具有不可压缩流的理想和电阻MHD等离子体的螺旋对称平衡

IF 1 4区数学

Applied Mathematics-A Journal of Chinese Universities Series B Pub Date : 2023-06-23 DOI:10.1007/s11766-023-3848-z

S. M. Moawad, O. H. El-Kalaawy, H. M. Shaker

{"title":"具有不可压缩流的理想和电阻MHD等离子体的螺旋对称平衡","authors":"S. M. Moawad, O. H. El-Kalaawy, H. M. Shaker","doi":"10.1007/s11766-023-3848-z","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation (PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.</p></div>","PeriodicalId":55568,"journal":{"name":"Applied Mathematics-A Journal of Chinese Universities Series B","volume":"38 2","pages":"192 - 209"},"PeriodicalIF":1.0000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows\",\"authors\":\"S. M. Moawad, O. H. El-Kalaawy, H. M. Shaker\",\"doi\":\"10.1007/s11766-023-3848-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation (PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.</p></div>\",\"PeriodicalId\":55568,\"journal\":{\"name\":\"Applied Mathematics-A Journal of Chinese Universities Series B\",\"volume\":\"38 2\",\"pages\":\"192 - 209\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-06-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics-A Journal of Chinese Universities Series B\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11766-023-3848-z\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-A Journal of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-023-3848-z","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

本文研究了具有螺旋对称的不可压缩质量流的磁流体动力学方程的精确解问题。对于理想流动，采用相似约简法得到了几种非线性变马赫数MHD流动的精确解。对于平行于磁场的电阻流，导出了控制平衡方程。螺旋对称不可压缩流的MHD平衡状态由螺旋磁通函数的二阶椭圆偏微分方程(PDE)控制。得到了后一个方程的精确解。同时，导出了不可压缩流重力等离子体的平衡方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Helically symmetric equilibria for some ideal and resistive MHD plasmas with incompressible flows

In this paper, the problem of finding exact solutions to the magnetohydrodynamic (MHD) equations in the presence of incompressible mass flows with helical symmetry is considered. For ideal flows, a similarity reduction method is used to obtain exact solutions for several MHD flows with nonlinear variable Mach number. For resistive flows parallel to a magnetic field, the governing equilibrium equation is derived. The MHD equilibrium state of a helically symmetric incompressible flow is governed by a second-order elliptic partial differential equation (PDE) for the helical magnetic flux function. Exact solutions for the latter equation are obtained. Also, the equilibrium equations of a gravitating plasma with incompressible flow are derived.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Mathematics-A Journal of Chinese Universities Series B MATHEMATICS, APPLIED-

自引率

10.00%

发文量

期刊介绍： Applied Mathematics promotes the integration of mathematics with other scientific disciplines, expanding its fields of study and promoting the development of relevant interdisciplinary subjects. The journal mainly publishes original research papers that apply mathematical concepts, theories and methods to other subjects such as physics, chemistry, biology, information science, energy, environmental science, economics, and finance. In addition, it also reports the latest developments and trends in which mathematics interacts with other disciplines. Readers include professors and students, professionals in applied mathematics, and engineers at research institutes and in industry. Applied Mathematics - A Journal of Chinese Universities has been an English-language quarterly since 1993. The English edition, abbreviated as Series B, has different contents than this Chinese edition, Series A.