On behalf of the organizing committee and of the Royal Institute of Technology I wish you welcome to this symposium. I need not stress the importance of the subject which we are going to discuss—as participants in this symposium all of us are aware of it. You also know very well how this field has been opened by Birkeland and Störmer, by Chapman, Cowling and Ferraro, by Hale, Swann, and many others. However, it is not until the last decade that the interest in this subject has become more general. Many different research groups are active but their ideas differ very much, which gives a good reason for meeting and exchanging ideas.

This symposium is held under the auspices of the International Astronomical Union at the department of electronics of a technical university. This combination of astronomy and technical electronics has already become so familiar, that it hardly strikes us as peculiar. This shows how strongly the case for electric and magnetic phenomena in a wide variety of astrophysical problems has been proven. However, all of this is comparatively recent history. One glance at an older epoch may illustrate this point and, perhaps, may help us to take fewer things for granted during our discussions.

The general theory of magneto-hydrodynamic waves in an ideal conducting fluid embedded in a uniform field of magnetic induction, and the application of the theory to the systematic analysis of the various modes of propagation in incompressible and compressible fluids have been presented by the author in two earlier papers[1, 2]. In these papers, however, no effort was made to include the thermodynamics of the situation, which amounts to the tacit assumption that the fluid is of zero heat conductivity. In this case the resulting modes are of two kinds: isothermal (v-modes) and adiabatic (p-modes).

In this paper we first establish the conservation laws of momentum and energy for a (macroscopic) compressible fluid with finite viscosity and finite thermal and electrical conductivities, which is embedded in a uniform field of magnetic induction, and we then derive quite generally the exact (nonlinearized) equation governing the distribution of temperature in such a fluid. Next, making use of the linearized magneto-hydrodynamic wave equation in the fluid velocity, combined with the resulting heat diffusion equation and with the equation of state of the fluid, and applying the mathematical techniques developed earlier, we obtain a higher order partial differential equation in the fluid temperature from which ensue all the temperature modes.

In particular, we examine in detail the behavior of plane homogeneous waves, and it is shown that a compressible fluid with the indicated properties sustains altogether six different modes, two of which are pure shear modes, devoid of density, pressure, and hence temperature fluctuations (v-modes), while the remaining four are shear-compression waves accompanied necessarily by density, pressure, and temperature fluctuations (p-modes). The two shear modes, which are isothermal, comprise a slightly attenuated Alfvén wave, and a highly attenuated viscous mode, sometimes referred to as a vorticity mode. The four shear-compression modes have in general very complex properties, but in the low frequency and low heat conductivity case they are easily identified as (1) a modified (adiabatic) sound wave slightly attenuated; (2) a slightly attenuated modified Alfvén p-wave; (3) a highly attenuated viscous wave; and (4) a highly attenuated thermal wave governed in the main by the thermal properties of the medium.

The possibility that a simply connected perfectly conducting fluid body could generate an increasing external magnetic field by acting as a self-excited dynamo is demonstrated by exhibiting a cycle of motions that doubles the external field each cycle. The essential feature of the motion is that interior points become surface points. This requires points which were originally adjacent to become widely separated. The possibility of such motions is demonstrated and some of the conditions that might lead to their development are considered.

1. The behaviour of the magnetic field of a star was investigated by Cowling, Lamb and Wrubel on the assumption of the star as a solid body and on the assumption that the field variations caused by the extinction do not create any motions of the stellar matter. The important results obtained make possible the interpretation of magneto-hydrodynamical processes in stars only quite roughly. When motions of stellar matter caused by the electromagnetic forces are taken into account new properties may be revealed and the non-stability of the magneto-hydrodynamical processes in stars established. Entangled magnetic fields are the general expression of non-stability.

2. The mathematical criterion of a confused stellar magnetic field is given in the preceding paper from the magneto-hydrodynamical equations for an ideal incompressible fluid. The conception of a confused field as a superposition of various fields of different scales is introduced.

3. It is known that the presence of a magnetic field causes an increase of the stability of hydrodynamical processes, as compared with processes in the absence of a magnetic field. It may most probably be concluded that the extent of confusion of a magnetic field is not the same, as it happens as a result of ordinary turbulent motions in a liquid. However, owing to magneto-hydrodynamical formulae, it may be stated in the present paper that if the field confusion is considered as a superposition of fields of different dimensions and not as a field of entangled magnetic lines, no stability of the above kind can be expected.

4. The theory of a totally entangled magnetic field, as a field in a state of maximum confusion is examined. A very close similarity between a totally entangled magnetic field and the turbulent motion in a viscous liquid is established. The question of the time of extinction of a magnetic field of a star is discussed.

Note. Sections 1, 2, 4 of the paper are based upon the results obtained by the author, reported by him at the 4th Cosmological Conference. Section 3 contains unpublished results.

Recent work at the Yerkes Observatory has been concerned with the study of configurations in which the magnetic and velocity fields possess a common axis of symmetry. In those cases where the density ρ may be assumed constant, it has proved advantageous to employ a representation suggested by Lüst and Schlüter[1]: in cylindrical co-ordinates (ω, ϕ, z) let and where is a unit vector and T, P, V, and U are independent of the azimuthal angle Φ. The hydrodynamic equation may then be replaced by the pair of equations (cf. Ghandrasekhar [2]) and where Δ5 is the Laplacian operator in 5 dimensions. The equation for the magnetic field, may similarly be replaced by the pair of equations and

Comparisons are made between magneto-hydrodynamics on cosmical and on laboratory scale. Magneto-hydrodynamic waves, turbulence, the generation of magnetic fields and thermal convection are discussed and a review is given of earlier experimental investigations. The possibilities are examined of realizing cosmical phenomena of this type in the laboratory.

This paper will summarize the experimental work at the University of Chicago on the problem of the onset of thermal instability in a layer of fluid heated from below. The purpose of this work has been to test certain theoretical predictions of the Rayleigh number at which instability sets in, and to determine the type of instability which appears at the critical point. The earlier experiments of this series were done at the hydrodynamics laboratory of the University of Chicago in connexion with a program of meteorological reseach[1, 2, 3, 4]. The current work is being done at the newly organized hydromagnetics laboratory of the Enrico Fermi Institute of Nuclear Studies. This laboratory utilizes the magnet of the old Chicago cyclotron, with pole pieces 92·7 cm in diameter and a gap of 22·1 cm. The magnet was reconstructed to allow the field strength to be varied from 0 to 13,000 gauss; the field is uniform to better than 1 % over the experimental area. The new laboratory is under the administrative supervision of Professors S. K. Allison and S. Chandrasekhar; the experiments are being done by Y. Nakagawa. The theoretical investigations are primarily the work of Chandrasekhar[5, 6, 7, 8, 9, 10] and it will be convenient to review some of his results before discussing the experiments.

The ionized gas is described as a mixture of several fluids; each obeying a quasi-hydrodynamic equation of motion with additional terms describing the mechanical interaction. Particularly, two- and three-fluid models are considered. The nature of the approximations (‘quasi-neutrality’, ‘creeping diffusion’) is discussed. Conservation-laws are formulated for the case of negligible effect of mutual encounters and of pressure diffusion. These models lead to a generalization of Ohm's law; it is shown that the additional terms are of practical importance if one has three components, of which one may be neutral.

The electromagnetic state of vacuum is characterized by two vector quantities, namely E and B. They are related to current and charge density by the equations Sometimes it is suitable and possible to introduce two new quantities, H and D, so defined that the equations (1) and (2) appear in the new form (Strattonm) and with a linear relation between E and D and also between B and H. This formalism is common when dealing with fluid and solid media, and has also been introduced to ionized media of zero temperature (Nichols and Schelleng[2], Alfven[3], p. 85, Astrom[4]). Here we shall say a few words about this matter for ionized media of non-zero temperature. In this connexion we also get an opportunity to discuss the meaning of the conception of diamagnetism.

A plasma source can be used to project ionized matter across a magnetic field. The configuration of plasma observed when an electromagnetic braking action is produced by the presence of low-pressure gas (about 1 μ) in the vacuum chamber provides an insight into the manner in which magnetic-field lines can be dragged and twisted. By firing several sources simultaneously, it is possible to simulate the production of spiral galaxies and barred spirals. The paper presented here forms an extension of earlier experiments performed by the author on plasmoids[1].

Standard formulae for the electrical resistance and for the radiating properties of a fully ionized gas have been combined with pinch effect relations to obtain the stationary state radial distribution functions and current—voltage characteristics of a filamentary current. The calculations suggest that the radiation cooling permits a pinched discharge to exist, with a maximum current of about one or two million amperes.

A historical account of the subject's development is attempted. Prior to 1940, the most significant papers were those by Larmor (1919) and Cowling (1934) on dynamo theories of solar fields: by Kiepenheuer (1935) on the corona; and by Ferraro (1937) on isorotation. These indicated the importance of electromagnetic forces and were groping towards the idea of frozen-in fields. The latter idea was, however, not clearly stated before Alfvén's 1941–2 papers.

Theory since then is divided into sections concerned with mechanical effects of magnetic fields, theories of sunspots, and the nature and origin of solar magnetic fields. The first includes theories of magnetic control of support of coronal filaments and prominences (van de Hulst, Alfvén, Dungey) and theories of magnetic influence on sunspot equilibrium. The second includes Alfvén's and Walén's theories of the solar cycle, and Biermann's explanation of sunspot coolness in terms of magnetic inhibition of convection. Sunspot theories, being discussed more fully by Biermann, are considered only briefly.

Electromagnetic heating covers theories of coronal heating and flares, discharge phenomena, particle acceleration and radio emission. Many of the older theories (Alfvén's on coronal heating, Giovanelli's on flares, that of Bagge and Biermann on cosmic rays) are set aside because of their neglect of self-induction effects and inadequacy of the mechanism of conversion. The relative motion of charged particles and neutral atoms (Piddington, Cowling) is described as supplying a powerful heating effect.

As regards the magnitude of the general solar magnetic field, it is suggested that the observed value can be discarded only if decisive reasons are given. Other theories having so far proved inadequate, dynamo theories of the origin of solar fields are regarded as the most promising. These can be partial, as when a toroidal field capable of explaining spot fields is supposed to be generated from the general field (Walén and others), or when a turbulent field is supposed to be generated from a smaller regular field (Alfvén and others): or total, when a simultaneous explanation of all fields is attempted (e.g. Parker). A general appraisal is made of the different theories.

1. Brief summary of the dynamics of flare development, based on the analysis of moving picture and spectroscopic data. Some new spectroscopic data on the fine structure of emission in active regions, evidencing the peculiar character of motions in them: outbursts of corpuscules, ascending grains of continuous emission, explosive processes and shock-waves.

2. Summary of the observational data on the motions in prominences. Regular electromagnetic and turbulent motions, ‘explosive’ motions and their admissible interpretation. Some data on the coronal forms above active regions and on the possible role of hydromagnetics in their formation.

3. Some remarks on the role of hydromagnetics, admissible, from the observational aspect.

It is shown that under certain conditions hydrostatic equilibrium becomes unstable in a conducting medium in the presence of a magnetic field containing a neutral point if the gas pressure is less than a limiting value.

The motion resulting from breakdown of hydrostatic equilibrium in the solar chromosphere above complex sunspot groups could produce solar flares and cosmic ray particles.

The discharge theory has been criticized by Professor Cowling in §5·3 of The Sun, ed. Kuiper (Chicago[1]). A discharge theory requires the thickness of the accelerating layer to be only 5 m, which he finds unacceptable. This criticism is not soundly based, because no lower limit for the layer width is obtained from observation.

Secondly, Cowling invokes Lenz's law: ‘the effect of induced currents is always to oppose the change to which they are due.’ Lenz's law needs verifying for conducting fluids, however, and though it is usually true, it is shown to be false when there is a neutral point. Since Lenz's law refers to electromagnetic induction, other effects such as the pressure gradient may be omitted in this test, and then a completely rigorous proof is possible: it is shown that in an ideal fluid which is perfectly conducting, perfectly compressible and inviscid, the current density at a neutral point must become infinite.

The pressure gradient is irrelevant to Lenz's law, but it usually opposes any motion and should also be discussed. A physical picture suggests that the pressure gradient will not stop a vortical motion, but merely retard it. The related problem of equilibrium between the pressure gradient and the electromagnetic force may be discussed mathematically for the special case with two-dimensional symmetry. It is found that equilibrium requires an infinite current density at the neutral point. This is a subsidiary argument in favour of discharges at neutral points.

A hitherto undisclosed source of absorption of hydromagnetic waves, due to the presence of neutral atoms, is investigated quantitatively. In the chromosphere the rate of absorption due to this effect may be 1010 times greater than that due to ordinary viscosity.

General solar heating, due to hydromagnetic waves caused by granules, is investigated and order-of-magnitude agreement with observational data is found.

The new effect is discussed in connexion with heating near sunspots and with flares.

Prominences which extend into the million degree temperature region of the corona will, in the absence of magnetic fields, be heated up to temperatures of the same order of magnitude in the course of at most a few hours. A magnetic field of reasonable magnitude inside the prominence, will, however, be sufficient to cut down thermal conduction and turbulence to such an extent that the long life of some prominences seems understandable.

A report is given of a ten-year observational program directed toward the discovery and investigation of the magnetic fields of stars through the Zeeman effect in their spectra. The emphasis has been on the sharp-line stars of type A, of which ten have been found to show irregular magnetic fluctuations without reversal of polarity, ten others to fluctuate irregularly with occasional reversals of polarity, and six to show essentially periodic variations; of the latter group, four are large-amplitude reversers with periods near one week.