大纵横比仿星器中的有限轨道宽度效应
Finite orbit width effects in large aspect ratio stellarators
摘要：
推导了镜比接近1的大纵横比仿星器中低碰撞新经典通量的新轨道平均方程。该方程采用第二绝热不变量$J$作为速度空间坐标，保留了有限轨道宽度效应，并已在轨道平均新经典程序KNOSOS中实现.这些方程被用来研究$1/ν$区域和低碰撞区域。对于镜像比接近于1的一般大纵横比仿星器，随着碰撞频率的降低，$1/ν$机制直接过渡到$ν$机制，而不通过$\sqrtν$机制。得到了$ν$区新经典通量的显式表达式。该公式包括在不同类型的阱之间过渡的粒子的影响。虽然这些过渡产生的随机散射的碰撞频率在速度空间中的值无关，在真实空间中的扩散保持成比例的碰撞频率。$\sqrtν$机制仅在接近全方位的大纵横比仿星器中恢复：具有大镜比的大纵横比仿星器和镜比接近1的优化的大纵横比仿星器。利用\cite{calvo17}导出的轨道平均方程，可以计算具有大镜比的大展弦比仿星器中的新经典输运。在这些仿星器中，$\sqrtν$区域存在于碰撞间隔$ε|\ln ε| \ll ν_{ii} R a/ρ_i v_{ti} \ll 1/ε$中。在优化的大长宽比仿星器中，镜比接近1，$\sqrtν$区域发生在一个碰撞间隔中，该间隔取决于与全向$δ$：$δ^2 |\ln δ| \ll ν_{ii} R a/ρ_i v_{ti} \ll 1$的偏差。
英文摘要：
New orbit averaged equations for low collisionality neoclassical fluxes in large aspect ratio stellarators with mirror ratios close to unity are derived. The equations retain finite orbit width effects by employing the second adiabatic invariant $J$ as a velocity space coordinate and they have been implemented in the orbit-averaged neoclassical code KNOSOS. The equations are used to study the $1/ν$ regime and the lower collisionality regimes. For generic large aspect ratio stellarators with mirror ratios close to unity, as the collision frequency decreases, the $1/ν$ regime transitions directly into the $ν$ regime, without passing through a $\sqrtν$ regime. An explicit formula for the neoclassical fluxes in the $ν$ regime is obtained. The formula includes the effect of particles that transition between different types of wells. While these transitions produce stochastic scattering independent of the value of the collision frequency in velocity space, the diffusion in real space remains proportional to the collision frequency. The $\sqrtν$ regime is only recovered in large aspect ratio stellarators close to omnigeneity: large aspect ratio stellarators with large mirror ratios and optimized large aspect ratio stellarators with mirror ratios close to unity. Neoclassical transport in large aspect ratio stellarators with large mirror ratios can be calculated with the orbit-averaged equations derived by \cite{calvo17}. In these stellarators, the $\sqrtν$ regime exists in the collisionality interval $ε|\ln ε| \ll ν_{ii} R a/ρ_i v_{ti} \ll 1/ε$. In optimized large aspect ratio stellarators with mirror ratios close to unity, the $\sqrtν$ regime occurs in an interval of collisionality that depends on the deviation from omnigeneity $δ$: $δ^2 |\ln δ| \ll ν_{ii} R a/ρ_i v_{ti} \ll 1$.
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