by Pyotr FRIK, Dr. Sc. (Phys. & Math.), Head of Physical Hydrodynamics Laboratory, Institute of Continuum Mechanics, RAS Ural Branch (Perm)

When Academician of the Latvian Academy of Sciences Igor Kirko came to Perm in 1972, the spectrum of conducted studies was expanded by magnetohydrodynamics (MHD), a section of mechanics which studies flows of electroconducting liquids and their interaction with magnetic fields. Today the physical hydrodynamics laboratory of the Institute of Continuum Mechanics is perhaps the only scientific division in Russia which carries out theoretical and experimental work on practically all problems in this area of knowledge, from galactic magnetic fields, stellar and planetary magnetism to applied problems associated with formation and monitoring of liquid metal flows in production conditions.

BIRTH OF A NEW SCIENCE

As far as magnetohydrodynamics is concerned, nonexpert can imply a range of phenomena which have no direct relationship with man's life and the environment. But it is not the case. The natural magnetic fields not only exist in many cosmic objects-from planets and stars to pulsars and galaxies but also largely determine their evolution. And if magnetic fields of galaxies, quasars, accretion disks and neutron stars excite interest in a relatively small circle of astrophysical scientists and astronomy enthusiasts, the similar fields of the Sun and the Earth have a direct effect on human life. The Solar magnetic field which is largely responsible for flashes causing bombardment of our planet by particle flows, complies with the eleven-year cycle of activity changing its direction to the opposite one every time upon its

completion. But the Earth's magnetic field which protects it from dangerous cosmic particles seems to be constant and unchanged. In reality it is not so, and its manifestations bear a lot of mystery. According to specialists during a whole period of history of our planet's existence, its magnetic field "turned over" several hundreds of times. The instances of these "turns" follow randomly one after another, and the interval between them varies from 10,000 to 100 mln years. During a polarity reversal, which can last for centuries, the magnetic field disappears (hence "the shield" disappears also), and it is impossible to predict them up to date.

Of course, the facts are interesting, but what hydrodynamics and conducting liquids do here? The point is that magnetic fields of celestial bodies and our planet are created by fluxes of conducting liquid which is in the form of a liquid metal in the outer core of the Earth and plasma in the convective shell of the Sun. It is interesting to note that the very problem of the origin of cosmic fields was a topmost incentive for development of magnetohydrodynamics. The Solar magnetic field was the first puzzle, and to interpret its nature the Irish physicist and mathematician, Professor of the Cambridge University Joseph Larmor was the first who in 1919 advanced a hypothesis on its possible generation by a moving conducting plasma in the convective shell of the star.

It was long assumed that the interstellar medium was vacuum. Sure enough, density of its substance makes up only from 0.1 to 1,000 atoms per cubic centimeter. When in 1937 the pioneer of research in the MHD theory Swedish scientist and specialist in plasma physics Hannes Alfven voiced for the first time a hypothesis that the interstellar medium was filled with ionized gas, the scientific community did not accept it. He supposed that if plasma filled the Universe, it was capable to conduct electrical currents but the latter gave rise to a galactic magnetic field which in its turn worked on passage of cosmic rays. Later these ideas were confirmed and are now universally recognized. Hannes Alfven has a number of other discoveries and hypotheses which form the basis of a new science, namely magnetohydrodynamics, i.e. discovery of a new type of wave motion of conducting medium in magnetic field (later named the Alfven waves), attempts to explain the formation of protuberances, solar spots, magnetic storms and aurora polaris. In 1970 the scientist was awarded the Nobel Prize, and in 1971 the USSR Academy of Sciences noted his services with its top award the Great Golden Medal named after Lomonosov.

At about the same time with the appearance of Alfven's ideas, Julius Hartmann (Denmark) carried out the first experiments in MHD, namely, studies of mercury flow resistance in the pipe under action of a lateral magnetic field.

The above-mentioned Acad. Igor Kirko was one of the founders of magnetohydrodynamics (MHD) in the Soviet Union, the initiator of scientific schools in Riga and Perm, the founder of the Magnetohydrodynamics journal. He headed the physical hydrodynamics laboratory in our institute from 1972 to 1986 and played a significant role in selection of the studied problems.

MHD-DYNAMO

The process of magnetic field generation by conducting liquid (gas) flows was named MHD-dynamo. This scientific problem formulated almost a century ago remains one of the most intriguing in modern fundamental science, first of all in hydrodynamics and astrophysics. The first self-consistent model describing the nature of solar dynamo was suggested by the American astrophysicist Eugene Parker in 1955. In the next decade a number of fundamental steps were taken for understanding of the dynamo process. Without specifying all important results of this period we shall mention the famous "Zeldovich's eight"* which he demonstrated at a conference by means of a belt taken from one of the participants and explained in general terms how a liquid

*Yakov Zeldovich-Soviet physicist, one of the creators of atomic and hydrogen bombs in the USSR.-Ed.

flow could transform into a magnetic loop to strengthen a magnetic flux. We must also mention the research of German physicists Max Steenbeck, Friedrich Krause and Karl-Heinz Radier, who proved that the key dynamo problem, i.e. positive feedback in induction equation, could be solved at a level of small-scale turbulence (the required electromotive force was created not by an ordered motion of liquid but a collective attack of chaotic small-scale vortexes). It is just the above works which were followed by rapid development of the M H D dynamo theory but exhaustive comprehension of this extremely complex nonlinear phenomenon was still a long way off. As it is impossible to perform a total mathematical modelling of the MHD dynamo up to date (statistics of interactions at different scales is required, which needs a gigantic calculation time even using supercomputers), while space observations are limited with hopes put on laboratory experiments.

But experiments are also not an easy matter. Just a few fluxes are known (and all of them have a rather complex structure) which can provide the dynamo operation, and in each such case the dynamo-effect can arise only on achieving certain "threshold" modes. Real values of critical parameters are such that the desired phenomenon can arise only in large quantities of liquid at its sufficiently rapid movement and fair electrical conductivity. Lower conductivity can be compensated by still greater sizes or velocities.

In conditions of cosmic scales the sizes and velocities are so great that dynamo works even at a very low conductivity of the medium. But under the laboratory conditions it is difficult to achieve dynamo mode. Liquid sodium is the most suitable material for such experiments. It is a dangerous material but has two great advantages, i.e. it has good electrical conductivity and is very light, its density and viscosity are similar to those of water. To reach critical parameters it is necessary to achieve the flow sizes of about a meter and velocity of about 10 m/s. The existing plants pump through tons of liquid sodium with velocities close to the designed value, which stipulates a high cost of such plants and an immense amount of consumed energy. But the listed conditions are not enough. The origin of dynamo requires a movement of a special type, i.e. liquid must move in helical trajectories.

The laboratory dynamo experiments have long remained a dream of specialists though the first attempt to realize them was made as early as the 1980s by researchers from the Institute of Physics (Riga) and Yefremov Research Institute of Electrophysical Equipment (Leningrad). The attempt ended in failure because the laboratory plant broke down in the process of approaching sought for regimes. At the end of the 1990s a new series of experimental research started all over the world. Two competitive large teams in the laboratories of Riga and Karlsruhe (Germany) succeeded in achieving the MHD dynamo effect at an interval of literally one month. Since then almost fifteen years have passed. But despite a hard work of a number of research teams only one new example of generation of a large-scale magnetic field moving by means of liquid metal appeared in all these years. The successful experiment was carried out in Cadarach (France). But not all specialists appraise it identically as dynamo was obtained only after solid magnetic particles, more precisely ferromagnetic parts, were introduced into the flux. Properly speaking, scientists have not managed yet to create a direct analog of the natural dynamo as in all three mentioned experiments solid metal parts played a key role (electric conductivity of walls in the Riga plant, guide tubes of a complex form in Karlsruhe, and ferromagnetic parts in Cadarach), which however by no means diminishes results of these experiments in development of magnetothermodynamics.

About fifteen years ago the physical hydrodynamics laboratory of the Institute of Continuum Mechanics (Perm) decided to participate in a "world race" for discovering MHD dynamo effect. (Let us point out here that at the same time preparations for dynamo-experiments were started, apart from the above-mentioned research institutions, in Los Alamos and in the universities of Madison and Maryland, USA.) Such decision was anything but simple as science at that time was financed in Russia on the "leftover" principle, which placed us on an unequal footing with our competitors. The desire to rally the research team round the "super-mission", which was in the traditions of the laboratory, won the day. We did not possess even a tenth of the financial resources available to foreign researchers and therefore strived for a great result at low expenses.

An original method was suggested in Perm, which meant abandoning the idea of dynamo realization in a stable metal flow. Instead they advanced an idea of achieving the desired effect in conditions of a pulse mode. What is it in practice? Liquid sodium is placed in a toroidal channel which gathers momentum to high speeds thus accumulating substantial reserves of kinetic energy. After acceleration the channel stops dead, and inertia forces make run liquid metal through special impeller diverters and provide intense flow with the prescribed geometry in the channel. Substantial advantages of such scheme of the experiment include a sharp drop in the volume of required liquid sodium (about 100 kg instead of several tons) and reduction of engine power (by an order of magnitude). The disadvantage lies in the fact that the scheme can realize only pulse (nonstationary) helical flow which secures the dynamo mode during a short period of time (about 1 s). But even this relatively simple configuration of the plant required long preliminary studies and theoretical works.

The idea of creation of an intense pulse flow of liquid metal in a fast-rotating channel by its sudden braking proved to be fruitful for laboratory studies of MHD-flows with moderate and high magnetic Reynolds numbers*, but it is not brought up yet to the dynamo effect. As of today the plant has already produced a number of fundamentally important results. In particular, the so-called alpha-effect was first recorded in a pulse flow of liquid sodium, which provides excitation of electromotive force in a turbulent flow directed along the magnetic field. The beta-effect was also quantitatively studied at the same plant, i.e. direct measurements of effective conductance of liquid metal in a turbulent flow (conductivity in which differs from conductivity of an immovable or slow-flowing analog). The alpha- and beta-effects are two key turbulent constituents in the dynamo theory of mean fields, on the basis of which all realistic models of cosmic dynamo are created.

Studies of spontaneous occurrence effect of the magnetic field can find quite a practical application. For example, liquid sodium has more and more widespread application as coolant in some atomic reactors. With an increase in capacity of these plants, the volumes of liquid metal increase which possesses high conductance

* Magnetic Reynolds number is a criterion in magnetohydrodynamics which determines the role of hydrodynamic effects in a magnetic field induction and is an analog of the known Reynolds' criterion, named after the British physicist and engineer Osborne Reynolds.-Ed.

and moves at a high speed. As a consequence, a magnetic field can originate spontaneously, which can change a process of heat and mass transfer in the reactor. We must foresee and prevent such possibility.

COSMIC MAGNETIC FIELDS

The problem of cosmic magnetic fields is attractive for hydrodynamics not only in the context of revealing physical mechanisms of magnetic field generation (which is a prime objective of laboratory experiments). Of no less interest are they for specialists in turbulence as the very astrophysical objects set examples of turbulent fluxes with the highest values of the Raynolds' number, a parameter responsible for a "degree of turbulization" of the flux. Besides, as applied to astrophysics it is mainly MHD turbulence in which velocity (vortex) and magnetic fields interact.

The turbulence models for limit modes not accessible for direct numerical simulation are another longstanding preoccupation of the laboratory workers. They made it possible to study in detail the behavior of a spiral MHD turbulence which is usual in cosmic systems. These models were used also in the process of computer reproduction of galactic dynamo for correct description of contribution of interstellar medium turbulence supported by supernova explosions.

It should be noted that the laboratory workers came to the problems of cosmic magnetic fields quite suddenly. For many years engaged in modelling of turbulent flows and analyzing signals generated by them, the laboratory specialists actively used a mathematical apparatus called the wavelet analysis. At the very beginning of its formation (1995), a specialized seminar on the wavelet analysis was organized within the framework of the continuum mechanics school at our institute. Among the seminar participants there were also astrophysicists, representatives of the school of Acad. Yakov Zeldovich, namely Dmitry Sokolov from the Lomonosov Moscow State University and Anvar Shukurov from the Institute of Terrestrial Magnetism and Radiowave Propagation (Troitsk), who evaluated the means of the method and suggested taking up the subject related to an analysis of magnetic fields in outer space. The tasks appeared to be of interest and resulted in close cooperation which is still in progress. An analysis of data on the solar activity was carried out in cooperation with astronomers from

the observatories of Paris and Nice, and a set of research work on the activity of solar stars was conducted in partnership with the colleagues from the Harvard University. The most productive cooperation was established with a research team of Rainer Beck from the Institute of Radioastronomy (Bonn, Germany) specializing in observations of polarized radio emission, a major source of information on galactic magnetic fields.

The data analysis provided a conclusion on the magnetic field structure both of the external galaxies and also our galaxy, i.e. the Milky Way. All of them are gigantic and at the same time compact physical systems in whose evolution the well-known natural phenomena manifest themselves. Magnetism occupies a special place among them. Magnetic fields play a key role in the formation of new stars and the cosmic climate in the already existing planetary systems. Luminescence of clusters of stars creates a bright spiral design well known from astronomical pictures. Less known is a fact that magnetic fields also form spiral structures. Among the last important results obtained by the laboratory workers together with scientists from the Lomonosov Moscow State University, the University of Manchester and the Institute of Radioastronomy in Bonn, is a multi-scale model of a galactic magnetic field generation which predicts the origin of inversions of a large-scale magnetic field and formation of spiral arms. Magnetic arms are not "tied" to gas arms, they can interpenetrate. Therefore in the process of evolution the planetary systems will enter and come out of magnetic arms. If the latter have a periodic structure, it will lead to a "seasonal" (hundreds of millions of years duration) change of the cosmic climate around planets.

APPLIED STUDIES

Despite cosmic motivation of its development magnetohydrodynamics has numerous terrestrial applications especially topical in metallurgy. The point is that electromagnetic field exerts influence on liquid metal. By changing its value and also the value of electric current passing through liquid metal we can control its flows. Scientifically the cosmic dynamo and MHD generators occupy two extreme regions in magnetohydrodynamics, where dynamo is a limit of enormous scales and heavy flows leading to generation of a field, and MHD generators are a limit of immense electric currents and strong magnetic fields which form metal flows and provide their control.

Introduction of MHD technologies to metallurgical production provides transition to pumps which are reliable and simple to control and service, raise labor efficiency and improve quality of cast metal and working conditions of the founder. Magnetohydrodynamic mixers for metals and alloys are designed for crystallization front levelling and grain refining in ingots, provide even distribution of an admixture in them, accelerate the process of alloy preparation and a higher quality of ingots.

The laboratory is carrying on works for studies and practical application of the so-called vortex flows in electroconducting liquid. The phenomenon lies in the fact that electric current passing through liquid conduc-

tor causes forces in the latter which are conditioned by interaction of the latter and its own magnetic field. In case of sufficiently strong electric currents electromagnetic forces can generate different flows of liquid metal through which this current passes.

Based on the conducted studies of vortex flows, the Institute of Continuum Mechanics worked out different MHD pumps and separators for transfer, mixing and refining of liquid metals. The absence of special electric coils for creation of a magnetic field which are sensitive to the influence of different aggressive factors of foundry production is an advantage of this equipment. Besides, due to the absence of coils such pumps can be lowered below the liquid metal level thus making them submerged. They are convenient in service as they do not need vacuum pumping during preliminary filling of the channel with metal. MHD facility with a corresponding pump has no moving parts; therefore metal does not mix with bottom sediments and is delivered cleaner to the conveyer. Besides, MHD facility provides simple control of the ingot pouring process and maximum isolation of metal from outer atmosphere, thus avoiding harmful gases in the atmosphere of the foundry shop and reducing the risk of occupational diseases.

The physical hydrodynamics laboratory worked out a new class of vortex pumps for transfer of nonferrous metals. This equipment passed experimental operation at the Berezniki Titano-Magnesium Integrated Plant and Solikamsk Magnesium Plant. The liquid aluminum mixer for preparation of semicontinuous ingots developed and manufactured in our laboratory found application at the All-Russia Aluminum-Magnesium Institute (St. Petersburg), Kamensk-Uralsky Metallurgical Works, Rossendorf Research Center (Germany) and Cidaut company (Spain).

The research works carried out in our laboratory are reflected in publications both of leading foreign periodicals (more than 10 per year in the Web of Science journals) and also national periodicals (more than 10 per year in the Russian Science Citation Index). And also survey articles published in the Uspekhi fizicheskikh nauk (Russia) and the Physical Reports (the Netherlands). Two specialized conferences were held in Perm "Perm Dynamo Days" and "Russian Magnetohydrodynamics". They aroused great interest in the Russian and international fellowship.

Today the physical hydrodynamics laboratory represents a sufficiently young team, which includes above 20 scientists. Annually new postgraduates join the team, and many of them continue their work with the laboratory even after taking a degree.

Apart from studies in the sphere of magnetohydrodynamics, the laboratory workers participate in research related to nonconducting liquid dynamics, medicine, mathematical methods of signal processing and geophysical flows.