{"title":"查普曼-恩斯科格等离子体的动力学稳定性","authors":"Archie F.A. Bott, S.C. Cowley, A.A. Schekochihin","doi":"10.1017/s0022377824000308","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$\\lambda$</span></span></img></span></span> of constituent particles is short compared with the length scale <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$L$</span></span></img></span></span> over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$\\lambda /L \\ll 1$</span></span></img></span></span>, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$\\beta$</span></span></img></span></span>, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (<span>viz.</span> plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$\\lambda$</span></span></img></span></span>, the electron inertial scale <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$d_e$</span></span></img></span></span> and the plasma <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$\\beta$</span></span></img></span></span>. This work is of general consequence in emphasising the fact that high-<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$\\beta$</span></span></img></span></span> collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$\\beta \\gtrsim L/\\lambda$</span></span></img></span></span>. In this situation, the determination of transport coefficients via the standard CE approach is not valid.</p>","PeriodicalId":16846,"journal":{"name":"Journal of Plasma Physics","volume":"28 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Kinetic stability of Chapman–Enskog plasmas\",\"authors\":\"Archie F.A. Bott, S.C. Cowley, A.A. Schekochihin\",\"doi\":\"10.1017/s0022377824000308\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline1.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\lambda$</span></span></img></span></span> of constituent particles is short compared with the length scale <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline2.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$L$</span></span></img></span></span> over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline3.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\lambda /L \\\\ll 1$</span></span></img></span></span>, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline4.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\beta$</span></span></img></span></span>, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (<span>viz.</span> plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline5.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\lambda$</span></span></img></span></span>, the electron inertial scale <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline6.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$d_e$</span></span></img></span></span> and the plasma <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline7.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\beta$</span></span></img></span></span>. This work is of general consequence in emphasising the fact that high-<span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline8.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\beta$</span></span></img></span></span> collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240503074510309-0931:S0022377824000308:S0022377824000308_inline9.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\beta \\\\gtrsim L/\\\\lambda$</span></span></img></span></span>. In this situation, the determination of transport coefficients via the standard CE approach is not valid.</p>\",\"PeriodicalId\":16846,\"journal\":{\"name\":\"Journal of Plasma Physics\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Plasma Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1017/s0022377824000308\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, FLUIDS & PLASMAS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Plasma Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1017/s0022377824000308","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, FLUIDS & PLASMAS","Score":null,"Total":0}
引用次数: 0
摘要
在本文中,我们研究了经典碰撞等离子体的动力学稳定性--即组成粒子的平均自由路径 $\lambda$ 与等离子体中场和体运动宏观变化的长度尺度 $L$ 相比很短,碰撞时间与演化时间相比很短的等离子体。流体方程通常用于描述这类等离子体,因为它们的分布函数接近于麦克斯韦分布函数。与麦克斯韦分布的微小偏差是通过$\lambda /L \ll 1$中的查普曼-恩斯科格(CE)展开来计算的,它决定了等离子体中的宏观动量和热通量。只有当基本的 CE 分布函数在无碰撞长度尺度和/或时间尺度上稳定时,这种计算才有效。我们发现,在等离子体的$\beta$足够高的情况下,CE分布函数在很大的尺度范围内会受到许多微观不稳定性的影响。对于强磁化等离子体(即粒子的拉莫尔周期远小于碰撞时间的等离子体)中产生的 CE 分布函数的一种特殊形式,我们提供了所有重要微不稳定性的详细分析特征,包括峰值增长率及其相关的波数。特别值得注意的是,我们发现了几种新的微不稳定性,包括一种亚电子拉莫尔尺度的微不稳定性("耳语不稳定性"),与其他不稳定性相比,它在某些参数区的增长率很大。我们的方法使我们能够根据$\lambda$、电子惯性尺度$d_e$和等离子体$\beta$来构建经典双物种碰撞等离子体的动力学稳定性图。这项工作的普遍意义在于强调了一个事实:高$\beta$碰撞等离子体在动力学上可能是不稳定的;对于强磁化CE等离子体,不稳定的条件是$\beta \gtrsim L/\lambda$。在这种情况下,通过标准 CE 方法确定传输系数是无效的。
In this paper, we investigate the kinetic stability of classical, collisional plasma – that is, plasma in which the mean-free-path $\lambda$ of constituent particles is short compared with the length scale $L$ over which fields and bulk motions in the plasma vary macroscopically, and the collision time is short compared with the evolution time. Fluid equations are typically used to describe such plasmas, since their distribution functions are close to being Maxwellian. The small deviations from the Maxwellian distribution are calculated via the Chapman–Enskog (CE) expansion in $\lambda /L \ll 1$, and determine macroscopic momentum and heat fluxes in the plasma. Such a calculation is only valid if the underlying CE distribution function is stable at collisionless length scales and/or time scales. We find that at sufficiently high plasma $\beta$, the CE distribution function can be subject to numerous microinstabilities across a wide range of scales. For a particular form of the CE distribution function arising in strongly magnetised plasma (viz. plasma in which the Larmor periods of particles are much smaller than collision times), we provide a detailed analytic characterisation of all significant microinstabilities, including peak growth rates and their associated wavenumbers. Of specific note is the discovery of several new microinstabilities, including one at sub-electron-Larmor scales (the ‘whisper instability’) whose growth rate in certain parameter regimes is large compared with other instabilities. Our approach enables us to construct the kinetic stability maps of classical, two-species collisional plasma in terms of $\lambda$, the electron inertial scale $d_e$ and the plasma $\beta$. This work is of general consequence in emphasising the fact that high-$\beta$ collisional plasmas can be kinetically unstable; for strongly magnetised CE plasmas, the condition for instability is $\beta \gtrsim L/\lambda$. In this situation, the determination of transport coefficients via the standard CE approach is not valid.
期刊介绍:
JPP aspires to be the intellectual home of those who think of plasma physics as a fundamental discipline. The journal focuses on publishing research on laboratory plasmas (including magnetically confined and inertial fusion plasmas), space physics and plasma astrophysics that takes advantage of the rapid ongoing progress in instrumentation and computing to advance fundamental understanding of multiscale plasma physics. The Journal welcomes submissions of analytical, numerical, observational and experimental work: both original research and tutorial- or review-style papers, as well as proposals for its Lecture Notes series.