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Register a new userRelative field-line helicity in bounded domains
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Models for astrophysical plasmas often have magnetic field lines that leave the boundary rather than closing within the computational domain. Thus, the relative magnetic helicity is frequently used in place of the usual magnetic helicity, so as to restore gauge invariance. We show how to decompose the relative helicity into a relative field-line helicity that is an ideal-magnetohydrodynamic invariant for each individual magnetic field line, and vanishes along any field line where the original field matches the reference field. Physically, this relative field-line helicity is a magnetic flux, whose specific definition depends on the gauge of the reference vector potential on the boundary. We propose a particular `minimal gauge that depends only on the reference field and minimises this boundary contribution, so as to reveal topological information about the original magnetic field. We illustrate the effect of different gauge choices using the Low-Lou and Titov-Demoulin models of solar active regions. Our numerical code to compute appropriate vector potentials and relative field-line helicity in Cartesian domains is open source and freely available.
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Plasma relaxation in the presence of an initially braided magnetic field can lead to self-organization into relaxed states that retain non-trivial magnetic structure. These relaxed states may be in conflict with the linear force-free fields predicted by the classical Taylor theory, and remain to be fully understood. Here, we study how the individual field line helicities evolve during such a relaxation, and show that they provide new insights into the relaxation process. The line helicities are computed for numerical resistive-magnetohydrodynamic simulations of a relaxing braided magnetic field with line-tied boundary conditions, where the relaxed state is known to be non-Taylor. Firstly, our computations confirm recent analytical predictions that line helicity will be predominantly redistributed within the domain, rather than annihilated. Secondly, we show that self-organization into a relaxed state with two discrete flux tubes may be predicted from the initial line helicity distribution. Thirdly, for this set of line-tied simulations we observe that the sub-structure within each of the final tubes is a state of uniform line helicity. This uniformization of line helicity is consistent with Taylor theory applied to each tube individually. However, it is striking that the line helicity becomes significantly more uniform than the force-free parameter.
One of the greatest challenges in solar physics is understanding the heating of the Suns corona. Most theories for coronal heating postulate that free energy in the form of magnetic twist/stress is injected by the photosphere into the corona where the free energy is converted into heat either through reconnection or wave dissipation. The magnetic helicity associated with the twist/stress, however, is expected to be conserved and appear in the corona. In previous work we showed that helicity associated with the small-scale twists undergoes an inverse cascade via stochastic reconnection in the corona, and ends up as the observed large-scale shear of filament channels. Our ``helicity condensation model accounts for both the formation of filament channels and the observed smooth, laminar structure of coronal loops. In this paper, we demonstrate, using helicity- and energy-conserving numerical simulations of a coronal system driven by photospheric motions, that the model also provides a natural mechanism for heating the corona. We show that the heat generated by the reconnection responsible for the helicity condensation process is sufficient to account for the observed coronal heating. We study the role that helicity injection plays in determining coronal heating and find that, crucially, the heating rate is only weakly dependent on the net helicity preference of the photospheric driving. Our calculations demonstrate that motions with 100% helicity preference are least efficient at heating the corona; those with 0% preference are most efficient. We discuss the physical origins of this result and its implications for the observed corona.
Context:In 2020 May-June, six solar energetic ion events were observed by the Parker Solar Probe/ISoIS instrument suite at 0.35 AU from the Sun. From standard velocity-dispersion analysis, the apparent ion path length is 0.625 AU at the onset of each event. Aims:We develop a formalism for estimating the path length of random-walking magnetic field lines, to explain why the apparent ion pathlength at event onset greatly exceeds the radial distance from the Sun for these events. Methods:We developed analytical estimates of the average increase in pathlength of random-walking magnetic field lines, relative to the unperturbed mean field. Monte Carlo simulations of fieldline and particle trajectories in a model of solar wind turbulence are used to validate the formalism and study the path lengths of particle guiding-center and full-orbital trajectories. The formalism is implemented in a global solar wind model, and results are compared with ion pathlengths inferred from ISoIS observations. Results:Both a simple estimate and a rigorous theoretical formulation are obtained for fieldlines pathlength increase as a function of pathlength along the large-scale field. From simulated fieldline and particle trajectories, we find that particle guiding centers can have pathlengths somewhat shorter than the average fieldline pathlength, while particle orbits can have substantially larger pathlengths due to their gyromotion with a nonzero effective pitch angle. Conclusions:The long apparent path length during these solar energetic ion events can be explained by 1) a magnetic field line path length increase due to the field line random walk, and 2) particle transport about the guiding center with a nonzero effective pitch angle. Our formalism for computing the magnetic field line path length, accounting for turbulent fluctuations, may be useful for application to solar particle transport in general.
The fast solar winds high speeds and nonthermal features require that significant heating occurs well above the Suns surface. Two leading theories have seemed incompatible: low-frequency Alfvenic turbulence, which transports energy outwards but struggles to explain the observed dominance of ion over electron heating; and high-frequency ion-cyclotron waves (ICWs), which explain the heating but lack an obvious source. We unify these paradigms via the novel helicity barrier mechanism. Using six-dimensional plasma simulations, we show that in imbalanced turbulence (as relevant to the solar wind) the helicity barrier limits electron heating by inhibiting the turbulent cascade of energy to the smallest scales. The large-scale energy grows in time to eventually generate high-frequency fluctuations from low-frequency turbulence, driving ion heating by ICWs. The resulting turbulence and ion distribution function provide a compelling match to in-situ observations from Parker Solar Probe and other spacecraft, explaining, among other features, the steep transition range in the magnetic spectrum.
In our earlier study of this series (Park et al. 2020, Paper I), we examined the hemispheric sign preference (HSP) of magnetic helicity flux $dH/dt$ across photospheric surfaces of 4802 samples of 1105 unique active regions (ARs) observed during solar cycle 24. Here, we investigate any association of the HSP, expressed as a degree of compliance, with flaring activity, analyzing the same set of $dH/dt$ estimates as used in Paper I. The AR samples under investigation are assigned to heliographic regions (HRs) defined in the Carrington longitude-latitude plane with a grid spacing of 45$^circ$ in longitude and 15$^circ$ in latitude. For AR samples in each of the defined HRs, we calculate the degree of HSP compliance and the average soft X-ray flare index. The strongest flaring activity is found to be in one distinctive HR with an extremely low HSP compliance of 41% as compared to the mean and standard deviation of 62% and 7%, respectively, over all HRs. This sole HR shows an anti-HSP (i.e., less than 50%) and includes the highly flare-productive AR NOAA 12673, however this AR is not uniquely responsible for the HRs low HSP. We also find that all HRs with the highest flaring activity are located in the southern hemisphere, and they tend to have lower degrees of HSP compliance. These findings point to the presence of localized regions of the convection zone with enhanced turbulence, imparting a greater magnetic complexity and a higher flaring rate to some rising magnetic flux tubes.
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