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News notice: This fall and winter the University of Vienna is hosting a lecture series, “History and Foundations of Modern Physics,” and Christoph Lehner will present the first lecture, on Schrödnger’s equation, on October 1. Further details, including how to watch the lectures online, can be found here.

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Last month, an international group of researchers announced new observations made with the Daniel K. Inouye Solar Telescope in Hawaii that showed clear visual evidence of Kelvin-Helmholtz instability on the Sun’s surface. The instability is a swirling pattern in the Sun’s plasma linked to the movement of magnetic energy and could explain mysteries such as why magnetic energy can build up at certain points and why the Sun’s outer atmosphere is extremely hot. Beyond that, the discovery is also the latest testament to the power of magnetohydrodynamics (MHD)—the science of electrically conducting fluids—to explain and hypothesize about solar behavior.

Historian Alex Blum and physicist Arnab Rai Choudhuri note in a recent open-access article that no thorough history of MHD has apparently ever been compiled. Seeking to assemble a history of theoretical MHD, they also aim to explain certain features of the history, particularly why MHD initially emerged only slowly before it became an area of intensive work in the mid-20th century. In addition, they examine the strategies used to construct MHD, observing that, as a synthesis of the existing theories of electrodynamics and hydrodynamics, it was built around “very specific idealizations and approximations in the physics of plasmas.”

Early theorization about solar magnetism

Blum and Choudhuri find that MHD’s origins trace clearly to attempts to understand magnetic activity on the Sun. That solar activity influenced magnetic activity on Earth was well known by the 19th century. In the early 20th century, George Ellery Hale, the director of the then-new Mount Wilson Solar Observatory, concluded, based on observations of Zeeman splitting in spectral lines, that sunspots were areas of extremely strong magnetic field. He also asserted that the Sun possessed a general magnetic field, though that was not decisively shown until later. Around the same time, John Evershed, working at the Kodaikanal Solar Observatory in India, discovered that gases in the peripheral areas of sunspots flowed outwards.

It also became clear that gases on the Sun are highly ionized, forming what is now called a plasma. In 1919, the British physicist Joseph Larmor suggested that the motion of such matter in the Sun could possibly generate a magnetic field by acting as a “self-exciting dynamo.” This suggestion would become the foundation for MHD but was slow to be taken up. Still, the 1930s did see the publication of two papers in Britain that Blum and Choudhuri argue were crucial to the later development of MHD, including its theoretical structure, despite not yet including the full set of MHD equations.

The first was by Thomas Cowling. Cowling was a postdoctoral researcher under Sydney Chapman, one of the few scientists to take an interest in Larmor’s idea, which Cowling attempted to adapt to explain the magnetic fields of sunspots. Whereas an earlier effort to model streams of ionized particles moving through magnetic fields attempted to work out the complicated dynamics between electrons and ions and their interactions with the magnetic field, Cowling treated the streams as an undifferentiated ionized gas, which, Blum and Choudhuri note, became the central idealization of MHD.

Cowling also introduced another simplification, that the sunspot system was symmetrical around an axis. Blum and Choudhuri explain the technical consequences of this quite thoroughly; the upshot was that, under this assumption, Larmor’s self-exciting dynamo idea could be shown to be unworkable.

The second paper was by Vincenzo Ferraro, who had himself been a student of Chapman and set out to determine how the conducting fluid flows would affect the magnetic fields of sunspots, even if, per Cowling’s model, those flows weren’t responsible for creating and maintaining the field. It was known by this point that the Sun’s rotation was not uniform at the surface: the speed of rotation varies by latitude. This implied that the solar rotation below the surface was also nonuniform, and Ferraro wanted to work out what this nonuniform rotation would do to the magnetic field.

Ferraro, like Cowling, introduced key assumptions simplifying the equations, most importantly that the azimuthal component of the magnetic field should be zero. This work resulted in what came to be called Ferraro’s law of isorotation, but his assumption turned out to be misplaced: Eugene Parker would later demonstrate that a strong azimuthal magnetic field was necessary to explain the origin of sunspots. Significantly, for Blum and Choudhuri, Ferraro’s incorrect assumption, along with Cowling’s negative conclusion about the dynamo effect, delayed the emergence of MHD.

Alfvén’s key insight

Blum and Choudhuri stress that MHD’s acceptance was not achieved by abandoning simplifying assumptions but in choosing the “right” assumptions. As it happened, the full equations of modern MHD were formulated in the early 1940s by Swedish physicist Hannes Alfvén in two papers predicting a new kind of “electromagnetic-hydrodynamic” wave.

Alfvén’s papers analogized magnetic field lines in an ionized fluid to elastic strings, showing that the lines oscillated and supported transverse waves and that the coupling of the fluid and the field meant that the oscillations were not only magnetic but material as well. This determination that the magnetic field and ionized fluid move in concert became the core of modern MHD.

Acceptance of Alfvén’s waves in the physics community was slow, in part because it would be years before their existence was experimentally demonstrated. A bigger problem, however, was Alfvén’s immediately subsequent work applying his equations to the problem of sunspots: why their magnetic fields were so concentrated, why they were cooler than their surroundings, why they appeared in pairs of opposite polarity, and why they displayed an 11-year cycle in frequency.

Alfvén’s attempts to answer these questions were received negatively, with physicists pointing out numerous flaws to his approach. And, Blum and Choudhuri point out, few had sufficient expertise in the area to see the virtues of his work on waves through his flawed work on sunspots, and, as a result, his work inspired few followers.

Then in the early 1950s, Cowling, one of Alfvén’s most significant critics, applied Alfvén’s equations not only to phenomena already studied through that lens, such as the origin of the solar magnetic field and sunspots, but also to solar flares. In addition, he published a review article that provided a general mathematical proof of “flux freezing,” that is the interlocked movement of field lines and physical material that Alfvén derived for the case of his waves.

In so doing, Cowling also provided a conceptual anchor to help researchers and students understand MHD better. In traditional laboratory physics, magnetic fields are produced by sending a current through a coil, and so the current appears fundamental while the magnetic field is an epiphenomenon. In an astrophysical setting, it can make more sense to view the magnetic field as fundamental. As Cowling himself put it, “In the laboratory, the causal order is normally that the electric force and the conductivity determine the current flowing, and this determines the magnetic field. In cosmic masses the order must be reversed.” This conceptual shift obviated some of the main difficulties physicists had with MHD, making it, in Blum and Choudhuri’s words, “a much more attractive and easier subject to learn.”

In 1957, Cowling published a comprehensive textbook on the theory and its applications, titled simply Magnetohydrodynamics, a term Alfvén had coined in the 1940s. A book review by Walter Elsasser declared, “After a protracted infancy, the field of magnetohydrodynamics has rather suddenly entered what might be called its adolescence. This is largely due to the tremendous extension of observational material, both geophysical and astrophysical, that has become available during the past ten years or so.”

The strange estrangement of Alfvén

Providing a historical account and explanation for that “protracted infancy” is the primary objective of Blum and Choudhuri’s paper, which they accomplish with a technical rigor and sophistication that can’t be captured in a brief synopsis. The growth of MHD in the latter half of the 20th century and beyond is outside their scope. They do, however, close by highlighting a significant irony that emerged in the years following their narrative.

Alfvén went on to receive the Nobel Prize in Physics for his work on MHD in 1970. This came after a full decade during which he was nominated each year. At the same time, though, he began distancing himself from MHD. In the late 1960s he began advocating for a “second approach to cosmical electrodynamics.” In fact, in his 1970 Nobel Prize lecture, he attacked MHD—though not by that name—as “mathematically elegant” but having “very little to do with reality.” Five years later, in his introductory lecture to the 1975 Nobel Symposium on magnetospheric physics, he decried MHD approaches to solar physics as “pseudo-plasma theories.”

His alternative approaches appeared, in Blum and Choudhuri’s words, “obscure and incomprehensible” to other researchers. The Nobel laureate who had formalized the conceptual and mathematical foundations of MHD found himself unable to publish in US journals, even as the field he essentially established became the dominant paradigm for understanding the magnetic and hydrodynamic aspects of astrophysical phenomena.

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Jon Phillips
American Institute of Physics
jphillips@aip.org

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