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Test of divertor materials under simulated plasma disruption conditions at the SOM electron beam facility
ELSEVIER
Journal of Nuclear Materials 220-222 (1995) 1071-1075
ii;,!:l;;r
Test of divertor materials under simulated plasma disruption conditions at the SOM electron beam facility V. Engelko a, R. Kurunov a, I. Landman b, B. Ljublin a, L. Smirnov a, H. Wiirz c Efremov Institute of Electrophysical Apparatus, 189631 St. Petersburg, Russian Federation b Troitsk Institute for Innovation and Fusion Research, 142092 Troitsk, Russian Federation c Kernforschungszentrum Karlsruhe, Postfach 36 40, 76021 Karlsruhe, Germany
a
Abstract
The SOM electron beam facility at the Efremov Institute at St. Petersburg was used for exploratory plasma stream target experiments under conditions aiming the thermal quench phase of ITER tokamak plasma disruptions. The SOM facility uses a vacuum diode with multipoint explosive emission cathode for e-beam formation and a downstream increasing magnetic field for beam transportation and focusing onto the target. The beam energy is around 100 keV. Pulse durations up to 200 Ixs and energy densities at the target up to 4.5 M J / m 2 are achieved. Optical interferometry and spectroscopy allowed to study the formation and properties of the plasma formed from vaporized target materials in front of the target. Target erosion was also determined. For carbon erosion starts after reaching a threshold energy density value of 1 M J / m 2. The onset of target plasma formation strongly depends on beam power density and for 2 M W / c m 2 starts only after 80 p,s. Temperature and density of the target plasma remain low and the fraction of neutrals is high. Modeling was done with a radiation hydrodynamic code in one-dimensional planar geometry. Multifrequency radiation transport was treated in forward reverse transport approximation. The modeling results in terms of vapor shield formation, target plasma temperature and erosion are in good agreement with the experimental results. Vapor shield formation is negligible. The erosion is mainly determined by the power density of the unattenuated beam. 1. Introduction
During the thermal quench phase of a plasma disruption and during ELMs, the divertor plates are hit by an intense particle flow (electrons and ions). In ITER this flow has the following parameters: particle energy up to 30 keV, pulse duration larger than 100 ixs, energy densities up to 150 M J / m 2 for disruptions and up to 10 M J / m 2 ELMs. Up to now there is no experimental facility which allows the simulation of the disruption conditions adequately in terms of plasma flow parameters. Investigations are carried out with laser and electron beams and with plasma streams [1-3]. Each of these methods has its merits and demerits. The merit of the electron beam facilities is their possibility to define the beam parameters with sufficient accuracy and to control them in a wide range. The disadvantage of the e-beam facilities is the rather high energy of the beam elec-
trons. To establish an effective vapor shield thus requires either rather high beam energy densities or measures to distribute a part of the translational electron energy into gyrational motion. An important problem in disruption simulation is the investigation of the shielding effect of the target plasma formed in front of the divertor plate under the influence of the impinging stream. Numerical simulation is of importance because of the absence of facilities which adequately simulate the disruptive particle stream. To validate and improve the numerical models, experimental investigations of the target plasma characteristics and their dependence on the impinging flow parameters are necessary. First results of such investigations carried out with the electron beam facility SOM are discussed in the present report. Modeling is done in one-dimensional planar geometry by using the radiation hydrodynamics code F O R E V [4]. The multifrequency radiation transport is treated
0022-3115/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00476-5
1072
lA Engelko et al. /Journal of Nuclear Materials 220-222 (1995) 1071-1075
E 6 < 5 insulat
4
-O a/ ta
cathode
1
anode
!
0
window
~I ili I~ diaphragm (~ ,, target
vacuum lock chamber
thermocouple
Fig. 1. Experimental facility SOM.
in forward reverse transport approximation with multigroup Planck opacities. Plasma diffusion across magnetic field lines, heat conduction into the bulk target erosion and melt front propagation into the target are taken into account.
2. Experimental facility SOM The scheme of the SOM facility is shown in Fig. 1. The electrons are produced in a vacuum diode using a multipoint explosive emission cathode [5]. The beam is formed by the Pierce gun in the magnetic field which additionally provides the transport and focusing of the beam to the target. The magnetic field in the cathode region is ~ 0.01 T and in the beam transportation region ~ 0.2-0.3 T. Cylindrical ferromagnetic material inserted behind the target is used for additional focusing of the beam to increase the power density at the target. The beam energy is in the range of 60 to 150 keV, pulse duration is up to 200 Ixs, and at the target energy densities up to 4.5 M J / m 2 are achieved. The maximum beam diameter is around 2 cm. The radial distribution of the current density in the transport region is shown in Fig. 2. In the central beam region up to a radius of around 0.8 cm there exists a rather homogeneous current density. This part of the beam is
0.2
0.4
i
,
0.6
0.8
1.0 1.2 radius (cm)
#
Fig. 2. Radial distribution of beam current density.
used in the experiments. The region with the highest current density is cut off by a graphite diaphragm placed at a distance of -- 1 cm from the target surface. The diameter of the hole in the diaphragm is 10 mm. The transverse electron energy in the transport region amounts up to around 18% of the total energy. By simply measuring the target beam current I t and the accelerating voltage U the power and energy density of the beam are obtained according to UI P = S ,
1 E =
UI t d t ,
with S the beam area. In Fig. 3 typical time dependent voltage and current oscillograms and the beam power density at the target are given for a graphite target. The average diode voltage { U } is 110 kV. The power density fairly well rectangularly shaped amounts up to 2.2 M W / c m 2. The erosion of irradiated materials was determined by weighing the samples before and after irradiation. In these first experiments target orientation always was perpendicular to the guiding magnetic field lines.
u (kV) 100-
•
60- ~
o
V
It
40--
~
10
.~
_
-I 1
a.
20--
a
............... 50
"1, 100
150 time
-1o 200
(ps)
Fig. 3. Typical operational parameters of the SOM facility for graphite targets.
1073
V. Engelko et aL /Journal of Nuclear Materials 220-222 (1995) 1071-1075
0
Plasma expansion across magnetic field lines was not investigated up to now.
j 3. Diagnostics for target plasma analysis For analysis of the target plasma optical interferometry, visible spectroscopy and measurement of the absolute intensity of the plasma continuum radiation were applied. From the interferometer signal the electron density is determined according to K Ne = 2.2 x 1 0 1 3 )tl' with K the measurable displacement of the fringes; A the wavelength of the probing laser radiation and l the thickness of the plasma layer. Assuming the minimum measurable displacement Kmin as 0.1 and A = 6943 and l = 1 cm the minimum detectable plasma electron density is N e m i n = 3 X 1 0 1 6 cm -3. For spectroscopy measurements a spectrograph with gratings of 600 and 1200 l i n e s / m m was used. For registration of the integral plasma spectrum a photofilm o is used. The registered spectrum range 3800-6000 A is defined by the photofilm used and the glass window. The spatial range observed extends from the target surface up to the diaphragam i.e. up to a distance of 1.1 cm from the target. To distinguish lines from continuum radiation and to measure time dependent intensities a monochromator with a grating of 1200 l i n e s / m m and 50 , ~ / m m reverse linear dispersion was used. A photomultiplier is placed behind the exit slit of the monochromator. The wavelength registration region was limited to the visible spectrum range. For absolute registration of the plasma continuum radiation a two channel system with collimators and photomultipliers is used. Calibration was done with a tungsten lamp of known brightness.
4. Experimental results The following regimes at the SOM facility were used for beam target experiments with carbon targets: beam current at the target 7-10 A; average diode voltage ( U ) = 125 kV, pulse duration up to 160 i~s. Within the observable spatial range of 1 cm only continuum radiation and the system of Svan's molecular lines but no line radiation from neutral and ionized atoms was detected. The expansion velocity of the plasma close to the target is 2 × 105 cm/s. This low velocity and the lack of spectrum lines of carbon atoms indicate a plasma temperature below 1 eV. The plasma electron temperature was determined from the spectral distribution of the continuum radiation. Shot to shot registration was used. The continuum intensity was
1 2 3 4
-1
oc~ 2
Nmstart= 1017cm'3 Nmstart= 5 1017cm"3 Nmstart= 1018cm3 / N m s 51018cm' t a r3 t 4 ~ =
I -4,
-6.
I
! .~,
I
I
I
i
1018
rlol 6 ..~ 1
I
0.6
I
0.7 0~8 01.9 1'.0 plasmatemperature(eV) Fig. 4. Continuum radiation intensities and plasma electron densities for graphite as function of plasma temperature, for different molecular densities Nmstart. measured for the four different spectral regions 4000 + 1 , 5 0 0 0 + 1 , 6 0 0 0 + 1 and 7 0 0 0 + 1 ,~. From the wavelength dependent radiation intensity an electron temperature of about 0.7 eV was obtained. From a comparison of the absolutely determined intensity of the continuum radiation with a theoretical calculation the plasma electron temperature and the electron density were obtained [6]. Continuum plasma radiation mainly is produced by bremsstrahlung and recombination processes. For the calculation of plasma continuum radiation additionally the radiation sources bremsstrahlung from interaction of free electrons with neutral molecules, with neutral atoms and molecular ions were taken into account [7]. Calculated radiation intensities and electron densities as function of the density of molecules are shown in Fig. 4 for the wavelength 6920 ,~. The small difference in the plasma density values demonstrates that the continuum radiation is mainly caused by the interaction of plasma ions and electrons. The maximum absolute intensity of the continuum radiation for the carbon plasma close to the target is 10 -3 W / ( c m 3 ,~ sr). According to Fig.4 this corresponds to a plasma density of 7 × 1016 cm -3. At a distance of 1 cm from the target the density decreases to 1016 cm -3. From the interferograms it was concluded that the fringe shift is due to carbon atoms produced by target material evaporation under the impinging electron beam. The density of neutrals near the surface of the graphite sample was obtained to be 5 × 1018 cm -3. So the ionization fraction of the target plasma is rather small. Mass loss results for carbon targets are shown in Fig. 5. For E > 200 J / c m 2 the mass loss rate increases
1074
V. Engelko et al. /Journal of Nuclear Materials 220-222 (1995) 1071-1075
rapidly. The existence of a threshold value for the energy density means that erosion can take place only if the energy density of the electron beam exceeds the density handled by heat conduction into the bulk material. From the time evolution of the continuum radiation it is seen that the formation of the target plasma cloud is considerably delayed. For power densities of 2 M W / c m 2 it starts after about 80 p.s, indicating a threshold energy density for erosion of about 160 J / c m 2.
5. Modeling of plasma stream target interaction
10
",8
F
) 6
).4 -
,t;
| ?, @ 25.0
| 5(?.0
i 75.0
, 100.0
i 125.0
~ 1500
i i i 175.0 2 0 0 0 225.0 250 t i m e (ps)
Modeling was done with the radiation hydrodynamics code FOREV in 1D geometry [4]. Radiation transport is treated in forward reverse transport approximation. The hydrodynamic motion of the plasma is calculated along and across magnetic field lines, heat conduction into the bulk target, erosion and melt front propagation into the target, electron beam stopping and surface and volumetric target heating are taken into account. Calculations for the SOM facility were performed for graphite. Multigroup Planck opacities were obtained from absorption coefficients calculated by using a collisional radiative model thus taking into account that radiation can influence the level population [8]. A monoenergetic electron beam of energy of 110 keV was assumed. Typical results for carbon are shown in Fig. 6. There are shown the time evolution of the target heat flux due to the external electron beam (1), the edge velocity of the target plasma (2), the erosion (3) and the maximum target plasma electron temperature (4). The heat load due to direct heating from the electron beam during all the time dominates. The radiative heat
30, E"
~L
25,
I 2
Vaporization Vaporization
g •~, o
/
h e a t 23 k J / g 59 kJlg
heat
/
/
A
/ 20
A
/ /
15
/
/
8 &
1/
10 /
I
I~
150
200
t
i
f2 /
/
I
300
/
• • • e
80kV lOOkV 110kV
Fig. 6. Typical modeling results for carbon. Monoenergetic electron beam with energy of 110 keV and power density of 2 MW/cm 2.
load remains negligible, no effective vapor shield is formed. The temperature of the target plasma amounts up to 0.65 eV. Vaporization of the target starts with a delay of 70 p~s. Calculated erosion values are shown in Fig. 5 for the two values of the vaporization heat 23 and 59 kJ/g. For 23 k J / g the erosion is 33 p,m, for 59 kJ/g it is 19 ~m for an energy density of 430 J / c m 2. The measured erosion is in between the calculated ones for the two vaporization heat values.
6. Conclusions The rather good agreement between experimental and theoretical results demonstrates the adequacy of the models for electron beam stopping, for heat conduction into the bulk target and for volumetric heating used in the calculations. The limited power density achievable at the SOM facility and the rather high energy of the electron beam do not allow formation of an effective vapor shield. Therefore the observed erosion is rather high and not tokamak typical. To come to a more realistic simulation of the tokamak disruption situation in electron facilities with pulsed diodes the longitudinal part of the electron energy has to be decreased and the beam energy density has to be increased. This possibility will be realized in the upgraded facility ELDIS being under testing now at Efremov. ELDIS is intended to achieve beam power densities of at least 10 M W / c m 2 at a longitudinal energy of about l0 keV and a total energy of about 70 keV.
I 400
beam energy density (J/cm 2) Fig. 5. Measured and calculated erosion for carbon. The average diode voltage is indicated, the heat of vaporization used are 23 and 59 kJ/g.
References [1] Van der Laan et al., Proc, 2nd Int. Syrup. on Fusion Nucl. Technology, Karlsruhe, June 2-7, 1991, Part C, p. 135.
V. Engelko et al. /Journal of Nuclear Materials 220-222 (1995) 1071-1075 [2] M. Akiba et al., Proc 13th Syrup. on Fusion Engeneering, Knoxwille, 1989, p. 529. [3] N.I. Arkhipov et al., Proc. Int. Conf. on Phenomena in Ionized Gases, ICPIG 21, Sept. 19-24, 1993, Bochum, vol. II, p. 169. [4] I. Landman et al., Proc. Int. Conf. on Phenomena in Ionized Gases, ICPIG 21, Sept. 19-24, 1993, Bochum, vo. II, p. 201.
1075
[5] E.P. Bolshakov et al., Prib. Tech. Eksp. 6 (1988) 18. [6] V.A. Burzev and B.V. Ljublin, Plasma Phys. 9 (2) (1983) 308. [7] B.M. Smirnov, Physics of weakly ionized gases, Moscow, Science (1972) p. 416. [8] B.N. Bazylev et al., Phys. Eng. J. 58 (6) (1990) 1012 (in Russian).
Journal of Nuclear Materials 220-222 (1995) 1071-1075
ii;,!:l;;r
Test of divertor materials under simulated plasma disruption conditions at the SOM electron beam facility V. Engelko a, R. Kurunov a, I. Landman b, B. Ljublin a, L. Smirnov a, H. Wiirz c Efremov Institute of Electrophysical Apparatus, 189631 St. Petersburg, Russian Federation b Troitsk Institute for Innovation and Fusion Research, 142092 Troitsk, Russian Federation c Kernforschungszentrum Karlsruhe, Postfach 36 40, 76021 Karlsruhe, Germany
a
Abstract
The SOM electron beam facility at the Efremov Institute at St. Petersburg was used for exploratory plasma stream target experiments under conditions aiming the thermal quench phase of ITER tokamak plasma disruptions. The SOM facility uses a vacuum diode with multipoint explosive emission cathode for e-beam formation and a downstream increasing magnetic field for beam transportation and focusing onto the target. The beam energy is around 100 keV. Pulse durations up to 200 Ixs and energy densities at the target up to 4.5 M J / m 2 are achieved. Optical interferometry and spectroscopy allowed to study the formation and properties of the plasma formed from vaporized target materials in front of the target. Target erosion was also determined. For carbon erosion starts after reaching a threshold energy density value of 1 M J / m 2. The onset of target plasma formation strongly depends on beam power density and for 2 M W / c m 2 starts only after 80 p,s. Temperature and density of the target plasma remain low and the fraction of neutrals is high. Modeling was done with a radiation hydrodynamic code in one-dimensional planar geometry. Multifrequency radiation transport was treated in forward reverse transport approximation. The modeling results in terms of vapor shield formation, target plasma temperature and erosion are in good agreement with the experimental results. Vapor shield formation is negligible. The erosion is mainly determined by the power density of the unattenuated beam. 1. Introduction
During the thermal quench phase of a plasma disruption and during ELMs, the divertor plates are hit by an intense particle flow (electrons and ions). In ITER this flow has the following parameters: particle energy up to 30 keV, pulse duration larger than 100 ixs, energy densities up to 150 M J / m 2 for disruptions and up to 10 M J / m 2 ELMs. Up to now there is no experimental facility which allows the simulation of the disruption conditions adequately in terms of plasma flow parameters. Investigations are carried out with laser and electron beams and with plasma streams [1-3]. Each of these methods has its merits and demerits. The merit of the electron beam facilities is their possibility to define the beam parameters with sufficient accuracy and to control them in a wide range. The disadvantage of the e-beam facilities is the rather high energy of the beam elec-
trons. To establish an effective vapor shield thus requires either rather high beam energy densities or measures to distribute a part of the translational electron energy into gyrational motion. An important problem in disruption simulation is the investigation of the shielding effect of the target plasma formed in front of the divertor plate under the influence of the impinging stream. Numerical simulation is of importance because of the absence of facilities which adequately simulate the disruptive particle stream. To validate and improve the numerical models, experimental investigations of the target plasma characteristics and their dependence on the impinging flow parameters are necessary. First results of such investigations carried out with the electron beam facility SOM are discussed in the present report. Modeling is done in one-dimensional planar geometry by using the radiation hydrodynamics code F O R E V [4]. The multifrequency radiation transport is treated
0022-3115/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3115(94)00476-5
1072
lA Engelko et al. /Journal of Nuclear Materials 220-222 (1995) 1071-1075
E 6 < 5 insulat
4
-O a/ ta
cathode
1
anode
!
0
window
~I ili I~ diaphragm (~ ,, target
vacuum lock chamber
thermocouple
Fig. 1. Experimental facility SOM.
in forward reverse transport approximation with multigroup Planck opacities. Plasma diffusion across magnetic field lines, heat conduction into the bulk target erosion and melt front propagation into the target are taken into account.
2. Experimental facility SOM The scheme of the SOM facility is shown in Fig. 1. The electrons are produced in a vacuum diode using a multipoint explosive emission cathode [5]. The beam is formed by the Pierce gun in the magnetic field which additionally provides the transport and focusing of the beam to the target. The magnetic field in the cathode region is ~ 0.01 T and in the beam transportation region ~ 0.2-0.3 T. Cylindrical ferromagnetic material inserted behind the target is used for additional focusing of the beam to increase the power density at the target. The beam energy is in the range of 60 to 150 keV, pulse duration is up to 200 Ixs, and at the target energy densities up to 4.5 M J / m 2 are achieved. The maximum beam diameter is around 2 cm. The radial distribution of the current density in the transport region is shown in Fig. 2. In the central beam region up to a radius of around 0.8 cm there exists a rather homogeneous current density. This part of the beam is
0.2
0.4
i
,
0.6
0.8
1.0 1.2 radius (cm)
#
Fig. 2. Radial distribution of beam current density.
used in the experiments. The region with the highest current density is cut off by a graphite diaphragm placed at a distance of -- 1 cm from the target surface. The diameter of the hole in the diaphragm is 10 mm. The transverse electron energy in the transport region amounts up to around 18% of the total energy. By simply measuring the target beam current I t and the accelerating voltage U the power and energy density of the beam are obtained according to UI P = S ,
1 E =
UI t d t ,
with S the beam area. In Fig. 3 typical time dependent voltage and current oscillograms and the beam power density at the target are given for a graphite target. The average diode voltage { U } is 110 kV. The power density fairly well rectangularly shaped amounts up to 2.2 M W / c m 2. The erosion of irradiated materials was determined by weighing the samples before and after irradiation. In these first experiments target orientation always was perpendicular to the guiding magnetic field lines.
u (kV) 100-
•
60- ~
o
V
It
40--
~
10
.~
_
-I 1
a.
20--
a
............... 50
"1, 100
150 time
-1o 200
(ps)
Fig. 3. Typical operational parameters of the SOM facility for graphite targets.
1073
V. Engelko et aL /Journal of Nuclear Materials 220-222 (1995) 1071-1075
0
Plasma expansion across magnetic field lines was not investigated up to now.
j 3. Diagnostics for target plasma analysis For analysis of the target plasma optical interferometry, visible spectroscopy and measurement of the absolute intensity of the plasma continuum radiation were applied. From the interferometer signal the electron density is determined according to K Ne = 2.2 x 1 0 1 3 )tl' with K the measurable displacement of the fringes; A the wavelength of the probing laser radiation and l the thickness of the plasma layer. Assuming the minimum measurable displacement Kmin as 0.1 and A = 6943 and l = 1 cm the minimum detectable plasma electron density is N e m i n = 3 X 1 0 1 6 cm -3. For spectroscopy measurements a spectrograph with gratings of 600 and 1200 l i n e s / m m was used. For registration of the integral plasma spectrum a photofilm o is used. The registered spectrum range 3800-6000 A is defined by the photofilm used and the glass window. The spatial range observed extends from the target surface up to the diaphragam i.e. up to a distance of 1.1 cm from the target. To distinguish lines from continuum radiation and to measure time dependent intensities a monochromator with a grating of 1200 l i n e s / m m and 50 , ~ / m m reverse linear dispersion was used. A photomultiplier is placed behind the exit slit of the monochromator. The wavelength registration region was limited to the visible spectrum range. For absolute registration of the plasma continuum radiation a two channel system with collimators and photomultipliers is used. Calibration was done with a tungsten lamp of known brightness.
4. Experimental results The following regimes at the SOM facility were used for beam target experiments with carbon targets: beam current at the target 7-10 A; average diode voltage ( U ) = 125 kV, pulse duration up to 160 i~s. Within the observable spatial range of 1 cm only continuum radiation and the system of Svan's molecular lines but no line radiation from neutral and ionized atoms was detected. The expansion velocity of the plasma close to the target is 2 × 105 cm/s. This low velocity and the lack of spectrum lines of carbon atoms indicate a plasma temperature below 1 eV. The plasma electron temperature was determined from the spectral distribution of the continuum radiation. Shot to shot registration was used. The continuum intensity was
1 2 3 4
-1
oc~ 2
Nmstart= 1017cm'3 Nmstart= 5 1017cm"3 Nmstart= 1018cm3 / N m s 51018cm' t a r3 t 4 ~ =
I -4,
-6.
I
! .~,
I
I
I
i
1018
rlol 6 ..~ 1
I
0.6
I
0.7 0~8 01.9 1'.0 plasmatemperature(eV) Fig. 4. Continuum radiation intensities and plasma electron densities for graphite as function of plasma temperature, for different molecular densities Nmstart. measured for the four different spectral regions 4000 + 1 , 5 0 0 0 + 1 , 6 0 0 0 + 1 and 7 0 0 0 + 1 ,~. From the wavelength dependent radiation intensity an electron temperature of about 0.7 eV was obtained. From a comparison of the absolutely determined intensity of the continuum radiation with a theoretical calculation the plasma electron temperature and the electron density were obtained [6]. Continuum plasma radiation mainly is produced by bremsstrahlung and recombination processes. For the calculation of plasma continuum radiation additionally the radiation sources bremsstrahlung from interaction of free electrons with neutral molecules, with neutral atoms and molecular ions were taken into account [7]. Calculated radiation intensities and electron densities as function of the density of molecules are shown in Fig. 4 for the wavelength 6920 ,~. The small difference in the plasma density values demonstrates that the continuum radiation is mainly caused by the interaction of plasma ions and electrons. The maximum absolute intensity of the continuum radiation for the carbon plasma close to the target is 10 -3 W / ( c m 3 ,~ sr). According to Fig.4 this corresponds to a plasma density of 7 × 1016 cm -3. At a distance of 1 cm from the target the density decreases to 1016 cm -3. From the interferograms it was concluded that the fringe shift is due to carbon atoms produced by target material evaporation under the impinging electron beam. The density of neutrals near the surface of the graphite sample was obtained to be 5 × 1018 cm -3. So the ionization fraction of the target plasma is rather small. Mass loss results for carbon targets are shown in Fig. 5. For E > 200 J / c m 2 the mass loss rate increases
1074
V. Engelko et al. /Journal of Nuclear Materials 220-222 (1995) 1071-1075
rapidly. The existence of a threshold value for the energy density means that erosion can take place only if the energy density of the electron beam exceeds the density handled by heat conduction into the bulk material. From the time evolution of the continuum radiation it is seen that the formation of the target plasma cloud is considerably delayed. For power densities of 2 M W / c m 2 it starts after about 80 p.s, indicating a threshold energy density for erosion of about 160 J / c m 2.
5. Modeling of plasma stream target interaction
10
",8
F
) 6
).4 -
,t;
| ?, @ 25.0
| 5(?.0
i 75.0
, 100.0
i 125.0
~ 1500
i i i 175.0 2 0 0 0 225.0 250 t i m e (ps)
Modeling was done with the radiation hydrodynamics code FOREV in 1D geometry [4]. Radiation transport is treated in forward reverse transport approximation. The hydrodynamic motion of the plasma is calculated along and across magnetic field lines, heat conduction into the bulk target, erosion and melt front propagation into the target, electron beam stopping and surface and volumetric target heating are taken into account. Calculations for the SOM facility were performed for graphite. Multigroup Planck opacities were obtained from absorption coefficients calculated by using a collisional radiative model thus taking into account that radiation can influence the level population [8]. A monoenergetic electron beam of energy of 110 keV was assumed. Typical results for carbon are shown in Fig. 6. There are shown the time evolution of the target heat flux due to the external electron beam (1), the edge velocity of the target plasma (2), the erosion (3) and the maximum target plasma electron temperature (4). The heat load due to direct heating from the electron beam during all the time dominates. The radiative heat
30, E"
~L
25,
I 2
Vaporization Vaporization
g •~, o
/
h e a t 23 k J / g 59 kJlg
heat
/
/
A
/ 20
A
/ /
15
/
/
8 &
1/
10 /
I
I~
150
200
t
i
f2 /
/
I
300
/
• • • e
80kV lOOkV 110kV
Fig. 6. Typical modeling results for carbon. Monoenergetic electron beam with energy of 110 keV and power density of 2 MW/cm 2.
load remains negligible, no effective vapor shield is formed. The temperature of the target plasma amounts up to 0.65 eV. Vaporization of the target starts with a delay of 70 p~s. Calculated erosion values are shown in Fig. 5 for the two values of the vaporization heat 23 and 59 kJ/g. For 23 k J / g the erosion is 33 p,m, for 59 kJ/g it is 19 ~m for an energy density of 430 J / c m 2. The measured erosion is in between the calculated ones for the two vaporization heat values.
6. Conclusions The rather good agreement between experimental and theoretical results demonstrates the adequacy of the models for electron beam stopping, for heat conduction into the bulk target and for volumetric heating used in the calculations. The limited power density achievable at the SOM facility and the rather high energy of the electron beam do not allow formation of an effective vapor shield. Therefore the observed erosion is rather high and not tokamak typical. To come to a more realistic simulation of the tokamak disruption situation in electron facilities with pulsed diodes the longitudinal part of the electron energy has to be decreased and the beam energy density has to be increased. This possibility will be realized in the upgraded facility ELDIS being under testing now at Efremov. ELDIS is intended to achieve beam power densities of at least 10 M W / c m 2 at a longitudinal energy of about l0 keV and a total energy of about 70 keV.
I 400
beam energy density (J/cm 2) Fig. 5. Measured and calculated erosion for carbon. The average diode voltage is indicated, the heat of vaporization used are 23 and 59 kJ/g.
References [1] Van der Laan et al., Proc, 2nd Int. Syrup. on Fusion Nucl. Technology, Karlsruhe, June 2-7, 1991, Part C, p. 135.
V. Engelko et al. /Journal of Nuclear Materials 220-222 (1995) 1071-1075 [2] M. Akiba et al., Proc 13th Syrup. on Fusion Engeneering, Knoxwille, 1989, p. 529. [3] N.I. Arkhipov et al., Proc. Int. Conf. on Phenomena in Ionized Gases, ICPIG 21, Sept. 19-24, 1993, Bochum, vol. II, p. 169. [4] I. Landman et al., Proc. Int. Conf. on Phenomena in Ionized Gases, ICPIG 21, Sept. 19-24, 1993, Bochum, vo. II, p. 201.
1075
[5] E.P. Bolshakov et al., Prib. Tech. Eksp. 6 (1988) 18. [6] V.A. Burzev and B.V. Ljublin, Plasma Phys. 9 (2) (1983) 308. [7] B.M. Smirnov, Physics of weakly ionized gases, Moscow, Science (1972) p. 416. [8] B.N. Bazylev et al., Phys. Eng. J. 58 (6) (1990) 1012 (in Russian).