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The effect of a magnetic field on electron mobility in a D.C. arc plasma
J. Quant. Spectrosc. Radiat. Transfer Vol. 31, No. I, pp. 91-95, I984 Printed in Great Britain.
0022-4073184 $3.00+ .00 Pergamon Press Ltd.
THE EFFECT OF A MAGNETIC FIELD ON ELECTRON MOBILITY IN A D.C. ARC PLASMA M. S. M. HAS•EM Department of Physics, Faculty of Science, Universityof Zagazig, Egypt
(Received 25 August 1981) Ahstract--A proposed method for electron mobility jze determination in a magnetized arc plasma is described. Applying a nonhomogeneousmagnetic field yields minimum electron mobility at the optimal value of magnetic induction. This value corresponds to the maximum enhancement of the spectral line intensity, the electron concentrationis a maximum, and the plasma temperature is elevated. 1. INTRODUCTION In order to determine the electron mobility of a d.c. arc plasma, the electron concentration n~ and the electrical conductivity (~ = J[E) of the plasma must be determined. The electron mobility can be easily determined for a free burning d.c. arcJ For a magnetized plasma it is very difficult to determine this quantity, since the arc plasma has a conical shape 2-5 in the presence of magnetic induction. It is known that the cathode and anode falls (Vc + V~) vary markedly with both the specimen and the electrode shapes (Ref. 1, p. 44). For this reason, when a magnetic field is applied, both the specimen and the electrodes are not altered and the sum (Vc + V~) is kept constant. 2. THEORETICAL INVESTIGATION Let Vf represent the total potential drop across the electrodes and (Vc + V,) the sum of the cathode and anode falls. Hence, the potential drop across the arc plasma is V~ = V, - ( V~ + Vo).
When measuring the arc current strength i, the quantity (~ = i/vp(f~-~), is proportional to the electrical conductivity (r, i.e., (r ~ (~,
(r = KcL
(1)
where or is calculated as usual ~ from .liE ( f y t cm-t) at zero Gauss, (~ is also calculated from iJVp (1]-1) at zero Gauss and K (cm -~) is the proportionality constant which depends on electrode shape, specimen and the experimental conditions. When K is determined at zero Gauss, the electrical conductivity ~r will be determined at any value of the magnetic induction [see Eq. (I)]. Therefore, the electron mobility /~e at any value of magnetic induction can be determined from
t~, = o'/ene,
(2)
where e is the electron charge (1.6 x 10-19c) and ne is the electron concentration. 3. EXPERIMENTAL STUDIES A Q-24, medium quartz spectrograph (Carl Zeiss, Jena) was used. The working conditions were 8 amp for the arc current and 4 mm for both the diameter and the depth of the graphite crater electrode. The processed plate was measured on a micorphotometer (G.II Carl Zeiss, Jena) and the Zaidel scale was used. The anode excitation technique employed. A graphite powder base containing different elements (amounts of 10- 6 - 10-~ g), thermometric species and manometric species was the charge of the anode crater. The thermometric line pair was Zn(I) 91
92
M.S.M. HASHEM
3072/Zn(I) 3076 A and log [(gAv)3ov2](gAv)3o76]= 2.580J The manometric line pair was Mg(II) 2796/Mg(I) 2780 ~, and log [(gAv)27961(gAv)278o]= -0.726, where A is the transition probability, g is the statistical weight and v is the frequency of transition. 4. PROPOSED METHOD FOR ELECTRON MOBILITY DETERMINATION IN THE MAGNETIZED ARC PLASMA The total voltage drop Vt across the electrodes was measured as a function of gap width for each value of magnetic induction (0, 20, 70, and 100 G). The results obtained are plotted in Fig, 1. The electric field strength E and the cathode and anode falls (Vc + Vo) are estimated from Fig. 1 and are given in Table 1. The arc plasma temperature, the electron concentration (he) and the total voltage drop across the arc gap Vt were estimated for the same values of magnetic
t
vott
90
70 G. 20 G.
80
70
_,260
0G.
u ci
5O
~0
30
I
I
1
I
I
I
0
2
z~
6
8
10
>
mm
Fig. 1. Plot of arc voltage Vt vs gap width at differentvalues of the magneticinduction.7
Table I. The effect of magneticfield on E and (Vc + Va).7 Magnetic Electricfield induction, strength, G E Gauss V/cm 0 20 70 100
30 60 75 80
Cathodeand anode falls (V~+ V~) Volt 36 36 37 37
The effect of a magnetic field on electron mobility in a d.c. arc plasma
93
induction. The results obtained are summarized in Table 2. The intensification ratio I[Io (I and I0 are the spectral line intensities with and without the magnetic field, respectively) of atom and ion lines of Mn(II) 2605 A and Mn(I) 2798 ,~ were determined at different values of magnetic induction. The results obtained are plotted in Fig. 2. Leushacks and Nickel 5 had found the same behaviour of atom and ion lines in the magnetized plasma, as shown in Fig. 3. This figure is plotted from their data. Using a crater diameter of 4 mm, Tables 1 and 2, an arc current of 8 amp, and Eq. (1), the proportionality constant K can be determined. At zero Gauss K was 3.2139 cm -1. By determining 6" at other values of the magnetic induction (20, 70, and 100 G), the corresponding values of electrical conductivity cr can be estimated as shown in Table 3. By substituting for the electrical conductivity o- in Eq. (2), the electron mobility bl,e at 20, 70, and 100 Gauss can be determined (see Table 4). The results obtained in Table 4 are plotted in Fig. 4. DISCUSSION
Most authors dealing with the subject found that the magnetic field at the optimal value gives a maximum enhancement in spectral line intensity. 3'~-1° Figures 2 and 4 show the effect of magnetic field on both the spectral line intensity (Fig. 2) and on electron mobility (Fig. 4). At the optimal value of magnetic induction (70 G), the spectral line intensities (atom and ion lines) are maxima, whereas the electron mobility is minimum, as shown in Figs. 2 and 4, respectively. It is clear that the spectral line intensity curve shows a contrary behaviour to the electron mobility curve. The decrease of electron mobility due to the magnetic field may be hindering the upward flow of excited particles (atoms, ions, and molecules) in the magnetized plasma which, in turn,
Table 2. The dependence of temperature, electron concentration, and voltage drop Vt across the arc on magnetic induction. Magnetic induction,
Arc plasma temperature,
Electron concentration,
Voltage drop across the gap (Vt),
Gauss
K
ne x 10is cm 3
Volt
0 20 70 100
6210 6250 6490 6650
0.69 1.38 2.80 2.07
48 60 67 69
I/To 5.0
z~.0
605 A°
3.0
~
2.0
2798 A°
1.0
0 0
l
I
l
i
J
r
20
40
60
80
100
120,
Gauss
Fig. 2. The effect of magnetic field on the intensification ration IIio of atom and ion lines for Mn(II2) 2605 ,~, and Mn(I) 2798 ~,.7
94
M.S.M. HASHEM
I/Io
0
12
0
0
I
I
I
I
I
t
I
I
50
100
~50
200
250
300
350
400
G.
Fig. 3. The effect of magnetic field on intensification ratio lJlo of atom and ion lines for Ca(ll) 3179/~ and Ca(I) 4302 A.
Table 3. The effect of magnetic induction on electrical conductivity o-.
Magnetic induction G
Electrical conductivity o-,
Gauss
Ohm i. cm-i
0 20 70 100
2,12 1,07 0.85 0.80
Table 4. The effect of magnetic field on electron mobility P-e.
Magnetic induction G,
Electron mobility o.,,
Gauss
cm 2 • V -~ • sec -~
0 20 70 100
1.92 x 104 0.48 x 104 0.18 x 104 0.24 × 104
The effect of a magneticfield on electron mobilityin a d.c. arc plasma
O[
95
F~ ~2.~.~. -1 -1
2.0
1.8C
1./-,,0
1.00
0.60
\ \
0.20[
~_o.~___J I
20
I
40
I
60
I
00
jy J
100
Gauss
Fig. 4. The effect of magneticfield on electron mobility t~e of a magnetizedplasma.
will increase the transit times u of these particles, which finally produce an increase in the spectral line intensities (atom and ion lines). Consequently, the electron mobility decrease may be one of the factors which increases the emitted spectral line intensities for magnetized plasmas. At the optimal value of magnetic induction (70 G), the electron concentration is a maximum and the arc plasma temperature is greater than that at B = 0 G , as shown in Table 2. Consequently, the increase in the spectral line intensity may be due to both an increase in electron concentration and in arc plasma temperature. Harizanov and Zadgorska 9 determined the electron pressure (P,) and the arc plasma temperature of magnetized plasma at one value of the magnetic induction. They found that the magnetic field causes an increase in both electron pressure and arc plasma temperature, These results are in a good agreement with our results. They performed their experiments on different gases at high temperatures.
REFERENCES 1. P. W. J. M. Boumans, Theory of Spectrochemical Excitation. Hilger and Watts, London (1966). 2. D. Lummersheimund H. Nickel, Z Anal. 245, 267 (1969). 3. M. Todorovic,V. Vukanovic,and V. Georgijevic,Spectrochimica Acta 2411,571 (1969). 4. J. Bril, G. Duverneuil.D. F. Leushacke, and H. Nickel, Spectrochimica Acta 27B, 35 (1972). 5. D. F. Leushacke und H. Nickel, Kernforschungsanlage Julieh, Institute fur Reaktorwerkstoffe, Interner Bericht, KFA-IRW-IB-7170, 31 (Juli 1970). 6, P. W. J. M. Boumans, and A. Lurio, Phys. Rev. 136A,376 (1964). 7. M. S, M. Hashem, "Effect of the Variation of the Shape of the External Magnetic Field on the Intensity of spectral Lines", Ph.D. Thesis, EI-AzharUniversity, Egypt (1979). 8. N. Krasnobaeva,Yu. Harizanov, and Z. Zadgorska, Spectrochimica Acta 2411,473 (1969). 9. Yu. Harizanov and Z. Zadgroska, Spectrochimica Acta 25B, 29 (1970). 10. B. Pavlovic and T. Mihalidi,Appl. Spectrosc. 30, 422 (1976). 11. V. Vukanovic,V. Georgijevic,N. Konjevic, and D. Vukanovic,Proc. 12th Colloq. Spectrosc. Int., Exter, p. 193 (1965).
0022-4073184 $3.00+ .00 Pergamon Press Ltd.
THE EFFECT OF A MAGNETIC FIELD ON ELECTRON MOBILITY IN A D.C. ARC PLASMA M. S. M. HAS•EM Department of Physics, Faculty of Science, Universityof Zagazig, Egypt
(Received 25 August 1981) Ahstract--A proposed method for electron mobility jze determination in a magnetized arc plasma is described. Applying a nonhomogeneousmagnetic field yields minimum electron mobility at the optimal value of magnetic induction. This value corresponds to the maximum enhancement of the spectral line intensity, the electron concentrationis a maximum, and the plasma temperature is elevated. 1. INTRODUCTION In order to determine the electron mobility of a d.c. arc plasma, the electron concentration n~ and the electrical conductivity (~ = J[E) of the plasma must be determined. The electron mobility can be easily determined for a free burning d.c. arcJ For a magnetized plasma it is very difficult to determine this quantity, since the arc plasma has a conical shape 2-5 in the presence of magnetic induction. It is known that the cathode and anode falls (Vc + V~) vary markedly with both the specimen and the electrode shapes (Ref. 1, p. 44). For this reason, when a magnetic field is applied, both the specimen and the electrodes are not altered and the sum (Vc + V~) is kept constant. 2. THEORETICAL INVESTIGATION Let Vf represent the total potential drop across the electrodes and (Vc + V,) the sum of the cathode and anode falls. Hence, the potential drop across the arc plasma is V~ = V, - ( V~ + Vo).
When measuring the arc current strength i, the quantity (~ = i/vp(f~-~), is proportional to the electrical conductivity (r, i.e., (r ~ (~,
(r = KcL
(1)
where or is calculated as usual ~ from .liE ( f y t cm-t) at zero Gauss, (~ is also calculated from iJVp (1]-1) at zero Gauss and K (cm -~) is the proportionality constant which depends on electrode shape, specimen and the experimental conditions. When K is determined at zero Gauss, the electrical conductivity ~r will be determined at any value of the magnetic induction [see Eq. (I)]. Therefore, the electron mobility /~e at any value of magnetic induction can be determined from
t~, = o'/ene,
(2)
where e is the electron charge (1.6 x 10-19c) and ne is the electron concentration. 3. EXPERIMENTAL STUDIES A Q-24, medium quartz spectrograph (Carl Zeiss, Jena) was used. The working conditions were 8 amp for the arc current and 4 mm for both the diameter and the depth of the graphite crater electrode. The processed plate was measured on a micorphotometer (G.II Carl Zeiss, Jena) and the Zaidel scale was used. The anode excitation technique employed. A graphite powder base containing different elements (amounts of 10- 6 - 10-~ g), thermometric species and manometric species was the charge of the anode crater. The thermometric line pair was Zn(I) 91
92
M.S.M. HASHEM
3072/Zn(I) 3076 A and log [(gAv)3ov2](gAv)3o76]= 2.580J The manometric line pair was Mg(II) 2796/Mg(I) 2780 ~, and log [(gAv)27961(gAv)278o]= -0.726, where A is the transition probability, g is the statistical weight and v is the frequency of transition. 4. PROPOSED METHOD FOR ELECTRON MOBILITY DETERMINATION IN THE MAGNETIZED ARC PLASMA The total voltage drop Vt across the electrodes was measured as a function of gap width for each value of magnetic induction (0, 20, 70, and 100 G). The results obtained are plotted in Fig, 1. The electric field strength E and the cathode and anode falls (Vc + Vo) are estimated from Fig. 1 and are given in Table 1. The arc plasma temperature, the electron concentration (he) and the total voltage drop across the arc gap Vt were estimated for the same values of magnetic
t
vott
90
70 G. 20 G.
80
70
_,260
0G.
u ci
5O
~0
30
I
I
1
I
I
I
0
2
z~
6
8
10
>
mm
Fig. 1. Plot of arc voltage Vt vs gap width at differentvalues of the magneticinduction.7
Table I. The effect of magneticfield on E and (Vc + Va).7 Magnetic Electricfield induction, strength, G E Gauss V/cm 0 20 70 100
30 60 75 80
Cathodeand anode falls (V~+ V~) Volt 36 36 37 37
The effect of a magnetic field on electron mobility in a d.c. arc plasma
93
induction. The results obtained are summarized in Table 2. The intensification ratio I[Io (I and I0 are the spectral line intensities with and without the magnetic field, respectively) of atom and ion lines of Mn(II) 2605 A and Mn(I) 2798 ,~ were determined at different values of magnetic induction. The results obtained are plotted in Fig. 2. Leushacks and Nickel 5 had found the same behaviour of atom and ion lines in the magnetized plasma, as shown in Fig. 3. This figure is plotted from their data. Using a crater diameter of 4 mm, Tables 1 and 2, an arc current of 8 amp, and Eq. (1), the proportionality constant K can be determined. At zero Gauss K was 3.2139 cm -1. By determining 6" at other values of the magnetic induction (20, 70, and 100 G), the corresponding values of electrical conductivity cr can be estimated as shown in Table 3. By substituting for the electrical conductivity o- in Eq. (2), the electron mobility bl,e at 20, 70, and 100 Gauss can be determined (see Table 4). The results obtained in Table 4 are plotted in Fig. 4. DISCUSSION
Most authors dealing with the subject found that the magnetic field at the optimal value gives a maximum enhancement in spectral line intensity. 3'~-1° Figures 2 and 4 show the effect of magnetic field on both the spectral line intensity (Fig. 2) and on electron mobility (Fig. 4). At the optimal value of magnetic induction (70 G), the spectral line intensities (atom and ion lines) are maxima, whereas the electron mobility is minimum, as shown in Figs. 2 and 4, respectively. It is clear that the spectral line intensity curve shows a contrary behaviour to the electron mobility curve. The decrease of electron mobility due to the magnetic field may be hindering the upward flow of excited particles (atoms, ions, and molecules) in the magnetized plasma which, in turn,
Table 2. The dependence of temperature, electron concentration, and voltage drop Vt across the arc on magnetic induction. Magnetic induction,
Arc plasma temperature,
Electron concentration,
Voltage drop across the gap (Vt),
Gauss
K
ne x 10is cm 3
Volt
0 20 70 100
6210 6250 6490 6650
0.69 1.38 2.80 2.07
48 60 67 69
I/To 5.0
z~.0
605 A°
3.0
~
2.0
2798 A°
1.0
0 0
l
I
l
i
J
r
20
40
60
80
100
120,
Gauss
Fig. 2. The effect of magnetic field on the intensification ration IIio of atom and ion lines for Mn(II2) 2605 ,~, and Mn(I) 2798 ~,.7
94
M.S.M. HASHEM
I/Io
0
12
0
0
I
I
I
I
I
t
I
I
50
100
~50
200
250
300
350
400
G.
Fig. 3. The effect of magnetic field on intensification ratio lJlo of atom and ion lines for Ca(ll) 3179/~ and Ca(I) 4302 A.
Table 3. The effect of magnetic induction on electrical conductivity o-.
Magnetic induction G
Electrical conductivity o-,
Gauss
Ohm i. cm-i
0 20 70 100
2,12 1,07 0.85 0.80
Table 4. The effect of magnetic field on electron mobility P-e.
Magnetic induction G,
Electron mobility o.,,
Gauss
cm 2 • V -~ • sec -~
0 20 70 100
1.92 x 104 0.48 x 104 0.18 x 104 0.24 × 104
The effect of a magneticfield on electron mobilityin a d.c. arc plasma
O[
95
F~ ~2.~.~. -1 -1
2.0
1.8C
1./-,,0
1.00
0.60
\ \
0.20[
~_o.~___J I
20
I
40
I
60
I
00
jy J
100
Gauss
Fig. 4. The effect of magneticfield on electron mobility t~e of a magnetizedplasma.
will increase the transit times u of these particles, which finally produce an increase in the spectral line intensities (atom and ion lines). Consequently, the electron mobility decrease may be one of the factors which increases the emitted spectral line intensities for magnetized plasmas. At the optimal value of magnetic induction (70 G), the electron concentration is a maximum and the arc plasma temperature is greater than that at B = 0 G , as shown in Table 2. Consequently, the increase in the spectral line intensity may be due to both an increase in electron concentration and in arc plasma temperature. Harizanov and Zadgorska 9 determined the electron pressure (P,) and the arc plasma temperature of magnetized plasma at one value of the magnetic induction. They found that the magnetic field causes an increase in both electron pressure and arc plasma temperature, These results are in a good agreement with our results. They performed their experiments on different gases at high temperatures.
REFERENCES 1. P. W. J. M. Boumans, Theory of Spectrochemical Excitation. Hilger and Watts, London (1966). 2. D. Lummersheimund H. Nickel, Z Anal. 245, 267 (1969). 3. M. Todorovic,V. Vukanovic,and V. Georgijevic,Spectrochimica Acta 2411,571 (1969). 4. J. Bril, G. Duverneuil.D. F. Leushacke, and H. Nickel, Spectrochimica Acta 27B, 35 (1972). 5. D. F. Leushacke und H. Nickel, Kernforschungsanlage Julieh, Institute fur Reaktorwerkstoffe, Interner Bericht, KFA-IRW-IB-7170, 31 (Juli 1970). 6, P. W. J. M. Boumans, and A. Lurio, Phys. Rev. 136A,376 (1964). 7. M. S, M. Hashem, "Effect of the Variation of the Shape of the External Magnetic Field on the Intensity of spectral Lines", Ph.D. Thesis, EI-AzharUniversity, Egypt (1979). 8. N. Krasnobaeva,Yu. Harizanov, and Z. Zadgorska, Spectrochimica Acta 2411,473 (1969). 9. Yu. Harizanov and Z. Zadgroska, Spectrochimica Acta 25B, 29 (1970). 10. B. Pavlovic and T. Mihalidi,Appl. Spectrosc. 30, 422 (1976). 11. V. Vukanovic,V. Georgijevic,N. Konjevic, and D. Vukanovic,Proc. 12th Colloq. Spectrosc. Int., Exter, p. 193 (1965).