A study of global magnetic helicity in self-consistent spherical dynamos

References

• Berger, M.A., Rigorous new limits on magnetic helicity dissipation in the solar corona. Geophys. Astrophys. Fluid Dyn. 1984, 30, 79–104.
   Web of Science ®Google Scholar
• Berger, M.A., Structure and stability of constant-alpha force-free fields. Astrophys. J., Suppl. Ser. 1985, 59, 433–444.
   Web of Science ®Google Scholar
• Berger, M.A. and Field, G.B., The topological properties of magnetic helicity. J. Fluid Mech. 1984, 147, 133–148.
   Web of Science ®Google Scholar
• Berger, M.A. and Hornig, G., A generalized poloidal-toroidal decomposition and an absolute measure of helicity. J. Phys. A Math. 2018, 51, 495501.
   Google Scholar
• Brandenburg, A., Advances in mean-field dynamo theory and applications to astrophysical turbulence. J. Plasma Phys. 2018, 84, 735840404.
   Google Scholar
• Brandenburg, A. and Subramanian, K., Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 2005, 417, 1–209.
   Web of Science ®Google Scholar
• Busse, F. and Simitev, R.D., Dynamos driven by convection in rotating spherical shells. Astron. Nachr. 2005, 326, 231–240.
   Web of Science ®Google Scholar
• Busse, F. and Simitev, R.D., Parameter dependences of convection-driven dynamos in rotating spherical fluid shells. Geophys. Astrophys. Fluid Dyn. 2006, 100, 341–361.
   Web of Science ®Google Scholar
• Busse, F. and Simitev, R., Toroidal flux oscillation as possible cause of geomagnetic excursions and reversals. Phys. Earth Planet. Inter. 2008, 168, 237–243.
   Web of Science ®Google Scholar
• Busse, F.H. and Simitev, R.D., Remarks on some typical assumptions in dynamo theory. Geophys. Astrophys. Fluid Dyn. 2011, 105, 234–247.
   Web of Science ®Google Scholar
• Cameron, R., Dikpati, M. and Brandenburg, A., The global solar dynamo. Space Sci. Rev. 2017, 210, 367–395.
   Web of Science ®Google Scholar
• Cantarella, J., DeTurck, D., Gluck, H. and Teytel, M., The spectrum of the curl operator on spherically symmetric domains. Phys. Plasma 2000, 7, 2766–2775.
   Web of Science ®Google Scholar
• Choudhuri, A.R., Chatterjee, P. and Nandy, D., Helicity of solar active regions from a dynamo model. Astrophys. J. Lett. 2004, 615, L57–L60.
   Google Scholar
• Christensen, U.R., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G.A., Grote, E., Honkura, Y., Jones, C., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wicht, J. and Zhang, K., A numerical dynamo benchmark. Phys. Earth Planet. Inter. 2001, 128, 25–34.
   Web of Science ®Google Scholar
• Faraco, D. and Lindberg, S., Proof of Taylor's conjecture on magnetic helicity conservation. Comm. Math. Phys. 2019, 373, 707–738.
   Web of Science ®Google Scholar
• Faraco, D., Lindberg, S., MacTaggart, D. and Valli, A., On the proof of Taylor's conjecture in multiply connected domains. Appl. Math. Lett. 2022, 124, 107654.
   Web of Science ®Google Scholar
• Hawkes, G. and Berger, M., Magnetic helicity as a predictor of the solar cycle. Solar Phys. 2018, 293, 1–25.
   Web of Science ®Google Scholar
• Lund, K., Jardine, M., Lehmann, L.T., Mackay, D.H., See, V., Vidotto, A.A., Donati, J.-F., Fares, R., Folsom, C.P., Jeffers, S.V., Marsden, S.C., Morin, J. and Petit, P., Measuring stellar magnetic helicity density. Mon. Notices Royal Astron. Soc. 2020, 493, 1003–1012.
   Web of Science ®Google Scholar
• Lund, K., Jardine, M., Russell, A.J.B., Donati, J.-F., Fares, R., Folsom, C.P., Jeffers, S.V., Marsden, S.C., Morin, J., Petit, P. and See, V., Field linkage and magnetic helicity density. Mon. Notices Royal Astron. Soc. 2021, 502, 4903–4910.
   Web of Science ®Google Scholar
• MacTaggart, D. and Hillier, A. (2020). Topics in Magnetohydrodynamic Topology, Reconnection and Stability Theory, CISM International Centre for Mechanical Sciences 2020 (Springer).
   Google Scholar
• Matsui, H., Heien, E., Aubert, J., Aurnou, J.M., Avery, M., Brown, B., Buffett, B.A., Busse, F., Christensen, U.R., Davies, C.J., Featherstone, N., Gastine, T., Glatzmaier, G.A., Gubbins, D., Guermond, J.L., Hayashi, Y.Y., Hollerbach, R., Hwang, L.J., Jackson, A., Jones, C.A., Jiang, W., Kellogg, L.H., Kuang, W., Landeau, M., Marti, P.H., Olson, P., Ribeiro, A., Sasaki, Y., Schaeffer, N., Simitev, R.D., Sheyko, A., Silva, L., Stanley, S., Takahashi, F., Ichi Takehiro, S., Wicht, J. and Willis, A.P., Performance benchmarks for a next generation numerical dynamo model. Geochem. Geophys. 2016, 17, 1586–1607.
   Web of Science ®Google Scholar
• Moffatt, H.K., The degree of knottedness of tangled vortex lines. J. Fluid Mech. 1969, 35, 117–129.
   Web of Science ®Google Scholar
• Pevtsov, A.A., Berger, M.A., Nindos, A., Norton, A.A. and van Driel-Gesztelyi, L., Magnetic helicity, tilt, and twist. Space Sci. Rev. 2014, 186, 285–324.
   Web of Science ®Google Scholar
• Pipin, V.V. and Pevtsov, A.A., Magnetic helicity of the global field in solar cycles 23 and 24. Astrophys. J. 2014, 789, 21.
   Web of Science ®Google Scholar
• Pipin, V.V., Pevtsov, A.A., Liu, Y. and Kosovichev, A.G., Evolution of magnetic helicity in solar cycle 24. Astrophys. J. Lett. 2019, 877, L36.
   Web of Science ®Google Scholar
• Silva, L.A.C. and Simitev, R.D. (2018). Pseudo-Spectral Code for Numerical Simulation of Nonlinear Thermo-Compositional Convection and Dynamos in Rotating Spherical Shells, zenodo.org.
   Google Scholar
• Simitev, R.D. and Busse, F.H., Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells. J. Fluid Mech. 2005, 532, 365–388.
   Web of Science ®Google Scholar
• Simitev, R.D. and Busse, F., Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells. Europhys. Lett. 2009, 85, 19001.
   Google Scholar
• Simitev, R.D. and Busse, F., How far can minimal models explain the solar cycle? Astrophys. J. 2012, 749, 9.
   Web of Science ®Google Scholar
• Taylor, J., Relaxation and magnetic reconnection in plasmas. Rev. Mod. Phys. 1986, 58, 741–763.
   Web of Science ®Google Scholar
• Tilgner, A., Spectral methods for the simulation of incompressible flows in spherical shells. Int. J. Numer. Meth. Fluids 1999, 30, 713–724.
   Web of Science ®Google Scholar
• Woltjer, L., A theorem on force-free magnetic fields. Proc. Natl. Acad. Sci. USA 1958, 44, 489–491.
   PubMed Web of Science ®Google Scholar
• Yang, S., Pipin, V.V., Sokoloff, D.D., Kuzanyan, K.M. and Zhang, H., The origin and effect of hemispheric helicity imbalance in solar dynamo. J. Plasma Phys. 2020, 86, 775860302.
   Google Scholar
• Zhang, H., Sakurai, T., Pevtsov, A., Gao, Y., Xu, H., Sokoloff, D.D. and Kuzanyan, K., A new dynamo pattern revealed by solar helical magnetic fields. Mon. Not. R. Astron. Soc. 2010, 402, L30–L33.
   Web of Science ®Google Scholar