The Self-Similar Nature of Cosmic Plasma

One of the underlying questions about the nature of the Universe is whether it is self-similar at different scales, i.e., do structures at different scales resemble each other? For example, Wilhelm Eduard Weber (1804-1891) developed a planetary model of the atom, one of the themes in Volume 4 of the works collected and translated under the supervision of André Assis¹.

In my post Kristian Birkeland Theorized that the Universe is Electric, I wrote about the fact that Kristian Birkeland (1867-1917) had first proposed that there were giant electric currents connecting celestial bodies in the cosmos. These ideas have been developed over the years by researchers such as Hannes Alfvén (1908-1995), Carl-Gunne Fälthammar (1931-2022) and Anthony L. Peratt (1940-), under the umbrella term plasma cosmology.

Alfvén wrote a summary paper for IEEE Transactions on Plasma Physics². Here are some key points.

• The same basic laws of plasma physics hold from laboratory and magnetospheric heliospheric plasmas out to interstellar and intergalactic plasmas.

• In order to understand the phenomena in a certain plasma region, it is necessary to map not only the magnetic but also the electric field and the electric currents.

• Space is filled with a network of currents which transfer energy and momentum over large or very large distances. The currents often pinch to filamentary or surface currents. The latter are likely to give space, as also interstellar and intergalactic space, a cellular structure.

For this post, what is most relevant is the first point, i.e., that plasmas resemble each other at all known scales.

Eric Lerner (1947-), in his The Big Bang Never Happened³, recounts that already by the 1950s, top-secret research had shown a pinching effect of a current discharged through a plasma, and that attempts to control plasma in laboratories were fraught with difficulty. (They still are!)

For decades scientists had known that if a high current is discharged through a plasma, the magnetic fields created pinch the current and the plasma together…. In the early fifties scientists in the U.S., England, and the Soviet Union, working in secret, showed that indeed superhot plasma can be created and confined with such pinches. But the plasma proved extraordinarily balky. Instead of smoothly pinching to high temperatures and staying stable while fusion occurred, it bucked and bowed like a wild bronco. The fusion scientists desperately needed a way to control the unruly plasma. [p.192]

According to Lerner, the theory was provided by Alfvén:

Alfvén provided the theory. In 1950 he had collected much of his unpublished work of the past decade into a ground-breaking textbook, Cosmic Electrodynamics. Covering a broad range of problems and phenomena, it was to become extremely influential, sometimes in rather surprising ways. The book provided for the first time a detailed theoretical analysis of how electrical discharges become constricted through their own magnetic fields. He applies this analysis to two cosmic problems he had long worked on—the aurora and the solar prominences. Here Alfvén shows that the filamentary structure of both can be explained in detail by the pinch effect.

Alfvén demonstrates that the problems of fusion in the lab and the prominences in space are closely linked. From Maxwell’s laws he derives rules with which a researcher can develop small-scale laboratory models of large-scale astrophysical processes. He also discusses how such processes can be used to predict plasma behavior in the lab. [p.192]

This is where it becomes fascinating. Cosmic phenomena over huge expanses, evolving through the aeons, can be simulated in laboratories of limited size and duration:

He found that certain key variables do not change with scale—electrical resistance, velocity, and energy all remained the same…. Other quantities do change: for example, time is scaled as size, so if a process is a million times smaller, it occurs a million times faster. Thus the stately processes of the cosmos, ranging from auroras lasting hours to prominences lasting days to galaxies lasting billions of years, can all be modeled in the lab by rapid discharges lasting millionths of a second. When densities of astronomical objects are scaled down to lab proportions, their densities become those of ordinary gases.

Equally important, though, is the converse use of these scaling rules. When the magnetic fields and currents of these objects are scaled down, they become incredibly intense—millions of gauss, millions of amperes, well beyond levels achievable in the laboratory. However, by studying cosmic phenomena, Alfvén shows, scientists can learn about how fusion devices more powerful than those now in existence will operate. In fact, they might learn how to design such devices from the lessons in the heavens. [pp.192-193]

And sure enough, laboratory modeling, such as that done by Winston H. Bostick (1916-1991) started to show the kinds of things that Alfvén predicted:

By 1956 fusion scientists, still under secrecy wraps, were gathering at the international conferences of cosmic electrodynamicists. That year, Alfvén hosted the International Astronomical Union Symposium on Electromagnetic Phenomena in Cosmic Physics in Stockholm. One researcher, Winston Bostick of Stevens Institute of Technology in Hoboken, New Jersey, reported just the sort of laboratory modeling Alfvén had described. Bostick found that tiny plasmas fired at high speed toward each other pinch and twist themselves into the graceful shapes of spiral galaxies. [p.193]

So let’s have a look at Cosmical Electrodynamics, whose second edition was coauthored by Alfvén and Fälthammar⁴:

If we want to apply the results obtained in a laboratory apparatus with the linear extension of 10 cm to cosmic phenomena, we have to increase the scale by a factor of 10^8-10^9 with regard to the conditions around the earth, a factor of 10^7-10^10 for the sun, 10^12 for interplanetary space, and 10^21-10^22 for the galaxy. Perhaps it is of more interest to go the other way, i.e. to transform the cosmic phenomena down to laboratory scale, because this gives us some hint concerning the general type of the phenomena. It shows what quantities are the most important ones, and indicates to what extent it is possible to make scale-model experiments illustrating cosmic phenomena. [p.139]

Just think, if their theory is correct, one can simulate, in a relatively small laboratory, phenomena 22 orders of magnitude greater than the simulation! This is simply mind-boggling! They go on, with a table that “shows how the similarity transformation may be applied to some important domains of cosmic physics.”

Table 4.2, p.140, Cosmic Electrodynamics

The table shows some features of interest. The first is that most densities are to be considered as very high. Except in the close vicinity of the earth there is no analogy to high-vacuum phenomena. The laboratory analogy of cosmic space is not the vacuum in a tank but a highly ionized gas of a very high density. [p.139, my emphasis]

This is a remarkable conclusion. Right from a young age, we are bombarded with expressions of the form “empty space” or the “vacuum of space”. But if we accept the scaling phenomena of the table, we should understand that cosmic entities of vast extent are in fact “as dense as our most dense laboratory plasmas”. It takes some adjustment in thinking before one can grasp what is really at stake.

But that is not all. The cosmic magnetic and electric fields, along with the electric currents that surge through them, are of incredible strength. Even when scaled down to laboratory-sized numbers, they are still of such strength that laboratories are not capable of producing them. (This was written in the early 1960s, I am not sure of the capabilities of today’s laboratories.)

Still more striking than the high densities are the very strong magnetic fields in the cosmos. In fact they are so strong that at present our laboratory resources do not suffice to produce field strengths large enough for model experiments. [p.139]

The powerful magnetic fields have two important consequences. The first is that the motion of charged particles is usually of a different type from what we are familiar with in the laboratory. The radius of curvature is very small and the particles move in the direction of the magnetic field or ‘drift’ perpendicular to it….

The other consequence is that strong electric fields are easily produced by any motion across the magnetic field…. To give an example, in a reduced magnetic field of 10^6 gauss, a velocity of 3.10^5 cm/sec causes an electric field of E = 10 e.s.u. = 3000 V/cm, and in a field of 10^10 gauss the same velocity gives 30.10^6 V/cm. Thus also the electric fields in the cosmos, when reduced to laboratory scale, are often very strong. [p.139]

Finally, it should be understood that what appear to be long, drawn-out phenomena at the cosmic scale are, when scaled down to laboratory-sized numbers, incredibly short-lived:

Finally, the time-scale transformation in Table 4.2 is of interest. Solar flares, coronal arcs, and also the initial phase of a magnetic storm should be regarded as very short-lived phenomena. In fact their equivalent duration is of the order of the ignition time of an electric discharge. This means that transient phenomena are very important in cosmical physics. [p.139]

For me, the self-similarity of plasma phenomena discovered by Hannes Alfvén and his colleagues, continuing on from the pioneering work of Kristian Birkeland, is truly exciting and deserves continued research.

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1. André Koch Torres Assis, editor. Wilhelm Weber’s Main Works on Electrodynamics Translated into English. Volume IV: Conservation of Energy, Weber’s Planetary Model of the Atom and the Unification of Electromagnetism and Gravitation. Montreal: Apeiron, 2021.

2. Hannes O.G. Alfvén. Cosmology in the Plasma Universe: An Introductory Exposition. IEEE Transactions on Plasma Physics 18(1):5-10, February 1990.

3. Eric J. Lerner. The Big Bang Never Happened. A Startling Refutation of the Dominant Theory of the Origin of the Universe. New York: Times Books, 1991.

4. Hannes Alfvén and Carl-Gunne Fälthammar. Cosmical Electrodynamics. Fundamental Principles. Second edition. Oxford University Press, 1963.