Riemann curvature-stretching coupling in dynamo torus laboratory and in UHF twisted plasma loops

Kleeorin, Rogachevskii, Tomin and Sokoloff [Phys Rev E79,046302,(2009)] have shown that Roberts slow dynamo can be transformed into a fast dynamo by allowing its coefficients randomly fluctuate. Stretching, fundamental for fast dynamo action, is increased by mean helicity flow. Previous investigation on slow dynamo plasma and anti-fast dynamo theorem in Riemannian geometry [Garcia de Andrade, Phys Plasmas 15(2008)], where Riemann curvature of astrophysical plasmas loops, is responsible for unstretching by plasma flow, one obtains a torus dynamos twisted flows slow dynamo such as in Moebius strip dynamo, considered by Shukurov, Stepanov and Sokoloff [Phys. Rev. E 78,025301,(2008)] to modelling Perm dynamo torus of liquid sodium. Diffusion and advection (stretching), which are competing effects for dynamo action, lead us to show plasma resistivity proportionality to Riemann curvature (folding). Shukurov et al, showed that in Ponomarenko dynamo torus model a broader channel produces a better dynamo. These results agree with Schekochihin et al [Phys Rev E (2002)] where random magnetic structures are strengthen by curvature inverse. Analysis of spectrum of chaotic fast dynamos, shows curvature acts as a damping, since growth 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. Curved plasma loop yields a R1212|Plasma ≈ 5.6×10 m. Perm torus has astronger one. Slow dynamos are favoured in laboratories rather than in plasma loops. Curvature-stretching flux rope dynamo coupling energy, coincides with minimum twist energy ǫtwist ≈ 10 TeV stored in flux ropes. Torus flux tubes around black-holes remain in the order of 2MeV and GBR are around 10TeV . R1212 is negative, and inflexionary flux tubes dynamos may be responsible for this CME mechanism. Resonant UHF frequencies of 100GHz are found in curved-twisted loops. This is close to plasma Tokamak 91GHz result.PACS numbers: 47.65.Md, 96.60.pc