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Keywords = gyrokinetic limit

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20 pages, 307 KiB  
Article
The Gyrokinetic Limit for the Two-Dimensional Vlasov–Yukawa System with a Point Charge
by Xianghong Hu and Xianwen Zhang
Mathematics 2025, 13(2), 320; https://doi.org/10.3390/math13020320 - 20 Jan 2025
Viewed by 647
Abstract
In this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued [...] Read more.
In this article, we study the asymptotic behavior of the two-dimensional Vlasov–Yukawa system with a point charge under a large external magnetic field. When the intensity of the magnetic field tends to infinity, we show that the kinetic system converges to the measure-valued Euler equation with a defect measure, which extends the results of Miot to the case of the Vlasov–Yukawa system. And compared with the Miot’s work, an important improvement is that our results do not require compact support conditions for spatial variables or uniform bound conditions for second-order spatial moments. In addition, the extra small condition for initial data is also not required. Full article
18 pages, 748 KiB  
Article
Investigation of a Multiple-Timescale Turbulence-Transport Coupling Method in the Presence of Random Fluctuations
by Jeffrey B. Parker, Lynda L. LoDestro and Alejandro Campos
Plasma 2018, 1(1), 126-143; https://doi.org/10.3390/plasma1010012 - 12 Jul 2018
Cited by 6 | Viewed by 3979
Abstract
One route to improved predictive modeling of magnetically confined fusion reactors is to couple transport solvers with direct numerical simulations (DNS) of turbulence, rather than with surrogate models. An additional challenge presented by coupling directly with DNS is the inherent fluctuations in the [...] Read more.
One route to improved predictive modeling of magnetically confined fusion reactors is to couple transport solvers with direct numerical simulations (DNS) of turbulence, rather than with surrogate models. An additional challenge presented by coupling directly with DNS is the inherent fluctuations in the turbulence, which limit the convergence achievable in the transport solver. In this article, we investigate the performance of one numerical coupling method in the presence of turbulent fluctuations. To test a particular numerical coupling method for the transport solver, we use an autoregressive-moving-average model to generate stochastic fluctuations efficiently with statistical properties resembling those of a gyrokinetic simulation. These fluctuations are then added to a simple, solvable problem, and we examine the behavior of the coupling method. We find that monitoring the residual as a proxy for the error can be misleading. From a pragmatic point of view, this study aids us in the full problem of transport coupled to DNS by predicting the amount of averaging required to reduce the fluctuation error and obtain a specific level of accuracy. Full article
(This article belongs to the Special Issue Multiscale Methods in Plasma Physics)
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