An adequate confinement of α-particles is fundamental for the operation of future fusion powered reactors. An even more critical situation arises for stellarator devices, whose complex magnetic geometry can substantially increase α-particle losses. A traditional approach to transport evaluation is based on a diffusive paradigm; however, a growing body of literature presents a considerable amount of examples and arguments toward the validity of non-diffusive transport models for fusion plasmas, particularly in cases of turbulent driven transport [R. Sanchez and D. E. Newman, Plasma Phys. Controlled Fusion 57, 123002 (2015)]. Likewise, a recent study of collisionless α-particle transport in quasi-toroidally symmetric stellarators [A. Gogoleva et al., Nucl. Fusion 60, 056009 (2020)] puts the diffusive framework into question. In search of a better transport model, we numerically characterized and quantified the underlying nature of transport of the resulting α-particle trajectories by employing a whole set of tools, imported from the fractional transport theory. The study was carried out for a set of five configurations to establish the relation between the level of the magnetic field toroidal symmetry and the fractional transport coefficients, i.e., the Hurst H, the spatial α, and the temporal β exponents, each being a merit of non-diffusive transport. The results indicate that the α-particle ripple-enhanced transport is non-Gaussian and non-Markovian. Moreover, as the degree of quasi-toroidal symmetry increases, it becomes strongly subdiffusive, although the validity of the fractional model itself becomes doubtful in the limiting high and low symmetry cases.

中文翻译：

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无碰撞 α 粒子传输的非扩散性质：仿星器几何形状中环形对称性的依赖

充分限制 α 粒子是未来聚变动力反应堆运行的基础。仿星器设备出现了更严重的情况，其复杂的磁几何形状会显着增加 α 粒子损失。传统的交通评估方法基于扩散范式；然而，越来越多的文献提供了大量关于聚变等离子体非扩散输运模型有效性的例子和论据，特别是在湍流驱动输运的情况下[R. Sanchez 和 DE Newman，等离子体物理学。受控聚变 57, 123002 (2015)]。同样，最近对准环形对称仿星器中无碰撞 α 粒子传输的研究 [A. Gogoleva 等人，Nucl。Fusion 60, 056009 (2020)] 对扩散框架提出质疑。为了寻找更好的传输模型，我们通过使用从分数传输理论导入的一整套工具，对所得 α 粒子轨迹的传输的潜在性质进行了数值表征和量化。该研究针对一组五个配置进行，以建立磁场环向对称性水平与分数传输系数之间的关系，即 Hurst H、空间 α 和时间 β 指数，每个指数都是一个优点非扩散运输。结果表明，α粒子波纹增强传输是非高斯和非马尔可夫的。此外，随着准环形对称度的增加，它变得强烈次扩散，尽管分数模型本身的有效性在有限的高对称和低对称情况下变得可疑。