Nonequilibrium gyrokinetic fluctuation theory and sampling noise in gyrokinetic particle-in-cell simulations

Krommes, John A.

doi:doi:10.1063/1.2759879

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Dust structures in cryogenic gas discharges

Results are given of experimental investigations of dust structures of monodisperse particles in a low-pressure dc glow discharge at temperatures of liquid nitrogen (T = 77 K) and liquid helium (T = 4.2 K). It is found that the cooling of discharge at invariant discharge current and neutral gas density causes a decrease in the interparticle spacing in structures and an increase in the kinetic energy of dust particles. The forming of a superdense dust structure with free boundaries is observed f...

The present state of the theory of fluctuations in gyrokinetic (GK) plasmas and especially its application to sampling noise in GK particle-in-cell (PIC) simulations is reviewed. Topics addressed include the Δf method, the fluctuation-dissipation theorem for both classical and GK many-body plasmas, the Klimontovich formalism, sampling noise in PIC simulations, statistical closure for partial differential equations, the theoretical foundations of spectral balance in the presence of arbitrary noise sources, and the derivation of Kadomtsev-type equations from the general formalism.

Article Outline

INTRODUCTION
1. Introductory remarks on noise, gyrokinetics, and the Δf simulation algorithm
2. Spectral balance: Basic concepts
3. Outline of the article
THE Δf EQUATIONS AND PIC SIMULATION
1. Δf versus δf
2. The Δf -PIC algorithm
DISCRETENESS-INDUCED FLUCTUATIONS
1. Fluctuation-dissipation theorem for plasmas
2. Introduction to the Klimontovich formalism
3. Fluctuation-dissipation theorem for gyrokinetics
  1. The gyrokinetic vacuum and gyrokinetic Poisson equation
  2. The gyrokinetic fluctuation-dissipation theorem
  3. Gyrokinetic fluctuations and normal modes
  4. Gyrokinetic fluctuations with an adiabatic species
4. Sampling noise in the Δf algorithm
  1. Monte Carlo sampling
  2. Markers and weights
  3. The weight equation
  4. Near-equilibrium spectrum with sampling noise
TURBULENT FLUCTUATIONS IN CONTINUUM PARTIAL DIFFERENTIAL EQUATIONS
1. Langevin dynamics
2. Statistical closures for quadratically nonlinear smooth PDEs
TURBULENT FLUCTUATIONS IN KLIMONTOVICH DESCRIPTIONS
1. Non-Gaussian PDFs and cumulant representations
2. Non-Gaussian initial conditions and the Klimontovich representation
  1. The renormalized equations of Rose
  2. Recovery of the weakly coupled fluctuation spectrum
  3. Structure of the particle direct-interaction approximation: A modified Kadomtsev equation
  4. Turbulent broadening and turbulent flux
NONEQUILIBRIUM SPECTRAL BALANCE WITH ΔF -PIC SAMPLING NOISE
DISCUSSION AND CONCLUSIONS

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KEYWORDS and PACS

Keywords

noise, partial differential equations, plasma fluctuations, plasma simulation

PACS

52.25.Gj

Fluctuation and chaos phenomena
52.65.Rr

Particle-in-cell method
52.65.Tt

Gyrofluid and gyrokinetic simulations
02.30.Jr

Partial differential equations

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http://link.aip.org/link/doi/10.1063/1.2759879

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1070-664X (print)

1089-7674 (online)

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American Institute of Physics

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