ELECTRON DENSITY IN A DECAYING PULSE-DISCHARGE PLASMA V. V. Tatarinov, L. T. Poleshchuk, and V. S. Mel'chenko Izvestiya VUZ. Fizika, Vol. 11, No. 3, pp. 131-133, 1968 UDC

533.951.2

It is of interest to determine the electron densities n e in order to study pulsed gas-discharge sources [1, 2]. However, such measurements are difficult to perform when the electron densities are very high [3, 4]. Under these conditions, it is convenient to perform the study by using a laser interferometer [5-7]. In this article, the laser interferometer shown in Fig. I is employed. The output intensity I is amplitude modulated by the change in positive feedback of the system MtM2Ms ; this quantity depends on the length MzMs. The appearance of a single burst in I corresponds to a X/2 change in the optical length of the plane-parallel resonator MsMs. By comparing the resonance condition for MzMs with the dispersion relation for a plasma [8], we can find the minimum electron density determining a single burst in I. In this case, 1.76.101~ nernht - - ~ (era-a),

(1)

where L is the length of the probed plasma section in centimeters. By fixing the appearance of the bursts when a plasma is created in MzMs for a unidirectional process, we can find the distribution ne(r, t). The drop in electron densities of an aperiodic pulse discharge was studied. Helium and argon plasmas were created in a tube 80 cm long and 2.5 cm in diameter. The capacitance of the capacitor bank was C = 40ttf and the initial voltage on the plates was 3.5 kV. Figure 2 shows the processed measurement results for He3 and Ar on a semilogarithmic scale (ln n e, t). The appearance time for the last burst increases with an increase in pressure p and, when we shift from a helium to an argon plasma, a significant discrepancy results. The decay rate 0ne/0t decreases as p and the ion mass increase. For electron densities of 1.1 9 101s-2 9 1016 cm - s , the experimental points lie very close to a straight line in the chosen coordinate system. This characterizes an exponential drop in the charged-particle density. ne = not e -tl~,

(2)

where n0e is the initial electron density and r is the decay time constant. The equation for the decay rate in electron density, allowing for the basic processes, is written as [9] On---Le = V (Dr he) - - an~ - - h~ne,

Ot

(3)

where D is the diffusion coefficient, cx is a coefficient for recombination with ions, h is the capture probability, and v is the electron-atom collision frequency. To understand the predominating process of electror~-density decrease, it is necessary to estimate the contribution of each term to (3). The capture and diffusion processes obey an exponential law, However, negative ions do not form in the inert gases. Moreover, the degree of ionization of the plasma under study is high; therefore, we can also ignore capture by attendant impurity atoms. If the electron-density decreases because of electron recombination with ions, the decrease in ne will be described by a straight line on the scale (1/n e, t); this does not agree with the experimental data. From (3) it also follows that the rate of decrease, when recombination predominates, remains constant as p changes. The possible change in One/0t

Fig. 1. Laser interferometer. RM3 = o% The wavelength generated by the laser is k = 6328 A. 76

does not agree with the obtained laws when the effect of temperature on the coefficient a as the pressure p changes is allowed for. The theoretical appearance times for the last bursts when ct = 10 - 7 cm s sec - i (dissociative recombination) is many times smaller than the times obtained experimentally (see Fig. 2). The contribution of recombination to the decrease in ne cannot be completely ignored; however, in our experiments, the recombination coefficient is small and limited to a value on the order of a < 10 -J= cm s see - 1 . Calculation of 0ne/St using (3) and allowing for 9 and ct <_ 10 - ~ cmz sec - I shows that the effect of the second term in Eq. (3) is negligible. The obtained values for the coefficient c~ evidently apply to recombination with radiation [9, 10]. We should note that the use of a laser interferometer for performing measurements in the high electron-density region makes it possible to easily measure the coefficient a; this is a complex problem when other methods are used [9, 10]. Thus, we can conclude that volume recombination is much less important than the diffusion runaway of charged particles:

~ne< DIA',

(4)

where A = (R/2.405) is the diffusion length of the vessel (L>> R) and R is the radius of the tube. In this case, Eq. (3) takes the form One n - - D [ 1 c) [r One ~ l at = Dv~ , - [ r Or ~, O r ] l "

(5)

The diffusion coefficients D were found from (5) and (2) for a diffusion length of A = 0.52 cm. For the gases used, the values of D lie within 6000-13 000 cmz sec - 1 for Hes and 1500-2700 cmz sec - 1 for At. Under the given conditions, diffusion is ambipolar [11,12]. The product pDa ~ const shows that the plasma was studied in the initial stages of decay when Te > Tgas. In [3], it was found that in the initial moments of decay, T e remains approximately constant; therefore, Da(t) = = Da(0) [14]. For this condition, we can write the solution to (5) as

(')

ne (r, t) = hoe e -tl" Jo 2 . 4 - ~ ,

(6)

where I0 is a zero-order Bessel function and r is the moving coordinate. The rate of decrease in ne at different distances from the tube axis r was measured for the same intervals and two different pressures (for Hea and At). In the (lnne, t) scale, the functions ne(t) for different r are

r

A '% I

.,, r.1 - \ i

k.

/6g $~s 48g t, .sec Fig. 2. Experimental graphs of ne(t) on the tube axis. 1) Oseillogram of discharge current; 2, 3) HeZ, initial p = = 0.6a and 2.58 m m H g ; 4, 5) At, initil p = 0.63 and 2.84 mm Hg. The curves for he(t) obtained for intermediate pressure are found between curves 2 and a for He and between curves 4 and 5 for At.

ge

O,6

REFERENCES

;\ X

0a

k

X \

02' a

\ O.J/ 0,gZ 0,.q3 ~, cm ig, 3. Distribution ne(r,t) for He 3, with p = 1.2 Hg. Dashes, calculated carve J0(2.4 r/R); C), experimental points for the time 50 ~sec; +, for 70 #sec; 9 for 80 psec.

straight lines converging to a single point; this shows that the active discharge uniformly fills the tube. From these graphs a set of curves for ne(r) was obtained for different moments in time. The distributions for ne(r, t) depends greatly on the time, pressure, and type of gas. These variables in (6) specify the product A(D, P, t)= hoe-t/r, which determines the electron density at the tube axis at some fixed moment in time. By normalizing the distribution ne(r) for particular A in the form

2-{el(Dr--)' ,gt= J 0 / \2 . 4 ( ,p, )

r ]

R]'

(7)

it was found that the experimental points in the cases under study closely follow the calculated curve for I0(2.4 r/R) (Fig, 3). This confirms that the initial stage of plasma decay is characterized by (5).

1. I. S. Marshak, Pulsed Light Sources [in Russian], Gosenergoizdat, Moscow- Leningrad, 1963. 2. S. G. Kulagin, V. M. Likhachev, M. S. Rabinovich, and V. Ms 8utavskii, ZhP8 [3ournal of Applied Spectroscopy], 5, no. 4, 534, 1966. 3. A. V. Chernetskii, O. A. Zinov'ev, and O. V. Kozlov, Equipment and Techniques for Plasma Diagnostics [in Russian], Atomizdat, Moscow, 1965. 4. V. D. Rusanov, Modern Methods in Plasma Diagnostics [in Russian], Oosatomizdat, Moscow, 1962. 5. D. E. Ashby and T. F. Iepheoot, Appl. Phys. Letters., 8, no. 1, 13, 1963. 6. I. B. Gerardo, J. T. Verdeyen, and M. A. Ousinow, J. Appl. Phys., 36, no. i1, 3526, 1965. 7. I. M. P. Quinn, J. NucL Energy, C7, no. 2, 113, 1965. 8. V. L. Ginzburg, Propagation of Electromagnetic Waves in Plasma [in Russian], Fizmatgiz, Moscow, 1960. 9. I. Hasted, The Physics of Atomic Collisions [Russian translation], Izd. Mir, Moscow, 1964. 10, G. Frensis, Ionization Phenomena in Oases, Atomizdat, Moscow, 1964. 11. D. Bates, ed., Atomic and Molecular Processes, Mir, Moscow, 1964. 12. S. A. Syrgii and V. L. Granovskii, Radiotekhnika i eiektronika, 4, no. i, 1854, 1959. 18. V. S. Egorov, ZhTF, 31, no. 9, 352, 1961. 14. V. L. Granovskii, Radiotekhnika i elektronika, 11, no. S, 371, 1966. i3 ]uly 1967

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