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\begin{document}

\title{Optimization of Magnetic Flux Ropes Modeled with the RBSL Method}



\author[1]{Viacheslav Titov}%
\author[1]{Cooper Downs}%
\author[1]{Tibor Torok}%
\author[1]{Jon Linker}%
\author[2]{Ronald Caplan}%
\author[1]{Roberto Lionello}%
\affil[1]{Predictive Science Inc.}%
\affil[2]{Predictive Science Inc}%


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  \date{June 17, 2024}


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\begin{abstract}
The so-called regularized Biot-Savart laws (RBSLs, Titov et al. 2018)
provide an efficient and flexible method for modeling pre-eruptive
magnetic configurations whose characteristics are constrained by
observational image and magnetic-field data. This method allows one to
calculate the field of magnetic flux ropes (MFRs) with small circular
cross-sections and an arbitrary axis shape. The field of the whole
configuration is constructed as a superposition of (1) such a flux-rope
field, (2) an ambient potential field determined, for example, by the
radial field component of an observed magnetogram, and (3) a so-called
compensating potential field that counteracts deviations of the radial
field caused by the axial current of the MFR. The RBSL kernels are
determined from the requirement that the MFR field for a straight
cylinder must be exactly force-free. For a curved MFR, however, the
magnetic forces are generally unbalanced over the whole path of the MFR.
To reduce this imbalance, we apply a modified Gauss-Newton method to
minimize the magnitude of the residual magnetic forces per unit length
and the unit axial current of the MFR. This is done by iteratively
adjusting the MFR axis path and axial current. We then try to relax the
resulting optimized configuration in a subsequent line-tied zero-beta
MHD simulation toward a force-free equilibrium. By considering several
examples, we demonstrate how this approach works depending on the
initial parameters of the MFR and the ambient magnetic field. Our method
will be beneficial for both the modeling of particular eruptive events
and theoretical studies of idealized pre-eruptive magnetic
configurations. This research is supported by NSF, NASA's HSR, SBIR, and
LWS Programs, and AFOSR%
\end{abstract}%



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