Long time gyrokinetic equations

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Quarterly of Applied Mathematics Pub Date : 2023-06-15 DOI:10.1090/qam/1666

C. Cheverry, Shahnaz Farhat

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引用次数: 2

Abstract

The aim of this text is to elucidate the oscillating patterns (see C. Cheverry [Res. Rep. Math. (2018)]) which are generated in a toroidal plasma by a strong external magnetic field and a nonzero electric field. It is also to justify and then study new modulation equations which are valid for longer times than before. Oscillating coherent structures are induced by the collective motions of charged particles which satisfy a system of ODEs implying a large parameter, the gyrofrequency ε − 1 ≫ 1 \varepsilon ^{-1} \gg 1 . By exploiting the properties of underlying integrable systems, we can complement the KAM picture (see G. Benettin and P. Sempio [Nonlinearity 7 (1994), pp. 281–303]; M. Braun [SIAM Rev. 23 (1981), pp. 61–93]) and go beyond the classical results about gyrokinetics (see M. Bostan [Multiscale Model. Simul. 8 (2010), pp. 1923–1957]; A. J. Brizard and T. S. Hahm [Rev. Modern Phys. 79 (2007), pp. 421–468]). The purely magnetic situation was addressed by C. Cheverry [Comm. Math. Phys. 338 (2015), pp. 641–703; J. Differential Equations 262 (2017), pp. 2987–3033]. We are concerned here with the numerous additional difficulties due to the influence of a nonzero electric field.

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长时间陀螺动力学方程

本文的目的是阐明振荡模式(见C. Cheverry [Res. Rep. Math])。(2018)])，它们是在强外磁场和非零电场作用下在环形等离子体中产生的。并对新的调制方程进行验证和研究，以期获得比以前更长的有效时间。振荡相干结构是由带电粒子的集体运动引起的，这些带电粒子满足一个包含大参数(陀螺频率ε−1 ^ 1 \varepsilon ^{-1} \gg 1)的ODEs系统。通过利用底层可积系统的性质，我们可以补充KAM图像(见G. Benettin和P. Sempio[非线性7 (1994)，pp. 281-303];M. Braun [SIAM Rev. 23 (1981)， pp. 61-93])，并超越了关于陀螺动力学的经典结果(见M. Bostan[多尺度模型]。仿真学报，8 (2010)，pp. 1923-1957;[中国科学:自然科学版，2007,p. 421-468]。C. Cheverry [Comm. Math]解决了纯磁性的情况。Phys. 338 (2015)， pp. 641-703;[j].微分方程学报，2017,pp. 391 - 391。我们在这里所关心的是由于非零电场的影响而产生的许多额外的困难。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Quarterly of Applied Mathematics 数学-应用数学

CiteScore

1.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Quarterly of Applied Mathematics contains original papers in applied mathematics which have a close connection with applications. An author index appears in the last issue of each volume. This journal, published quarterly by Brown University with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.