Finite-duration vortical generation and subsequent spectral evolution of hypermagnetic seeds from a high-scale first-order phase transition

We investigate the finite-duration generation of hypermagnetic seeds by vortical plasma motion associated with a high-scale first-order phase transition. Starting from a vanishing initial hypermagnetic field, the source is described by an effective parity-odd vortical electromotive response within a reduced battery diffusion framework. Transition localized Gaussian sources are used to quantify how the seed depends on the inverse transition duration parameter (β/H∗), while broad coherent sources provide an upper envelope comparison within the reduced source closure. In the perturbative coherent regime, the generated hypermagnetic energy and helicity depend quadratically on the vortical response amplitude, with the helicity sign determined by the kinetic helicity of the source. For 100≤β/H∗≤1000, the localized-source energy and helicity decrease approximately as (β/H∗)^ -3 and remain several orders of magnitude below the broad coherent reference. An unequal time analysis further shows that temporal coherence controls the seed normalization in addition to the source duration. Subsequent spectral evolution is analyzed separately from seed generation. In the ideal limit, the source-free nonlinear transfer shows only a weak direct transfer tendency, whereas, for the adopted finite conductivity benchmark, the migration toward larger magnetic scales is largely reproduced by Ohmic dissipation alone. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.