AI 中文总结
研究旋转p-11B等离子体中多流体平衡，提出VEQ-MF框架。通过耦合多种方程扩展公式，以其为工具扫描质子和硼旋转频率，经后处理获聚变与轫致辐射功率，识别多流体效应，展现快速求解优势，为相关研究提供支持。
AI 中文摘要
我们提出了VEQ-MF，这是一种用于二维轴对称多流体平衡的快速光谱参数扫描框架，具有规定的与物种相关的环形旋转。该求解器耦合了广义玻尔兹曼密度响应、准中性静电极化和广义Grad-Shafranov方程，将简化参数的Grad-Shafranov和VEQ公式扩展到多物种旋转平衡。旋转的p-11B球形托卡马克构型被用作一个具有挑战性的测试案例。在EHL-2和EHL-3B几何结构中对质子和硼的旋转频率进行了独立扫描。然后对计算得到的场进行后处理，以从漂移麦克斯韦反应速率系数获得聚变功率，并从解析辐射模型获得轫致辐射功率。三个EHL-3B有限差分基准测试给出的全局储能、轫致辐射功率和聚变功率差异为1.7%-3.4%，而一个代表性的收敛性检查表明，增加光谱参数数量时灵敏度低于1%，对高斯网格细化敏感度可忽略不计。对于重复扫描，核心平衡求解仍然很快，在MATLAB中，EHL-3B的代表性非零案例每点需要0.032-0.050秒，不包括后处理、插值、绘图和文件导出。扫描识别出两种相互竞争的多流体效应。在等旋转下，向外的硼积累增加了体积积分的n_e^2，因此聚变与轫致辐射功率比R_fb随着旋转增加而降低。与物种相关的环形旋转减弱了离心极化并降低了轫致辐射功率，而较大的EHL-3B几何结构中的相对环形流提高了漂移麦克斯韦反应速率系数，从而改变了聚变功率。
英文摘要
We present VEQ-MF, a fast spectral parameter-scan framework for two-dimensional axisymmetric multi-fluid equilibria with prescribed species-dependent toroidal rotation. The solver couples generalized Boltzmann density responses, quasineutral electrostatic polarization, and a generalized Grad--Shafranov equation, extending reduced-parameter Grad-Shafranov and VEQ formulations to multi-species rotating equilibria. Rotating $p\text{-}^{11}\text{B}$ spherical-tokamak configurations are used as a demanding test case. Independent scans of the proton and boron rotation frequencies are performed in EHL-2 and EHL-3B geometries. The computed fields are then post-processed to obtain fusion power from a drift-Maxwellian reaction-rate coefficient and bremsstrahlung power from an analytical radiation model. Three in-range EHL-3B finite-difference benchmarks give global stored-energy, bremsstrahlung-power, and fusion-power differences of $1.7$--$3.4\%$, while a representative convergence check shows sub-percent sensitivity to increasing the spectral-parameter number and negligible sensitivity to Gaussian-grid refinement. The core equilibrium solve remains fast for repeated scans, with representative nonzero EHL-3B cases requiring $0.032$--$0.050$~s per point in MATLAB, excluding post-processing, interpolation, plotting, and file export. The scans identify two competing multi-fluid effects. Under iso-rotation, outward boron accumulation increases the volume-integrated $n_e^2$, so the fusion-to-bremsstrahlung power ratio $\mathcal{R}_{\mathrm{fb}}$ decreases with increasing rotation. Species-dependent toroidal rotation weakens centrifugal polarization and lowers bremsstrahlung power, while the relative toroidal flow in the larger EHL-3B geometry raises the drift-Maxwellian reaction-rate coefficient and thereby modifies fusion power.
Comments29 pages, 21 figures
