MHD Kamchatnov-Hopf Soliton in the Model of Primordial Solar Nebula

V. Salmin

Siberian Federal University, Krasnoyarsk, Russia

Stereographic projection of Hopf field on the 3-sphere into Euclidean 3-space is used as a model of 3D steady flow of ideal compressible fluid in MHD. In such case, flow lines are Villarceau circles lying on tori corresponding to the levels of Bernoulli function. Existence of an optimal torus with minimal relative surface free energy is shown. Beat of oscillations with wave numbers corresponding to structural radii of optimal torus leads to scaling of optimal tori. Spatial intersection of homothetic tori within one torus result in formation of cluster with the size depending on scaling factor. Optimal tori are considered as precursors of planetary orbits.