NEW INSTRUMENTS AND METHODS OF MEASUREMENT

OBTAINING HIGH TEMPERATURES (UP TO 55,000°) UNDER LABORATORY CONDITIONS*)

O. Prainig

1. GENERAL REMARKS ON THE CONCEPT AND MEASUREMENT OF HIGH TEMPERATURES

When passing into the region of very high temperatures, it is first of all necessary to clarify both the very concept of temperature in this region and the state in which matter is found here.

Temperature, as is known, is a characteristic of a state determined by the average kinetic energy of “molecules,” and it is usually assumed that thermodynamic equilibrium exists, i.e., an identical, on the average, distribution of energy over all degrees of freedom of all types of molecules. The expression “molecules” here has a thermodynamic meaning, i.e., it includes both molecules in the narrow sense of the word and atoms, various ions, and electrons. A further essential prerequisite in substantiating the concept of temperature, as goes without saying, is the consideration of a sufficiently large number of molecules. One therefore cannot speak of temperature in the ordinary sense of the word in a very small volume or at very low pressure, when this prerequisite is not fulfilled.

Most processes leading to very high temperatures proceed comparatively rapidly. To establish thermodynamic equilibrium, however, a certain time is necessary. It may therefore often turn out that equilibrium is absent. If, for example, the energy used for heating is absorbed directly by only one kind of particle (say, electrons), then the energy is concentrated primarily in particles of this kind, and an equilibrium state will be established only gradually.

*) Österreichische Chemiker-Zeitung 55, No. 5/6, March (1954). Translated from the German by V. V. Bredel.

In the region of high temperatures it is therefore necessary to distinguish the temperatures of individual kinds of particles (electronic, atomic, and ionic temperatures¹), of different degrees of freedom (translational and rotational² temperatures), as well as temperatures of ionization and excitation. By each of these temperatures one should understand the temperature that a monatomic gas would have if the average kinetic energy of its molecules were equal to the average kinetic energy of the corresponding kind of particles, of the corresponding degrees of freedom, or to the average energy of the corresponding states of ionization or excitation.

If we assume that we are dealing with some gas in thermodynamic equilibrium, then at high temperature there will occur dissociation of molecules into atoms, and then thermal ionization of atoms with the formation of atomic ions and free electrons. With a further rise in temperature, the ionization of atomic ions will continue until, finally, only the bare atomic nucleus remains as the “last ion.” An electrically neutral equilibrium mixture of atoms, various ions, and electrons as a whole is customarily called a “thermal plasma.” Its quantitative composition is described by the Eggert—Saha theory³,⁴*).

If, for the atoms participating in the formation of the plasma, the energies of single, double, etc. ionization are known, then by the law of mass action the degree of ionization can be calculated as a function of temperature and pressure. Thanks to measurements carried out in atomic physics, all the necessary values of ionization energy are now known with sufficient accuracy. The Eggert—Saha theory is therefore applicable to any gases and to any mixtures of them.

Before proceeding to describe methods for obtaining high and the highest temperatures, let us briefly dwell on certain principally possible methods for their measurement and estimation.

For a radiator whose properties are close to those of a black body, the temperature can be determined from its radiation, either by measuring the total intensity of the radiation in a specified wavelength interval, or by comparing the radiation intensities for two different wavelengths, or else by measuring the absolute radiation intensity for one wavelength only. More often, however, the assumption that the radiation is close to black-body radiation is not fulfilled. The methods mentioned can therefore serve only for estimating the temperature; great accuracy should not be expected from them.

*) A review may be found in the book¹.

A completely different method of measuring temperature could be based on the use of the Stark effect. It is known that, as temperature rises, a broadening of spectral lines is observed (chiefly as a result of the increase in electron density). By measuring, therefore, the width of the lines, we could, generally speaking, determine the temperature. In doing so, however, considerable theoretical and experimental difficulties arise. For many substances, for example, the constants of the Stark effect are unknown; moreover, it is very difficult to measure the line width accurately. In this connection the method indicated has not yet acquired substantial significance.^5

Various other methods of determining high temperatures most often correspond to methods of obtaining these temperatures. If, for example, a short-lived nonstationary electric discharge is used to obtain a given temperature, then there must necessarily be a relation between the geometrical and electrical parameters of the discharge, on the one hand, and the temperature, on the other. This relation, however, is difficult to express analytically, since the ionization conditions enter essentially into the calculation in the form of coordinate-dependent functions. Therefore up to the present time all calculations have been carried out only under very crude simplifications. (In order to use, for example, Gvozdover’s formula^6 for the mobility of electrons, G. Glaser^3 proceeded from the assumption of complete, but only single, ionization of the entire discharge space.)

For stationary processes the conditions are more favorable. Certain special methods of measuring temperatures will be considered in more detail later; the most important of them are based on measuring the intensity of spectral lines corresponding to definite ionized atoms, for example \( \mathrm{O}^{+} \) or \( \mathrm{O}^{++} \), present in the plasma as a result of thermal ionization of \( \mathrm{O} \) atoms.

Determination of high temperatures by various methods most often leads to very different results. In practice, therefore, the temperature is usually measured by as large a number as possible of independent methods, and on the basis of the individual measurement results, which often differ substantially from one another (discrepancies by a factor of two are not rare), a more or less arbitrary “reasonable mean value” is obtained.

2. SHORT-TERM PRODUCTION OF HIGH TEMPERATURES

At the present time we are already able to create very high temperatures for a relatively short time by several different methods. At our disposal are the following possibilities: a) nuclear reactions, b) explosions, c) explosions of wires by electric current, d) superpowerful sparks.

The only stationary method for solving the same problem so far is the super-powerful arc, which will be considered separately in Section 3. Although at present, for laboratory practice, it is chiefly the new forms of arc discharge that are of importance, for the sake of completeness and for purposes of comparison we shall also briefly describe or mention other methods.

a) Nuclear reactions

The possibilities associated with this method are generally known. It requires the expenditure of large resources and cannot as yet be realized under laboratory conditions. Therefore we shall not discuss it here.

b) Explosions

The method of obtaining high temperatures by means of explosions, i.e., by chemical reactions, is probably the oldest; it has been known for centuries. Considerable successes have been achieved by means of this method.

Already 30 years ago Wartenberg\(^7\), photographing the collision of explosive waves, discovered a region of very high temperature that did not coincide with the centers of the explosions. It was stated that temperatures of \(17\,000^\circ\) were observed in this case. The collision of explosive waves therefore leads to the appearance of high temperatures. If one uses not two, as Wartenberg did, but a very large number of individual explosive waves, creating them so that they all arrive simultaneously at one point, then the possibility should thereby arise of obtaining still higher temperatures. Such a possibility is practically realized in a shaped charge, whose geometry is reflected by its name. Upon explosion in such a charge there arises a “concentric compression wave,” by which one should understand an explosive wave converging to a point. G. Guderley\(^8\) showed theoretically that at small distances \(r\) from the point of convergence the pressure increases as \(\left(\dfrac{1}{r}\right)^{0.792}\). At the very point of convergence, therefore, an infinitely large pressure should theoretically arise. Since the indicated process must proceed adiabatically, a very considerable rise in temperature should correspondingly also arise.

Under real conditions the pressure and temperature can increase in the compression zone only until complete ionization of all atoms occurs, i.e., until they have lost their entire electron shell. The effective cross section of atoms, or better—of atomic ions, is then reduced from \(10^{-8}\ \text{cm}\) to \(10^{-12}\ \text{cm}\) (the nuclear radius). Correspondingly, the mean free path increases by approximately \(10^8\) times.

free path. It thereby becomes so large that the compression zone must dissipate.

On the basis of the arguments indicated, E. Sänger \(^{9}\) made a theoretical estimate of the temperatures that can be attained by this method. As an upper limit he found (not very reliably) the value \(1.94 \cdot 10^{9}\) degrees. Here the question is only of translational temperature (see above). The temperatures found are already so great that thermal excitation of nuclear reactions no longer seems completely impossible.

Some progress in the field of attaining high temperatures was also promoted by the development of rocket technology. E. Sänger \(^{10}\) theoretically investigated the conditions obtaining in rocket engines. He describes the processes occurring in them approximately as follows.

Let us consider a reaction engine in the regime of steady combustion. Suppose that the engine has already been started by introducing the corresponding combustible substances. The reagents, for example petroleum and oxygen, are injected into the combustion chamber of the engine. First of all, even before the beginning of the reaction itself, they pass in the chamber through a preparatory stage, i.e., they evaporate and mix. The heat needed for evaporation is most often supplied by radiation from hot gases*), by radiation arising during the reaction, and, finally, by convection. Mixing is achieved by the rational arrangement of nozzles and the creation of turbulence, and also, though to a lesser extent, by diffusion. The question of which of the listed processes plays the main role in any given case depends, of course, on the shape and size of the combustion chamber, the kind of fuel, and the method of its injection. After the fuel has been sufficiently prepared, the reaction begins. The chemical energy released in this process is initially converted entirely into the energy of the translational motion of gas particles, which leads to a strong increase in pressure and to the emergence of a temperature that is purely translational. Only later is thermodynamic equilibrium gradually established.

As an example, let us indicate the conditions obtaining in a 100-atmosphere reaction engine of continuous operation, working on a mixture of vaporous petroleum and oxygen. Vaporous petroleum and oxygen are injected into the mixing space. Here, right up to the beginning of the reaction itself, an increase in the temperature of the mixture is observed. The reaction itself, i.e., the conversion of chemical energy into the energy of translational motion of gas particles, takes place during an extremely short interval of time, correspond-

*) Hot gases are those gases which, after the reaction, have reached thermodynamic equilibrium.

... corresponding approximately to one free path of the molecules. During the next ten collisions of the molecules (i.e., in approximately \(10^{-9}\) sec.) a translational temperature of \(26\,000^\circ\) is established, and the corresponding pressure is \(4300\) atm. All the energy is then distributed only among the degrees of freedom of translational motion. After approximately a thousand collisions (\(10^{-7}\) sec.) one can already speak of the establishment of a rotational temperature. Under the given conditions it is about \(16\,000^\circ\). During a time corresponding to approximately 100,000 collisions, a vibrational temperature is also established, close to \(6000^\circ\). Finally, after 10,000,000 collisions (after \(10^{-3}\) sec.) equilibrium is reached; by this time the temperature has decreased to \(3700^\circ\) (the equilibrium temperature of hot gases), and the pressure to 100 atm.

c) Explosions of wires\(^{11}\)

If a large capacitor (for example, \(1\ \mu\mathrm{F}\), \(20\text{–}50\ \mathrm{kV}\)) is discharged through a thin wire (0.1 mm in diameter), the latter evaporates explosively. This method has long been developed (since 1920) by astrophysicists, chiefly in order to create, near or in the exploding wires themselves (or in the clouds of metallic vapor arising from them), possibly high temperatures required for carrying out certain spectroscopic investigations. Rough estimates of the temperature, made on the basis of measuring the total brightness of the glow, gave values from \(15\,000\) to \(20\,000^\circ\). However, such temperatures can be obtained only during a very short interval of time (of the order of \(10^{-6}\) sec.). The mechanical and electrical processes in experiments with wire explosions are very intricate; for example, stratification of the vapor cloud is observed. Therefore determining the temperature of the explosion at its various points and at various moments of time is probably a difficult task.

d) Superpower spark\(^{3}\)

If a large capacitor is discharged through a spark gap, then for a short time a strong current will flow along the discharge channel. If, moreover, the discharge channel is further narrowed by creating high pressure in the discharge gap and by using the most suitable gases, then it is possible to achieve the release of a large power in a small space and thereby ensure a strong rise in temperature. In order that the discharge current be sufficiently large, the period of oscillations of the discharge must be of the order of \(10^{-6}\) sec. (It is known that, for given values of the capacitance of the capacitor and of the voltage applied to it, the maximum value of the discharge current is the greater, the smaller the period of oscillations...

tions.) In the type of discharge under consideration, energy is at first transferred practically only to the electrons.

Equalization between the electron temperature and the gas temperature is effected, in the best case, only after \(10^{-5}\) sec.\(^1\) (this value should perhaps be increased somewhat), and consequently one cannot speak of an equilibrium temperature immediately after the start of the discharge. It is true that the oscillations of the discharge do not die out very strongly, so that one may count on the electron temperature approaching the gas temperature after several periods of oscillation, when the maximum value of the current has not yet decreased too much.

Temperature measurements in superpowerful sparks were made by various methods, which for understandable reasons yielded very different results. For different methods of measurement, temperature values between \(35\,000^\circ\) and \(60\,000^\circ\) were obtained under the following conditions:

3. OBTAINING VERY HIGH TEMPERATURES UNDER STATIONARY CONDITIONS BY MEANS OF A SUPERPOWERFUL ARC

The common feature of all the methods considered so far is that they all make it possible to obtain high temperatures only for a short time. Therefore, if in connection with these methods it is at all permissible to speak of thermodynamic equilibrium, then only with the corresponding reservations.

The situation is different in the case of methods that use an electric arc to obtain high temperatures. An arc discharge is a stationary process, and therefore at every point of the arc thermodynamic equilibrium prevails (the temperature of the arc is a function of the coordinates). It goes without saying that temporary disturbances of this equilibrium may sometimes also be observed, caused, for example, by strong diffusion of ions, etc.

Almost from the very beginning of the study of arc discharge, numerous attempts were made to raise the temperature of a burning arc. As early as 1910 these attempts led to the discovery of Beck’s arc. Obtaining this type of arc is based on the following principle: if measures are taken so that, when the current is increased, the flame of the arc cannot spread beyond the edge of the positive carbon electrode, then it is possible to overload considerably the arc burning between carbon electrodes with a “core-

“...type” (i.e., between carbon electrodes in which channels drilled along their axis were filled with metal salts), and thereby to achieve a considerable increase in the temperature and brightness of the arc.

The further improvement of the arc continued in the same direction. In this connection it is enough to recall the numerous works on high-current carbon arcs and on the study of the influence of the composition of carbons on the arc discharge¹². But even in a freely burning high-current carbon arc, at a current of \(1500\ a\), the temperatures are not very high; they scarcely exceed \(10\,000^\circ\).

The reason preventing the attainment of higher temperatures is that the temperature depends on the power released per unit volume, and hence on the current density, which is difficult to make greater than a certain value. Indeed, if the current is increased, then the cross section of the discharge simply increases, while the current density remains unchanged. Thus, for example, in the case when the end surface of the anode becomes too small for the development of the arc, the flame of the latter spreads over the side surface of the anode, so that the current density, and consequently also the power released per unit volume and the temperature, do not increase.

This circumstance led H. Gerdien¹³ to the idea of increasing the release of power per unit volume by preventing the base of the arc from spreading over the side surface of the anode. He placed on the anode a cylindrical shell (a diaphragm), the edges of which projected beyond the end surface of the carbon electrode. The base of the arc was thus located in an artificial crater, which narrowed its cross section near the anode. Naturally, the diaphragm was arranged symmetrically with respect to the axis of the arc. The indicated spatial restriction of the arc should lead, as may be expected, to an increase in the current density and therefore to an increase in temperature near the axis of the arc.

There is, however, no material that could withstand the working temperatures to which the diaphragm is subjected. In order to protect it from the action of the hot gases of the arc and reliably to prevent a possible jumping of the arc onto the diaphragm, Gerdien designed it in such a way that it was covered with a film of water. This idea proved decisive for the entire subsequent development of the superpower arc.

The first apparatus designed by Gerdien was, admittedly, still technically imperfect; above all, the problem of providing insulation between the carbon electrode and the diaphragm washed by water proved very difficult. However, Gerdien soon succeeded in establishing that, by artificially narrowing the arc at any point of the discharge column, one can obtain by simpler means the same results as when narrowing the arc in its anode ...

parts. This led him to invent the nozzle that was named after him.

The Gerdien nozzle is shown schematically in Fig. 1. It consists of a cylindrical plate a, along whose axis an opening b is drilled; the arc burns through this opening. From the peripheral annular channel v to the central opening, tangentially to its walls, narrow channels g lead. Water is supplied through these channels, as a result of which the walls of opening b, through which the arc burns and which narrows it, are protected from the action of the arc gases by a thin film of water.

Fig. 1. Diagram of the Gerdien nozzle.

Fig. 2. Diagram for calculating the emissivity of the zones of an electric arc.

The Gerdien arc was subsequently investigated in many respects^14. The discovery in the arc of multiply ionized oxygen atoms already made it possible at that time to suppose that temperatures exceeding \(20\,000^\circ\) develop in it. An exact determination of the temperature, however, was achieved only in 1950 by Laurence^15, who improved for this purpose the astrophysical method of temperature measurement based on determining the intensities of the lines of the emission spectrum of the ions \(O^+\) and \(O^{++}\).

In this method the image of the column of the Gerdien arc is projected onto the slit of a spectrograph in such a way that the arc column and the slit are mutually perpendicular, which makes it possible to investigate the transverse section of the arc for different wavelengths. By photometrically measuring individual wavelengths across the spectrum, one can determine the dependence between the emissivity, established experimentally, of individual zones of the arc and the distance from the arc axis.

The calculation is carried out in the following way (Fig. 2). If the emissivity as a function of the distance \(r\) from the arc axis is denoted by \(E(r)\), and the intensity determined along a monochromatic line of the image of the transverse section of the arc column as a function of the distance \(y\) from the image of the arc axis by \(I(y)\), then we obtain, as is immediately evident from Fig. 2,

the following relation between these quantities:

\[ I(y)=2\int_{0}^{\sqrt{r_0^2-y^2}} E\left(\sqrt{x^2+y^2}\right)\,dx, \]

where \(r_0\) is the radius of the arc column. The integral equation obtained is solved numerically.

On the other hand, if it is possible to calculate theoretically the spectral emissivity of the arc plasma as a function of temperature (and pressure), then we can immediately determine the radial distribution of temperature in the arc by comparing the coordinates of the experimental and theoretical emissivity functions. In the theoretical determination of the functional dependence between emissivity and temperature, certain difficulties arise, connected with ignorance of the values of the absolute intensities of the corresponding spectral lines (transition probabilities). These difficulties, however, can be overcome by introducing “normalized radiation functions” in the following way.

The emissivity of the plasma has, for a given spectral line at a given temperature, a maximum. Indeed, at first, as the temperature increases, the number \(n(T)\) of ions emitting the given line also increases; however, with a further increase in temperature, the intensity of emission of this line must decrease, since the number \(n(T)\) of emitting ions decreases owing to the formation of atomic ions with a large positive charge. The values of the degree of ionization of ions of a definite multiplicity as a function of temperature, needed for the calculation, can be obtained from the Eggert—Saha theory. The intensity \(i(T)\) of the radiation depends, as stated, chiefly on the concentration of the corresponding ions. Taking into account the excitation of ions to a definite level corresponding to the excitation energy \(U_a\), we obtain for the intensity of the corresponding spectral line:

\[ i(T)\sim n(T)e^{-\frac{U_a}{kT}}/Z(T). \]

The Boltzmann factor \(e^{-\frac{U_a}{kT}}/Z(T)\) increases monotonically with increasing temperature, while \(n(T)\) reaches a maximum at a definite temperature. From the practical point of view, certain lines of atomic oxygen ions are important. Calculations by Burgoyne, Mäger, and Peters \(^{16}\) showed, for example, that the intensity maxima of the line \(\lambda=4651\,\text{\AA}\) of the ion \(\mathrm{O}^+\) and the line \(\lambda=3447\,\text{\AA}\) of the ion \(\mathrm{O}^{++}\) correspond to temperatures \(32\,000^\circ\) and \(52\,000^\circ\). As for the “function

of “radiation” of a given line, then it is normalized by setting the intensity at the temperature corresponding to the maximum equal to unity. The emissivity as a function of distance from the arc axis is normalized in an analogous way, i.e., the emissivity corresponding to the maximum is also set equal to unity. In this case, at the distance from the arc axis corresponding to the maximum of the radial radiation function, the temperature corresponding to the maximum of the temperature curve of the emissivity naturally predominates. For other distances from the arc axis, as has already been noted, the temperature is easily determined by comparing the corresponding coordinates.

This method, applicable, to be sure, only to a superpower arc stabilized by water, as the Gerdien arc and the various modifications of the arc developed on its basis are commonly called, makes it possible to determine the temperature considerably more accurately than all the methods considered earlier. The assumption of transparency of the arc column, which underlies the method, is in practice almost completely justified*).

Larens determined, by means of the indicated method, the temperature on the axis of the Gerdien arc[^17]. With a discharge current of 500 A and a diaphragm diameter of 3 mm he found a temperature of 35,000° on the arc axis.

Larens also determined the dependence of the temperature \(T_a\) on the arc axis on the current strength. Whereas at small current strengths \(T_a\) increases rapidly, this increase is considerably slowed at large values of the current strength. It follows from this that, by means of this method, no further substantial rise of temperature can be attained.

The last step in the development of methods for obtaining high temperatures was made by Maecker[^18].

Fig. 3. “Turbine” for obtaining a channel arc.

If a strong increase in temperature is already ensured by the narrowing of only a limited part of the arc column, then an even greater increase in temperature should be expected from confining almost the entire arc in a channel. This idea led to the development of the so-called channel arc. The scheme of the channel is shown in Fig. 3. The arc burns in the air cavity of a water vortex.

The hollow cylinder \((a)\) is closed by two plates \((b)\). Along the axis of the cylinder, holes are drilled in the plates. Into the middle part

*) For an opaque arc column, determination of \(E(r)\) from \(I(y)\) would be impossible without knowledge of the dependence of absorption on the region of the arc column under consideration.

cylinder, tangentially to its walls, a water jet strikes (e). The water rotates rapidly in the hollow cylinder and is forced outward by centrifugal force. Around the axis of the cylinder there is thus formed a cylindrical cavity free of water. The diameter of this cavity is determined mainly by the diameter of the holes in the plates closing the cylinder. By giving these plates a definite shape, it is possible, by means of centrifugal forces and cohesion forces, to ensure that the water, on leaving the cylinder, does not splash, but flows over the surface of the plates.

When igniting the arc it often has to be “drawn” through the channel with the aid of an auxiliary electrode. The water forming the channel strongly cools the walls (an arc bounded by a stabilized wall!).

The temperature of the channel arc was determined by the Lorenz method described above.^17 At a current of 1450 a and a channel diameter of 2.4 mm, the temperature on the arc axis proved to be 55,000°.

The dependence of the temperature near the axis of the channel arc on the current resembles the analogous dependence for Gerdien’s arc. Therefore, in a channel arc as well, it will probably not be possible to increase the temperature appreciably by merely increasing the current.

In contrast, however, to all the methods described earlier, this method makes it possible to obtain such high temperatures for practically as long as desired.

Measuring the temperature (admittedly a comparatively low one) and, in particular, the electron density for a definite channel arc, G. Jürgens^19 verified the correctness of temperature determination by Lorenz’s method. The channel arc used by Jürgens was characterized by the following data:

Coals 13 mm thick were used as electrodes. Along the axis of the coals, holes 5.2 mm in diameter were drilled. Thanks to these holes Jürgens was able to make observations along the axis of the arc. In addition, observations were made in a direction normal to the axis of the arc.

Comparing the results of observations in directions along and across the arc, Jürgens succeeded in proving that the radiation passing through the hole in the carbon electrode does not depend, near the arc axis, on the absorption coefficient and therefore corresponds to black-body radiation. In this connection he was able to determine the temperature of the arc in several ways: a) by measuring the absolute intensity of the \(H_\alpha\) line in the direction along the arc axis, b) by measuring the absolute value of the intensity in the transverse direction, c) by relative measurements of the intensity distribution-

OBTAINING HIGH TEMPERATURES

...ties in the Balmer series and d) from the Stark effect. Averaging the results obtained by different methods, he found the temperature to be equal to \(12650^\circ \pm 100^\circ\) K, which agrees quite well with the temperature determined by Laurentz’s method.

Apart from the intrinsically interesting possibility of obtaining very high temperatures under stationary conditions, a water-stabilized super-power arc may find numerous other applications.

In the “water-free channel” there are products of the thermal dissociation of water molecules. The atoms present here are multiply ionized. The high temperature prevailing in the channel is associated with a corresponding expansion of the gas. As a result of this expansion, the gas flows out of both ends of the channel and, after cooling, again forms water. It is therefore possible to observe how from the channel of such an arc “jets of plasma are ejected,” turning at the end of their path into flames of burning detonating gas. This phenomenon is seen in Fig. 4, in which the channel can also be distinguished on the right. After contact with the electrodes, the plasma jets, of course, no longer carry charge. A water-stabilized super-power arc can therefore make it possible to study an easily accessible, electrically neutral, thermal plasma.

Fig. 4. Burning channel arc. From the channel a jet of plasma is ejected (a), turning at the end of its path into flames of burning detonating gas (b). A slightly incandescent carbon electrode (c) is illuminated by the arc. The plastic (d) flowing around it is illuminated by the arc. Arc characteristics: current \(62\) a, field strength \(35\) V/cm, channel diameter \(9\) mm, temperature about \(14000^\circ\) near the arc axis. Exposure time: \(1/500\) sec.

A channel arc can also be used to determine the probabilities of transitions between specified excitation states of an atom or atomic ion. For this it is only necessary to introduce into the water used for stabilizing the arc a soluble compound containing the element under investigation, or to use for stabilization a liquid in whose composition this element is already present. The indicated method was already used by Maecker\(^{20}\), who, with the aid of a channel arc stabilized by water and alcohol, determined the transition probabilities corresponding to certain lines of C and C+.

After all that has been said it is clear that a water-stabilized super-power arc is a means enabling us to study, under laboratory conditions, the properties of matter at very high temperatures.

References

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