THE PROBLEM OF STRONG MAGNETIC FIELDS AND THE WORK OF P. L. KAPITSA

L. G. Dorfman, Leningrad.

Introduction

It will hardly be an exaggeration to say that magnetic phenomena still constitute the least developed field of physics. Recent decades have revealed many new magnetic phenomena and have shown the closest connection of magnetism with the most fundamental laws governing the structure of atoms and molecules; questions of the structure of metals and questions of chemical valence have turned out, in essence, to be almost magnetic questions. All these data have broadened the horizon of what had seemed to many an almost barren and “narrow” field of magnetism, but they have not explained the accumulated experimental material.

One of the chief difficulties in the investigation of magnetic phenomena is their relative smallness. Leaving aside ferromagnetic phenomena, it must be said that magnetic properties, for their study, require extraordinarily refined means. Most of these phenomena usually begin to be observable in magnetic fields of strength \(10\,000\)—\(20\,000\) gauss, whereas the strongest fields accessible to investigators do not exceed \(30\,000\)—\(40\,000\) gauss. The study of the action of a magnetic field on various processes can be the more fruitful the wider the range of fields that can be varied. Therefore, obviously, magnetic investigations can develop in two directions: 1) in the direction of increasing the sensitivity of methods so that

to be able to observe magnetic phenomena already in weak fields, and 2) toward increasing the strength of magnetic fields. The second path is all the more interesting because in extremely strong magnetic fields we may expect the manifestation of new properties, of qualitatively new phenomena. Indeed, one may confidently expect that in a field of \(10^6\)—\(10^7\) gauss we would be able to observe magnetic saturation in many paramagnetic substances; further, as may be predicted from magneto-optical data, fields of this order of magnitude are capable of causing the most profound perturbation of the motion of electrons in atoms and molecules. As a result, the problem of obtaining strong magnetic fields is of enormous interest.

By what means, then, can one hope to obtain such strong fields? Increasing the current strength in modern electromagnets or changing the shape of the pole pieces cannot yield any substantial results; here the maximum is a field of \(7 \times 10^4\) gauss, but in a volume of about \(1\ \mathrm{mm}^3\), i.e. it is practically impossible to make use of it. This volume can be increased only by significantly increasing the dimensions of the electromagnet itself. At present, in the Cotten laboratory in Paris, according to the calculations of Cotten and P. Weiss, a gigantic electromagnet weighing \(100\ t\) is being completed, the transverse section of whose cores is \(1\ \mathrm{m}^2\). In this electromagnet it is expected to obtain \(100\,000\) gauss in a volume in which it will be quite convenient to investigate various substances. In all these electromagnets their field maximum is limited by the saturation of iron or iron-cobalt.1 One way of increasing the field would be to find other materials for the cores. But it is still unknown whether ferromagnetic substances exist outside the family of metals of the iron group. There is reason to think that ferromagnetism exists among the group of the so-called rare earths, but their study has so far been hindered by the difficulty of obtaining these substances in the metallic state. Obtaining them in large quanti-

THE PROBLEM OF STRONG MAGNETIC FIELDS

…substances is in any case extremely difficult, in view of their rarity and value. Even if ferromagnetic metals were found among these substances, it may be said almost with certainty that replacing iron (or Fe—Co) by them in ordinary electromagnets and even in Cotton’s electromagnet would increase the magnetic field by no more than up to \(200—400 \times 10^3\) gauss. Although this path undoubtedly is of very great interest, for reasons of a material nature none of the researchers can yet follow it.

But if in electromagnets with a core the upper limit of the field is assumed to be the saturation value of the core material, then the possibilities of generating a field by means of a solenoid without a core are in principle unlimited. For this, however, enormous currents are required, causing considerable heat evolution. In such a case the question of cooling the solenoid becomes cardinal. The construction of a solenoid already for \(25—45 \times 10^3\) gauss presents serious technical difficulties. Delandre and Perot constructed a solenoid which, in a volume of about \(0.1\ \mathrm{cm^3}\), gave a field up to 60,000 gauss. The expenditure of energy was about 500 kW. Further improvement was proposed to be achieved by various means. Upon the discovery of the phenomenon of superconductivity, it was considered possible to make the solenoid of a superconductor, but this idea proved utopian, for superconductivity disappears completely already in very small fields (100—200 gauss). Another idea was natural, first expressed by Perot, of cooling the solenoid with liquid air. The very lowering of the temperature to \(-180^\circ\ \mathrm{C}\) should have reduced the resistance of the winding approximately by half. Fabry subjected this idea to a careful calculation and showed, however, that in order to obtain \(100 \times 10^3\) gauss in a solenoid of internal diameter \(1\ \mathrm{cm}\), the consumption of liquid air would be \(24\ \mathrm{l/sec}\) at a current-source power of 400 kW. Consequently, the idea of using liquid air is likewise impracticable in practice.

P. L. Kapitza and Wall took a different path. They abandoned the idea of creating magnetic fields lasting a long time and turned to the creation of the strongest instantaneous magneti—

fields. Since almost all molecular processes are established approximately within \(10^{-8}\)—\(10^{-12}\) sec, it is sufficient if the field exists for \(10^{-3}\) sec, so that these processes already occur exactly as in a constant field. Of course, the very method of measuring fields and observing phenomena must in such a case be adapted to small time intervals.

The creation of powerful instantaneous discharges can, of course, be accomplished by the most varied methods. A field of 1,000,000 gauss would require 50,000 kW. If, however, the field is created for short intervals of time, then one can manage with a source of considerably smaller power; for this it is only necessary that, in the intervals between the operation of the solenoid, energy be accumulated in some way, and then, during the discharge, the accumulated reserve be released.

The simplest of such methods is the method of discharging a capacitor, first carried out (although in an extremely imperfect form) by Wills. In his apparatus there were several capacitors, each of 50 \(\mu\mathrm{F}\) (at a voltage of 2,000 V). These capacitors were charged from a small generator (20 W), connected in series with a storage battery up to 2,200 V. A large resistance was included in the charging circuit, in order to avoid an excessive rise of the current during charging. The charging lasted several minutes. Then the capacitors were discharged through a solenoid located in oil. In order to avoid destruction of the solenoid, owing to the enormous mechanical forces arising between the turns in Wills’s apparatus, the solenoid was fastened in a special frame. The current in the solenoid and the voltage were measured with an oscillograph. However, Wills’s apparatus had two serious shortcomings: first, no measures were taken to ensure that the current in the oscillograph changed in the same way as in the solenoid, i.e. there was no guarantee that the oscillograms corresponded to the current; and, second, a rapidly alternating oscillatory discharge was obtained, which could not be used for any investigations.

According to the calculations of P. L. Kapitsa, the method of capacitor discharge could be applied for generating strong insta-

...fields, and this would require a capacitance of \(20\,\mu\mathrm{F}\), charged to \(50\,000\ \mathrm{V}\). The other two methods were successfully proposed and carried out by P. L. Kapitsa.

The first method consists in the instantaneous discharge of storage batteries of special construction. Let us turn to a more detailed description of it.

Method of Discharging Storage Batteries

To obtain short and powerful discharges it was necessary to construct a special storage battery. Each battery consisted of 71 lead plates, \(35 \times 35\ \mathrm{cm}^2\) in area and \(1.5\ \mathrm{mm}\) thick. These plates were separated from one another by ebonite plugs. Along the outer edge, between the plates, there were also narrow rubber gaskets. Thus the space between two plates constituted, as it were, a flat vessel, closed on two sides by rubber and with a rubber bottom, filled with a 30% solution of sulfuric acid. Each lead plate bounded two neighboring vessels. Each vessel constituted a storage cell, so that when current was passed through the battery each lead plate was charged positively on one side and negatively on the other. The thickness of the lead served as the connecting conductor between the separate cells. Since the current passed through thin layers of acid and through the lead plates perpendicular to the surface, the resistance of such a battery proved to be extremely small—\(0.02\ \Omega\). There were 4 such batteries, and they were connected with one another in parallel. They were charged by a current of \(2\)--\(3\ \mathrm{A}\) at \(220\ \mathrm{V}\). On discharge it was possible to obtain about \(1{,}000\ \mathrm{kW}\), the current reaching \(7{,}000\)--\(10{,}000\ \mathrm{A}\).

In studying the variation of the discharge current with time for different resistances of the conductor by which the circuit was closed, it turned out that with an external resistance of \(0.025\ \Omega\) it was possible, during the first \(0.01\ \mathrm{s}\), to obtain considerable power, but the current fell rapidly. With a resistance greater than \(0.025\ \Omega\), the current fell more slowly, but the power was smaller.

The first difficulty in these works was the necessity of rapidly switching on and off a current of the order of 10,000 A. This difficulty was overcome in the following way. First the batteries were charged. The circuit from the accumulators to the solenoid contained one special switch and, in series with it, a second special switch shunted by a thin wire. The switches were very complex mechanisms, in which brushes consisting of several copper strips could be brought into contact with copper plates extremely quickly. A whole series of mechanical devices prevented the brushes from rebounding after contact, ensuring precision of motion. The first switch, by means of a pawl and a lever, was connected with the second in such a way that the closing of the first switch instantly entailed the closing of the second as well, i.e. the discharge of the accumulators through the solenoid. Then the second switch automatically interrupted the connection again at once, and the current rushed into the thin shunt. From the gigantic current the shunt melted within 0.01 sec, after which the current was interrupted completely. The closing of the first and second switches lasted \(1/40\) sec. The apparatus operated so precisely that simultaneity of switching could be ensured with an accuracy of up to 0.0001 sec. Serious attention was paid to the resistance of the switches and the lead-in cables; it was made equal to \(0.0016\,\Omega\). Thus only about 7–10% of the current was lost in the wiring.

By this method P. L. Kapitza succeeded in obtaining fields of the order of 500,000 gauss in a solenoid with an internal cross-section of about \(1\,\mathrm{mm}^2\) for \(0.003\) sec. In a volume of about \(2\,\mathrm{cm}^3\) one could have about 80,000 gauss, which already represented an enormous success in comparison with the fields obtained in ordinary electromagnets.

The generation of such strong instantaneous fields required a special methodology for measuring the currents, voltages, and the fields themselves. The measurements were made by means of special oscillographs. We shall return to this question below.

As was already stated in the description of Ull’s apparatus, the enormous currents flowing through the solenoid cause in

PROBLEM OF STRONG MAGNETIC FIELDS

extremely large mechanical forces (interaction between turns). This circumstance presented a serious obstacle. When P. L. Kapitsa in 1925 installed an even more powerful apparatus (see below), the solenoids were shattered almost at every experiment. Only thanks to an extremely ingenious construction of the solenoid was it finally possible to overcome this difficulty as well. We shall also return to the description of the solenoid later.

We shall now turn to another method for producing strong fields, likewise carried out by P. L. Kapitsa—the method of short-circuiting a generator.

The Method of Short-Circuiting a Generator.

In order to create a field of the order of 1,000,000 gauss, it is necessary to have a reserve of energy 50–100 times greater than the energy reserve of the accumulator battery described above, i.e., about 50,000 kW. Moreover, the accumulators deteriorated comparatively quickly. Finally, it is very difficult to switch on and off sharply and definitely a direct current of such enormous strength.

A far more suitable source of energy may be a generator short-circuited for a brief interval of time. The mechanical energy accumulated by the rotor is discharged at the moment of closing; the rotor is braked, and an enormous current runs through the circuit. In order to have a sufficient amount of energy, the generator must be designed for a steady power of 2,000 kW. In order to switch the current on and interrupt it easily, the generator must be an alternating-current generator; in that case switching on and off can be carried out at the moments when the current curve passes through zero.

It is evident that, for the problem at hand, the design of the generator must be such that: 1) the current curve has a flat maximum (i.e., the current is constant for a certain interval of time), 2) at the moment of short-circuiting a very large current arises, then slowly decreasing. Both these features, characteristic of a special generator capable of serving for the production of instantaneous strong

...currents sharply contradict the requirements imposed on ordinary generators. Precisely these two characteristic features distinguishing the given generator are regarded as defects in ordinary electrical engineering. These defects had to be brought to the point of hypertrophy—such was the designer’s task. This task was solved by P. L. Kapitsa himself (an electrical engineer by training), together with Eng. M. Kostenko, Prof. Miles Walker, and others, and the generator was built by the Vickers company.

With rational calculation it proved possible to reduce considerably the constant power of the machine, bringing the instantaneous maximum power during a short circuit up to 220,000 kW.

The flat maximum of the current curve is attained by a quite definite ratio of the windings. The winding consists of two parts.

The mechanical strength of the machine is very important, since at the moment of short circuit gigantic forces develop. In addition, the apparent resistance (impedance) of the machine had to be reduced to a minimum. Since the generator is short-circuited on a solenoid, whose apparent resistance is approximately equal to the apparent resistance of the winding, the machine gives only 110,000 kW, and of these only about 55,000 kW can be used in the solenoid. At the moment of short circuit the rotor speed decreases by 10%, and, consequently, 20% of the kinetic energy is drawn off. The machine is set in motion by an 80 HP direct-current motor mounted on the same shaft as the generator rotor.

An extremely serious obstacle was encountered in the fact that at the moment of short circuit a very strong elastic wave arises, which, despite a number of measures taken, shakes the laboratory building. This difficulty was circumvented with rare ingenuity. The solenoid and measuring instruments were placed about 20 m away from the generator, to which a thick cable was laid. Since the very process of recording the current and of the other measurements lasts, like the short circuit itself, about 0.01 sec, the elastic wave, traveling through the ground at a speed of 2,000–3,000 m/sec, does not yet have time to reach the instruments when the experiment is already over, the photographic records have been made, etc. After several

THE PROBLEM OF STRONG MAGNETIC FIELDS

the circuit is closed every few minutes, but again the wave does not have time to interfere with the experiment. The laboratory of P. L. Kapitza in Cambridge is housed in a special building. In order to avoid accidents, at the moment when the generator is switched on, the doors of the laboratory are automatically closed by special electromagnetic mechanisms and signal lamps are lit.

The most serious question here, as in the method of discharging accumulators, is the question of the design of the switch and of the synchronizing devices. In practice it is impossible to switch the current on and off exactly at the moment when the current curve passes through zero. It is enough to deviate by 0.0003 sec in one direction or the other already to encounter a current of 3,000–6,000 A. If this current is interrupted without an arc, the accumulated energy will charge the generator to a high potential, which may lead to a breakdown of the insulation of the winding. It is therefore necessary to connect, at the moment of switching off the current, a capacitance of 50 μF. The brushes of the switch begin to move away from one another somewhat ahead of time so that an arc is struck, which then dies out after 0.0005 sec without causing harm. There then continues a weak oscillatory discharge.

The switch must operate with an accuracy of up to 0.0003 sec with respect to the zero moment. In order to move apart brushes weighing 1 kg over a distance of 0.5 mm in not more than 0.0003 sec, they must be given an acceleration 1,000 times greater than the acceleration of gravity, i.e. a force of the order of 1 t must be applied. These few considerations already show what difficulties had to be overcome in designing the switch. Moreover, the very manufacture of it from special steel requires exceptional care. We shall not enter into a consideration of the details of this masterpiece. It is interesting to note yet another difficulty: considerable heating of the solenoid changes its resistance, and hence the current regime, and the synchronization may be disturbed.

The moment of switching the current on and off is connected in time with a whole series of manipulations, such as: the release of falling pla-

plates of the oscillographs and by the inclusion of a whole series of safety relays. All this works without fail.

We now turn to the method of measuring currents and fields.

Measurement of Currents and Fields.

P. L. Kapitsa used an ordinary type of Duddell oscillograph for measuring both current strength and voltage. The current strength was measured by a shunted oscillograph. For measuring the voltage, another oscillograph was used, in whose circuit an additional resistance of \(300\ \Omega\) was included.

The oscillographs, however, had to be constructed anew so that they would meet the requirements of the installation.

There were two such requirements: first, the current strength in the oscillograph had to vary in the same way as in the solenoid, and, second, the oscillograph had to record extremely rapid changes, i.e. it had to be designed for a frequency of \(20\,000\)—\(30\,000\) oscill./sec.

The condition satisfying the first requirement follows from the equation:

\[ ir + l\frac{di}{dt} = JR + L\frac{dJ}{dt}, \]

where \(i\) is the current strength in the oscillograph, \(J\) is the current strength in the solenoid, \(r\) is the resistance of the oscillograph, \(R\) is the resistance of the solenoid, \(l\) is the self-inductance of the oscillograph, \(L\) is the self-inductance, and \(t\) is time.

If now:

\[ \frac{r}{l}=\frac{R}{L}, \]

then it follows that

\[ i=\frac{R}{r}\,J, \]

i.e. the current in the oscillograph is proportional to the current in the solenoid. This condition, as already indicated above, was by no means observed by Ollom in his installation, and the magnitude of his field is therefore unknown.

The second requirement is satisfied, as theory shows, by reducing the length of the oscillograph filament. P. L. Kapitza constructed the corresponding miniature oscillograph. The shunt included in the oscillograph circuit was made non-inductive and consisted of thick wires.

The field \(H\) was measured from the current in the solenoid. Before the experiment, the constant \(X\) of the solenoid was determined, i.e., at fields of lesser strength the dependence was established

\[ H = xJ, \]

and then, knowing \(J\), it was always possible to find \(H\).

Subsequently, a method of direct ballistic measurement of fields was applied. Inside the solenoid a special small coil was fixed, connected to a ballistic galvanometer. It is quite obvious, however, that if the galvanometer is connected during the whole time while the current rises and falls, the instrument will give no reading. Therefore a special automatic switch was arranged, which connected the galvanometer at any moment and simultaneously gave a light mark on the current-strength oscillogram. The greatest difficulty here was presented by the necessity of careful bifilar wiring from the coil to the galvanometer.

Let us now turn to the construction of the solenoid itself.

Construction of the solenoid.

A solenoid through which current passes is subjected to forces of various directions: first, radial forces, tending to tear apart each turn, and, second, axial forces, pressing one turn against the neighboring one. We shall not dwell here on the analysis of these forces, reaching 1 ton/cm\(^2\), which was carried out in detail by P. L. Kapitza.

The basis of the solenoid is a cylinder made of an alloy of copper with 2% cadmium (this alloy has an electrical conductivity equal to 90% of the electrical conductivity of copper and, being hardened, is four times stronger than copper). This cylinder is wound

...with a strip 5 mm wide of the same alloy, insulated with oilcloth and mica. The inner end of the winding is soldered to the cylinder; the outer one carries a sliding contact. The contact must be made sliding, because, owing to the enormous magnetic radial forces, the solenoid expands slightly when a current passes through it. However strange at first sight the arrangement of a sliding contact may seem at 30,000 A, the short duration of the passage of the current renders it harmless. The solenoid is impregnated with bakelite, which fills all the cavities, and is then enclosed in a strong steel (special steel) bandage. In a field of 400,000 gauss the bandage experiences a pressure of 100 tons. The presence of steel, as experiments have shown for fields inside the solenoid greater than 40,000 gauss, no longer plays any role, since then the field outside the solenoid is sufficiently large to bring the steel to saturation.

This solenoid has so far successfully withstood 329,000 gauss—the greatest field to which P. L. Kapitza has in practice so far attained in his investigations.

Physical phenomena in strong magnetic fields.

It is still too early to speak of the results of P. L. Kapitza’s investigations, for they have only just begun. It should be noted that the short duration of the existence of strong fields requires an entirely special experimental technique, different from the generally accepted one. And this technique is still only in the stage of development. First of all, P. L. Kapitza attempted to measure the Zeeman effect in these fields in the spectra of various substances. It turned out that it is possible to observe the Paschen–Back phenomenon in those spectra in which, up to now, owing to the weakness of our ordinary fields, it had not been possible to observe it. The splitting itself was so large that it could be studied with a simple spectroscope.

Recently P. L. Kapitza published an investigation of the influence of a magnetic field on the electrical conductivity of bismuth. It turned out that in such strong fields the very form of the dependence

of the change of resistance with field strength varies; instead of the quadratic law, discovered at one time by Goldhammer and occurring in weak fields, a linear law is found. We shall return to all these questions on some future occasion.

The works of P. L. Kapitsa already published show, in any case, that the region of strong magnetic fields, like the regions of low temperatures, high pressures, and high voltages, is a region not only of quantitatively, but also qualitatively new phenomena: therein lies their chief interest.

Literature

P. L. Kapitsa (P. Kapitza). Proceedings of the Royal Society, A, 105, 691, 1924; 106, 602, 1924; 109, 227, 1925; 115, 658, 1927.

Wall. Applied Magnetism, 1926.

1. Iron-cobalt has a saturation about 10% higher than iron. ↩