发电机环实验室和UHF扭曲等离子体环中的黎曼曲率-伸缩耦合
Riemann curvature-stretching coupling in dynamo torus laboratory and in UHF twisted plasma loops
摘要：
将等离子体环扭曲黎曼模型应用于环面发电机扭曲流，其导致诸如在Moebius带发电机中的缓慢发电机，最近由Shukurov、Stepanov和Sokoloff [Phys. Rev. \textbf{E 78}，025301，（2008）]考虑对液体钠中的Perm发电机环面进行建模。由于扩散和平流（拉伸），是发电机行动的竞争效应，等离子体电阻率项被证明是成比例的循环黎曼曲率（折叠）。Shukurov等人还表明，基于Ponomarenko发电机，更宽的环面通道产生更好的发电机。这些结果与Schekochihin等人[Phys Rev \textbf{E}（2002）]的结果一致，其中随机磁场磁场通过曲率得到加强。对混沌快速发电机的频谱分析表明，由于磁场增长率与黎曼曲率成反比，黎曼曲率起着阻尼作用。与广义相对论MHD发电机方程的比较表明，扩散项中也出现了黎曼张量的压缩形式Ricci张量。等离子体环的曲率是${R^{1}_{212}}|_{\textbf{Plasma}}\approx{5.6{\times}10^{-19}m^{-2}}$，而彼尔姆环形的曲率肯定更高。因此，在发电机实验室中，慢发电机比在等离子体回路中更受欢迎。结果表明，弯曲拉伸磁通绳发电机耦合能与磁通绳中储存的最小扭转能$ε_{\textbf{twist}}\approx{10^{30}TeV}$相一致。黑洞周围的环面通量管仍保持在$2MeV$和GBR的顺序是围绕$10^{52}TeV$。由于${R^{1}}_{212}$是负的，因此，在UHF等离子体环中，这种CME机制可能是由非线性通量管快速发电机引起的。
英文摘要：
A plasma loop twisted Riemannian model is applied to torus dynamos twisted flows it leading to a slow dynamo such as in Moebius strip dynamo, recently considered by Shukurov, Stepanov and Sokoloff [Phys. Rev. \textbf{E 78},025301,(2008)] to modelling Perm dynamo torus in liquid sodium. Since diffusion and advection (stretching), are competing effects for dynamo action, plasma resistivity term is shown to be proportional to loops Riemann curvature (folding). Shukurov et al, also showed that based on Ponomarenko dynamo, a broader torus channel produces a better dynamo. These results agree with Schekochihin et al [Phys Rev \textbf{E} (2002)] where random filamentary magnetic fields are strengthen by curvature. Analysis of spectrum of chaotic fast dynamos, shows that Riemann curvature acts as a damping, since growth magnetic field rate is inversely proportional to Riemann curvature. Comparison with general relativistic MHD dynamo equation, shows that the Ricci tensor, which is a contraction of the Riemann tensor also appears in the diffusion term. Curvature of plasma loop is ${R^{1}_{212}}|_{\textbf{Plasma}}\approx{5.6{\times}10^{-19}m^{-2}}$, while for Perm torus is certainly higher. Thus slow dynamos are favoured in dynamo laboratories rather than in plasma loops. It is shown that the curvature-stretching flux rope dynamo coupling energy, coincides with the minimum twist energy $ε_{\textbf{twist}}\approx{10^{30}TeV}$ stored in flux ropes. Torus flux tubes around black-holes remain in the order of $2MeV$ and GBR are around $10^{52}TeV$. Since the ${R^{1}}_{212}$ is negative, inflexionary flux tubes fast dynamos may be responsible for this CME mechanism in UHF plasma loops.
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