{"title":"用中心极限定理求脉冲有源力作用下的松弛时间","authors":"J.L. Domenech-Garret","doi":"10.1016/j.physa.2025.131002","DOIUrl":null,"url":null,"abstract":"<div><div>We study the relaxation time of a generic plasma which is perturbed by means of a time-dependent pulsed force. This time pulse is modelled using a Gaussian superposition. During such a pulse two forces are considered: An inhomogeneous oscillating electric force and the corresponding ponderomotive force. The evolution of that ensemble is driven by the Boltzmann Equation, and the perturbed population is described by a power-law distribution function. In this work, as a new feature, instead the usual techniques the transient between both distributions is analysed using the moments of such distribution function and the Central Limit Theorem. This technique, together with the, ad hoc solved, equation of motion of the charges under this particular system of pulsed forces, allows to find the corresponding expressions relating the time pulse with the relaxation times and the dynamic conditions. We validate that new technique by comparison with the analytical expression using the corresponding relaxation time using an exact collision operator. Moreover, we parameterise this plasma to make numerical estimates in order to analyse the impact of relevant parameters involved in the physical process on such a relaxation time.</div></div>","PeriodicalId":20152,"journal":{"name":"Physica A: Statistical Mechanics and its Applications","volume":"679 ","pages":"Article 131002"},"PeriodicalIF":3.1000,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Relaxation times under pulsed ponderomotive forces using the Central Limit Theorem\",\"authors\":\"J.L. Domenech-Garret\",\"doi\":\"10.1016/j.physa.2025.131002\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We study the relaxation time of a generic plasma which is perturbed by means of a time-dependent pulsed force. This time pulse is modelled using a Gaussian superposition. During such a pulse two forces are considered: An inhomogeneous oscillating electric force and the corresponding ponderomotive force. The evolution of that ensemble is driven by the Boltzmann Equation, and the perturbed population is described by a power-law distribution function. In this work, as a new feature, instead the usual techniques the transient between both distributions is analysed using the moments of such distribution function and the Central Limit Theorem. This technique, together with the, ad hoc solved, equation of motion of the charges under this particular system of pulsed forces, allows to find the corresponding expressions relating the time pulse with the relaxation times and the dynamic conditions. We validate that new technique by comparison with the analytical expression using the corresponding relaxation time using an exact collision operator. Moreover, we parameterise this plasma to make numerical estimates in order to analyse the impact of relevant parameters involved in the physical process on such a relaxation time.</div></div>\",\"PeriodicalId\":20152,\"journal\":{\"name\":\"Physica A: Statistical Mechanics and its Applications\",\"volume\":\"679 \",\"pages\":\"Article 131002\"},\"PeriodicalIF\":3.1000,\"publicationDate\":\"2025-09-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica A: Statistical Mechanics and its Applications\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0378437125006545\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica A: Statistical Mechanics and its Applications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378437125006545","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
Relaxation times under pulsed ponderomotive forces using the Central Limit Theorem
We study the relaxation time of a generic plasma which is perturbed by means of a time-dependent pulsed force. This time pulse is modelled using a Gaussian superposition. During such a pulse two forces are considered: An inhomogeneous oscillating electric force and the corresponding ponderomotive force. The evolution of that ensemble is driven by the Boltzmann Equation, and the perturbed population is described by a power-law distribution function. In this work, as a new feature, instead the usual techniques the transient between both distributions is analysed using the moments of such distribution function and the Central Limit Theorem. This technique, together with the, ad hoc solved, equation of motion of the charges under this particular system of pulsed forces, allows to find the corresponding expressions relating the time pulse with the relaxation times and the dynamic conditions. We validate that new technique by comparison with the analytical expression using the corresponding relaxation time using an exact collision operator. Moreover, we parameterise this plasma to make numerical estimates in order to analyse the impact of relevant parameters involved in the physical process on such a relaxation time.
期刊介绍:
Physica A: Statistical Mechanics and its Applications
Recognized by the European Physical Society
Physica A publishes research in the field of statistical mechanics and its applications.
Statistical mechanics sets out to explain the behaviour of macroscopic systems by studying the statistical properties of their microscopic constituents.
Applications of the techniques of statistical mechanics are widespread, and include: applications to physical systems such as solids, liquids and gases; applications to chemical and biological systems (colloids, interfaces, complex fluids, polymers and biopolymers, cell physics); and other interdisciplinary applications to for instance biological, economical and sociological systems.