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Modelling of the impurity pumping by a tokamak scrape-off layer
194
Journal of Nuclear Materials 121 (1984) 194-198 North-Holland, Amsterdam
MODELLING OF THE IMPURITY PUMPING BY A TOKAMAK SCRAPEOFF LAYER J. NEUHAUSER,
W. SCHNEIDER,
R. WUNDERLICH
and K. LACKNER
Max - Planck - Institut ftir Plasmaphysik, E URA TOM Association, D - 8046 Garching, Fed. Rep. Germany
and K. BEHRINGER
*
JET Joint Undertaking Culham, UK
The impurity flow along magnetic field lines in a collisional tokamak scrape-off layer is numerically investigated using a testfluid approach. Transport perpendicular to the magnetic field is approximately included by a local loss time constant rl. Results for various impurities and hydrogen background plasma parameters show the significance of thermal forces in the high recycling, subsonic flow regime. In this case, impurity flow reversal on “hot” field lines may cause impurity circulation in the scrap-off layer and, as a consequence, a stronger coupling between the main plasma and a separate pumping chamber than previously assumed.
1. Iatmduetlon
2. Model
While a lot of theoretical and experimental work has been done in the past concerning impurity transport in the bulk plasma, there is much less knowledge about the impurity behaviour in the equally important, highly inhomogeneous boundary layer. Recent experimental results, especially from divertor tokamaks yielded encouraging results with respect to global impurity control. On the other side, specific impurity puffing experiments at ASDEX [l] revealed a rather complex impurity flow history in the high recycling divertor regime, partly in severe contradiction to simple impurity recycling and pumping models. The theoretical approach and the results described below may be an important step towards the understanding of these results and their extrapolation to large fusion machines. The testfluid model used is especially adapted to the high density, low temperature edge presently favoured. It complements alternative single particle or kinetic approaches more appropriate for lower collisionality.
In the high recycling regime of present-day tokamaks like ASDEX or of future experiments like INTOR, the mean free path of all relevant particles in the scrape-off layer is small compared with typical system dimensions and a fluid description may be adequate. In view of the low impurity content measured in ASDEX and the small tolerable impurity contamination in future fusion experiments, a test fluid approach seems to be justified. This requires n,Z’ -=zn,, where ne is the electron density and nz is the density of the Z times ionized impurities. In this limit we may neglect collisions between impurities and also their influence on the background hydrogen plasma. Each ionization stage is then treated as a separate fluid which is coupled to neighbouring states via ionization and recombination and to the hydrogen background plasma via collisions and the ambipolar electric field E [2],
l
On leave from Max-Planck-Institut
fur Plasmaphysik.
n,eE = -ape/as
- 0.714 a(kT,)/ar,
pe = n,kT,, T, = electron temperature, e = 1.6 X lo-l9 As. For simplicity, the impurity temperature T, is assumed to be equal to the hydrogen ion temperature Ti, instead of solving an energy equation for each charge state. s is the spatial coordinate along field lines. Presently only the impurity flow along field lines is treated
0022-3115/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J. Neuhauser et al. /
Model&g of impurity pumping
in detail, while the perpendicular transport (diffusion and drift motion across field lines) is simulated by a local impurity loss time constant TV . The physical interpretation of r1 will be discussed later on in more detail. Altogether we solve the following set of equations:
--aZ"Z
a(e) -_-sznz!p
=sz-IPZ-,Vz-I
+R pZ=mznz,
as
-(Sz-IPZ-I +RZ+IPZ+I)~Z
z+lPz+lvz+I - mzVzdz, Pz=nzkTz,
lgZ
mz
is the impurity mass, Sznz and R,n, are the ionization and recombination rates, V, is the impurity flow velocity and d,(s) is an externally prescribable impurity source depending on the scenario to be considered. 7z is the Spitzer slowing-down time [3]. For the electron thermal force coefficient, following the derivation of Braginski [2], we get a, = 0.71Z2. For the ion thermal force coefficient fiz, the expression given by Chapman [4] is used, the asymptotic value for heavy impurities being Bz = 2.65Z2. Except for the perpendicular loss term, these equations and their numerical solution are the same as in ref. [5], where the principle mechanisms involved in the parallel impurity transport have been investigated. It will be shown, however, that the perpendicular transport is crucial for a realistic assessment of the impurity pumping efficiency of a divertor or pumped limiter. Since we are following the spatial distribution of individual charged states, the calculation of the instantaneously radiated power or the electron cooling rate is straight forward. In fact, the charge state distribution is usually far from coronal equilibrium. Charge exchange recombination with neutral hydrogen is also included. The hydrogen background plasma parameters and the neutral hydrogen density are taken from the one-dimensional hydrodynamic scrape-off model described in ref. [6].
4. Rate coefficients and radiation data The ionization rate coefficients are calculated proposed by Lotz [7]. The radiative recombination
as is
195
treated the usual way, i.e. applying the hydrogen formula and introducing effective quantum numbers. For dielectronic recombination, the Burgess prescription [8] has been used basically, but taking into account modifications by Merts et al. [9]. A density dependence of the latter rate coefficients has been adopted as suggested in ref. [lo]. For calculating resonance line radiation the van Regemorter formula [ll] is applied, the Gaunt factors being taken from Mewe [12]. In order to calculate the total power emitted by line radiation, two effective resonance lines have been defined for each ionization stage as to account for An = 0 and An + 0 transitions. For this purpose we use processed data sets taken from Wiese et al. [13] for light impurities (He to Ne) and from Fuhr et al. [14] for iron. In the case of optically forbidden lines, the f-values of the allowed lines are used and the Gaunt factors are taken again from Mewe’s prescription 1121.The resonance line data for allowed transitions are also used for calculating the dielectronic recombination rate coefficients. Charge exchange recombination cross sections were taken from ref. [15].
5. Hydrogen scmpe-off plasma at high recycling The results of the hydrodynamic scrape-off layer model [6] show that the flow velocity is highly subsonic outside the divertor in case of strong target recycling and the total plasma pressure becomes constant there along field lines. Fig. 1 shows a typical high recycling case calculated for ASDEX geometry. The temperatures and the hydrogen density and flow velocity are given along field lines from the midplane (s = 0) through the divertor throat (s = 12 m) to the target plates (S = 15 m). The data correspond to a total particle loss of 2 X 1021 s-’ and an energy loss of 1.5 MW, if an average scrape-off layer width of 2 cm and a double-null divertor are assumed. The ratio of the ion to electron energy input (1: 20 in this case) determines the relation between q and T, and their spatial gradients and is therefore an important parameter. The hydrogen atom density in the divertor plasma is around no = 6 x 10” cmw3. The Mach number in the plateau outside the divertor is very low, M,, = 0.03. These parameters are assumed to be representative for the hot layer near the separatrix, where most of the energy is transported away. Farther out in the low temperature wing, however, the energy flow and the corresponding recycling decrease, resulting in a higher local Mach number as indicated by the hydrodynamic code results. A more detailed discussion of the scaling
1%
J. Neuhauser et al. / Modelling of impurity pumping
1.0
- *.
Fe
j I
I
I
0.25 0
3
slml
12
15
Fig. 1. Variation of the hydrogen plasma parameters along magnetic field lines for an ASDEX-type configuration and high divertor recycling conditions (s = 0: midplane; s = 15 m: target plate; s = 12 m: divertor throat).
0
0 3 12 15 a Iml Fig. 2. Normalized density profiles for individual iron charged states along magnetic field lines (Z= total iron density). A homogeneous Fe II source is chosen for 0
of the scrape-off layer parameters and their physical origin is given in ref. [6]. A two-dimensional code has been written, but results are not yet available in sufficient detail.
6. Results and discussion
It has been shown in a previous paper [S] that at high Mach number (M = l), the impurities are swept onto the target plates together with the hydrogen. For sufficiently low Mach number and large temperature gradients, however, impurity flow reversal was found with subsequent accumulation near the divertor throat or even in the main chamber. The flow reversal was caused by thermal forces (mainly between the impurities and hydrogen ions) pointing towards high temperature. A simple criterion for practical cases (T, = Ti) is that flow reversal occurs if the local Mach number M becomes smaller than the ratio of the ion mean free path Xi to the temperature gradient length X,, i.e. M < A,/&. No transport across field lines was considered in this strictly one-dimensional model. In the present paper, the two-dimensional structure of the scrape-off layer is approximated by sub-dividing the scrape-off layer into two regions: a hot part close to the separatrix, where most of the parallel energy flow is concentrated, and a cold scrape-off layer wing. The impurity transport is treated in detail in the hot layer only because of the variety of competing processes occurring there. In the low temperature wing frictional coupling is likely to be dominant and impurities can be removed on the millisecond time scale. This cold layer and eventually wall pumping (in case of metallic impurities) is taken into account only by assuming a loss time TV from the hot layer.
It is assumed that there is no net outflux at the bulk plasma side in the final stationary state. Of course, a reasonable choice for r1 requires already some idea about the two-dimensional structure of the hydrogen background plasma, especially the radial variation of the parallel flow velocity V. In order to get a rough idea about the pumping efficiency of the scrape-off layer, we consider two qualitatively different scenarios. In the first scenario, we assume an iron source near the torus midplane, absorption plus self-sputtering at a stainless steel target plate and TV = 1 ms. Fig. 2 shows the charge state distribution and the total density along field lines. Clearly, iron tends to accumulate near the midplane. The density is however, limited by cross diffusion and pumping at the wall or outflow along outer field lines and is therefore proportional to the loss time TV. A small part of the iron ions is driven into the divertor in the hot layer itself by the impurity pressure gradient. Only these ions have the chance to sputter target material, since their final kinetic energy is high [S]. The penetration depth of secondary iron particles has been somewhat arbitrarily chosen to get a strong self-sputtering flux enhancement, just at the starting point of an avalanche. Nevertheless these secondary particles are efficiently isolated from the main plasma, since they are concentrated in the high Mach number region near the target plate, where backward thermal forces are small compared to friction. If, however, iron is sputtered in or near to the divertor throat by energetic hydrogen neutrals, it would rapidly drift into the main chamber. In the second scenario a fixed amount of neon is assumed in the vessel, obtained by a short neon puff in the main chamber or the divertor. 100% recycling of neon (Ne II source in the divertor) and TV = 1 ms is
J. Neuhawer et al. / Modeling of impurity pumping
assumed. The final state is then determined by a homogeneous neon (Ne II) recycling source in the divertor. The fact that hydrogen neutrals penetrate farther into the divertor throat than neon neutrals is taken into account by a .dightly narrower neon recycling source width along field lines. The result is rather sensitive to this choice, indicating the importance of an optimum throat design. The resulting neon radiation profile along field lines is shown in fig. 3. The density profiles are similar, since the radiation efficiency of these low-Z states is only weakly dependent on Z. Charge exchange recombination turns out to be a small effect. The maximum of 1.6 W/ems corresponds to about 1% neon in the divertor. For such a impurity level the testfluid approach is still valid, but radiation loss would be already a non-negligible contribution to the power balance. An important difference from iron is that neon, being a rare gas, is not pumped at the target plate or the divertor walls and therefore fills the whole divertor. A small part is re-ionized close to the narrow divertor throat and quickly driven into the main chamber by the thermal force drift motion. From there it may eventually return to the divertor on “cold” field lines, simulated here by r,, = 1 ms. Obviously, the neon distribution between the main chamber and the divertor (i.e. the average neon retention in the divertor) is determined by three major processes: The neon recycling profile in the divertor compared to that of hydrogen, especially near the divertor throat, the thermal force drift velocity into the main chamber, and the backflow from the main chamber on the cool scrape-off layer wing. Until now, the recycling profile in the divertor and the cross diffusion and backflow time constant 71 are only rough estimates based on the ASDEX geometry. A two-dimen-
-0
3
sfml
Fig. 3. Neon radiation profiles obtained for a fixed total number of particks in the vessel, rL = 1 ms and 100% recycling in the divertor chamber. The absolute values correspond to 1% neon at the point of maximum radiation (S = 14 m).
197
sional scrape-off layer model and a Monte Carlo recycling description should allow for a more quantitative answer. We emphasize that this model assumes a quite rapid circulation of impurities in the scrape-off layer, the average divertor retention being determined by the balance of inflow and outflow, which in turn is strongly dependent on the hydrogen background pattern and the throat design.
7. Summary On the basis of a multi-testfluid model for impurity flow along magnetic field lines [S] we have constructed pumping scenarios for metallic and gaseous (i.e. recycling) impurities. A hydrogen background plasma characterized by strong recycling in a separate chamber (pumped limiter or divertor) and highly subsonic flow outside the chamber has been chosen, The impurity transport in the high temperature, subsonic scrape-off layer close to the separatrix was simulated in detail because of the variety of competing processes occurring there. Cross field transport to the wall or to the low recycling, high Mach number wing of the scrape-off region was simulated by a local loss time constant TV. It was shown that impurity removal from the main chamber is strongly inhibited in the hot part of the scrape-off layer because of thermal forts pointing towards high temperature. Impurities ionized near the throat of the pumping chamber (metallic or gaseous) are even flowing back into the main chamber on these “hot” field lines because of the same thermal forces. For gaseous impurities a rapid circulation in the scrapeoff layer may be set up by pumping along “cold” field lines and backflow along “hot” field lines, causing a stronger impurity coupling between the main plasma and a separate pumping chamber than assumed previously. The final density distribution is then determined by the balance of inflow and outflow, and depends on details of the chamber recycling of hydrogen and impurities and the two-dimensional structure of the scrape-off layer. Only metallic impu~ti~ born in the vicinity of the target plates, where N = 1 holds, are efficiently isolated from the main chamber. According to this general picture, an optimization of the divertor action will require a careful design of the throat region. In the present model the cross field transport was not specified in detail. In fact, a locally varying radial drift motion between hydrogen and impurities could significantly influence the flow pattern and cause an up-down asymmetry in a double-null configuration. Also transport near an X-point has not been considered.
198
J. Neuhauser et al. / Modelling
Comparing with experimental results from ASDEX [l] the impurity flow pattern postulated above seems to produce much fewer inconsistencies than previous models assuming a backflow of impurities from the divertor in form of neutral atoms. The low hydrogen Mach number case (Mr = 0.03) chosen for demonstration of the principle effects may be an extreme case for ASDEX, though the general features prevail also for higher M. However, Mach numbers of only a few percent are in fact envisaged for INTOR [16].
AClClSO_tS We thank Dr. Fussmann and the ASDEX team for discussions concerning their experimental results.
[l] G. Fussmano et al., J. Nucl. Mater. 121 (1984) 164 (these proceedings). [2] S.I. Braginsky, in: Reviews of Plasma Physics, Vol. 1, Ed. M.A. Leontovich (Consultants Bureau, New York, 1965) p. 205. [3] L. Spitzer, Jr., Physics of Fully Ionized Gases, 2nd ed. (Interscience, New York, 1962). [4] S. Chapman, Proc. Phys. Sot. 72 (1958) 353.
of impurity pumping
[5] J. Neuhauser, W. Schneider and R. Wunderlich, in: Proc. 11th Europ. Conf. on Controlled Fusion and Plasma Physics, Aachen, Germany, 5-9 Sept. 1983; Vol. II, 475. see also: J. Neuhauser et al., Lab. Report IPP l/216 (1983) Garching, Germany. [6] R. Chodura, K. Lackner, J. Neuhauser and W. Schneider; in: Proc. 9th Intern. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, Baltimore, USA, 1982, Vol. 1 (IAEA, Vienna,) p. 313, paper CN-41/D-3-1; W. Schneider et al., J. Nucl. Mater. 121 (1984) 178 (these proceedings). [7] W. Lots, Lab. Reports IPP l/62 (1967) and IPP l/76 (1968) Garching, Germany. [8] A. Burgess, Astrophys. J. 141 (1968) 1588. [9] A.L. Merts, R.D. Cowan and N.H. Magee, Los Alamos Scientific Laboratory Report LA-6220-MS (1976). [lo] D.E. Post, R.V. Jensen, C.B. Tarter, W.H. Grasberger and W.A. Lokke, Atomic Data and Nuclear Data Tables 20 (1977) 397. [ll] H. van Regemorter, Astrophys. J. 136 (1%2) 906. [12] R. Mewe, Astron. Astrophys. 20 (1972) 215. [13] W.L. Wiese, M.W. Smith and B.M. Glennon, National Bureau of Standards, Report NSRDS-NBS4 (1966). [14] J.R. Fuhr, G.A. Martin, W.L. Wiese, S.M. Younger, J. Phys. Chem. Ref. Data 10 (1981) 305. [15] M.E. Puiatti, C. Breton, C. DeMichelis and M. Mattioli; Plasma Phys. 23 (1981) 1075. [16] M.F.A. Harrison, P.J. Harbour and E.S. Hotston, Lab. Report CLM-P668,1982, Culham, UK.
Journal of Nuclear Materials 121 (1984) 194-198 North-Holland, Amsterdam
MODELLING OF THE IMPURITY PUMPING BY A TOKAMAK SCRAPEOFF LAYER J. NEUHAUSER,
W. SCHNEIDER,
R. WUNDERLICH
and K. LACKNER
Max - Planck - Institut ftir Plasmaphysik, E URA TOM Association, D - 8046 Garching, Fed. Rep. Germany
and K. BEHRINGER
*
JET Joint Undertaking Culham, UK
The impurity flow along magnetic field lines in a collisional tokamak scrape-off layer is numerically investigated using a testfluid approach. Transport perpendicular to the magnetic field is approximately included by a local loss time constant rl. Results for various impurities and hydrogen background plasma parameters show the significance of thermal forces in the high recycling, subsonic flow regime. In this case, impurity flow reversal on “hot” field lines may cause impurity circulation in the scrap-off layer and, as a consequence, a stronger coupling between the main plasma and a separate pumping chamber than previously assumed.
1. Iatmduetlon
2. Model
While a lot of theoretical and experimental work has been done in the past concerning impurity transport in the bulk plasma, there is much less knowledge about the impurity behaviour in the equally important, highly inhomogeneous boundary layer. Recent experimental results, especially from divertor tokamaks yielded encouraging results with respect to global impurity control. On the other side, specific impurity puffing experiments at ASDEX [l] revealed a rather complex impurity flow history in the high recycling divertor regime, partly in severe contradiction to simple impurity recycling and pumping models. The theoretical approach and the results described below may be an important step towards the understanding of these results and their extrapolation to large fusion machines. The testfluid model used is especially adapted to the high density, low temperature edge presently favoured. It complements alternative single particle or kinetic approaches more appropriate for lower collisionality.
In the high recycling regime of present-day tokamaks like ASDEX or of future experiments like INTOR, the mean free path of all relevant particles in the scrape-off layer is small compared with typical system dimensions and a fluid description may be adequate. In view of the low impurity content measured in ASDEX and the small tolerable impurity contamination in future fusion experiments, a test fluid approach seems to be justified. This requires n,Z’ -=zn,, where ne is the electron density and nz is the density of the Z times ionized impurities. In this limit we may neglect collisions between impurities and also their influence on the background hydrogen plasma. Each ionization stage is then treated as a separate fluid which is coupled to neighbouring states via ionization and recombination and to the hydrogen background plasma via collisions and the ambipolar electric field E [2],
l
On leave from Max-Planck-Institut
fur Plasmaphysik.
n,eE = -ape/as
- 0.714 a(kT,)/ar,
pe = n,kT,, T, = electron temperature, e = 1.6 X lo-l9 As. For simplicity, the impurity temperature T, is assumed to be equal to the hydrogen ion temperature Ti, instead of solving an energy equation for each charge state. s is the spatial coordinate along field lines. Presently only the impurity flow along field lines is treated
0022-3115/84/$03.00 0 Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
J. Neuhauser et al. /
Model&g of impurity pumping
in detail, while the perpendicular transport (diffusion and drift motion across field lines) is simulated by a local impurity loss time constant TV . The physical interpretation of r1 will be discussed later on in more detail. Altogether we solve the following set of equations:
--aZ"Z
a(e) -_-sznz!p
=sz-IPZ-,Vz-I
+R pZ=mznz,
as
-(Sz-IPZ-I +RZ+IPZ+I)~Z
z+lPz+lvz+I - mzVzdz, Pz=nzkTz,
lgZ
mz
is the impurity mass, Sznz and R,n, are the ionization and recombination rates, V, is the impurity flow velocity and d,(s) is an externally prescribable impurity source depending on the scenario to be considered. 7z is the Spitzer slowing-down time [3]. For the electron thermal force coefficient, following the derivation of Braginski [2], we get a, = 0.71Z2. For the ion thermal force coefficient fiz, the expression given by Chapman [4] is used, the asymptotic value for heavy impurities being Bz = 2.65Z2. Except for the perpendicular loss term, these equations and their numerical solution are the same as in ref. [5], where the principle mechanisms involved in the parallel impurity transport have been investigated. It will be shown, however, that the perpendicular transport is crucial for a realistic assessment of the impurity pumping efficiency of a divertor or pumped limiter. Since we are following the spatial distribution of individual charged states, the calculation of the instantaneously radiated power or the electron cooling rate is straight forward. In fact, the charge state distribution is usually far from coronal equilibrium. Charge exchange recombination with neutral hydrogen is also included. The hydrogen background plasma parameters and the neutral hydrogen density are taken from the one-dimensional hydrodynamic scrape-off model described in ref. [6].
4. Rate coefficients and radiation data The ionization rate coefficients are calculated proposed by Lotz [7]. The radiative recombination
as is
195
treated the usual way, i.e. applying the hydrogen formula and introducing effective quantum numbers. For dielectronic recombination, the Burgess prescription [8] has been used basically, but taking into account modifications by Merts et al. [9]. A density dependence of the latter rate coefficients has been adopted as suggested in ref. [lo]. For calculating resonance line radiation the van Regemorter formula [ll] is applied, the Gaunt factors being taken from Mewe [12]. In order to calculate the total power emitted by line radiation, two effective resonance lines have been defined for each ionization stage as to account for An = 0 and An + 0 transitions. For this purpose we use processed data sets taken from Wiese et al. [13] for light impurities (He to Ne) and from Fuhr et al. [14] for iron. In the case of optically forbidden lines, the f-values of the allowed lines are used and the Gaunt factors are taken again from Mewe’s prescription 1121.The resonance line data for allowed transitions are also used for calculating the dielectronic recombination rate coefficients. Charge exchange recombination cross sections were taken from ref. [15].
5. Hydrogen scmpe-off plasma at high recycling The results of the hydrodynamic scrape-off layer model [6] show that the flow velocity is highly subsonic outside the divertor in case of strong target recycling and the total plasma pressure becomes constant there along field lines. Fig. 1 shows a typical high recycling case calculated for ASDEX geometry. The temperatures and the hydrogen density and flow velocity are given along field lines from the midplane (s = 0) through the divertor throat (s = 12 m) to the target plates (S = 15 m). The data correspond to a total particle loss of 2 X 1021 s-’ and an energy loss of 1.5 MW, if an average scrape-off layer width of 2 cm and a double-null divertor are assumed. The ratio of the ion to electron energy input (1: 20 in this case) determines the relation between q and T, and their spatial gradients and is therefore an important parameter. The hydrogen atom density in the divertor plasma is around no = 6 x 10” cmw3. The Mach number in the plateau outside the divertor is very low, M,, = 0.03. These parameters are assumed to be representative for the hot layer near the separatrix, where most of the energy is transported away. Farther out in the low temperature wing, however, the energy flow and the corresponding recycling decrease, resulting in a higher local Mach number as indicated by the hydrodynamic code results. A more detailed discussion of the scaling
1%
J. Neuhauser et al. / Modelling of impurity pumping
1.0
- *.
Fe
j I
I
I
0.25 0
3
slml
12
15
Fig. 1. Variation of the hydrogen plasma parameters along magnetic field lines for an ASDEX-type configuration and high divertor recycling conditions (s = 0: midplane; s = 15 m: target plate; s = 12 m: divertor throat).
0
0 3 12 15 a Iml Fig. 2. Normalized density profiles for individual iron charged states along magnetic field lines (Z= total iron density). A homogeneous Fe II source is chosen for 0
of the scrape-off layer parameters and their physical origin is given in ref. [6]. A two-dimensional code has been written, but results are not yet available in sufficient detail.
6. Results and discussion
It has been shown in a previous paper [S] that at high Mach number (M = l), the impurities are swept onto the target plates together with the hydrogen. For sufficiently low Mach number and large temperature gradients, however, impurity flow reversal was found with subsequent accumulation near the divertor throat or even in the main chamber. The flow reversal was caused by thermal forces (mainly between the impurities and hydrogen ions) pointing towards high temperature. A simple criterion for practical cases (T, = Ti) is that flow reversal occurs if the local Mach number M becomes smaller than the ratio of the ion mean free path Xi to the temperature gradient length X,, i.e. M < A,/&. No transport across field lines was considered in this strictly one-dimensional model. In the present paper, the two-dimensional structure of the scrape-off layer is approximated by sub-dividing the scrape-off layer into two regions: a hot part close to the separatrix, where most of the parallel energy flow is concentrated, and a cold scrape-off layer wing. The impurity transport is treated in detail in the hot layer only because of the variety of competing processes occurring there. In the low temperature wing frictional coupling is likely to be dominant and impurities can be removed on the millisecond time scale. This cold layer and eventually wall pumping (in case of metallic impurities) is taken into account only by assuming a loss time TV from the hot layer.
It is assumed that there is no net outflux at the bulk plasma side in the final stationary state. Of course, a reasonable choice for r1 requires already some idea about the two-dimensional structure of the hydrogen background plasma, especially the radial variation of the parallel flow velocity V. In order to get a rough idea about the pumping efficiency of the scrape-off layer, we consider two qualitatively different scenarios. In the first scenario, we assume an iron source near the torus midplane, absorption plus self-sputtering at a stainless steel target plate and TV = 1 ms. Fig. 2 shows the charge state distribution and the total density along field lines. Clearly, iron tends to accumulate near the midplane. The density is however, limited by cross diffusion and pumping at the wall or outflow along outer field lines and is therefore proportional to the loss time TV. A small part of the iron ions is driven into the divertor in the hot layer itself by the impurity pressure gradient. Only these ions have the chance to sputter target material, since their final kinetic energy is high [S]. The penetration depth of secondary iron particles has been somewhat arbitrarily chosen to get a strong self-sputtering flux enhancement, just at the starting point of an avalanche. Nevertheless these secondary particles are efficiently isolated from the main plasma, since they are concentrated in the high Mach number region near the target plate, where backward thermal forces are small compared to friction. If, however, iron is sputtered in or near to the divertor throat by energetic hydrogen neutrals, it would rapidly drift into the main chamber. In the second scenario a fixed amount of neon is assumed in the vessel, obtained by a short neon puff in the main chamber or the divertor. 100% recycling of neon (Ne II source in the divertor) and TV = 1 ms is
J. Neuhawer et al. / Modeling of impurity pumping
assumed. The final state is then determined by a homogeneous neon (Ne II) recycling source in the divertor. The fact that hydrogen neutrals penetrate farther into the divertor throat than neon neutrals is taken into account by a .dightly narrower neon recycling source width along field lines. The result is rather sensitive to this choice, indicating the importance of an optimum throat design. The resulting neon radiation profile along field lines is shown in fig. 3. The density profiles are similar, since the radiation efficiency of these low-Z states is only weakly dependent on Z. Charge exchange recombination turns out to be a small effect. The maximum of 1.6 W/ems corresponds to about 1% neon in the divertor. For such a impurity level the testfluid approach is still valid, but radiation loss would be already a non-negligible contribution to the power balance. An important difference from iron is that neon, being a rare gas, is not pumped at the target plate or the divertor walls and therefore fills the whole divertor. A small part is re-ionized close to the narrow divertor throat and quickly driven into the main chamber by the thermal force drift motion. From there it may eventually return to the divertor on “cold” field lines, simulated here by r,, = 1 ms. Obviously, the neon distribution between the main chamber and the divertor (i.e. the average neon retention in the divertor) is determined by three major processes: The neon recycling profile in the divertor compared to that of hydrogen, especially near the divertor throat, the thermal force drift velocity into the main chamber, and the backflow from the main chamber on the cool scrape-off layer wing. Until now, the recycling profile in the divertor and the cross diffusion and backflow time constant 71 are only rough estimates based on the ASDEX geometry. A two-dimen-
-0
3
sfml
Fig. 3. Neon radiation profiles obtained for a fixed total number of particks in the vessel, rL = 1 ms and 100% recycling in the divertor chamber. The absolute values correspond to 1% neon at the point of maximum radiation (S = 14 m).
197
sional scrape-off layer model and a Monte Carlo recycling description should allow for a more quantitative answer. We emphasize that this model assumes a quite rapid circulation of impurities in the scrape-off layer, the average divertor retention being determined by the balance of inflow and outflow, which in turn is strongly dependent on the hydrogen background pattern and the throat design.
7. Summary On the basis of a multi-testfluid model for impurity flow along magnetic field lines [S] we have constructed pumping scenarios for metallic and gaseous (i.e. recycling) impurities. A hydrogen background plasma characterized by strong recycling in a separate chamber (pumped limiter or divertor) and highly subsonic flow outside the chamber has been chosen, The impurity transport in the high temperature, subsonic scrape-off layer close to the separatrix was simulated in detail because of the variety of competing processes occurring there. Cross field transport to the wall or to the low recycling, high Mach number wing of the scrape-off region was simulated by a local loss time constant TV. It was shown that impurity removal from the main chamber is strongly inhibited in the hot part of the scrape-off layer because of thermal forts pointing towards high temperature. Impurities ionized near the throat of the pumping chamber (metallic or gaseous) are even flowing back into the main chamber on these “hot” field lines because of the same thermal forces. For gaseous impurities a rapid circulation in the scrapeoff layer may be set up by pumping along “cold” field lines and backflow along “hot” field lines, causing a stronger impurity coupling between the main plasma and a separate pumping chamber than assumed previously. The final density distribution is then determined by the balance of inflow and outflow, and depends on details of the chamber recycling of hydrogen and impurities and the two-dimensional structure of the scrape-off layer. Only metallic impu~ti~ born in the vicinity of the target plates, where N = 1 holds, are efficiently isolated from the main chamber. According to this general picture, an optimization of the divertor action will require a careful design of the throat region. In the present model the cross field transport was not specified in detail. In fact, a locally varying radial drift motion between hydrogen and impurities could significantly influence the flow pattern and cause an up-down asymmetry in a double-null configuration. Also transport near an X-point has not been considered.
198
J. Neuhauser et al. / Modelling
Comparing with experimental results from ASDEX [l] the impurity flow pattern postulated above seems to produce much fewer inconsistencies than previous models assuming a backflow of impurities from the divertor in form of neutral atoms. The low hydrogen Mach number case (Mr = 0.03) chosen for demonstration of the principle effects may be an extreme case for ASDEX, though the general features prevail also for higher M. However, Mach numbers of only a few percent are in fact envisaged for INTOR [16].
AClClSO_tS We thank Dr. Fussmann and the ASDEX team for discussions concerning their experimental results.
[l] G. Fussmano et al., J. Nucl. Mater. 121 (1984) 164 (these proceedings). [2] S.I. Braginsky, in: Reviews of Plasma Physics, Vol. 1, Ed. M.A. Leontovich (Consultants Bureau, New York, 1965) p. 205. [3] L. Spitzer, Jr., Physics of Fully Ionized Gases, 2nd ed. (Interscience, New York, 1962). [4] S. Chapman, Proc. Phys. Sot. 72 (1958) 353.
of impurity pumping
[5] J. Neuhauser, W. Schneider and R. Wunderlich, in: Proc. 11th Europ. Conf. on Controlled Fusion and Plasma Physics, Aachen, Germany, 5-9 Sept. 1983; Vol. II, 475. see also: J. Neuhauser et al., Lab. Report IPP l/216 (1983) Garching, Germany. [6] R. Chodura, K. Lackner, J. Neuhauser and W. Schneider; in: Proc. 9th Intern. Conf. on Plasma Physics and Controlled Nuclear Fusion Research, Baltimore, USA, 1982, Vol. 1 (IAEA, Vienna,) p. 313, paper CN-41/D-3-1; W. Schneider et al., J. Nucl. Mater. 121 (1984) 178 (these proceedings). [7] W. Lots, Lab. Reports IPP l/62 (1967) and IPP l/76 (1968) Garching, Germany. [8] A. Burgess, Astrophys. J. 141 (1968) 1588. [9] A.L. Merts, R.D. Cowan and N.H. Magee, Los Alamos Scientific Laboratory Report LA-6220-MS (1976). [lo] D.E. Post, R.V. Jensen, C.B. Tarter, W.H. Grasberger and W.A. Lokke, Atomic Data and Nuclear Data Tables 20 (1977) 397. [ll] H. van Regemorter, Astrophys. J. 136 (1%2) 906. [12] R. Mewe, Astron. Astrophys. 20 (1972) 215. [13] W.L. Wiese, M.W. Smith and B.M. Glennon, National Bureau of Standards, Report NSRDS-NBS4 (1966). [14] J.R. Fuhr, G.A. Martin, W.L. Wiese, S.M. Younger, J. Phys. Chem. Ref. Data 10 (1981) 305. [15] M.E. Puiatti, C. Breton, C. DeMichelis and M. Mattioli; Plasma Phys. 23 (1981) 1075. [16] M.F.A. Harrison, P.J. Harbour and E.S. Hotston, Lab. Report CLM-P668,1982, Culham, UK.