One of the main codes to analyze and optimize stellarator configurations is the EMC3 code, which implements a state-of-the-art 3D Monte Carlo plasma edge transport code. However, so far, a self-consistent treatment of the E x B drift is absent. This plasma drift is known to significantly impact the particle and heat distribution in the plasma edge. It is desirable to incorporate this drift into EMC3 to improve the predictive capabilities of the code. The calculation of the E x B drift requires the approximation of the electric field E, which is proportional to the gradient of the electric potential $ \varphi $. In previous work, the gradient was calculated with a least squares method based on a finite difference approximation of the electric potential. However, due to the stochastic nature of EMC3, the output plasma fields computed by the code are inherently noisy. The finite difference method further amplifies the noise, with the amplification growing as the grid size decreases. We continue from, which introduced a new noise-robust method for 1D derivatives. We extend the noise-robust method to 2D and apply it to the electric potential. We show that a PDE can be derived that describes the evolution of the electric field in case of a uniform diffusion coefficient. This PDE allows us to approximate the electric field directly with a Monte Carlo simulation, thus avoiding the need for a finite difference approximation. We illustrate the accuracy of the method and the noise robustness with a test case.

翻译：分析与优化仿星器位形的主要代码之一是EMC3代码，该代码实现了先进的3D蒙特卡洛等离子体边缘输运程序。然而，迄今为止，其中尚未包含对E x B漂移的自洽处理。已知这种等离子体漂移会显著影响等离子体边缘的粒子和热分布。为了提升该代码的预测能力，需要将这种漂移纳入EMC3中。E x B漂移的计算需要近似求解电场E，该电场与电势$ \varphi $的梯度成正比。在先前的工作中，梯度是基于电势的有限差分近似、采用最小二乘法进行计算的。然而，由于EMC3的随机特性，该代码计算输出的等离子体场本质上具有噪声。有限差分法会进一步放大噪声，且放大效应随网格尺寸减小而增强。我们基于先前引入的一种新型一维导数抗噪声方法继续展开研究。我们将该抗噪声方法推广至二维，并将其应用于电势计算。我们证明，在均匀扩散系数的情况下，可以推导出一个描述电场演化的偏微分方程。该偏微分方程使我们能够直接通过蒙特卡洛模拟来近似求解电场，从而避免了有限差分近似的需要。我们通过一个测试案例展示了该方法的准确性和抗噪声鲁棒性。