| Summary: | Using the results of numerical simulations and solar observations, this study shows that the transition from deterministic chaos to hard turbulence in the magnetic field generated by the emerging small-scale, near-surface (within the Sun’s outer 5–10% convection zone) solar MHD dynamos occurs through a randomization process. This randomization process has been described using the concept of distributed chaos, and the main parameter of distributed chaos <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>β</mi></semantics></math></inline-formula> has been employed to <i>quantify</i> the degree of randomization (the wavenumber spectrum characterising distributed chaos has a stretched exponential form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow><mo>∝</mo><mo form="prefix">exp</mo><mo>−</mo><msup><mrow><mo>(</mo><mi>k</mi><mo>/</mo><msub><mi>k</mi><mi>β</mi></msub><mo>)</mo></mrow><mi>β</mi></msup></mrow></semantics></math></inline-formula>). The dissipative (Loitsianskii and Birkhoff–Saffman integrals) and ideal (magnetic helicity) magnetohydrodynamic invariants govern the randomization process and determine the degree of randomization <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>β</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula> at various stages of the emerging MHD dynamos, directly or through Kolmogorov–Iroshnikov phenomenology (the magnetoinertial range of scales as a precursor of hard turbulence). Despite the considerable differences in the scales and physical parameters, the results of numerical simulations are in quantitative agreement with solar observations (magnetograms) within this framework. The Hall magnetohydrodynamic dynamo is also briefly discussed in this context.
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