The Particle Kinetics of Plasmas

C e n t r u m v o o r W i s k u n d e e n I n f o r m a t i c a Modelling, Analysis and Simulation Modelling, Analysis and SimulationDeviations from the local field approximation in negative streamer heads C. Li, W.J.M. Brok, U. Ebert, J.J.A.M. van der Mullen Deviations from the local field approximation in negative streamer heads ABSTRACT Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is <= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field. REPORT MAS-E0706 FEBRUARY 2007 Mathematics Subject Classification: 82D10Keywords and Phrases: streamers; ionization front; particle model; local field approximation Note: This work was carried out under project "Multiscale Modelling and Nonlinear Dynamics"-"Electric discharges and plasma technology". The authors acknowledge support by the Dutch national program Bsik, in the ICT project BRICKS, theme MSV1. arXiv:physics/0702129v1 15 Feb 2007Deviations from the local field approximation in negative streamer heads Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is ≤ 50 kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200 kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60 % higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, ...

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“…The resulting equations are continuity equations for density, momentum, kinetic energy, etc. [52,53,54].…”

Section: Derivation From the Boltzmann Equationmentioning

confidence: 99%

“…Fluid models in general are derived from the Boltzmann equation [51,52,53]. For each species k, this equation describes the temporal development of the 6-dimensional phase space density f k (x, v).…”

Section: Derivation From the Boltzmann Equationmentioning

confidence: 99%

Deviations from the local field approximation in negative streamer heads

Brok

Ebert

et al. 2007

Journal of Applied Physics

170

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“…It is now universally agreed that it extends to about 1 Debye length. Proper justification for this is found in the advanced Liouville equation theory, but heuristic reasons can be found in almost any book on plasma physics (see, for example, [20]). The general conclusion is that, if one ignores the fact that the collisions are not binary and the Debye cutoff is used, the momentum transfer in the collision is the same as that obtained by a more exact treatment.…”

Section: Appendix Dmentioning

confidence: 99%

Coulomb scattering within a spherical beam bunch in a high current linear accelerator

Gluckstern

Fedotov

1999

Phys. Rev. ST Accel. Beams

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Beam halo formation issues are important for the design of high current linear ion accelerators. Various mechanisms can potentially cause beam halo. Some recent studies suggested that Coulomb collisions in the beam bunch can contribute significantly to beam bunch growth and halo development in linear accelerators. Despite the general belief that collisions are not important, it is clear that a rigorous treatment of this question is needed. In an effort to explore this issue in detail we have undertaken an analysis of the effects of Coulomb scattering between ions in a self-consistent spherical bunch.[S1098-4402(99)

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“…In order to solve the Boltzmann equation, an expansion of the distribution function and collision operator can be made in Cartesian tensors [26]. Under the assumption that the distribution is only weakly perturbed from equilibrium, retaining only the first two terms is sufficient for an accurate description of transport:…”

Section: Lorentzian Plasma: Analytical Treatmentmentioning

confidence: 99%

“…Once the form of f 1 is known, the electric current and total heat flow are calculated via integrations over momentum space [26]:…”

Section: Lorentzian Plasma: Analytical Treatmentmentioning

confidence: 99%

Transport coefficients of a relativistic plasma

Pike

Rose

2016

Phys. Rev. E

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In this work, a self-consistent transport theory for a relativistic plasma is developed.Using the notation of Braginskii [S. I. Braginskii, in Reviews of Plasma Physics, ed. M. A. Leontovich (1965), Vol. 1, p.174], we provide semi-analytical forms of the electrical resistivity, thermoelectric and thermal conductivity tensors for a Lorentzian plasma in a magnetic field.This treatment is then generalized to plasmas with arbitrary atomic number by numerically solving the linearized Boltzmann equation. The corresponding transport coefficients are fitted by rational functions in order to make them suitable for use in radiation-hydrodynamic simulations and transport calculations. Within the confines of linear transport theory and on the assumption that the plasma is optically thin, our results are valid for temperatures up to a few MeV. By contrast, classical transport theory begins to incur significant errors above k B T ∼ 10 keV, e.g., the parallel thermal conductivity is suppressed by 15% at k B T = 20 keV due to relativistic effects.

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The Particle Kinetics of Plasmas

Cited by 293 publications

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Deviations from the local field approximation in negative streamer heads

Deviations from the local field approximation in negative streamer heads

Coulomb scattering within a spherical beam bunch in a high current linear accelerator

Transport coefficients of a relativistic plasma

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