Deriving the Continuous β-FPUT Model for Decayless Solar Coronal Oscillations Directly from Resistive MHD
Abstract
We present an analytical framework deriving the fluid-continuum β-Fermi-Pasta-Ulam-Tsingou (β-FPUT) system directly from a third-order resistive magnetohydrodynamics (MHD) expansion to explain persistent, decayless transverse oscillations observed in solar coronal loops. For a continuous wave field propagating along a longitudinal magnetic field with cross-field density variations, a multi-scale expansion demonstrates that quadratic 𝒪(2) advective and Maxwell tension terms vanish identically due to out-of-plane polarization symmetry. Instead, the quadratic longitudinal ponderomotive force drives field-aligned density modulations that back-react on the primary transverse wave, yielding a cubic 𝒪(3) restoring force. In the long-wavelength limit, the governing equations reduce to a fluid-continuum Modified Korteweg-de Vries (mKdV) system where cross-field profile variation provides the non-linear dispersive mechanism. We prove that this internal fluid mechanism establishes stable, amplitude-dependent frequency self-focusing, which phase-locks adjacent elements and prevents phase-mixing wave attenuation without requiring external steady driving parameterizations. This framework enables macro-scale coronal seismology, providing closed-form expressions to invert observed decayless wave-packet durations to compute the unresolved cross-field density gradient scale length (Lx) and the internal volumetric filling factor (fV) without relying on traditional emission measure or spectroscopic line-ratio diagnostics. Much like famous Enrico Fermi's historic use of macro-scale displacements to estimate complex atomic explosion yields, this framework establishes a paradigm where monitoring macroscopic oscillation durations empowers observers to extract fine-scale, otherwise unresolvable waveguide properties.
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BibTeX
@misc{tsiklauri2026deriving,
title = {{Deriving the Continuous $β$-FPUT Model for Decayless Solar Coronal Oscillations Directly from Resistive MHD}},
author = {D. Tsiklauri},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06953},
eprint = {2610.06953},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06953},
}
RIS
TY - UNPB
TI - Deriving the Continuous β-FPUT Model for Decayless Solar Coronal Oscillations Directly from Resistive MHD
AU - D. Tsiklauri
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2610.06953
UR - https://arxiv.org/abs/2610.06953
AB - We present an analytical framework deriving the fluid-continuum β-Fermi-Pasta-Ulam-Tsingou (β-FPUT) system directly from a third-order resistive magnetohydrodynamics (MHD) expansion to explain persistent, decayless transverse oscillations observed in solar coronal loops. For a continuous wave field propagating along a longitudinal magnetic field with cross-field density variations, a multi-scale expansion demonstrates that quadratic 𝒪(2) advective and Maxwell tension terms vanish identically due to out-of-plane polarization symmetry. Instead, the quadratic longitudinal ponderomotive force drives field-aligned density modulations that back-react on the primary transverse wave, yielding a cubic 𝒪(3) restoring force. In the long-wavelength limit, the governing equations reduce to a fluid-continuum Modified Korteweg-de Vries (mKdV) system where cross-field profile variation provides the non-linear dispersive mechanism. We prove that this internal fluid mechanism establishes stable, amplitude-dependent frequency self-focusing, which phase-locks adjacent elements and prevents phase-mixing wave attenuation without requiring external steady driving parameterizations. This framework enables macro-scale coronal seismology, providing closed-form expressions to invert observed decayless wave-packet durations to compute the unresolved cross-field density gradient scale length (L_x) and the internal volumetric filling factor (f_V) without relying on traditional emission measure or spectroscopic line-ratio diagnostics. Much like famous Enrico Fermi's historic use of macro-scale displacements to estimate complex atomic explosion yields, this framework establishes a paradigm where monitoring macroscopic oscillation durations empowers observers to extract fine-scale, otherwise unresolvable waveguide properties.
ER -