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Numerical investigation of a neutral helium beam as a diagnostic probe in the plasma edges
ELSEVIER
Journal of Nuclear Materials 220-222 (1995) 1057-1060
Numerical investigation of a neutral helium beam as a diagnostic probe in the plasma edges Ken Takiyama
a,
Katsuhiro Mizuno b Tadahiro Katsuta Toshiatsu Oda a
a
Toshihide Ogawa
c
a Department of Applied Physics and Chemistry, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima 724, Japan b Plasma Physics Institute, University of California, Davis and Lawrence Livermore National Laboratory, Livermore, California, USA e Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan
Abstract
We have made a simulation study of the interaction of a He neutral beam and the JFT-2M tokamak plasma by using a set of coupled rate equations. Our objective is to develop a spectroscopic diagnostic based on the He neutral beam to study plasma parameters in the edge region of the tokamak plasma. One of the important issues is the spatial evolution of the metastable helium. Numerical results indicated that the He metastable density was large enough for the measurements in the interaction region, and that the several lower level populations (21p, 31D, etc.) were almost linearly proportional to the plasma density. Hence it is possible to measure the plasma density by observing the emission line originating from the levels. We have also studied the forbidden excitation by a tunable laser (Stark effect) to measure the electric field induced in the plasma edge region.
1. Introduction
Extensive studies have recently been made in the development of diagnostic neutral particle beam techniques for measurement of the ion temperature profile, localized plasma density turbulence and plasma current profile in magnetic fusion plasmas [1-5]. For these purposes elaborate collisional-radiative atomic processes have been utilized. A neutral hydrogen beam has been used in the most cases. A neutral helium beam will be useful as a diagnostic beam, especially in the plasma edges. It is possible to have a significant amount of metastable population in the He beam. Hence, helium is a good candidate for a diagnostic neutral beam. We have developed a diagnostic system based on laser-aided particle probe spectroscopy using a He beam [6,7] for the measurement of high electric fields of a free electron laser (FEL) in the microwave tokamak experiment (MTX) [8]. A metastable He beam was also used to observe density turbulence in the Phaedrus-T tokamak [9]. A time-dependent collisional radiative model was used to numerically investigate the propagation of a
He beam in the tokamak plasmas [10]. More detailed studies, however, are needed with taking into account updated data of the proton-impact cross sections and other effects. In this paper, we describe a numerical simulation study of the He excited states in a neutral beam injected into a medium-size tokamak plasma. The spatial evolutions of the metastable He population were estimated. We are interested in measurements of the electric field induced in the plasma-edge region as well as of the plasma density. We evaluated laser-induced fluorescence emission due to a forbidden transition by the Stark effect.
2. Coilisional radiative model
2.1. Rate equations
A collisional-radiative model is applied to temporal and spatial behavior of the population density nk(X , t) of an excited level of helium atom in a neutral helium
0022-3115/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00473-0
K Takiyama et al. /Journal of Nuch'ar Materials 220-222 (1995) 1057-1060
1(158
beam passing through a plasma. A set of rate equations for nk(x, t) is given by Onk
Onk
3~- + t'b 3X =
-
E i
-
, U A ~ , -
sured the triplet metastable He population in a He beam by observing the laser-induced fluorescences of 388.9 nm (33p-23S) and 706.5 nm (33S-23p) [7]. Our results suggest a possibility to yield the metastable helium by 5% in the initial He beam.
E.~.4x)<~,'o>k, i 3. N u m e r i c a l r e s u l t s a n d d i s c u s s i o n
F_,n~n~(x)<,,~,,~>~, + Y'. n,A,~ i
+ Enine(X)
i>k
3.1. Plasma-density profile and population densities of the excited levels in tokamak
Y',nino(x)(~rpvo)ik i
+(6kl--6km)llm(t)(nmBml--nlBlm),
(1)
where v b is the beam velocity, x is the distance the atom travels in the plasma, n~(x) and no(x) are the electron and proton densities as a function of x, respectively, Aki is the spontaneous transition probability from level k to i, (treVe)ki is the rate coefficient for electron-impact and (~pvp)k, is the rate coefficient for ion impact including the charge exchange processes. The last term on the right hand side corresponds to the laser excitation of the level l to m, where 6kl(6k, ,) is the Kronecker's delta, Itm(t) the laser power density and Bmt(Btm) the induced emission (absorption) coefficient. The number of the levels included in Eq. (1) is 35 for the principal quantum number n = 1-6. For the present calculations we make the following simplifying assumptions. First, the incident beam flux is kept constant, so that the spatial evolution of the level populations can be obtained by putting 8nk/~t = 0 and Ilm(t) = 0. Second, we assume ne(X)= no(x), and the plasma density profile is assumed to be n~,p(x) = n¢,p(a) [1 - ((a - x ) / a ) 2 ] 2, where a is the radius of the plasma column and n~,p(a) denotes the plasma density at the column center. Third, as an example we consider here the following He beam: a beam energy of 50 keV (the corresponding velocity is 1.55 x 10 s c m / s ) , a He atom density of 1 X 10 9 c m - 3 and a beam cross section of 2 x 2 cm 2. T h e n the beam current is 100 mA. The rate coefficients for electron-impact processes of the helium atom were calculated according to Fujimoto [11]. For ion-impact processes, the following data of the cross sections are available: excitations from the ground state to the niL state, where L is the orbital angular m o m e n t u m [12], as well as ionization and charge excange processes [13].
Fig. 1 shows some results on evolutions of nk(x) of several lower levels in the beam propagating across the plasma under conditions of n e = 1 x 1013 cm -3 at the plasma center and Te = 1 keV over the plasma column. The ground state atom density is only slightly attenuated over the plasma column. The singlet metastable level population sharply increases due to strong excitation in the plasma along the beam path and is almost saturated at the plasma center because the metastable atom is hardly destroyed in the opposite side of the plasma with lower plasma density. The 21p level population as well as the 31p level reaches its peak value at the plasma center and decreases with the plasma density in the boundary region of the plasma because these excited levels are rapidly decayed through the strong radiative transition down to the ground state. As shown in Fig. 2, this evolution of the 21P level population agrees almost perfectly with the plasmadensity profile, if both peak values are normalized at
I0"
= } ..... :
:::...... ~
=i
:
{
.'"
=
~"~Ju:°
I S ~
,c,9
o
cz3~
~ , 10 4
10 8
--~
.N
~-:7~:~-~::-~
"
2~s= . . . . . ~
'=
T 31S
10 2
106
2.2. Production of metastable atoms Several data are available for the production of metastable helium by charge exchange processes [14]. The maximum production rate of the metastable atom in hydrogen gas, which is calculated with the data, is a few %. A rate of more than 10% is achieved in alkali-atom gases. In our previous experiments we mea-
!'-
1o' 0
i 10
20
30
_i
:
•
40
50
60
1° ~
70
Distance [cml Fig. 1. Spatial evolutions of the population densities of the He atom levels in the plasma column with a plasma density of l X 1013 cm 3 and at Te.o = l keV.
BL Takiyama et aL /Journal of Nuclear Materials 220-222 (1995) 1057-1060
1059
3.2. Plasma density dependence of level populations in the plasma edge
1.0
0.8
~0.6
~0.4
0.2
0.0 0
10
20
30 40 50 60 70 Distance [cm] Fig. 2. The plasma density profile and a normalized evolution of the 21p level population.
the plasma center. The corresponding evolution of the 3~P level was found to be also well fitted with the plasma-density profile. These results indicate that the electron density measurement can be accurately performed by observing the emitted lines of 58.4 nm (21p-11S) a n d / o r 501.6 nm (31p-21S). The latter line is definitely easily observed.
As shown in Figs. 1 and 2, the level population is rather small in the plasma edge region without the initial 21S level population although the evolution of the calculated level population is well fitted to the plasma density profile. We calculated several level populations versus the plasma density, when we have the metastable level population yielded by 5% in the initial He beam. Fig. 3 shows the calculated results of both (a) the singlet levels and (b) the triplet levels at 6 cm from the plasma edge. Here, the effective plasma density shown on the abscissa means an averaged density over the distance (6 cm) passed by the beam from the plasma edge. The values of the level populations are clearly much larger than the corresponding ones shown in Fig. 1. The population density increases linearly with plasma density for the levels 21p, 31p, 31D, etc. Hence these results indicate that it is possible to measure the plasma density in the edge region by observing the emission lines originating from the levels.
3.3. Laser-induced fluorescence for electric field measurement We can apply the He diagnostic beam to the electric field measurements in tokamak plasma. A helium neu-
(a) 108
{b} 101°
10s
_-
1010
'7 lO,
109 oE
10 7
8
f/? _/
= 106
108 "~
.~
.~
0
""~ ~
0
l0 s
[0 7
o ¢:~
108 .~
= 106
o
e-, o -~.~
105
10 7
E
~
z /
104 10It
1012 Effective plasma density [cm-3]
106 1013
104 10It
1012
J06 1013
Effective plasma density [cm-3]
Fig. 3. (a) The singlet He level populations versus the plasma density when the 21S population is yielded by 5% in the initial He beam. (b) The triplet He level populations versus the plasma density when the 23S population is yielded by 5% in the initial He beam density.
1060
K. Takiyama et al. /Journal of Nuclear Materials 220-222 (1995) 1057-1060 electric field measurements, a slow velocity helium beam is required to minimize the motional Stark effect. 1C E ~~ 1C
Acknowledgements
We would like to thank Dr. H. Maeda of the Japan Atomic Energy Research Institute for his encouragement and interest throughout this study. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture.
e-
c~ 10 © ,~
.
.
!
i
3]D
i
References 2
°
10 0 ~
~
10
15
20
Distance lcm] Fig. 4. Spatial evolution of the calculated enhancement of the 31D level population due to the forbidden excitation for an electric field of 1 kV/cm.
tral beam will be irradiated by a tunable laser to excite the 21S atoms to the 31D level. The excitation is possible due to a forbidden transition by the Stark effect, if an electric field is present. T h e n the resulting fluorescence intensity at 667.8 nm (31D-21P) is proportional to the square of the electric field strength. Fig. 4 shows an example of our calculation for spatial evolution of the enhancement of the 31D level population due to the forbidden excitation for the electric field of 1 k V / c m . The tunable laser has a wavelength width of 4 pm and a power of 4 M W / c m 2. The estimated photon number emitted from the interaction region is 2.6 x 1014 cm -3 s -1. This number is large enough to measure the electric field in a tokamak plasma. It is also noted that an electric field of the order of 100 V / c m may be measurable using a higher level of helium, such as the 41D level. For the
[1] R.J. Fonck, D.S. Darrow and K.P. Jeahning, Phys. Rev. A 29 (1984) 3288. [2] R.J. Fonck, P.A. Duperrex and S.F. Paul, Rev. Sci. Instr. 61 (1990) 3487. [3] Y.J. Kim, R.A. Breun, D. Brouchous and R.J. Fonck, Rev. Sci. Instr. 61 (1990) 3046. [4] A. Boileau, M. von Hellerman et al., J. Phys. B 22 (1989) L145. [5] F.M. Levinton, R.J. Fonck et al., Phys. Rev. Lett. 63 (1989) 2060. [6] T. Oda, K. Odajima et al., Rev. Sci. Instr. 61 (1990) 2964. [7] T. Oda, K. Odajima et al., Proc. 1992 Int. Conf. on Plasma Phys., Innsbruck, 1992, vol. 2, eds. W. Freysinger et al., (Europ. Phys. Soc.) p. 1191. [8] S.L. Allen, M.D. Brown et al., Phys. Rev. Lett. 72 (1994) 1348. [9] H. Evensen, D. Brouchous et al., Rev. Sci. Instr. 63 (1992) 4928. [10] F.M. Levinton, Rev. Sci. Instr. 57 (1986) 1834. [11] T. Fujimoto, J. Quant. Spectrosc. Radiat. Transfer 21 (1979) 439. [12] F.J. de Heer et al., Atomic and Plasma-Material Interaction Data for Fusion, Suppl. J. Nucl. Fusion 3 (1992) 47. [13] R.K. Janev et al., Elementary Processes in HydrogenHelium Plasmas, (Springer, Berlin, 1987). [14] R.E. Miers et al., Phys. Rev. 183 (1969) 213.
Journal of Nuclear Materials 220-222 (1995) 1057-1060
Numerical investigation of a neutral helium beam as a diagnostic probe in the plasma edges Ken Takiyama
a,
Katsuhiro Mizuno b Tadahiro Katsuta Toshiatsu Oda a
a
Toshihide Ogawa
c
a Department of Applied Physics and Chemistry, Faculty of Engineering, Hiroshima University, Higashi-Hiroshima 724, Japan b Plasma Physics Institute, University of California, Davis and Lawrence Livermore National Laboratory, Livermore, California, USA e Japan Atomic Energy Research Institute, Tokai, Ibaraki 319-11, Japan
Abstract
We have made a simulation study of the interaction of a He neutral beam and the JFT-2M tokamak plasma by using a set of coupled rate equations. Our objective is to develop a spectroscopic diagnostic based on the He neutral beam to study plasma parameters in the edge region of the tokamak plasma. One of the important issues is the spatial evolution of the metastable helium. Numerical results indicated that the He metastable density was large enough for the measurements in the interaction region, and that the several lower level populations (21p, 31D, etc.) were almost linearly proportional to the plasma density. Hence it is possible to measure the plasma density by observing the emission line originating from the levels. We have also studied the forbidden excitation by a tunable laser (Stark effect) to measure the electric field induced in the plasma edge region.
1. Introduction
Extensive studies have recently been made in the development of diagnostic neutral particle beam techniques for measurement of the ion temperature profile, localized plasma density turbulence and plasma current profile in magnetic fusion plasmas [1-5]. For these purposes elaborate collisional-radiative atomic processes have been utilized. A neutral hydrogen beam has been used in the most cases. A neutral helium beam will be useful as a diagnostic beam, especially in the plasma edges. It is possible to have a significant amount of metastable population in the He beam. Hence, helium is a good candidate for a diagnostic neutral beam. We have developed a diagnostic system based on laser-aided particle probe spectroscopy using a He beam [6,7] for the measurement of high electric fields of a free electron laser (FEL) in the microwave tokamak experiment (MTX) [8]. A metastable He beam was also used to observe density turbulence in the Phaedrus-T tokamak [9]. A time-dependent collisional radiative model was used to numerically investigate the propagation of a
He beam in the tokamak plasmas [10]. More detailed studies, however, are needed with taking into account updated data of the proton-impact cross sections and other effects. In this paper, we describe a numerical simulation study of the He excited states in a neutral beam injected into a medium-size tokamak plasma. The spatial evolutions of the metastable He population were estimated. We are interested in measurements of the electric field induced in the plasma-edge region as well as of the plasma density. We evaluated laser-induced fluorescence emission due to a forbidden transition by the Stark effect.
2. Coilisional radiative model
2.1. Rate equations
A collisional-radiative model is applied to temporal and spatial behavior of the population density nk(X , t) of an excited level of helium atom in a neutral helium
0022-3115/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00473-0
K Takiyama et al. /Journal of Nuch'ar Materials 220-222 (1995) 1057-1060
1(158
beam passing through a plasma. A set of rate equations for nk(x, t) is given by Onk
Onk
3~- + t'b 3X =
-
E i
-
, U A ~ , -
sured the triplet metastable He population in a He beam by observing the laser-induced fluorescences of 388.9 nm (33p-23S) and 706.5 nm (33S-23p) [7]. Our results suggest a possibility to yield the metastable helium by 5% in the initial He beam.
E.~.4x)<~,'o>k, i 3. N u m e r i c a l r e s u l t s a n d d i s c u s s i o n
F_,n~n~(x)<,,~,,~>~, + Y'. n,A,~ i
+ Enine(X)
i>k
3.1. Plasma-density profile and population densities of the excited levels in tokamak
Y',nino(x)(~rpvo)ik i
+(6kl--6km)llm(t)(nmBml--nlBlm),
(1)
where v b is the beam velocity, x is the distance the atom travels in the plasma, n~(x) and no(x) are the electron and proton densities as a function of x, respectively, Aki is the spontaneous transition probability from level k to i, (treVe)ki is the rate coefficient for electron-impact and (~pvp)k, is the rate coefficient for ion impact including the charge exchange processes. The last term on the right hand side corresponds to the laser excitation of the level l to m, where 6kl(6k, ,) is the Kronecker's delta, Itm(t) the laser power density and Bmt(Btm) the induced emission (absorption) coefficient. The number of the levels included in Eq. (1) is 35 for the principal quantum number n = 1-6. For the present calculations we make the following simplifying assumptions. First, the incident beam flux is kept constant, so that the spatial evolution of the level populations can be obtained by putting 8nk/~t = 0 and Ilm(t) = 0. Second, we assume ne(X)= no(x), and the plasma density profile is assumed to be n~,p(x) = n¢,p(a) [1 - ((a - x ) / a ) 2 ] 2, where a is the radius of the plasma column and n~,p(a) denotes the plasma density at the column center. Third, as an example we consider here the following He beam: a beam energy of 50 keV (the corresponding velocity is 1.55 x 10 s c m / s ) , a He atom density of 1 X 10 9 c m - 3 and a beam cross section of 2 x 2 cm 2. T h e n the beam current is 100 mA. The rate coefficients for electron-impact processes of the helium atom were calculated according to Fujimoto [11]. For ion-impact processes, the following data of the cross sections are available: excitations from the ground state to the niL state, where L is the orbital angular m o m e n t u m [12], as well as ionization and charge excange processes [13].
Fig. 1 shows some results on evolutions of nk(x) of several lower levels in the beam propagating across the plasma under conditions of n e = 1 x 1013 cm -3 at the plasma center and Te = 1 keV over the plasma column. The ground state atom density is only slightly attenuated over the plasma column. The singlet metastable level population sharply increases due to strong excitation in the plasma along the beam path and is almost saturated at the plasma center because the metastable atom is hardly destroyed in the opposite side of the plasma with lower plasma density. The 21p level population as well as the 31p level reaches its peak value at the plasma center and decreases with the plasma density in the boundary region of the plasma because these excited levels are rapidly decayed through the strong radiative transition down to the ground state. As shown in Fig. 2, this evolution of the 21P level population agrees almost perfectly with the plasmadensity profile, if both peak values are normalized at
I0"
= } ..... :
:::...... ~
=i
:
{
.'"
=
~"~Ju:°
I S ~
,c,9
o
cz3~
~ , 10 4
10 8
--~
.N
~-:7~:~-~::-~
"
2~s= . . . . . ~
'=
T 31S
10 2
106
2.2. Production of metastable atoms Several data are available for the production of metastable helium by charge exchange processes [14]. The maximum production rate of the metastable atom in hydrogen gas, which is calculated with the data, is a few %. A rate of more than 10% is achieved in alkali-atom gases. In our previous experiments we mea-
!'-
1o' 0
i 10
20
30
_i
:
•
40
50
60
1° ~
70
Distance [cml Fig. 1. Spatial evolutions of the population densities of the He atom levels in the plasma column with a plasma density of l X 1013 cm 3 and at Te.o = l keV.
BL Takiyama et aL /Journal of Nuclear Materials 220-222 (1995) 1057-1060
1059
3.2. Plasma density dependence of level populations in the plasma edge
1.0
0.8
~0.6
~0.4
0.2
0.0 0
10
20
30 40 50 60 70 Distance [cm] Fig. 2. The plasma density profile and a normalized evolution of the 21p level population.
the plasma center. The corresponding evolution of the 3~P level was found to be also well fitted with the plasma-density profile. These results indicate that the electron density measurement can be accurately performed by observing the emitted lines of 58.4 nm (21p-11S) a n d / o r 501.6 nm (31p-21S). The latter line is definitely easily observed.
As shown in Figs. 1 and 2, the level population is rather small in the plasma edge region without the initial 21S level population although the evolution of the calculated level population is well fitted to the plasma density profile. We calculated several level populations versus the plasma density, when we have the metastable level population yielded by 5% in the initial He beam. Fig. 3 shows the calculated results of both (a) the singlet levels and (b) the triplet levels at 6 cm from the plasma edge. Here, the effective plasma density shown on the abscissa means an averaged density over the distance (6 cm) passed by the beam from the plasma edge. The values of the level populations are clearly much larger than the corresponding ones shown in Fig. 1. The population density increases linearly with plasma density for the levels 21p, 31p, 31D, etc. Hence these results indicate that it is possible to measure the plasma density in the edge region by observing the emission lines originating from the levels.
3.3. Laser-induced fluorescence for electric field measurement We can apply the He diagnostic beam to the electric field measurements in tokamak plasma. A helium neu-
(a) 108
{b} 101°
10s
_-
1010
'7 lO,
109 oE
10 7
8
f/? _/
= 106
108 "~
.~
.~
0
""~ ~
0
l0 s
[0 7
o ¢:~
108 .~
= 106
o
e-, o -~.~
105
10 7
E
~
z /
104 10It
1012 Effective plasma density [cm-3]
106 1013
104 10It
1012
J06 1013
Effective plasma density [cm-3]
Fig. 3. (a) The singlet He level populations versus the plasma density when the 21S population is yielded by 5% in the initial He beam. (b) The triplet He level populations versus the plasma density when the 23S population is yielded by 5% in the initial He beam density.
1060
K. Takiyama et al. /Journal of Nuclear Materials 220-222 (1995) 1057-1060 electric field measurements, a slow velocity helium beam is required to minimize the motional Stark effect. 1C E ~~ 1C
Acknowledgements
We would like to thank Dr. H. Maeda of the Japan Atomic Energy Research Institute for his encouragement and interest throughout this study. This work was supported in part by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture.
e-
c~ 10 © ,~
.
.
!
i
3]D
i
References 2
°
10 0 ~
~
10
15
20
Distance lcm] Fig. 4. Spatial evolution of the calculated enhancement of the 31D level population due to the forbidden excitation for an electric field of 1 kV/cm.
tral beam will be irradiated by a tunable laser to excite the 21S atoms to the 31D level. The excitation is possible due to a forbidden transition by the Stark effect, if an electric field is present. T h e n the resulting fluorescence intensity at 667.8 nm (31D-21P) is proportional to the square of the electric field strength. Fig. 4 shows an example of our calculation for spatial evolution of the enhancement of the 31D level population due to the forbidden excitation for the electric field of 1 k V / c m . The tunable laser has a wavelength width of 4 pm and a power of 4 M W / c m 2. The estimated photon number emitted from the interaction region is 2.6 x 1014 cm -3 s -1. This number is large enough to measure the electric field in a tokamak plasma. It is also noted that an electric field of the order of 100 V / c m may be measurable using a higher level of helium, such as the 41D level. For the
[1] R.J. Fonck, D.S. Darrow and K.P. Jeahning, Phys. Rev. A 29 (1984) 3288. [2] R.J. Fonck, P.A. Duperrex and S.F. Paul, Rev. Sci. Instr. 61 (1990) 3487. [3] Y.J. Kim, R.A. Breun, D. Brouchous and R.J. Fonck, Rev. Sci. Instr. 61 (1990) 3046. [4] A. Boileau, M. von Hellerman et al., J. Phys. B 22 (1989) L145. [5] F.M. Levinton, R.J. Fonck et al., Phys. Rev. Lett. 63 (1989) 2060. [6] T. Oda, K. Odajima et al., Rev. Sci. Instr. 61 (1990) 2964. [7] T. Oda, K. Odajima et al., Proc. 1992 Int. Conf. on Plasma Phys., Innsbruck, 1992, vol. 2, eds. W. Freysinger et al., (Europ. Phys. Soc.) p. 1191. [8] S.L. Allen, M.D. Brown et al., Phys. Rev. Lett. 72 (1994) 1348. [9] H. Evensen, D. Brouchous et al., Rev. Sci. Instr. 63 (1992) 4928. [10] F.M. Levinton, Rev. Sci. Instr. 57 (1986) 1834. [11] T. Fujimoto, J. Quant. Spectrosc. Radiat. Transfer 21 (1979) 439. [12] F.J. de Heer et al., Atomic and Plasma-Material Interaction Data for Fusion, Suppl. J. Nucl. Fusion 3 (1992) 47. [13] R.K. Janev et al., Elementary Processes in HydrogenHelium Plasmas, (Springer, Berlin, 1987). [14] R.E. Miers et al., Phys. Rev. 183 (1969) 213.