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Examining solar corona formations has prompted Paul Bellan, a Caltech professor of applied physics, along with his previous graduate pupil Yang Zhang (PhD ’24), to uncover a novel equilibrium state of the magnetic field alongside its corresponding plasma. The solar corona, which is the outermost layer of the Sun’s atmosphere, possesses a significantly lower density than the Sun’s surface yet is a millionfold hotter. The corona is made up of powerful magnetic fields that confine plasma, a gaseous mixture of charged particles (electrons and ions). The newly discovered equilibrium, termed a double helix, is applicable not only to the solar corona but also to considerably larger astrophysical structures like the Double Helix Nebula, found near the heart of the Milky Way galaxy.
Solar corona formations, including flares, frequently manifest as magnetic flux ropes: twisted tubes composed of plasma-filled magnetic fields. This configuration can be imagined as a plasma-filled garden hose with a helical stripe spiraled around it. An electric current traverses the length of the hose, with the helical stripe indicative of the twisted magnetic field. Given that plasma carries an electric charge, it conducts currents and is effectively “frozen” into magnetic fields.
Magnetic flux ropes emerge in a variety of contexts, ranging from the human scale—such as in laboratory settings—to the astronomically large: solar flares that extend several hundred thousand kilometers. Astrophysical entities featuring magnetic flux ropes can extend across hundreds or even thousands of light-years.
Within a large laboratory vacuum chamber, Bellan and Zhang (currently a NASA Jack Eddy postdoctoral fellow at Princeton) created replicas of solar flares measuring between 10 and 50 centimeters in length. “We set up two electrodes inside the vacuum chamber, equipped with coils generating a magnetic field that spans the electrodes. We then apply high voltage across these electrodes to ionize the initially neutral gas, resulting in plasma formation,” Yang elaborates. “This resulting magnetized plasma configuration naturally assembles into a braided structure.”
This braided formation consists of two flux ropes interweaving around each other to create a double helix structure. During the experiments, this double helix was noted to exist in a stable equilibrium—in essence, it maintains its structure without a tendency to twist tighter or untwist. In a recent paper, Zhang and Bellan showcase that the stable equilibrium of these double-helix flux ropes can be comprehended, analyzed, and accurately predicted through mathematical means.
Although the characteristics of single flux ropes are well-documented, braided flux ropes were not thoroughly understood—particularly configurations in which the electric currents flow in the same direction along both braided segments. Researchers have previously modeled the alternative scenario—where currents flow in one direction in one flux rope and in the reverse direction in the other—but this configuration is deemed unlikely in nature.
The same-current configuration is especially critical because it is prone to kinking and expansion propelled by hoop forces—phenomena noted in braided solar structures as well as in laboratory experiments. Such kinking and expansion are not expected to occur when currents flow in opposing directions along the braided strands (a “no-net-current” state).
Previously, scientists presumed that braided flux ropes where the strands carry current in the same direction would always merge, due to the magnetic attraction of parallel currents. However, in 2010, researchers at Los Alamos National Laboratory discovered that these flux ropes instead repel each other as they approach.
“Clearly, there was something more complex occurring when the flux ropes are braided, and now we have elucidated what that is,” Bellan remarks. “When electrical currents traverse two helical wires that entwine to form a braided structure, as observed in our laboratory, the components of both currents flowing along the lengths of the wires are parallel and attractive, but those components flowing in the wrapping direction are anti-parallel and repulsive. This combination of both attractive and repulsive forces entails a specific helical angle at which these opposing forces counterbalance, yielding an equilibrium. If the helical flux ropes twist more tightly, excessive magnetic repulsion occurs; if they twist more loosely, excessive magnetic attraction does. At the critical twist angle, the helical structure attains its minimal energy state, or equilibrium.”
The subsequent objective was to formulate a mathematical model for this behavior—an endeavor that had not previously been undertaken. Utilizing what Bellan refers to as “brute force mathematics,” Zhang devised a series of equations applicable to multiple flux tubes in varying configurations, including braided ropes, and demonstrated that a state exists where the attractive and repulsive forces balance each other, leading to equilibrium. “As an unanticipated benefit, Yang is able to compute the magnetic fields both inside and outside the flux ropes, as well as the current and pressure within them,” Bellan states, “providing a comprehensive overview of these braided structures’ behaviors.”
Zhang validated his mathematical model against the Double Helix Nebula, an astrophysical plasma entity situated 25,000 light-years away from Earth, covering a 70 light-year expanse of space, to ascertain whether the equations could also characterize a vast model as effectively as they did the structures developed in the laboratory by him and Bellan. “What was particularly remarkable about this calculation is that Yang didn’t require extensive knowledge about the nebula,” Bellan shares. “By merely understanding the diameter of the strands and the periodicity of the twist—figures that can be observed astronomically—Yang successfully predicted the angle of twist that resulted in an equilibrium structure, which aligned with the observations of this nebula. One of the most thrilling aspects of this research is that magnetohydrodynamics, the theory encompassing magnetized plasmas, proves to be remarkably scalable. Initially, I believed that magnetic structures at varying scales were qualitatively similar; however, given their vastly different sizes, they couldn’t be described by the same equations. It turns out that this is not the case. What we observe in laboratory experiments and in solar and astrophysical observations is governed by the same equations.”
The paper, entitled “Magnetic Double Helix,” was published in Physical Review Letters. The research was supported by the National Science Foundation.
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