基于贝叶斯分析的托卡马克平衡推断和力平衡模型验证的统一方法
A Unified Method for Inference of Tokamak Equilibria and Validation of Force-Balance Models Based on Bayesian Analysis
摘要：
提出了一种新的方法，贝叶斯分析的基础上，统一的等离子体平衡参数的推断，在托卡马克的能力，以量化推断的平衡和梯度Shafranov力平衡解决方案之间的差异。该技术的核心是观测分裂的新方法，该方法允许多个正演模型与单个诊断观测相关联。这个新的想法随后提供了一种方法，通过这种方法，GS解决方案的空间可以有效地通过先验分布来表征。此外，通过将力平衡直接折叠到一组前向模型中并在另一组中利用简单的Biot-Savart响应，等离子体参数本身的贝叶斯推断产生对两组模型之间的相对一致性敏感的证据（推断的后验分布的归一化常数）。然后，该证据可用于帮助确定测试的力平衡模型在几次放电/时间内的相对准确度。这些想法已经在称为BEAST（贝叶斯均衡分析和模拟工具）的代码中实现，该代码使用Skilling的嵌套采样算法的特殊实现[Skilling，Bayesian Analysis 1（4），833- 859（2006）]来对高维非高斯后验进行采样和证据计算。初始BEAST平衡推理结果为两个高性能的MAST放电。
英文摘要：
A new method, based on Bayesian analysis, is presented which unifies the inference of plasma equilibria parameters in a Tokamak with the ability to quantify differences between inferred equilibria and Grad-Shafranov force-balance solutions. At the heart of this technique is the new method of observation splitting, which allows multiple forward models to be associated with a single diagnostic observation. This new idea subsequently provides a means by which the the space of GS solutions can be efficiently characterised via a prior distribution. Moreover, by folding force-balance directly into one set of forward models and utilising simple Biot-Savart responses in another, the Bayesian inference of the plasma parameters itself produces an evidence (a normalisation constant of the inferred posterior distribution) which is sensitive to the relative consistency between both sets of models. This evidence can then be used to help determine the relative accuracy of the tested force-balance model across several discharges/times. These ideas have been implemented in a code called BEAST (Bayesian Equilibrium Analysis and Simulation Tool), which uses a special implementation of Skilling's nested sampling algorithm [Skilling, Bayesian Analysis 1(4), 833--859 (2006)] to perform sampling and evidence calculations on high-dimensional, non-Gaussian posteriors. Initial BEAST equilibrium inference results are presented for two high-performance MAST discharges.
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