ISOBARIC JOULE HEATING

43

gcm

1.5

MPa

1.0

0.5

0

0

0.5

1.0

1.5

2.0

˚C

Fig. 2.20. Thermodynamic equation of state for cesium (Alekseev et al. 1970a).

returning to the radiating piezoelectric transducer. The di erence between the in–phase time coordinates of both pulses gives rise to the time taken by the sound wave to pass the speed base. This enables one to calculate the sound velocity. This procedure is described in more detail by Kulik et al. (1984).

The measurement results are given in Fig. 2.24. One can see the rise in the slope of isobars, especially in the liquid phase, as the critical point is approached. The behavior of supercritical isobars becomes smooth. Apparently, the smoother it is, the higher the value of p/pc. The vS(ρ) relationship, derived during the rearrangement of these data, clearly reveals a kink in the case of a density of 9 g cm−3. It is known that at this density mercury becomes metallized.

2.2Isobaric Joule heating

Isobaric Joule heating is realized in a capillary or in an atmosphere of inert gas. These methods help to attain a high concentration of charged particles (up to 1020 cm−3 ) and high temperatures (up to 105 K) at pressures of up to 0.1 GPa. However, the plasma generated proves to be substantially inhomogeneous. Moreover, in this case, one fails to realize direct reliable measurements of temperature, density and pressure.

2.2.1Isobaric heating in a capillary

This technique was developed to investigate the properties of a nonideal plasma of cesium and, later, of sodium, potassium and lithium (Kulik et al. 1984). A

44 ELECTRICAL METHODS OF NONIDEAL PLASMA GENERATION

g cm

.

.

.

.

.

					˚
.	.	.	.

Fig. 2.21. Curve of phase equilibrium for cesium (Jungst et al. 1985).

schematic of the apparatus is shown in Fig. 2.25. A transparent quartz (or glass) capillary 0.7 mm in diameter and 20 mm long is filled with liquid cesium (or it can accommodate a wire of solid potassium, sodium, or lithium). Cesium is subjected to constant argon pressure maintained throughout the experiment. Filled with argon simultaneously, the volume serves as an expander for cesium, part of which is forced out of the capillary upon heating. The cesium in the capillary is heated by a current pulse shaped by an electric circuit comprising a capacitor bank, inductor and a control thyristor. The apparatus was greatly improved in the course of subsequent studies.

In the experiment, the current–voltage characteristic is measured (from the oscillogram). In the oscillogram, the region corresponding to steady–state conditions is recorded. It is obvious that in doing so, the capillary is completely filled with plasma. By processing the data of the oscillogram, one can obtain the F (i) dependence, where F is the electric field intensity and i the discharge current. This dependence provides the initial experimental data used to obtain, by calculations, the isobars of electrical conductivity, σ(T ), and thermal conductivity, χ(T ).

The basic equations include the heat balance equation, which is known in the physics of gas discharge as the Elenbaas–Heller equation, and ohm’s law. For a su ciently long capillary, these equations take the form

ISOBARIC JOULE HEATING

45

g cm

.

.

.

.

.

.

.

cm

Fig. 2.22. Curve of phase equilibrium for cesium (Jungst et al. 1985).

Fig. 2.23. Cell for measuring the sound velocity in mercury (Suzuki et al. 1977): 1, quartz piezoelectric transducers; 2, niobium ampoule; 3, sound ducts; 4, heater; 5, niobium ring; 6, high–pressure chamber.

	1 d			rκ	dT	+ σF 2 = 0,	(2.5)
	r dr				dr

46 ELECTRICAL METHODS OF NONIDEAL PLASMA GENERATION

m s

MPa

.

.

.

Fig. 2.24. Isobars of the sound velocity in mercury (Suzuki et al. 1977).

b

Fig. 2.25. Schematic of an apparatus for isobaric heating in a transparent capillary (Barolskii et al. 1972). (a): 1, capillary; 2, electrodes; 3, liquid cesium; 4, argon purge. (b) The behavior of the time dependence of plasma temperature.

R
i = 2πF	σr dr,	(2.6)

0

where r is the distance from the capillary axis and R is its radius. The boundary conditions are: dT /dr = 0 at r = 0; T = Ts at r = R, where Ts is the pyrometrically measured temperature of the outside surface of the plasma.

In the plasma under investigation, the main mechanism for the extraction of heat and the shaping of the temperature distribution T (r) is provided by radiation transfer. Since the mean radiation path length, that is, the Rosseland length, is lR R, the radiative thermal conductivity approximation is valid while κ(T ) is equal to the coe cient of radiative thermal conductivity κR(T ). The sought-for functions κR(T ) and σ(T ) were obtained as a result of substitution in