Integral and Lagrangian simulations of particle and radiation transport in plasma

Accurate integral and Lagrangian models of transport in plasmas, in which the models reflect the actual physical behaviour as closely as possible, are presented. These methods are applied to the behaviour of particles and photons in plasmas. First, to show how these types of models arise in a wide range of plasma physics applications, an application to radiation transport in a lighting discharge is given. The radiation transport is solved self-consistently with a model of the discharge to provide what are believed to be very accurate 1D simulations of fluorescent lamps. To extend these integral methods to higher dimensions is computationally very costly. The wide utility of 'treecodes' in solving massive integral problems in plasma physics is discussed, and illustrated in modelling vortex formation in a Penning trap, where a remarkably detailed simulation of vortex formation in the trap is obtained. Extension of treecode methods to other integral problems such as radiation transport is under consideration.

[1]  J. Lawler,et al.  Radiation trapping of the Hg 254 nm resonance line , 2005 .

[2]  J. Lawler,et al.  Experimental and numerical study of a low-pressure Hg–Ar discharge at high current densities , 2002 .

[3]  C. V. Trigt ANALYTICALLY SOLVABLE PROBLEMS IN RADIATIVE TRANSFER. II. , 1970 .

[4]  T. Holstein Imprisonment of Resonance Radiation in Gases , 1947 .

[5]  P. J. Walsh,et al.  Effect of Simultaneous Doppler and Collision Broadening and of Hyperfine Structure on the Imprisonment of Resonance Radiation , 1959 .

[6]  J. Fajans,et al.  Experimental dynamics of a vortex within a vortex. , 2000, Physical review letters.

[7]  Colin B. Macdonald,et al.  Parallel High-Order Integrators , 2010, SIAM J. Sci. Comput..

[8]  John P. Verboncoeur,et al.  A treecode algorithm for simulating electron dynamics in a Penning-Malmberg trap , 2004, Comput. Phys. Commun..

[9]  G. J. Parker,et al.  Radiation trapping simulations using the propagator function method: complete and partial frequency redistribution , 1993 .

[10]  L. A. Gritzo,et al.  Fast Multipole Solvers for Three-Dimensional Radiation and Fluid Flow Problems , 1999 .

[11]  Robert Krasny,et al.  Computation of vortex sheet roll-up in the Trefftz plane , 1987, Journal of Fluid Mechanics.

[12]  D. Uhrlandt,et al.  Metastable and resonance atom densities in a positive column: II. Application to light source modelling , 2005 .

[13]  Jerold W. Emhoff Simulation of ion optics using particle-in-cell and treecode methods , 2005 .

[14]  W. Hitchon,et al.  Physics-based description of gas breakdown , 2007 .

[15]  Peijun Li,et al.  A Cartesian treecode for screened coulomb interactions , 2009, J. Comput. Phys..

[16]  C. V. Trigt Analytically Solvable Problems in Radiative Transfer. I , 1969 .

[17]  G. J. Parker,et al.  Plasma chemistry at long mean‐free‐paths , 1994 .

[18]  Piet Hut,et al.  A hierarchical O(N log N) force-calculation algorithm , 1986, Nature.

[19]  G. J. Parker,et al.  Radiation trapping simulations using the propagator function method , 1993 .

[20]  S. E. Coe,et al.  GLOMAC : a one dimensional numerical model for steady state low pressure mercury-noble gas discharges , 1993 .

[21]  A gridless solution of the radiative transfer equation for fire and combustion calculations , 1999 .

[22]  Daniel J. Koch,et al.  An efficient scheme for convection-dominated transport , 1989 .

[23]  C. V. Trigt Complete redistribution in the transfer of resonance radiation , 1976 .

[24]  Iain D. Boyd,et al.  Kinetic description of flow past a micro-plate , 2004 .

[25]  G. Lister Collisional and radiative processes in fluorescent lamps , 2003 .

[26]  Parker,et al.  Transport of sputtered neutral particles. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[27]  Paul Gibbon,et al.  Many-body tree methods in physics , 1996 .

[28]  J. Lawler,et al.  Resonance radiation transport in inhomogeneous media: Cylindrical glow discharges , 1999 .

[29]  J. Lawler,et al.  Propagator description of radiation transport, applied to lighting discharges , 2007 .

[30]  Jerold W. Emhoff,et al.  Grid-free plasma Simulation techniques , 2006, IEEE Transactions on Plasma Science.

[31]  John P. Verboncoeur,et al.  Simulation of a positive column discharge with a one-dimensional radial radiation transport coupled particle-in-cell model , 2001 .

[32]  G. S. Hurst,et al.  Effect of correlations between absorbed and emitted frequencies on the transport of resonance radiation , 1974 .

[33]  J. Giuliani,et al.  Non-local radiation transport via coupling constants for the radially inhomogeneous Hg–Ar positive column , 2005 .

[34]  Deborah A. Fixel,et al.  Convective scheme solution of the Boltzmann transport equation for nanoscale semiconductor devices , 2007, J. Comput. Phys..

[35]  A. Ghoniem,et al.  Grid-free simulation of radiative transport in a participating medium , 1999 .

[36]  Andreas F. Molisch,et al.  Radiation Trapping in Atomic Vapours , 1999 .

[37]  K. Lindsay,et al.  A particle method and adaptive treecode for vortex sheet motion in three-dimensional flow , 2001 .