Mechanism selecting spectral representation of the magnetic-helicity cascade

Determine what physical mechanism selects whether the common magnetic-helicity cascade is realized as a power-law magnetic spectrum with index -3/4 or as a stretched-exponential distributed-chaos spectrum with exponent 1/5 in a given solar-wind or outer-heliosheath situation.

Background

The paper derives a magnetic-helicity-driven cascade whose scaling form produces a magnetic energy spectrum proportional to k{-3/4} in the statistically robust regime. It then compares this result with a distributed-chaos construction based on the same amplitude scaling, which instead yields a stretched-exponential spectrum proportional to exp[-(k/k_beta){1/5}].

Observations are presented as displaying both forms in different settings, including solar-wind reservoirs and the outer heliosheath. The paper states that these may represent different projections of a single underlying cascade result, but does not identify the physical conditions or mechanism that determine which spectral representation appears.

References

The fundamental and tantalizing question of what physically determines which projection is realized in a given situation remains open for future investigations (see also Ref. and references therein).

— Cascade models of anisotropic turbulence in magnetized plasma of solar wind  (2609.10418 - Bershadskii, 9 Sep 2026) in Section "Distributed chaos dominated by magnetic helicity"