Numerical study of plasma–wall transition in an oblique magnetic field

Valsaque, Fabrice; Manfredi, Giovanni

doi:10.1016/s0022-3115(00)00454-2

Cited by 27 publications

(17 citation statements)

References 5 publications

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“…The second numerical tool is a Vlasov-Eulerian code. [31][32][33][34] It computes directly the ion distribution function on a grid corresponding to the phase space variables (x,v), which are both sampled with 200-400 points. As it will be presented in the following, results from both numerical approaches are in good agreement in all the cases studied.…”

Section: Resultsmentioning

confidence: 99%

Kinetic simulations of ion temperature measurements from retarding field analyzers

et al. 2002

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Retarding field analyzers (RFA) provide an integral of the ion velocity distribution in tokamak edge plasmas, leading, in principle, to an estimate of the ion temperature. However, the presence of the RFA itself perturbs the ambient plasma, such that the measured distribution is distorted with respect to the unperturbed one far from the probe. Here, collisionless kinetic modeling is employed to investigate the modification of the plasma characteristics (temperature, particle flux, density, and electric potential) in the presheath of the RFA. The kinetic equations are solved independently by means of two different numerical methods, which provide a reliable check of their results. Moreover, they are interpreted in light of a simplified kinetic analytical model. Systematic numerical studies are performed for a large range of values of the ion-to-electron temperature ratio and the parallel drift speed. In the same way that a Mach probe measures upstream–downstream asymmetries of ion saturation current in flowing plasmas, RFAs are expected to measure important asymmetries of sheath potential and ion temperature. These asymmetries can be used to estimate accurately the ion temperature in the absence of the probe perturbation.

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Section: Resultsmentioning

confidence: 99%

Kinetic simulations of ion temperature measurements from retarding field analyzers

et al. 2002

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“…However, in cases where the physics of interest is in a region of low plasma density, smooth convergence seems to be necessary for precise measurements. For a variety of practical problems indeed (including backward Raman scattering [3], plasma-wall transitions [4,5], halo formation in beams [6] and development of electron holes in the presence of a guide field [7]) physicists often need to resort to (grid based) Vlasov or Semi-Lagrangian solvers in order to obtain sufficient accuracy. Unfortunately these methods are known to be numerically expensive to run and challenging to implement, as they require the mesh to cover the whole phase space and can suffer from diffusive effects.…”

Section: Introductionmentioning

confidence: 99%

Noiseless Vlasov–Poisson simulations with linearly transformed particles

Pinto

Sonnendrücker

Friedman

et al. 2014

Journal of Computational Physics

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We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts to using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme [J. Denavit, J. Comp. Physics 9, 75 (1972)]. However, it has recently been established [M. Campos Pinto, "Smooth particle methods without smoothing", arXiv:1112.1859 (2012)] that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

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“…The function W is continuous, decreasing and has a limit as ϕ → −∞ which is such that lim ϕ→−∞ W(φ) > 0. Therefore the equation (29) has a unique negative solution if and only W(0) < 0 which is the inequality (13). The equation (29) is then solved using a standard Newton method.…”

Section: Summary Of the Numerical Methodsmentioning

confidence: 99%

“…In all the sequel, we shall assume that the incoming ions density f inc i : (0, +∞) → R + is at least piecewise continuous so that the upcoming quadrature formulas make sense. Moreover, we assume φ wall < 0 to solve exactly or approximately the equation (29). We begin with introducing a uniform discretization of the interval [0, 1] of size ∆x = 1/(N + 1) where N + 1 denotes the number of intervals of discretization so that x j = j∆x for 0 ≤ j ≤ N +1.…”

Section: The Numerical Schemementioning

confidence: 99%

“…Convergence and stability analysis of these methods can be found in the mentioned references. In the specific context of plasma sheaths, some of these numerical methods have been used [29,19,21,25] with their own specificity according to the model under consideration. We mention that non stationary based numerical methods are often more generic in a sense, and enable to avoid dealing with the delicate problem of selecting the boundary conditions that reproduce the physics of sheaths.…”

Section: Introductionmentioning

confidence: 99%

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A stable fixed point method for the numerical simulation of a kinetic collisional sheath

Badsi

Berthon

Crestetto

2021

Journal of Computational Physics

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This work introduces a numerical fixed point method to approximate the solutions of a Vlasov-Poisson-Boltzmann boundary value problem which arises when modeling a bi-species collisional sheath. Our method relies on the exact integration of the transport equations by means of the characteristic curves. A special care is given about the choice of a suitable phase space discretization together with the use of adequate quadrature formulas so as to ensure that the numerical fixed point method is stable. Numerical experiments are carried out in order to illustrate the effects of the various physical parameters that are in the scope of the analysis. Some results going beyond the scope of the analysis are also given.

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Numerical study of plasma–wall transition in an oblique magnetic field

Cited by 27 publications

References 5 publications

Kinetic simulations of ion temperature measurements from retarding field analyzers

Kinetic simulations of ion temperature measurements from retarding field analyzers

Noiseless Vlasov–Poisson simulations with linearly transformed particles

A stable fixed point method for the numerical simulation of a kinetic collisional sheath

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