Milovanov Alexander V, Rasmussen Jens Juul, Dif-Pradalier Guilhem
ENEA National Laboratory, Centro Ricerche Frascati, I-00044 Frascati, Rome, Italy and Space Research Institute, Russian Academy of Sciences, 117997 Moscow, Russia.
Physics Department, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
Phys Rev E. 2021 May;103(5-1):052218. doi: 10.1103/PhysRevE.103.052218.
A new basis has been found for the theory of self-organization of transport avalanches and jet zonal flows in L-mode tokamak plasma, the so-called "plasma staircase" [Dif-Pradalier et al., Phys. Rev. E 82, 025401(R) (2010)PLEEE81539-375510.1103/PhysRevE.82.025401]. The jet zonal flows are considered as a wave packet of coupled nonlinear oscillators characterized by a complex time- and wave-number-dependent wave function; in a mean-field approximation this function is argued to obey a discrete nonlinear Schrödinger equation with subquadratic power nonlinearity. It is shown that the subquadratic power leads directly to a white Lévy noise, and to a Lévy fractional Fokker-Planck equation for radial transport of test particles (via wave-particle interactions). In a self-consistent description the avalanches, which are driven by the white Lévy noise, interact with the jet zonal flows, which form a system of semipermeable barriers to radial transport. We argue that the plasma staircase saturates at a state of marginal stability, in whose vicinity the avalanches undergo an ever-pursuing localization-delocalization transition. At the transition point, the event-size distribution of the avalanches is found to be a power law w_{τ}(Δn)∼Δn^{-τ}, with the drop-off exponent τ=(sqrt[17]+1)/2≃2.56. This value is an exact result of the self-consistent model. The edge behavior bears signatures enabling to associate it with the dynamics of a self-organized critical (SOC) state. At the same time the critical exponents, pertaining to this state, are found to be inconsistent with classic models of avalanche transport based on sand piles and their generalizations, suggesting that the coupled avalanche-jet zonal flow system operates on different organizing principles. The results obtained have been validated in a numerical simulation of the plasma staircase using flux-driven gyrokinetic code for L-mode Tore-Supra plasma.
已为L模托卡马克等离子体中传输雪崩和喷流带状流的自组织理论找到了一个新基础，即所谓的“等离子体阶梯”[迪夫 - 普拉达利耶等人，《物理评论E》82，025401(R) (2010年) PLEEE81539 - 375510.1103/PhysRevE.82.025401]。喷流带状流被视为由一个依赖于时间和波数的复波函数表征的耦合非线性振荡器的波包；在平均场近似中，该函数被认为服从具有亚二次幂非线性的离散非线性薛定谔方程。结果表明，亚二次幂直接导致白噪声，以及用于测试粒子径向输运的噪声分数福克 - 普朗克方程（通过波粒相互作用）。在自洽描述中，由白噪声驱动的雪崩与喷流带状流相互作用，喷流带状流形成了一个对径向输运的半透性屏障系统。我们认为等离子体阶梯在边际稳定状态饱和，在其附近雪崩经历持续的局域化 - 非局域化转变。在转变点，发现雪崩的事件大小分布是幂律(w_{τ}(Δn)∼Δn^{-τ})，衰减指数(τ = (\sqrt{17} + 1)/2≃2.56)。该值是自洽模型的精确结果。边缘行为具有一些特征，使其能够与自组织临界（SOC）状态的动力学相关联。同时，发现与该状态相关的临界指数与基于沙堆及其推广的经典雪崩输运模型不一致，这表明雪崩 - 喷流带状流耦合系统基于不同的组织原则运行。使用通量驱动的陀螺动力学代码对L模托雷 - 苏普拉等离子体的等离子体阶梯进行数值模拟，验证了所获得的结果。
