distributions with different temperatures. The result can be used in the kinetic investigations of Collisional effects on the energetic ion behavior, including variational studies of the energetic ion Fokker–Planck equation.

Eero Hirvijoki - One of the best experts on this subject based on the ideXlab platform.

  • energy momentum density and positivity preserving spatio temporal discretizations for the nonlinear landau Collision Operator with exact h theorems
    arXiv: Plasma Physics, 2018
    Co-Authors: Eero Hirvijoki, J W Burby, Michael Kraus
    Abstract:

    This paper explores energy-, momentum-, density-, and positivity-preserving spatio-temporal discretizations for the nonlinear Landau Collision Operator. We discuss two approaches, namely direct Galerkin formulations and discretizations of the underlying infinite-dimensional metriplectic structure of the Collision integral. The spatial discretizations are chosen to reproduce the time-continuous conservation laws that correspond to Casimir invariants and to guarantee the positivity of the distribution function. Both the direct and the metriplectic discretization are demonstrated to have exact H-theorems and unique, physically exact equilibrium states. Most importantly, the two approaches are shown to coincide, given the chosen Galerkin method. A temporal discretization, preserving all of the mentioned properties, is achieved with so-called discrete gradients. Hence the proposed algorithm successfully translates all properties of the infinite-dimensional time-continuous Landau Collision Operator to time- and space-discrete sparse-matrix equations suitable for numerical simulation.

  • metriplectic particle in cell integrators for the landau Collision Operator
    arXiv: Computational Physics, 2018
    Co-Authors: Eero Hirvijoki, Michael Kraus, J W Burby
    Abstract:

    In this paper, we present a new framework for addressing the nonlinear Landau Collision Operator in terms of particle-in-cell methods. We employ the underlying metriplectic structure of the Collision Operator and, using a macro particle discretization for the distribution function, we transform the infinite-dimensional system into a finite-dimensional time-continuous metriplectic system for advancing the macro particle weights. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of density, momentum, and energy, as well as the positive semi-definite production of entropy in both the time-continuous and the fully discrete system is demonstrated algebraically. The new algorithm is fully compatible with the existing particle-in-cell Poisson integrators for the Vlasov-Maxwell system.

  • metriplectic integrators for the landau Collision Operator
    Physics of Plasmas, 2017
    Co-Authors: Michael Kraus, Eero Hirvijoki
    Abstract:

    We present a novel framework for addressing the nonlinear Landau Collision integral in terms of finite element and other subspace projection methods. We employ the underlying metriplectic structure of the Landau Collision integral and, using a Galerkin discretization for the velocity space, we transform the infinite-dimensional system into a finite-dimensional, time-continuous metriplectic system. Temporal discretization is accomplished using the concept of discrete gradients. The conservation of energy, momentum, and particle densities, as well as the production of entropy is demonstrated algebraically for the fully discrete system. Due to the generality of our approach, the conservation properties and the monotonic behavior of entropy are guaranteed for finite element discretizations, in general, independently of the mesh configuration.

  • fluid moments of the nonlinear landau Collision Operator
    Physics of Plasmas, 2016
    Co-Authors: Eero Hirvijoki, Manasvi Lingam, D Pfefferle, Luca Comisso, J Candy, A Bhattacharjee
    Abstract:

    An important problem in plasma physics is the lack of an accurate and complete description of Coulomb Collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau Collision Operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary Collisionality and flow.

  • fluid moments of the landau Collision Operator
    arXiv: Plasma Physics, 2016
    Co-Authors: Eero Hirvijoki, Manasvi Lingam, D Pfefferle, Luca Comisso, J Candy, A Bhattacharjee
    Abstract:

    One important problem in plasma physics is the lack of an accurate and complete description of Coulomb Collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multi-dimensional Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau Collision Operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to weakly Collisional and strong flow regimes.

S Alexiou - One of the best experts on this subject based on the ideXlab platform.

  • IMPROVED CLOSED-FORM FORMULAS FOR THE Collision Operator FOR ISOLATED ION LINES IN THE STANDARD STARK-BROADENING THEORY
    Journal of Quantitative Spectroscopy and Radiative Transfer, 1999
    Co-Authors: A. Poquérusse, S Alexiou
    Abstract:

    Abstract In a recent paper, Alexiou and Maron gave a closed-form formula for the Collision Operator for Stark broadening of isolated ion lines. In this work we improve on the above-mentioned work by giving simpler and more accurate expressions. As in the work of Alexiou and Maron, the new expressions involve no integrations and assume a pure dipole interaction, and a Maxwellian electron velocity distribution. As in the original work by Alexiou and Maron, these expressions are exact within the stated approximations, and apply equally to hot and cold plasmas as long as the above approximations are satisfied. Further, they also give an estimate of the theoretical error. The present formulas should be useful for fast data analysis and for the calculation of a large number of lines, as, for example, in opacity calculations.

  • theoretically based closed form formulas for the Collision Operator for isolated ion lines in the standard stark broadening theory
    Journal of Quantitative Spectroscopy & Radiative Transfer, 1995
    Co-Authors: S Alexiou, Y Maron
    Abstract:

    Abstract In this work we obtain closed form expressions for the Collision Operator for Stark broadening of isolated ion lines in the semiclassical (dipole) impact approximation and for a Maxwellian electron velocity distribution. These expressions are simple in that no integrations are involved, exact within the stated approximations, and apply equally to hot and cold plasmas as long as the above approximations are satisfied. These formulas give widths with good accuracy, together with an estimate of the theoretical error. Therefore, they can be used for fast data analysis and also for the calculation of a large number of lines, as, for example, in opacity calculations. In addition, the behavior of the Collision Operator as a function of the energy separation of the perturbing levels, the temperature, and the cutoffs becomes more transparent.

Igitte Lucquindesreu - One of the best experts on this subject based on the ideXlab platform.

  • the fokker planck asymptotics of the boltzmann Collision Operator in the coulomb case
    Mathematical Models and Methods in Applied Sciences, 1992
    Co-Authors: Pierre Degond, Igitte Lucquindesreu
    Abstract:

    The Fokker-Planck Collision Operator is usually considered as an approximation of the Boltzmann Collision Operator when the Collisions become grazing. A mathematical framework to this approach has recently been given in Ref. 2, by assuming that the scattering cross-section is smooth and depends upon a small parameter e which tends to zero. However, the connection between e and the physical quantities is unclear. In the present paper, our main concern is the Boltzmann Operator for Coulomb Collisions and its Fokker-Planck approximation. In the case of Coulomb Collisions, the scattering cross-section has a non-integrable singularity when the relative velocity of the colliding particles tends to zero and a careful analysis is required. Furthermore, by a scaling of the Collision Operator, the small parameter which is involved in the Fokker-Planck asymptotics is clearly identified to the plasma parameter, and an expansion which is consistent with the physical observations is derived.

A Bhattacharjee - One of the best experts on this subject based on the ideXlab platform.

  • fluid moments of the nonlinear landau Collision Operator
    Physics of Plasmas, 2016
    Co-Authors: Eero Hirvijoki, Manasvi Lingam, D Pfefferle, Luca Comisso, J Candy, A Bhattacharjee
    Abstract:

    An important problem in plasma physics is the lack of an accurate and complete description of Coulomb Collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multivariate Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau Collision Operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to arbitrary Collisionality and flow.

  • fluid moments of the landau Collision Operator
    arXiv: Plasma Physics, 2016
    Co-Authors: Eero Hirvijoki, Manasvi Lingam, D Pfefferle, Luca Comisso, J Candy, A Bhattacharjee
    Abstract:

    One important problem in plasma physics is the lack of an accurate and complete description of Coulomb Collisions in associated fluid models. To shed light on the problem, this Letter introduces an integral identity involving the multi-dimensional Hermite tensor polynomials and presents a method for computing exact expressions for the fluid moments of the nonlinear Landau Collision Operator. The proposed methodology provides a systematic and rigorous means of extending the validity of fluid models that have an underlying inverse-square force particle dynamics to weakly Collisional and strong flow regimes.