The heritage of Hannes Alfvén

Phys. Chem. Earth, Vol. 22, No. 7-8, pp. 599-604, 1997 © 1997 Published by Elsevier Science Ltd. All rights reserved Printed in Great Britain 0079-1946/97 $17.00 + 0.00

Pergamon

PII: S0079-1946(97)00182-1

The Heritage of Hannes AlfvEn C.-G. Fiilthammar D i v i s i o n of P l a s m a Physics, Alfv6n Laboratory, Royal Institute of T e c h n o l o g y , SE-100 44 Stockholm, Sweden

Received 9 September 1996; accepted 12 December 1996

1

Hannes Alfv@nwas born on the 30th of May, 1908, in the town of Norrkping, in Sweden. Both heritage and environmental circumstances provided a foundation on which he built his achievements. Heritage, because he came from a h m i l y of high achievers, including a mother who was a pioneer as one of the first female physicians in Sweden and an uncle who was a famous composer Hugo Alfv@n . Environmental factors, because two childhood experiences had a significant influence on his intellectual development and scientific career. One was a book on popular astronomy by Camille Flammarion, which he was given at a young age and which kindled a lifelong fascination with astronomy and astrophysics. The other was the schools radio club where he was an active member and built radio receivers. This instilled in him a profound interest in electronics. It is a striking fact that the fresh perspective that he got by approaching astrophysical problems from an electromagnetic point of view was a valuable asset in his scientific work. When his book Cosmical Eleetrodynamics (Alfv~n 1950) was published, the author was by one of the reviewers, referred to as "an electrical engineer in Stockholm." His rapid academic career was marked by a doctors degree at the age of 24 and an appointment as full prolessor at the Royal Institute of Technology in Stockholm at the age of 32. As professor he was an exceptionally inspiring and generous leader, spreading fruitful ideas around him without any claim to co-authorship of publications deriving from them. His vigorous scientific activity led to the creation of a number of new professorships and departments. The three departments that most directly trace their origin to his work now form a separate entity within the Royal Institute of Technology, the Alfvdn Laboratory, founded in 1990. This, too, is part of his heritage. All of Hannes Alfv@ns scientific work reveals a profound physical insight and an intuition that allowed him to derive results of great generality from specific prob-

Introduction

As we open the first Alfvdn Conference of the European Geophysical Society we honour a man to whom our field of research owes so much. His fundamental discoveries laid essential parts of the scientific foundations of modern plasma physics and its applications, including solar terrestrial physics, to which these conferences will be devoted. Hannes Alfvdn (Figure 1) was awarded the 1970 Nobel Prize for Physics for "his contributions and fundamental

discoveries in magnetohydrodynamics and their fruitful applications in different areas of plasma physics." His scientific heritage is one of many facets. It includes the new fields of research that he opened, the powerful tools he invented and which greatly facilitate scientific work in our field, several brave new concepts, many stimulating, often controversial ideas, the vision of a new paradigm in cosmical physics the Plasma Universe and, not the least, the great inspiration that he gave to his students and colleagues all over the world. In addition to his most fundamental discoveries, Hannes Alfv@n made numerous important contributions to the physics of the magnetosphere, especially auroras and magnetic storms, as well as to solar and interplanetary physics, astrophysics and cosmology. Often his contributions were initially disregarded or opposed but vindicated later as a result of new experiments in the laboratory or measurements in space. How significant his contributions have been to the field of solar terrestrial physics is to some extent indicated by how often concepts bearing his name are mentioned at any conference in this field of science such as Alfv@n waves, Alfv~n number, Alfv@n layer etc. But only to some extent, because he also made important contributions where his role as originator is not widely known.

Correspondence to: Carl-Gunne F~lthammar 599

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C.-G. F~ilthammar

/

F i g . 1. H a n n e s A f f v 6 n , 1908 - 1995.

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The Heritage of Hannes Alfv6n lems. A paper on cosmic rays (Alfvdn 1933), which he published in Nature in his early twenties, reflects a principle that he adhered to in all of his work: Theories of cosmical phenomena must agree with what is known from laboratory experiments on the Earth, because the same laws of nature must apply everywhere.

2

Alfvdn Waves

His most well-known discovery, of what we now call AIfvdn waves, is in m a n y ways typical of his ability to achieve important general results from consideration of specific problems. In this case the specific problem was the nature and origin of sunspots and the sunspot cycle, but it led to his discovery of a new kind of waves and to the opening of a whole new field of research: magneto-

hydrodynamics. Until then electromagnetic theory and fluid dynamics had been well established but separate fields of physics. But as an "electrical engineer" Hannes Alfvdn realized that the magnetic fields observed in the sunspots must derive from electrical currents in the solar plasma, and that the currents and magnetic fields together must give rise to forces that affect the motion of this plasma, which in turn induces electric fields. He formulated this mutual interaction between electromagnetic fields and fluid motion, and the resulting waves, in an admirably simple and clear mathematical form in a Letter to Nature with the title "Existence of Electromagnetic-Hydrodynamic Waves" as shown in Figure 2 (Alfvdn 1942b). Incredible as it may seem to us today, it took many years before this discovery was taken seriously. Some of his critics maintained that if such waves existed, Maxwell would have discovered them. General acceptance came only in 1948, when Enrico Fermi acknowledged that such waves could exist, and his enormous prestige immediately swayed the attitude of the physics community. One reason for the long non-acceptance was the fact that the waves, although elegantly described in theory, were not demonstrated experimentally for several years. In Alfvdns laboratory Stig Lundquist proved their existence in mercury (Lundquist 1949) and Bo Lehnert in liquid sodium (Lehnert 1952). But the waves in liquid metals were very strongly damped, and it was not until around 1960 that Alfv6n waves were demonstrated in plasmas, about at the same time in Great Britain and in the United States. For example John Wilcox (who was later to become a well known solar physicist) generated Alfvdn waves in a laboratory plasma at the University of California, Berkeley, and confirmed their predicted propagation velocity as well as their behaviour when reflected by an obstacle (Wilcox et al. 1960). Since then Alfvdn waves have become a well known phenomenon in the laboratory as well as in space, and as we know they occur profusely in the sun, the solar at-

....

Existence

of

- E . l e c t r o m a g n e t i c - H y d r o_d y n a m _

c Waves

Ix a con¢iucting liquid is placed hz a constant magnetic "field,every motion of the 'liquid gives rise-to . :an. "~.K~r. which produoes"eleotrio currents:" O w i n g to the m .a~netio field,those currents glv~:meehanical forbes which changethe state of motion o'fthe liquid. Thus a kifid Of combined oleetromagnetis,hydrodynamic wav~ is produced which, So far as T.know, has as yet attr~to d no attontiom •The phenomenon m a y be described by the electrodynamic equations " 4r, . rot H ~ - - , C

I 4B c d4

rot E =

"

T)

=

a(E +.~

×

B);

.

together witll,the hydrodynamic equation dv 1 . ~ = .~.(~ X B ) gr~d ~ , [ where a is.theeleetri6conductivity, [~the permeability, a the mass density or the liquid, i the electriccurrent, v.the velocity of the liquid, and-~p the pressurd~: Consider.the simple case when a'=~ Go, ~ = I and • the imposed constant magnetic field'H0 i~ .homo-. gcneetm an d parallel to tlm z.axis. In order t0study a plane wave we assume that all variables dop0nd " upon the time ~ and z only. If the velocity ~ is.parallel to the z.v;xis, the Current i is parallel,to the y-axis and produces a variable magnetic field H t in the z-direction. B y elementary calculation we'obtain d'Il~ 4aa dSH" dz'

=

Ho'.

d~'

'

which .'moans a wave in the direction of the z-axis with the velocity v

_

"

W a ~ s of this sort m a y be of importance in solar physics. ,as the sun has a general magnetic field, 'and as solar matter is a good conductor, the conditions for the exist&tee of eleeta'om~gnotic-hydrodydamic waves are satisfied. If in ~ region of the sun we have 'He ffi=15 gauss and @ ~ffi0"005 gin. cm.7 ~, the velocity 'of the waves amounts to V --, 60 crn. eec.-'. This.is about the velocity Wlth which the sunspot .zone moves towards the equator during the sunspot cycle. The above values'ofH0 and 8 refer to a distance of about I0 *o cm. below the solar surface where tlie original cause of the sunspots m a y be found. Thus it is possible t h a t the smzspota ace associated with a magnetic and mechanical disturbance proceeding a s an eloctromagnotic.hyd~odyn'amic wave. " The matter is further'discussed in a p.apor which will appear in Ark'iv f6r matenta~ik, astronoml, od# fysil¢, l=I. A r . ~ N . ' I~g!.,Tolmiska HSgskolan, Stockholm. Aug. 24. .• Fig. 2. Hannes Alfv~n's Letter to N~ture, "Existence of Electroma4~netic-Hydrodynamic Waves" (Nature, 150, 405, 1942b).

C.-G. F/~lthammar

602

mosphere, interplanetary space and the magnetospheres of the Earth and other planets.

3

Magnetohydrodynamies

But the 1942 Letter to Nature meant much more than the discovery of a new kind of waves. It meant the opening of a whole new field of physics, namely magnetohydrodynamics. Combining the complexities of electromagnetism and hydrodynamics this field offers considerable challenge. This was expressed by 1948 Nobel Laureate Lord Blacket, who used to tell his students: "Electromagnetism is diffictilt, hydrodynamics is very difficult, but magnetohydrodynamics is damned difficult." At the time of its discovery, there were no known applications of magnetohydrodynamics, because plasmas rarely occur naturally on the Earth, and the technology of the 1940s had very limited capability of producing plasmas artificially. But this situation was soon to change. In the 1950s the beginning of the thermonuclear research effort led to technological developments that made it possible to generate high temperature plasmas artificially in laboratories on the Earth. And for these plasmas magnetohydrodynamics was of fundamental importance. In the same decade it became possible for man to send instruments into space. As almost all known matter beyond the Earths atmosphere is in the state of a magnetized plasma, magnetohydrodynamics became an indispensable tool in the emerging field of space physics. A special case of magnetohydrodynamics is magnetohydrostatics, which has important applications in solar terrestrial physics. Striking examples of essentially magnetohydrostatic states can sometimes be seen in solar prominences. As far as the problem of sunspots and the solar cycle is concerned, the particular solution that Hannes Alfvdn worked out has not been widely accepted, but the waves that he discovered in the process, and the field of magnetohydrodynamics that this opened, are of crucial importance in solar physics as well as in the physics of all space and astrophysicM plasmas.

4

Frozen-In M a g n e t i c Field Lines

In the case of sufficiently high electrical conductivity, one corollary of magnetohydrodynamics is the concept of frozen-in magnetic field lines. The expression originally used by Alfv~n (1942a,) was that the matter was "fastened to the lines of force." This well-known concept greatly simplifies physical reasoning about plasma physical problems, and is used profusely, but it is perhaps not always recognized as due to Alfv~n. It is a seductive concept, which has often led to careless reasoning in terms of "moving magnetic field lines."

As often stressed by Hannes Alfv6n, "motion" of magnetic field lines is an intrinsically meaningless concept, which can be given a meaning under certain restrictive conditions and should only be used with utter caution. In a rigorous definition, a state of frozen-in magnetic field lines is one where any two elements of the medium that are at one instant on a common magnetic field line will be on a common magnetic field line at any other instant. This definition does not rely on the concept of motion of magnetic field lines, but where the frozen condition in this sense holds, it can be used to "label" field lines and then define their "motion." According to classical theory of plasma conductivity, which was the only one known at the time, the frozen field condition should be easily satisfied in practically all space and astrophysical plasmas. But Hannes Alfv6n realized that the classical theory may not always apply in space plasmas. In particular, his study of the aurora, convinced him that the use of the concept of frozen-in magnetic field lines can sometimes be unjustified and dangerously misleading. In his later years he vigorously warned of unjustified use of the concept (Alfv6n 1976).

5

T h e G u i d i n g Centre A p p r o x i m a t i o n

Another contribution of far-reaching importance is the guiding centre approximation for charged particle motion. The Norwegian mathematician Carl St0rmer had studied the motion of electrons in the Earths dipole field. His object was to explain the auroral zones by tracing electron orbits from the sun to the Earth. These orbits were quite complicated, and for lack of computers it could take his assistants of the order of two weeks to calculate a single orbit. Hannes Alfv~n introduced an enormous simplification by separating the motion of the particle into a gyration transverse to the local magnetic field and a drift of the centre of this gyration, which he called the guiding centre. He used this as a tool in developing a theory of the aurora and magnetic storms, where he also analyzed the concept of a ring current in the Earths magnetic field. But when Hannes Alfv~n tried to publish this work, it was rejected by the leading journal at that time, Terrestrial Magnetism and Atmospheric Electricity, on the grounds that it did not agree with generally accepted theories. It was therefore published in the not very widely circulated Annals of the Royal Swedish Academy of sciences (Alfv~n 1939). Although the advantage of the guiding centre approximation is obvious already in the example of the Stormer orbits, which apply at cosmic ray energies, it is still much greater at the lower energies that are mostly encountered in auroral and magnetospheric physics. There, the actual orbits would not only be cumbersome to calculate, even with modern computers, but would also be less relevant than the guiding centre path.

The Heritage of Hannes Alfv~n In developing the guiding centre approximation, Hannes Alfv~n proved that the magnetic moment of the gyrating particle is invariant to a very good approximation. This became the starting point of what has since developed into the adiabatic theory of charged particle motion, which has reached a high degree of sophistication and become an indispensable tool in plasma physics. This is another example of how results of great generality have resulted from Hannes AlfvSns consideration of a specific problem, in this case the aurora.

6

T h e C r i t i c a l Ionization Velocity

A concept introduced by Hannes Alfv~n, but not widely known, is the Critical Ionization Velocity, nowadays often referred to as CIV. In developing a theory of how planets formed around the sun, and satellites around some planets (Alfv~n 1942c), he made a strange postulate. Considering neutral atoms failing toward the primordial sun, he postulated that when a particle reached a speed such that its kinetic energy was equal to its ionization energy, it would suddenly become ionized. This velocity, he called the critical velocity. The ion formed from the neutral atom would then be trapped in the magnetic field and remain at that distance from the sun where it reached its critical velocity. The strangeness of the postulate becomes obvious from realizing that when the neutral atom in this scenario collides with a resident particle (which is essentially at rest), the energy in the centre of mass system is less than the ionization energy, and ionization therefore energetically impossible. And even at higher energies the ionization yield of collisions between atoms and ions is small. Not surprisingly, the concept was met with massive disregard. But years later, in experiments with plasma and neutral gas in relative motion, Block and FaMeson found that as the relative speed reached a certain value, the neutral gas was rapidly ionized (Fahleson 1961). And this value of the relative speed turned out to be the one postulated by Alfv~n. Since then, the phenomenon has been found to occur in plasma experiments of many configurations and found to constitute an unwanted velocity limitation in certain thermonuclear experiments. It was most clearly demonstrated in experiments by Danielsson and Brenning (1970, 1975) in Hannes Alfv6ns laboratory. In space the phenomenon has proved to be more elusive. It seems to be the only explanation so far of the anomalous ionization of the Apollo 13 Lunar impact cloud (Lindeman et al. 1974). More importantly, its existence in space plasma has been convincingly demonstrated in one active experiment Haerendel (1982) but failed to show up in others. Therefore, it still remains to be determined precisely under which conditions the phenomenon occurs in space and astrophysical plasmas.

603

It took a long time before the phenomenon was explained theoretically (Sherman 1969). The explanation is, essentially, that an instability transfers part of the energy residing in the relative motion into energy of the electrons, which can then ionize very efficiently.

7

Electric fields

In the early years of the space age it was generally believed that space plasma could be described in terms of ideal magnetohydrodynamics. As a consequence it was thought that the electric feld, in case anybody were interested, could be calculated from the MHD equations. This view was challenged by Hannes Alfv~n, who strongly emphasized the importance of making direct measurements of electric fields in space (e.g., Alfv~n 1967a). Encouraged by him, his student Ulf Fableson did pioneering work on the double probe technique for measuring electric fields in space plasma (Fahleson 1967). And indeed, when direct measurements were finally made, it was found that the electric fields were much more complicated than foreseen in any theory. An example is the very strong, irregular and rapidly varying electric fields above the aurora. The observed contrast between the "turbulent" auroral electric fields and the weak and quiet fields in the subauroral plasma illustrates another concept introduced by Hannes Alfv~n, namely passive and active plasmas (Alfv~n 1981). Passive plasmas, among which he would count the subauroral plasma, carry little or no electric current and behave nearly classically. In contrast, active plasmas are those which carry electric current and are characterized by inhomogeneity in space, variability in time, "anomalous" behaviour and often by strong electric fields, including magnetic-field aligned components. Hannes Alfvdn emphasized that ideal magnetohydrodynamics and the validity of the frozen field condition could be violated locally by electric field components along the magnetic field. The existence of such components used to be considered impossible, because the essentially collisionless motion of electrons and ions in dilute space plasmas would cause any such components to be "shorted out." Therefore, no attention was given to his suggestion (Alfv~n 1958), that magnetic-field aligned electric fields, perhaps in structures called electric double layers, exist above the ionosphere and cause the downward acceleration of auroral primary electrons. Later Hannes Alfv6n and Carl-Gunne F~ilthammar (1963) suggested a specific mechanism for supporting magnetic-field aligned electric fields: the magnetic mirror effect in a collisionless plasma. Only after very extensive evidence from space measurements and active experiments, the existence of magnetic-field aligned electric fields became generally

6O4

C.-G. F~lthammar

accepted a n d is now considered a very i m p o r t a n t aspect of auroral electrodynamics.

8

Other contributions

Some of H a n n e s Alfvdns c o n t r i b u t i o n s were never generally recognized. For example, already in his early s t u d y of cosmic rays (Alfvdn 1933), H a n n e s Alfv~n concluded t h a t there m u s t exist a galactic m a g n e t i c field, b u t this proposal was generally dismissed, because space was considered to be a v a c u u m , u n a b l e to carry any current. Of course, it has later b e c o m e well established t h a t the galactic magnetic field does exist, b u t w i t h o u t recognition of Hannes Alfvdn's original proposal. It is also i n t e r e s t i n g to note t h a t Hannes Alfvdn (1941) used the observed scale height of the solar corona to conclude t h a t t h e corona m u s t indeed have a t e m p e r a t u r e of t h e order of a million K in a g r e e m e n t with Edldns identification of coronal spectral lines as due to highly ionized iron. Some of Hannes Alfvdns ideas are still unaccepted or controversial. One example is the concept of a special kind of p a r t i a l c o r o t a t i o n at a velocity equal to two t h i r d s of the Kepler velocity (Alfvdn 1967b). He introduced this concept p r i m a r i l y in an a t t e m p t to explain in great detail t h e s t r u c t u r e of the S a t u r n i a n ring system. B u t it also led h i m to predict t h a t Uranus would prove to have a ring system. He was u n a b l e to have this prediction accepted for publication, b u t the prediction proved correct. A n o t h e r e x a m p l e is the concept of s y m m e t r i c cosmology, which implies t h a t the Universe m a y consist of equal a m o u n t s of p l a s m a a n d a n t i p l a s m a , separated by t h i n b o u n d a r y layers, where intense a n n i h i l a t i o n takes place (Alfvdn a n d Klein 1962, see e.g., Alfv6n 1967c). T h e rad i a t i o n from this a n n i h i l a t i o n is unobservable, because the low density a n d s m a l l spatial size of the b o u n d a r y regions m a k e the resulting r a d i a t i o n too weak to be detected at t h e position of the E a r t h . These regions are analogous to the Leidenfrost layer formed u n d e r a drop of water on a h o t p l a t e .

9

Concluding Remark

Finally, I wish to emphasize t h a t Hannes Alfvdn has c o n t r i b u t e d to the progress of our field of research not only by his own work, b u t also t h r o u g h the extraordin a r y i n s p i r a t i o n t h a t he gave to his m a n y s t u d e n t s as well as to colleagues all over the world. It is now j u s t over a year since Hannes Alfvdn passed away, on April 2, 1995. T h i s left his m a n y friends with a feeling of great loss b u t also of deep g r a t i t u d e for all t h a t he has m e a n t as a scientist a n d as a friend. And his own scientific discoveries will r e m a i n a lasting heritage.

References Alfv6n, H., Origin of Cosmic Radiation, Nature 131,619, 1933. Alfv6n, H., A Theory of Magnetic Storms and of the Aurorae, Kgl. Sv. Vet. Ak. Handl., Tredje Set., Band 18, No 3, 1939. Alfv~n, H., On the Solar Corona, Arkiv ]r Matematik, Astronomi och Fysik, 27A, No. 25, 1941. Alfv6n, H., On the Existence of Electromagnetic-Hydrodynamic Waves, Arkiv ]r Matematik, Astronomi och Fysik, 29B, No. 2, 1942a. Alfv6n, H., Existence of Electromagnetic-Hydrodynamic Waves, Nature, 150, 405, 1942b. Alfv~n, H., On the Cosmogony of the Solar System, Stockholms Obs. Annaler, Band 14, No. 2, 1942c. Alfv6n, H., Cosmical Electrodynamics, Clarendon Press, Oxford 1950. Alfv6n, H., On the Origin of the Solar System, Oxford University Press, 1953. Alfv6n, H., On the Theory of Magnetic Storms and Aurorae, Tellus, 10, 104, 1958. Alfv6n, H., On the Importance of Electric Fields in the Magnetosphere and Interplanetary Space, Space Sci. Rev., 7, 140, 1967a. Alfv~n, H., Partial Corotation of a Magnetized Plasma, Icarus, 7, 387, 1967b. Alfv6n, H., Antimatter and Cosmology, Scientific American 216, 106, 1967c. Alfv6n, H., On Frozen-in Field Lines and Field-Line Recomaection, J. Geophys. Res. 81, 4019, 1976. Alfv~n, H., Cosmic Plasma, Astrophysics and Space Science Library Vol. 82., D. Reidel, Dordrecht, Holland, 1981. Alfv6n, H., and Arrhenius, G., Evolution of the Solar System, NASA Sp-345, National Aeronautics and Space Administration, Washington,D.C., 1976. Alfv6n, H., and F~iltharnmar, C.-G., Cosmical Electrodynamics, Fundamental Principles, Clarendon Press, Oxford 1963. Alfv~n, H., and Klein, O., Matter-Antimatter Annihilation and Cosmology, Arkiv f. Fysik, Band 23, No. 19, 1962. Danielsson, L., and Brenning, N., Experiment on the Interaction between a Plasma and a Neutral Gas, Physics of Fluids, 13, 2288, 1970. Danielsson, L., and Brerming, N., Experiment on the Interaction between a Plasma and a Neutral Gas - II, Physics of Fluids, 18, 661, 1975. Fahieson, U., Experiments with Plasma Moving Through Neutral Gas, Phys. Fluids, 4, 123, 1961 Fahleson, U., Theory of Electric Field Measurements Conducted in the Magnetosphere with Electrical Probes, Space Sci. Rev., 7, 238, 1967. Haerendel, G., Alfv~ns Critical Velocity Tested in Space. Z. Natnrforschung, 37a, 728, 1982. Lehnert, B., Magneto-hydrodynamic W'aves in Liquid Sodium, Phys. Rev. 94, 815, 1954. Lindeman, R., A., Vondrak, R., R., Freeman, J., W., and Snyder, C., W., The Interaction Between an Impact-Produced Neutral (3as Cloud and the Solar Wind at the Lunar Surface, J. Geophys. Res., 79, 2287, 1974. Lundquist, S., Experimental Demonstration of MagnetoHydrodynamic Waves, Phys. Rev., 76, 1805, 1949. Sherman, J., C., Some Theoretical Aspects of the Interaction between a Plasma Stream and a Neutral Gas in a Magnetic Field, Report TRITA-EPP 69-29, Dep. of Plasma Physics, Royal Institute of Technology, 1969. Also p. 315 in Proc. Nobel Symposium No.12, Almqvist and Wiksell, Uppsala, 1972. Wilcox, J., Boley, F., I., and De Silva, A., W., Experimental Study of Alfv~n Wave Propagation, Phys. Fluids, 3, 15, 1960.