Propagator methods for plasma simulations: application to breakdown

Wichaidit, C.; Hitchon, W. N. G.

doi:10.1016/j.jcp.2004.09.008

Cited by 14 publications

(10 citation statements)

References 48 publications

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“…Given these experimental challenges, computer simulations provide an alternative method of analysing high-pressure microplasmas, contributing to the advance in our current understanding of the underlying physics. Fluid (or hydrodynamic), particlein-cell (PIC) and hybrid methods can be used to simulate low-temperature plasmas [7][8][9][10][11]. In this study we focused on the first two methods and compared the results obtained when modelling a plasma needle.…”

Section: Introductionmentioning

confidence: 99%

Comparison of fluid and particle-in-cell simulations on atmospheric pressure helium microdischarges

Hong

Yoon

Iza

et al. 2008

J. Phys. D: Appl. Phys.

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Microdischarges at atmospheric pressure were studied by two computational methods. The first method is a typical one-dimensional fluid model in which the electron velocity distribution function is assumed to be Maxwellian and the energy equation is solved to determine the spatial profile of the electron temperature. The second method is a particle-in-cell (PIC) model with Monte-Carlo collisions (MCC). We compared the time-averaged density, electric field and power consumption profiles of helium microdischarges driven at 13.56 MHz and 2.45 GHz obtained with the two models. The agreement between the two models depends on the driving frequency. The kinetic information obtained from the PIC-MCC model indicates that the improved agreement at higher frequency is due to the evolution of the electron energy distribution function from a three-temperature distribution at 13.56 MHz to a close-to-Maxwellian distribution at 2.45 GHz.

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Section: Introductionmentioning

confidence: 99%

Comparison of fluid and particle-in-cell simulations on atmospheric pressure helium microdischarges

Hong

Yoon

Iza

et al. 2008

J. Phys. D: Appl. Phys.

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“…The direction of injection is critical for preventing a significantly troublesome form of numerical diffusion. If injection is along the coordinate axes, as transport inevitably will be in most finite difference schemes (but unlike a propagator scheme [3]) then density will spread along the axes, even in situations where the actual movement should fall between the axes. Suppose E x and E y are both nonzero.…”

Section: Energy Conservation and Density Injectionmentioning

confidence: 99%

“…The limitations on ( x, t) can be partially overcome by using a propagator (i.e. Lagrangian) scheme that also allows the density to grow exponentially with the gain in energy as particles move from cell to cell [2,3]. All of these schemes are subject to numerical diffusion to varying degrees, however, and this can be a severe problem in breakdown simulations.…”

Section: Introductionmentioning

confidence: 99%

Physics-based description of gas breakdown

Hitchon¹,

Wichaidit²

2007

J. Phys. A: Math. Theor.

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This paper develops an efficient method for simulation of breakdown in a gas, which explicitly makes use of the real underlying physics, in a case where standard numerical schemes are likely to fail. We develop a 'time-dependent capacitor model' (TDCM) for 2D or 3D, which ensures that the ionization rate is consistent with energy conservation and which disallows almost all numerical diffusion (and hence allows larger ( x, t)). To avoid spurious ionization in the TDCM, density is only added in a cell when the density and electric field are high enough so that the density could physically grow to the expected final density within the cell. Numerical diffusion is negligible in the TDCM, in part because we only inject density into cells/capacitors when enough time has elapsed for density to be physically present. The direction of injection is controlled, so if, for example, density from cell [i, j ] in reality moves to cell [i ± 1, j ± 1], it goes there directly, giving a physically correct direction of propagation. A simple scheme for accelerating convergence, exploiting the very different time scales which arise, is also discussed.

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“…Among a great variety of solution methods [7,9], for the last two decades, those semi-analytical approaches aided by numerical computation have roused great interest. In this group, the path-sum, path-integral or propagator methods describe the evolution of a distribution function by means of an approximate propagator or Green's function (see, for instance, [10][11][12][13] and references therein). An interesting discussion about the physical sense of this path-integral approach and its relation to continuous Markovian processes can also be found in the early works [14,15].…”

Section: Introductionmentioning

confidence: 99%

Integral propagator solvers for Vlasov–Fokker–Planck equations

Donoso¹,

Río²

2007

J. Phys. A: Math. Theor.

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We briefly discuss the use of short-time integral propagators on solving the so-called Vlasov–Fokker–Planck equation for the dynamics of a distribution function. For this equation, the diffusion tensor is singular and the usual Gaussian representation of the short-time propagator is no longer valid. However, we prove that the path-integral approach on solving the equation is, in fact, reliable by means of our generalized propagator, which is obtained through the construction of an auxiliary solvable Fokker–Planck equation. The new representation of the grid-free advancing scheme describes the inherent cross- and self-diffusion processes, in both velocity and configuration spaces, in a natural manner, although these processes are not explicitly depicted in the differential equation. We also show that some splitting methods, as well as some finite-difference schemes, could fail in describing the aforementioned diffusion processes, governed in the whole phase space only by the velocity diffusion tensor. The short-time transition probability offers a stable and robust numerical algorithm that preserves the distribution positiveness and its norm, ensuring the smoothness of the evolving solution at any time step.

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Propagator methods for plasma simulations: application to breakdown

Cited by 14 publications

References 48 publications

Comparison of fluid and particle-in-cell simulations on atmospheric pressure helium microdischarges

Comparison of fluid and particle-in-cell simulations on atmospheric pressure helium microdischarges

Physics-based description of gas breakdown

Integral propagator solvers for Vlasov–Fokker–Planck equations

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