发表机构
Princeton Plasma Physics Laboratory, Princeton University; The University of Tokyo（普林斯顿等离子体物理实验室，普林斯顿大学; 东京大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出利用模拟初期快速频率偏移迭代收敛以确定能量粒子模种子频率的方法，利用不完美时间尺度分离的残余实现自优化，为降阶建模提供输入。
AI 中文摘要
集成代码在模拟托卡马克等离子体中阿尔芬波与快离子相互作用时，对于不稳定性增长、饱和、啁啾和爆发以及输运等相对缓慢的过程采用微扰模型。阿尔芬模时空结构形成的更快过程被假定在其振荡周期$\tau_0 \equiv 2\pi/\omega_0$内已完成。这种时间尺度分离是微扰模型计算效率的基础，其中阿尔芬模的时间依赖性被简化为标量信号$s(t) = A(t)\sin(-\omega_0 t - \phi(t))$，具有可变振幅$A(t)$和相位$\phi(t)$。为此，需要以模的空间结构$\delta\Phi({\mathbf x})$、阻尼率$\gamma_{\rm d}$和初始频率$\omega_0$形式提供的准确输入数据。对于位于密集或连续谱中的模，$\delta\Phi$和$\gamma_{\rm d}$可以从连续谱和快离子轨道的形式估计，但难以猜测种子频率$\omega_0$。在此，我们报告数值实验的结果，表明可以通过模拟的前几百个时间步内发生的快速频率偏移来找到$\omega_0$。使用偏移频率重新启动迭代收敛到似乎最大化共振驱动的$\omega_0$值，表明存在自优化过程。迭代的需要归因于在推导微扰模型时截断了快速频率调整所需的项。同时，部分自优化之所以可能，归因于仅级数截断（无滤波）并不严格强制缓慢。数值实现中仍存在更快动力学的残余和串扰。这既带来不确定性，也带来实用性。
英文摘要
Integrated codes simulating interactions between Alfvén waves and fast ions in tokamak plasmas use perturbative models for the relatively slow processes of instability growth, saturation, chirping and bursting, and transport. Faster processes by which an Alfvén mode's spatiotemporal structure forms are assumed to have been completed within the mode's oscillation period, $τ_0 \equiv 2π/ω_0$. This separation of time scales underlies the computational efficiency of perturbative models, where the Alfvén mode's time-dependence is reduced to that of a scalar signal $s(t) = A(t)\sin(-ω_0 t - ϕ(t))$ with variable amplitude $A(t)$ and phase $ϕ(t)$. For this, accurate input data in the form of a mode's spatial structure $δΦ({\mathbf x})$, damping rate $γ_{\rm d}$, and initial frequency $ω_0$ are required. For modes residing in dense or continuous spectra, $δΦ$ and $γ_{\rm d}$ could be estimated from the form of the continua and fast ion orbits, but it is difficult to guess the seed frequency $ω_0$. Here, we report results of numerical experiments showing that it is possible to find $ω_0$ using a prompt frequency shift that occurs during the first few $100$ time steps of a simulation. Restarts with the shifted frequency iteratively converge to a value of $ω_0$ that seems to maximize the resonant drive, suggesting an auto-optimization process. The need for iteration is attributed to the fact that the terms required for rapid frequency adjustments were truncated when deriving the perturbative model. Meanwhile, the fact that partial auto-optimization is possible at all is attributed to the fact that series truncation alone (without filter) does not strictly enforce slowness. Remnants of and cross-talk with faster dynamics still occur in numerical implementations. This entails potential for both uncertainty and utility.
Comments17 pages. 7 figures
