来自巴西球形托卡马克数据的紧致黎曼等离子体装置中的慢发电机模
Slow dynamo modes in compact Riemannian plasma devices from Brazilian spherical tokamak data
摘要：
由于柯林反发电机定理自然地适用于轴对称装置和流动，在球马克等离子体装置实验中经常发现反发电机模。本文充分考虑了无边界紧致黎曼等离子体装置（如托卡马克、仿星器和扭转加速器）中慢发电机模的存在性。研究表明，衰减模式磁场作用下的扰动无扭流能够产生一种缓慢的有扭发电机等离子体流，其中无扰流也是一种定常流。当获得高雷诺磁数$Rm$的慢发电机极限时，未扰动的等离子体流达到平衡，如在spheromak。从国家空间研究所的巴西球形托卡马克获得的纵横比数据和其他数据被用来获得慢发电机作用的磁场的最大磁增长率的数值估计，即对于环形初始磁场$B_{0}\approx{0.4T}$和纵横比数据为1.5的托卡马克的$γ_{1max}\approx{\frac{0.26}{a}{\times}\frac{v_{1θ}}{B_{1s}}}$。对于$a\approx{0.2m}$的托卡马克内半径，得到慢发电机的最大增长率为$γ_{1max}\approx{1.3{\times}\frac{v_{1θ}}{B_{1s}}}$，其中$v_{1θ}$是极向扰动扩散流。安全因子由$q\approx{-1}$给出，它是$q<1$，表示球形托卡马克等离子体的稳定性。
英文摘要：
Anti-dynamo modes are usually found in spheromaks plasma devices experiments due to the fact that Cowling anti-dynamo theorem is naturally applied to axisymmetric devices and flows. In this paper full consideration is given to the existence of slow dynamo modes in the case of compact Riemannian plasma devices without boundaries, such as tokamaks, stellarators and torsatrons. It is shown that a perturbed untwisted flow given by a decaying mode magnetic field is able to generate a slow twisted dynamo plasma flow where the unperturbed flow is also a steady flow. When the slow dynamo limit is obtained for high Reynolds magnetic numbers $Rm$, the unperturbed plasma flow achieve equilibrium as in spheromaks. The data of aspect ratio and other data obtained from the Brazilian spherical tokamak at the National institute for space research are used to obtain a numerical estimate for the maximum magnetic growth rate of the magnetic field of the slow dynamo action as $γ_{1max}\approx{\frac{0.26}{a}{\times}\frac{v_{1θ}}{B_{1s}}}$ for a toroidal initial magnetic field $B_{0}\approx{0.4T}$ and an aspect data tokamak of 1.5. For a tokamak internal radius of $a\approx{0.2m}$ one obtains a maximum growth rate for the slow dynamo as $γ_{1max}\approx{1.3{\times}\frac{v_{1θ}}{B_{1s}}}$, where $v_{1θ}$ is the poloidal perturbed diffusive flow. The safety factor is given by $q\approx{-1}$ which is $q<1$ implying stability of spherical tokamak plasma.
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