HIGH–PRESSURE ELECTRIC DISCHARGES

53

sume that the plasma became homogeneous after 100 µs. The beginning of the monotonic resistance drop is a sign of the establishment of the homogeneous state. After 400 µs from the beginning of the process, the resistance starts to increase. Renaudin et al. (2002) connect this with plasma cooling as result of the radiative heat transfer. Analyzing the method of the conductivity measurements it is necessary to draw attention to many uncertainties and, first of all, to the problem of the distribution of measurable values in the plasma volume.

Korobenko et al. (2002) developed and used a method that makes it possible to investigate the transition of a metal from a condensed to a gaseous phase while maintaining almost uniform temperature and pressure distributions in the sample. The method consists in the pulsed Joule heating of a sample in the form of a thin foil strip placed between two relatively thick glass plates. This method was used to measure the conductivity of tungsten in a process during which the pressure in the sample is maintained at a level of 46 GPa and the density of the sample decreases from the normal solid density to a density 20 to 30 times lower. E ects connected to the sample evaporation are absent because these pressures exceed in several times the critical pressure of the liquid–gas phase transition. In Fig. 2.31 resistivity ρ of tungsten as a function of relative volume v/v0 (v0 is a specific volume of solid sample at normal conditions) obtained in the pulsed Joule heating experiments with tungsten foil strips placed in the cells of glass or sapphire. One can see that this dependence has di erent character in solid, liquid and gaseous states. In liquid state the specific resistivity is approximately proportional to specific volume, that is the ratio of specific conductivity to density remains almost constant. Over the range of relative volumes v/v0 from 9 to 11, the dependence changes its character (in experiments with the glass cell). For larger volumes, the resistivity approaches a constant value. Note that, for relative volumes larger than 5, the heating process was nearly isobaric. Thus, the dependence of resistivity on the specific volume changes its character along an isobar. As the pressure increases from 4 to 6 GPa, as it follows from the figure, the dependence becomes substantially flatter, in which case the range of relative volumes where the character of the dependence changes becomes larger by a factor of approximately 3. It should be noted that no such e ect was detected in nonisobaric processes. The new data on supercritical state of Al were obtained by Korobenko et al. (2005).

2.3High–pressure electric discharges

Because of a high density of material and high level of temperature, the charged particle concentration in a plasma of high–pressure electric arcs and discharges is as high as (1018–1021) cm−3. In such a plasma, the Coulomb nonideality parameter Γ may reach substantial values. Whilst doing so, at pressures p 1 MPa, the plasma of high–pressure discharge is locally equilibrium. This section will briefly characterize the principal approaches to the investigation of high–pressure discharge plasma. A good review of these studies was made by Asinovskii and Zeigarnik (1974).

54 ELECTRICAL METHODS OF NONIDEAL PLASMA GENERATION

µohm m

glass (4 GPa)

sapphire (6 GPa)

melting

Fig. 2.31. Specific resistivity of tungsten as a function of relative volume (Korobenko et al. 2002). The bend marked by the arrow corresponds to the end of melting. Stars refer to temperature in the range from 104 to 5·104, with a step 104. Triangles are for the data of Kloss et al. (1998) and Rakhel et al. (2002).

Facilities with steady high–pressure arcs appeared as a result of improvement of a wall–stabilized Maecker arc. In the late 1960s, facilities operating at pressures of up to 2 MPa were developed in a number of laboratories in the USSR and FRG. It gave a possibility performing of a series of investigations on the properties of nonideal plasma. Batenin and Minayev (1970) measured the electrical conductivity and emissivity of argon plasma with the following parameters: p = 1 MPa, T = (12–15)·103 K, ne = 1018 cm−3, nonideality parameter Γ 0.5, and specific power input to the discharge was 4.5 kW cm−1. In steady stabilized high–pressure arcs and high–pressure discharges, one manages, as a rule, to perform measurements of the electrical conductivity and emissivity of plasma. However, the possibilities of wall-stabilized arcs are greatly restricted from the standpoint of nonideal plasma generation. The relatively low level of specific power restricts the level of temperature and, consequently, the values of the degree of ionization.

High parameters of plasma were obtained by Peters (1953) who stabilized the arc with a liquid wall. The arc was burning in water vapors formed due to evaporation of liquid adjoining the discharge column. The liquid proper formed a rotating liquid wall. This was due to the rotation of the casing as a whole. The plasma parameters were as follows: p = 0.1 GPa, T = 18 · 103 K, ne = 8 · 1018 cm −3, Γ = 1.25, and a specific power of 120 kW cm−1.

Considerably more intensive studies were made into pulsed discharges, which featured a number of advantages. The problem of wall cooling is nonexistent. The specific power is readily increased to the 100 kW cm−1 level, thereby providing high degrees of ionization of the material. Quasisteady burning conditions

HIGH–PRESSURE ELECTRIC DISCHARGES			55

Fig. 2.32. Discharge tube (Radtke and G¨unter 1976): 1, quartz window; 2, auxiliary elec-

trode; 3, steel ring; 4, pressure sensor; 5, cathode; 6, tungsten probes; 7, anode.

are maintained in a typical arc for a period of approximately one millisecond, which is su cient to perform measurements and to establish local thermodynamic equilibrium. Because of high pressures and temperatures, the attainable concentrations of charged particles are two (and even three in the case of discharges in liquid) orders of magnitude higher than the characteristic electron concentrations in sustained arcs and reach (1019–1023) cm−3. However, a possibility arises with the emergence of inhomogeneities in plasma: wave phenomena, and even manifestations of nonequilibrium, are possible.

Pulsed discharges in gases are generated upon discharging a tank of capacitors through an interelectrode gap. The discharge techniques are rather varied. Figure 2.32 illustrates one of the possible designs for a discharge tube. A detailed description of this design was given by G¨unter (1968) and Radtke and G¨unter (1976). Essentially, it consists of a quartz tube with four electric leads: anode, cathode (comprising a pressure cell), and two measuring probes. Inside the tube, a movable auxiliary electrode required for ignition is mounted. The tube has a length of 10 cm and a diameter of 1 cm. It is filled with an inert gas at an initial pressure of up to 0.1 MPa.

The basic element of the discharge circuit includes several parallel-connected LC elements shaping a square pulse. Figure 2.33 is a schematic of the apparatus employed by Popovic et al. (1974). Measurements of the current strength i and axial field intensity F help to determine the mean electrical conductivity σ,

	R
	= (2/R2)	σ(r)r dr,	(2.9)
σ
0

where R is the radius of the tube. Since the radiation presents the main mechanism of heat transfer at high pressures, the transverse inhomogeneity of the plasma is relatively low. Figure 2.34 gives the radial profiles of the electron temperature measured in flash lamps which have a length of 1 m and radius of 13 mm and are filled with xenon at a pressure of 4·103 Pa.

Mitin (1977) developed a procedure for producing superhigh pressures (about 0.1 GPa) in the plasma of a high–pressure pulsed free arc. As distinct from stationary discharges, the power of a pulsed arc may be high, up to 10 kW cm−1. The discharge has a narrow central high–temperature zone (up to 7·104 K) and a

Fig. 2.34.

56 ELECTRICAL METHODS OF NONIDEAL PLASMA GENERATION

Optics

Starting Energy

Fig. 2.33. Schematic of the experimental apparatus of Popovic et al. (1974).

J

mm

Radial profiles of Te in a xenon plasma in a flash-lamp for di erent values of discharge energy (numerals by the curves) (Vitel et al. 1990).

peripheral low–temperature zone (approximately 104 K). Under these conditions, conventional optical diagnostic methods provide information about the discharge surface and the registered radiating power characterizes the integral properties of inhomogeneous plasma. A pulsed cascade arc, unlike a free one, makes it possible to produce a plasma column that is homogeneous along the axis. However, the inhomogeneity over the column cross–section persists. The coe cient of electrical conductivity of such a plasma was measured for the nonideality parameters of 0.1 ≤ γ ≤ 0.3. The density of material was measured by X–rays. An X–ray beam from a standard X–ray tube passed through a top hollow electrode (its end, turned into the chamber, had been sealed with a tungsten–tipped beryllium plug), axial region of the arc and a bottom electrode, and was recorded by a NaI photomultiplier.

In order to study the physical properties of the plasma at pressures above 10 MPa and temperatures of up to 20 000 K, special plasma generating sources must

HIGH–PRESSURE ELECTRIC DISCHARGES

57

P

P

BS

Fig. 2.35. Plasma source design and optical scheme of temperature measurements (Andreev and Gavrilova 1974). Plasma source : 1, quartz plates; 2, quartz spacers; 3, platinum electrodes; 4, tungsten cylinder. Transmission source: 5, Teflon capillary; 6, steel electrodes; M, monochromator; Φ, photomultiplier; O, oscillograph; P, ignition; BS, synchronizer; A-A, cross–section of the plasma source (see insertion).

be provided. Andreev and Gavrilova (1974, 1975a, 1975b) described a plasma source which was used to measure the electrical conductivity and emissivity of air. Its design is shown in Fig. 2.35. This source allows the derivation of an optically transparent plasma at pressures above 10 MPa with uniform and controlled distribution of temperature and density. The apparatus developed by Andreev and Gavrilova (1974, 1975a, 1975b) o ers great possibilities for investigations in a high region of parameters.

The plasma volume of 1.0 × 1.1 × 10 mm3 is defined by quartz plates 1 and spacers 2. Air–tightness was ensured by the high quality of machining performed on the plates and spacers and by tightly pressing the electrodes against the quartz. A bank of capacitors (C = 3.75 F) discharged through the plasma volume. The discharge mode was aperiodic (L = 0.51 H) with a current amplitude reaching 300 A and a duration of about 50 s. The radial fluctuations of plasma density cease after ignition in less than 5 s.

Measurements of brightness of the transmission source and transparency of the plasma helped to determine the temperature. Spatial resolution of the optical scheme allowed the derivation of the temperature (and density) distribution in the plasma volume. The regress of wall and electrode materials into the plasma was monitored spectroscopically.

Andreev and Gavrilova (1974) used this source to measure the electrical con-

ductivity of air at 13 400 K ≤ T				≤ 18 100 K and 9.5 ≤ p ≤ 15 MPa, thus
corresponding to N	e		1018–1019	cm−3		0.7–1. The plasma gap resis-
		=			and Γ =

tance was

58	ELECTRICAL METHODS OF NONIDEAL PLASMA GENERATION
	R(t) = U0		tm	i dt − L dt i−1.		(2.10)
		− C
		1			di
		0

At the moment of current passage through the maximum tm, it is su cient

tm

to know U0, i(tm), C−1 i dt. The measured values of R(tm) were on the order

0

of 1 ohm. The error in subsequent determination of the values of electrical conductivity did not exceed 15%, with the values of σ in the central region of the plasma volume di ering from its average value by only 8–10%. The measured values proved to be approximately twice lower than those given by the Spitzer formula. These results are discussed in Chapter 7.

The highest values of charged particle concentrations, ca. 1021 cm−3, were attained in pulsed discharges in liquids. In doing so, pressures of a tenth of a GPa are attained. The plasma is generated by discharging a bank of capacitors between two electrodes immersed in a liquid, usually water. The current-heated plasma tends to expand the discharge column. This is impeded by the mechanical inertia of the ambient water. Consequently, high pressures develop. For this purpose, the bank of capacitors must be discharged as soon as possible while the plasma column volume is still small. The discharge is shaped over a period of time of about 1 s. The plasma generated upon discharge in water has the following parameters: T = (1–5)·104 K, p = 0.1–5 GPa. Therefore, high pressures are combined with high temperatures, which may hardly be accomplished in other types of facilities. However, in view of the high temperature values, the parameter of nonideality is not very high, being Γ ≤ 1.5. The discharge is usually initiated by electric explosion of a thin wire interconnecting the electrodes. Therefore, the plasma consists of a multicomponent mixture of the products of water vapor decomposition with a small admixture of metal from which the wire was made.

The first investigations of a plasma of pulsed discharge in water were performed by Robinson (1957) and Martin (1960). At present, such discharges are employed in a wide range of investigations related to the development of advanced technologies (cf. Ivanov et al. 1982; Naugol’nykh and Roy 1971). Naturally, such investigations may yield interesting physical results as well.

The capillary discharge with evaporating wall is a pulsed discharge of a special kind. The characteristic feature of this discharge resides in the purging of the discharge channel by vapors of the wall material evaporating due to the Joule heat of the discharge. Ogurtsova et al. (1967, 1974) obtained a plasma with a charge concentration of up to 1020cm−3 at a temperature ranging from 3 ·104 to 105 K and at a pressure of 20–50 MPa. The chemical composition of the plasma depends solely on the composition of the wall material. The capillaries were manufactured from textolite. Therefore, the plasma had a complex elementary composition, namely, 47% hydrogen, 37% carbon, and 16% oxygen. The plasma was investigated under quasistationary conditions. To this end, (i) the discharge