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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Gyrokinetics ： ウィキペディア英語版 Gyrokinetics Gyrokinetics is a theoretical framework to study plasma behavior on perpendicular spatial scales comparable to the gyroradius and frequencies much lower than the particle cyclotron frequencies. These particular scales have been experimentally shown to be appropriate for modeling plasma turbulence.〔G.R. McKee, C.C. Petty, et al. Non-dimensional scaling of turbulence characteristics and turbulent diffusivity. Nuclear Fusion, 41(9):1235, 2001.〕 The trajectory of charged particles in a magnetic field is a helix that winds around the field line. This trajectory can be decomposed into a relatively slow motion of the guiding center along the field line and a fast circular motion, called gyromotion. For most plasma behavior, this gyromotion is irrelevant. Averaging over this gyromotion reduces the equations to six dimensions (3 spatial, 2 velocity, and time) rather than the seven (3 spatial, 3 velocity, and time). Because of this simplification, gyrokinetics governs the evolution of charged rings with a guiding center position, instead of gyrating charged particles. == Derivation of the gyrokinetic equation == Fundamentally, the gyrokinetic model assumes the plasma is strongly magnetized ( $\backslash rho\_\; \backslash ll\; L\_$ ), the perpendicular spatial scales are comparable to the gyroradius ( $k\_\; \backslash rho\_\; \backslash sim\; 1$ ), and the behavior of interest has low frequencies ( $\backslash omega\; \backslash ll\; \backslash Omega\_\; \backslash ll\; \backslash Omega\_$ ). We must also expand the distribution function, $f\_\; =\; f\_\; +\; f\_\; +\; \backslash ldots$, and assume the perturbation is small compared to the background ($f\_\; \backslash ll\; f\_$).〔G.G. Howes, S.C. Cowley, W. Dorland, G.W. Hammett, E. Quataert, and A.A. Schekochihin. Astrophysical gyrokinetics: Basic equations and linear theory. ApJ, 651(1):590, 2006.〕 The starting point is the Fokker–Planck equation and Maxwell's equations. The first step is to change spatial variables from the particle position $\backslash vec$ to the guiding center position $\backslash vec$. Then, we change velocity coordinates from $(v\_,v\_,v\_)$ to the velocity parallel $v\_\; \backslash equiv\; \backslash vec\; \backslash cdot\; \backslash hat$, the magnetic moment $\backslash mu\; \backslash equiv\; \backslash frac^\}$, and the gyrophase angle $\backslash varphi$. Here parallel and perpendicular are relative to $\backslash vec\; \backslash equiv\; \backslash vec/B$, the direction of the magnetic field, and $m\_$ is the mass of the particle. Now, we can average over the gyrophase angle at constant guiding center position, denoted by $\backslash left\backslash langle\; \backslash ldots\; \backslash right\backslash rangle\_$, yielding the gyrokinetic equation. The electrostatic gyrokinetic equation, in the absence of large plasma flow, is given by〔I. G. Abel, G. G. Plunk, E. Wang, M. Barnes, S. C. Cowley, W. Dorland, and A. A. Schekochihin. Multiscale Gyrokinetics for Rotating Tokamak Plasmas: Fluctuations, Transport and Energy Flows. http://arxiv.org/pdf/1209.4782.pdf〕 $\backslash frac\; +\; \backslash left(\; v\_\; \backslash hat\; +\; \backslash vec\_\; +\; \backslash left\backslash langle\; \backslash vec\_\; \backslash right\backslash rangle\_\; \backslash right)\; \backslash cdot\; \backslash vec\_\; -\; \backslash sum\_\; \backslash left\backslash langle\; C\; \backslash left(h\_,\; h\_\; \backslash right)\; \backslash right\backslash rangle\_\; =\; \backslash frac\}\}\; -\; \backslash frac\; \backslash left\backslash langle\; \backslash vec\_\; \backslash right\backslash rangle\_\; \backslash cdot\; \backslash vec\; \backslash psi$. Here the first term represents the change in the perturbed distribution function, $h\_\; \backslash equiv\; f\_\; +\; \backslash frac$, with time. The second term represents particle streaming along the magnetic field line. The third term contains the effects of cross-field particle drifts, including the curvature drift, the grad-B drift, and the lowest order E-cross-B drift. The fourth term represents the nonlinear effect of the perturbed $\backslash vec\; \backslash times\; \backslash vec$ drift interacting with the distribution function perturbation. The fifth term uses a collision operator to include the effects of collisions between particles. The sixth term represents the Maxwell–Boltzmann response to the perturbed electric potential. The last term includes temperature and density gradients of the background distribution function, which drive the perturbation. These gradients are only significant in the direction across flux surfaces, parameterized by $\backslash psi$, the magnetic flux. The gyrokinetic equation, together with gyro-averaged Maxwell's equations, give the distribution function and the perturbed electric and magnetic fields. In the electrostatic case we only require Gauss's law (which takes the form of the quasineutrality condition), given by〔F.I. Parra, M. Barnes, and A.G. Peeters. Up-down symmetry of the turbulent transport of toroidal angular momentum in tokamaks. Phys. Plasmas, 18(6):062501, 2011.〕 $\backslash sum\_\; Z\_\; e\; B\; \backslash int\; d\; v\_\; d\backslash mu\; d\backslash varphi\; h\_\; \backslash left(\backslash vec\backslash right)\; =\; \backslash sum\_\; \backslash frac\; e^\; n\_\; \backslash phi\}\{T\_\{s\}\}$. Usually solutions are found numerically with the help of supercomputers, but in simplified situations analytic solutions are possible. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Gyrokinetics」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.