- Email: [email protected]
Measurement of pre-sheath flow velocities by laser-induced fluorescence
Journal of Nuclear Materials 176 & 177 (1990) 1059-1063 North-Holland
1059
Measurement of pre-sheath flow velocities by laser-induced fluorescence S.L. Gulick, B.L. Stansfield, Z. Abou-Assaleh, and R. Marchand INRS-Energie,
C. Boucher, J.P. Matte, T.W. Johnston
CP 1020, Varennes, Quebec, Canada J3X IS2
For the first time, the pre-sheath ion flow velocity has been measured using the Doppler shift of laser-induced fluorescence in singly-ionized argon ions. The velocity shows a monotonic increase, from a value of about 0.15 of the sound speed V, far from the target to 0.5 of V, at a distance of 5 mm from the surface. The temperature, the floating potential and the density are calculated from cylindrical probe measurements taken in the same region under identical conditions. These experimental results are compared with those from a 1D isothermal single-ion fluid model of the pre-sheath and a kinetic electron/fluid ion model. Both models agree well with the density profile, but underestimate the potential change and overestimate the velocity. In addition, the bulk flow velocity has been independently determined from “Mach probe” measurements, using various candidate theories to relate the Mach number to the ratio of the upstream to downstream saturation currents. Comparison with the optical measurements indicate that the probe models which include viscosity provide reasonable agreement with our Mach probe data.
1. Introduction The flux of particles and energy from a hot plasma can cause considerable sputtering damage to a surface, as well as producing very high heat loads [l]. The impinging particles will be recycled (normally as neutral atoms or molecules) from the surface, and atoms from the solid will be sputtered as well. Their subsequent ionization will cause the particle flux to be amplified, and the temperature to fall. This results in a lowering in the bombarding energies and hence a (possibly drastic) reduction of the sputtering rates. The entrainment of the ionized sputtered atoms by the flowing plasma and their subsequent redeposition is a crucial factor in determining the lifetime of these material components. Most of these processes occur in the pre-sheath where there are gradients in the plasma density, temperatures, bulk velocitiy and electrostatic potential. The physics of the pre-sheath thus plays a dominant role in determining the details of the flow of particles and power to solid surfaces. In addition, the magnitude and direction of the particle flow velocities in the edge of tokamak plasmas are considered to be important indicators of the trans0022-3115/90/$03.50
port processes in the edge region, and in particular there should be a significant difference beween velocity profiles in the H and L modes [2,3]. The reliable measurement of these velocities is thus of crucial importance if we wish to compare experimental data to edge models. While probes (so-called “Mach probes”) have been used to measure velocity profiles [4,5], the differences in the theoretical models [4-71 used to calculate Mach numbers (from the measured ratios of “upstream” to “downstream” currents) have allowed a large range of ion flow velocities. Given the importance of such measurements, newer models incorporating viscosity have been recently proposed [S-lo] and experiments to test these models carried out [ll]. One element, and in fact the key one, has always been lacking: the direct measurement of the flow velocity. As pointed out by Chung et al. [ll], while the various models give similar results for the density calculated for a flowing plasma, the velocity measurement is a more sensitive means of discriminating between the models. The experiments reported here were undertaken to (i) verify in detail different models used to describe lD, recycling plasmas in contact with a surface, and (ii) to provide a benchmark for relating the current ratio mea-
0 1990 - Elsevier Science Publishers B.V. (North-Holland)
1060
S.L. Guhck et al. / Measurement
sured by a Mach probe to the flow velocity, thus providing a means for reliably interpreting Mach probe measurements.
2. Experiment The experiment is performed in a quasi-1D system: the plasma is created by an ECR source operated in a region where the magnetic field is slightly above the resonance condition. The argon plasma flows from the source along a slightly diverging magnetic field, to impact a target located about 1.5 meters from the source, in a region where the magnetic field is essentially constant and the plasma column has a diameter of about 70 mm. Laser-induced fluorescence is used to measure the singly-ionized ion velocity distribution either parallel to the magnetic field (the laser beam propagates axially along the field) or perpendicular to it (with the beam propagating across the field). The dye laser (Lumonics HyperDYE) is pumped by an Excimer laser (Lumonics HyperEX, operated with XeCl) and has a narrow linewidth (0.002 nm), with a pulsewidth of 30 ns. The laser is tuned to a 617.229 nm transition in ArII, while the fluorescence is observed at 458.993 nm to minimize interference from the laser beam. The laser line is swept across the absorption profile in wavelength steps of 0.001 nm using computer control, which allows us to average 100 laser shots at every wavelength setting. The light emitted from the focal volume is collected by a lens system and focused onto the slit of a 0.25 m grating monochromator. The signal is measured by a photomultiplier and the current pulse sent to a charge-integrating ADC (Lecroy 2249W); a 100 ns gate is applied to the ADC in synchronization with the dye laser pulse. The image of the slit in the plasma has a width of 400 pm; combined with a laser beam diameter of 2 mm, this provides extremely good spatial resolution. Since the laser linewidth is not negligible compared with the atomic absorption width or the Doppler shift, the measured profiles have been deconvoluted to obtain as good a representation as possible of the ion velocity distribution function. A modified Gaussian profile, slightly narrower than that measured perpendicular to the magnetic field, has been used as a measure of the “instrument function”. The plasma near the target is diagnosed by a single cylindrical Langmuir probe (to obtain local values of n,, Vr and T,); farther from the target we use a Mach probe [12] to measure the flow velocity. The single probe is a thin tungsten wire (0.5 mm diameter) pro-
ofpre-sheath flow
velocities
truding from a ceramic sheath, with a recessed insulated spacer to assure a well-defined collecting area. The Mach probe is composed of a graphite tip holding 3 tungsten pins; the 9.5 mm diameter graphite shaft shields the “upstream” from the “downstream” probes [12]. Since the Mach probe is quite large, the radius being necessarily larger than the ion Larmor radius, we must remain far enough from the target to assure that the wake does not intercept the target. The voltage on the probes is swept from -100 V to 0 V, and the current measured across a 1 kS2 resistor.
3. Modeling The experimental results are compared to different models for the pre-sheath: the isothermal fluid model of Stangeby [7] and a kinetic electron code (FPI) [13,14]. This latter model treats the electrons using a FokkerPlanck code, while the ions are treated in the fluid approximation. The two codes are alternated, using the FPI code to correct the fluid code’s electron transport properties while using the fluid code for the ion dynamics. In the simulations, a linear neutral density profile is assumed near the plate. This profile (density at the plate and decay length) is chosen to be consistent with recycling at the plate and with the ionization-charge exchange attenuation length of the released neutral atoms.
4. Results The deconvoluted LIF profiles taken at different positions in front of the target are shown in fig. 1. As we approach the plate, there is a noticeable Doppler shift in the fluorescence signal, indicating an appreciable acceleration of the ions in the pre-sheath. In addition, the total fluorescence signal increases somewhat, reaching a maximum around 30 mm from the target, and then drops as we get closer to the surface. The distribution function of the ions is somewhat skewed, showing a significant number of ions at velocities lower than the maximum. Both of these effects are indicative of the creation of ions in a region in front of, but close to, the plate. The velocity profile in front of the target is shown in fig. 2; the velocity plotted corresponds to that at the maximum of the distribution function. At 100 mm from the plate, the ions are moving at about 0.15 of the local sound speed while at the closest point (5 mm from the surface) the Mach number has risen to 0.5.
XL. Gulick et al. / Measurement
of pre-sheath flow velocities
1061
region. The electron density was calculated from the ion saturation current using the standard formula for unmagnetized plasmas. The flow velocity as measured by the laser-induced fluorescence experiment for a position relatively far (100 mm) from the target is used to calculate the local Mach number M. This value is shown in fig. 4, along with the ratio R between the upstream and downstream ion saturation currents measured by the Mach probe at the same position. Also shown are the relations between R and M obtained from different theoretical models
[47,8,151.
WAVELENGTH
SHIFT
(0.001
5. Discussion and conclusions
NM)
Fig. 1. Fluorescence signal versus wavelength shift measured at different distances (5, 10, 20, 30, 50 and 100 mm) from the target surface.
The laser fluorescence measurements show a definite acceleration of the ions into the presheath, while the probe data show a monotonic decrease of electron density and potential in the same region. The global features of the density variation can be reasonably well described by both the isothermal fluid model and the kinetic/fluid code if recycling is modeled by a fixed profile of neutral (argon) gas near the target plate. For the calculations shown in fig. 2 and 3, a profile has been assumed which varies linearly from zero at a distance of 100 mm from the surface to a value of 2 X 10” mW3 at
The measurements taken with the unmagnetized probe over the same region as covered by the laser experiment give a plasma electron temperature of about 14 eV and a plasma density of 3 X 10” rnm3; the variations of the floating potential and the density are shown in figs. 2 and 3. The electron temperature (not plotted) was found to be relatively constant over this
0.4
-1.6
0.0 0
80
160
240
-2.0 300
Wmm) Fig. 2. Spatial profiles of the measured ion flow velocity (0) and floating potential (A) in front of the Target surface, The theoretical profiles are calculated using the isothermal fluid model (A) and the kinetic electron/fluid ion model (B).
S. L. Gulick et al. / Measurement of pre-sheath flow velocities
1062
3
NiVf/NoV, 2
1
I.0
80
160 X(mm)
240
Fig. 3. Spatial profile of the measured profiles
are calculated
normalized electron density (A) and the ion flux (0) in front using the isothermal fluid model (A) and the kinetic electron/fluid
the plate. The thickness of this layer is consistent with the ionization mean free path for atoms of Argon being recycled from the surface with thermal (about 0.1 eV)
3.2
HARBOUR ITe=Til HUTCHINSON (APPROX) STANGEBY FLU10 x HUOIS/LIOSKY (Ti/Te=.
300' of the target. The theoretical ion model (B).
energies. The neutral density at the plate is also consistent with a large fraction of the incident ions being recycled as thermal atoms.
+ 0
I)
I
_
J
EXPERIMENT
MACH NUMBER Fig. 4. Ratio of the upstream
to downstream The experimental
saturation currents value is calculated
M
as a function of the Mach number from different using the measured electron temperature.
theoretical
models.
S.L. Gulick et al. / Measurement
Neither of the models considered provides a good description of the electrostatic potential variation or the ion flow velocity in the pre-sheath. In particular, the potential drop is much larger than predicted by any of the isothermal electron models [16], showing pre-sheath potential drops larger than T,. In addition, the Boltzmann relation between the electron density and the potential variation (obtained from the floating potential) is not obeyed, thus contradicting a fundamental assumption made in many previous fluid and kinetic models. The FPI kinetic-electron model produces a somewhat higher potential drop, but again does not reproduce the experimental results. On the other hand, the measured ion flow velocity is seen to be consistently lower than that predicted by the codes. In fact, unless a sudden acceleration takes place very close to the surface, the extrapolated to ion flow velocity would appear to be significantly less than the ion sound speed at the sheath edge. Finally, the anomalously large measured potential drop is seen to be completely inconsistent with the (pompously low) ion flow velocity. These disquieting results certainly require further experimental study. The models can be improved by including the effect of multiply charged species and charge exchange, but the results may well indicate the necessity to examine further the underlying physics of the theoretical models near the sheath edge. Turning now to the Mach probe results, the comparison between the Mach probe data and the LIF results gives a clear indication that the model developed by Hutchinson [S-lo] gives a good description for our plasma. The measurements, however, are not sufficiently accurate to allow a clear determinion of the effective ratio of viscosity to ~ffusi~ty. The Harbour and Proudfoot “particle” formula [4] relating M and R is shown assuming T, = Ti, although this is inapplicable in our case (Ti = 0.1 ev). The fluid model [7] is clearly not in agreement with our data, and would predict very high Mach numbers from the measured current ratio. The Hudis and Lidsky model [15] for an unma~et~ed plasma gives values only slightly higher than those of the fluid model. Based on these results, and on the fact that the fluid model predicts supersonic velocities, the Hutchinson model is the one which has been used to
ojpre-sheath
jlow velocities
1063
interpret the Mach probe data taken in the Tokamak de Varennes 1121.
Acknowledgements
The authors would like to acknowledge the technical assistance of S. Savoie and to thank J. Boucher for the loan of essential equipment used in the experiment. We would also like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada.
References [I] F. Engelmann, in: Physics of Plasma-Wall Interactions in Controlled Fusion, Eds. D.E. Post and R. Behrisch (Plenum Press, New York, 1986) p. 15. [2] KC. Shaing and E.C. Crume, Jr., Phys. Rev. Lett. 63 (1989) 2369. [3] R.J. Groebner, K.H. BurrelI and R.P. Seraydarian, General Atomics Report GA-A19813 (1989). [4] P.J. Harbour and G. Proudfoot, J. Nucl. Mater. 121 (1984) 222. [5] G. Proudfoot, P.J. Harbour, J. Allen and A. Lewis, J. Nucl. Mater. 128 & 129 (1984) 180. [6] P.C. Stangeby, J. Phys. D 15 (1982) 1007. [7] P.C. Stangeby, Pbys. Fluids 27 (1984) 2699. [8] I.H. Hutchinson, Phys. Fluids 30 (1987) 3777. [9] I.H. Hutchinson, Phys. Rev. A37 (1988) 4358. [lo] K.S. Chung and I.H. Hutchinson, Phys. Rev. A38 (1988) 4721. [ll] K.S. Chung, I.H. Hutchinson, B. LaBombard and R.W. COM. Phys. Fluids B 1 (1989) 2229. 1121 C. Boucher, C. MacLatchy, G. LeClair and J.L. Lachambre, in these Proceedings, J. Nucl. Mater. 176 L 177 (1990). [13] J.H. Rogers, J.S. DeGroot, Z. Abou-AssaIeh, J.P. Matte, T.W. Johnston and M.D. Rosen, Phys. FIuids Bl (1989) 741. f14] Z. Abou-Assaleh, R. Marchand, J.P.Matte, T.W. Johnston and K.J. Parbhakar, Contrib. Plasma Phys. 30 (1989) 37. [15] M. Hudis and L.M. Lidsky, J. Appl. Phys. 41 (1970) 5011. (161 R.C. Bissell, P.C. Johnson and P.C. Stangeby, Phys. Fluids Bl (1989) 1133.
1059
Measurement of pre-sheath flow velocities by laser-induced fluorescence S.L. Gulick, B.L. Stansfield, Z. Abou-Assaleh, and R. Marchand INRS-Energie,
C. Boucher, J.P. Matte, T.W. Johnston
CP 1020, Varennes, Quebec, Canada J3X IS2
For the first time, the pre-sheath ion flow velocity has been measured using the Doppler shift of laser-induced fluorescence in singly-ionized argon ions. The velocity shows a monotonic increase, from a value of about 0.15 of the sound speed V, far from the target to 0.5 of V, at a distance of 5 mm from the surface. The temperature, the floating potential and the density are calculated from cylindrical probe measurements taken in the same region under identical conditions. These experimental results are compared with those from a 1D isothermal single-ion fluid model of the pre-sheath and a kinetic electron/fluid ion model. Both models agree well with the density profile, but underestimate the potential change and overestimate the velocity. In addition, the bulk flow velocity has been independently determined from “Mach probe” measurements, using various candidate theories to relate the Mach number to the ratio of the upstream to downstream saturation currents. Comparison with the optical measurements indicate that the probe models which include viscosity provide reasonable agreement with our Mach probe data.
1. Introduction The flux of particles and energy from a hot plasma can cause considerable sputtering damage to a surface, as well as producing very high heat loads [l]. The impinging particles will be recycled (normally as neutral atoms or molecules) from the surface, and atoms from the solid will be sputtered as well. Their subsequent ionization will cause the particle flux to be amplified, and the temperature to fall. This results in a lowering in the bombarding energies and hence a (possibly drastic) reduction of the sputtering rates. The entrainment of the ionized sputtered atoms by the flowing plasma and their subsequent redeposition is a crucial factor in determining the lifetime of these material components. Most of these processes occur in the pre-sheath where there are gradients in the plasma density, temperatures, bulk velocitiy and electrostatic potential. The physics of the pre-sheath thus plays a dominant role in determining the details of the flow of particles and power to solid surfaces. In addition, the magnitude and direction of the particle flow velocities in the edge of tokamak plasmas are considered to be important indicators of the trans0022-3115/90/$03.50
port processes in the edge region, and in particular there should be a significant difference beween velocity profiles in the H and L modes [2,3]. The reliable measurement of these velocities is thus of crucial importance if we wish to compare experimental data to edge models. While probes (so-called “Mach probes”) have been used to measure velocity profiles [4,5], the differences in the theoretical models [4-71 used to calculate Mach numbers (from the measured ratios of “upstream” to “downstream” currents) have allowed a large range of ion flow velocities. Given the importance of such measurements, newer models incorporating viscosity have been recently proposed [S-lo] and experiments to test these models carried out [ll]. One element, and in fact the key one, has always been lacking: the direct measurement of the flow velocity. As pointed out by Chung et al. [ll], while the various models give similar results for the density calculated for a flowing plasma, the velocity measurement is a more sensitive means of discriminating between the models. The experiments reported here were undertaken to (i) verify in detail different models used to describe lD, recycling plasmas in contact with a surface, and (ii) to provide a benchmark for relating the current ratio mea-
0 1990 - Elsevier Science Publishers B.V. (North-Holland)
1060
S.L. Guhck et al. / Measurement
sured by a Mach probe to the flow velocity, thus providing a means for reliably interpreting Mach probe measurements.
2. Experiment The experiment is performed in a quasi-1D system: the plasma is created by an ECR source operated in a region where the magnetic field is slightly above the resonance condition. The argon plasma flows from the source along a slightly diverging magnetic field, to impact a target located about 1.5 meters from the source, in a region where the magnetic field is essentially constant and the plasma column has a diameter of about 70 mm. Laser-induced fluorescence is used to measure the singly-ionized ion velocity distribution either parallel to the magnetic field (the laser beam propagates axially along the field) or perpendicular to it (with the beam propagating across the field). The dye laser (Lumonics HyperDYE) is pumped by an Excimer laser (Lumonics HyperEX, operated with XeCl) and has a narrow linewidth (0.002 nm), with a pulsewidth of 30 ns. The laser is tuned to a 617.229 nm transition in ArII, while the fluorescence is observed at 458.993 nm to minimize interference from the laser beam. The laser line is swept across the absorption profile in wavelength steps of 0.001 nm using computer control, which allows us to average 100 laser shots at every wavelength setting. The light emitted from the focal volume is collected by a lens system and focused onto the slit of a 0.25 m grating monochromator. The signal is measured by a photomultiplier and the current pulse sent to a charge-integrating ADC (Lecroy 2249W); a 100 ns gate is applied to the ADC in synchronization with the dye laser pulse. The image of the slit in the plasma has a width of 400 pm; combined with a laser beam diameter of 2 mm, this provides extremely good spatial resolution. Since the laser linewidth is not negligible compared with the atomic absorption width or the Doppler shift, the measured profiles have been deconvoluted to obtain as good a representation as possible of the ion velocity distribution function. A modified Gaussian profile, slightly narrower than that measured perpendicular to the magnetic field, has been used as a measure of the “instrument function”. The plasma near the target is diagnosed by a single cylindrical Langmuir probe (to obtain local values of n,, Vr and T,); farther from the target we use a Mach probe [12] to measure the flow velocity. The single probe is a thin tungsten wire (0.5 mm diameter) pro-
ofpre-sheath flow
velocities
truding from a ceramic sheath, with a recessed insulated spacer to assure a well-defined collecting area. The Mach probe is composed of a graphite tip holding 3 tungsten pins; the 9.5 mm diameter graphite shaft shields the “upstream” from the “downstream” probes [12]. Since the Mach probe is quite large, the radius being necessarily larger than the ion Larmor radius, we must remain far enough from the target to assure that the wake does not intercept the target. The voltage on the probes is swept from -100 V to 0 V, and the current measured across a 1 kS2 resistor.
3. Modeling The experimental results are compared to different models for the pre-sheath: the isothermal fluid model of Stangeby [7] and a kinetic electron code (FPI) [13,14]. This latter model treats the electrons using a FokkerPlanck code, while the ions are treated in the fluid approximation. The two codes are alternated, using the FPI code to correct the fluid code’s electron transport properties while using the fluid code for the ion dynamics. In the simulations, a linear neutral density profile is assumed near the plate. This profile (density at the plate and decay length) is chosen to be consistent with recycling at the plate and with the ionization-charge exchange attenuation length of the released neutral atoms.
4. Results The deconvoluted LIF profiles taken at different positions in front of the target are shown in fig. 1. As we approach the plate, there is a noticeable Doppler shift in the fluorescence signal, indicating an appreciable acceleration of the ions in the pre-sheath. In addition, the total fluorescence signal increases somewhat, reaching a maximum around 30 mm from the target, and then drops as we get closer to the surface. The distribution function of the ions is somewhat skewed, showing a significant number of ions at velocities lower than the maximum. Both of these effects are indicative of the creation of ions in a region in front of, but close to, the plate. The velocity profile in front of the target is shown in fig. 2; the velocity plotted corresponds to that at the maximum of the distribution function. At 100 mm from the plate, the ions are moving at about 0.15 of the local sound speed while at the closest point (5 mm from the surface) the Mach number has risen to 0.5.
XL. Gulick et al. / Measurement
of pre-sheath flow velocities
1061
region. The electron density was calculated from the ion saturation current using the standard formula for unmagnetized plasmas. The flow velocity as measured by the laser-induced fluorescence experiment for a position relatively far (100 mm) from the target is used to calculate the local Mach number M. This value is shown in fig. 4, along with the ratio R between the upstream and downstream ion saturation currents measured by the Mach probe at the same position. Also shown are the relations between R and M obtained from different theoretical models
[47,8,151.
WAVELENGTH
SHIFT
(0.001
5. Discussion and conclusions
NM)
Fig. 1. Fluorescence signal versus wavelength shift measured at different distances (5, 10, 20, 30, 50 and 100 mm) from the target surface.
The laser fluorescence measurements show a definite acceleration of the ions into the presheath, while the probe data show a monotonic decrease of electron density and potential in the same region. The global features of the density variation can be reasonably well described by both the isothermal fluid model and the kinetic/fluid code if recycling is modeled by a fixed profile of neutral (argon) gas near the target plate. For the calculations shown in fig. 2 and 3, a profile has been assumed which varies linearly from zero at a distance of 100 mm from the surface to a value of 2 X 10” mW3 at
The measurements taken with the unmagnetized probe over the same region as covered by the laser experiment give a plasma electron temperature of about 14 eV and a plasma density of 3 X 10” rnm3; the variations of the floating potential and the density are shown in figs. 2 and 3. The electron temperature (not plotted) was found to be relatively constant over this
0.4
-1.6
0.0 0
80
160
240
-2.0 300
Wmm) Fig. 2. Spatial profiles of the measured ion flow velocity (0) and floating potential (A) in front of the Target surface, The theoretical profiles are calculated using the isothermal fluid model (A) and the kinetic electron/fluid ion model (B).
S. L. Gulick et al. / Measurement of pre-sheath flow velocities
1062
3
NiVf/NoV, 2
1
I.0
80
160 X(mm)
240
Fig. 3. Spatial profile of the measured profiles
are calculated
normalized electron density (A) and the ion flux (0) in front using the isothermal fluid model (A) and the kinetic electron/fluid
the plate. The thickness of this layer is consistent with the ionization mean free path for atoms of Argon being recycled from the surface with thermal (about 0.1 eV)
3.2
HARBOUR ITe=Til HUTCHINSON (APPROX) STANGEBY FLU10 x HUOIS/LIOSKY (Ti/Te=.
300' of the target. The theoretical ion model (B).
energies. The neutral density at the plate is also consistent with a large fraction of the incident ions being recycled as thermal atoms.
+ 0
I)
I
_
J
EXPERIMENT
MACH NUMBER Fig. 4. Ratio of the upstream
to downstream The experimental
saturation currents value is calculated
M
as a function of the Mach number from different using the measured electron temperature.
theoretical
models.
S.L. Gulick et al. / Measurement
Neither of the models considered provides a good description of the electrostatic potential variation or the ion flow velocity in the pre-sheath. In particular, the potential drop is much larger than predicted by any of the isothermal electron models [16], showing pre-sheath potential drops larger than T,. In addition, the Boltzmann relation between the electron density and the potential variation (obtained from the floating potential) is not obeyed, thus contradicting a fundamental assumption made in many previous fluid and kinetic models. The FPI kinetic-electron model produces a somewhat higher potential drop, but again does not reproduce the experimental results. On the other hand, the measured ion flow velocity is seen to be consistently lower than that predicted by the codes. In fact, unless a sudden acceleration takes place very close to the surface, the extrapolated to ion flow velocity would appear to be significantly less than the ion sound speed at the sheath edge. Finally, the anomalously large measured potential drop is seen to be completely inconsistent with the (pompously low) ion flow velocity. These disquieting results certainly require further experimental study. The models can be improved by including the effect of multiply charged species and charge exchange, but the results may well indicate the necessity to examine further the underlying physics of the theoretical models near the sheath edge. Turning now to the Mach probe results, the comparison between the Mach probe data and the LIF results gives a clear indication that the model developed by Hutchinson [S-lo] gives a good description for our plasma. The measurements, however, are not sufficiently accurate to allow a clear determinion of the effective ratio of viscosity to ~ffusi~ty. The Harbour and Proudfoot “particle” formula [4] relating M and R is shown assuming T, = Ti, although this is inapplicable in our case (Ti = 0.1 ev). The fluid model [7] is clearly not in agreement with our data, and would predict very high Mach numbers from the measured current ratio. The Hudis and Lidsky model [15] for an unma~et~ed plasma gives values only slightly higher than those of the fluid model. Based on these results, and on the fact that the fluid model predicts supersonic velocities, the Hutchinson model is the one which has been used to
ojpre-sheath
jlow velocities
1063
interpret the Mach probe data taken in the Tokamak de Varennes 1121.
Acknowledgements
The authors would like to acknowledge the technical assistance of S. Savoie and to thank J. Boucher for the loan of essential equipment used in the experiment. We would also like to acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada.
References [I] F. Engelmann, in: Physics of Plasma-Wall Interactions in Controlled Fusion, Eds. D.E. Post and R. Behrisch (Plenum Press, New York, 1986) p. 15. [2] KC. Shaing and E.C. Crume, Jr., Phys. Rev. Lett. 63 (1989) 2369. [3] R.J. Groebner, K.H. BurrelI and R.P. Seraydarian, General Atomics Report GA-A19813 (1989). [4] P.J. Harbour and G. Proudfoot, J. Nucl. Mater. 121 (1984) 222. [5] G. Proudfoot, P.J. Harbour, J. Allen and A. Lewis, J. Nucl. Mater. 128 & 129 (1984) 180. [6] P.C. Stangeby, J. Phys. D 15 (1982) 1007. [7] P.C. Stangeby, Pbys. Fluids 27 (1984) 2699. [8] I.H. Hutchinson, Phys. Fluids 30 (1987) 3777. [9] I.H. Hutchinson, Phys. Rev. A37 (1988) 4358. [lo] K.S. Chung and I.H. Hutchinson, Phys. Rev. A38 (1988) 4721. [ll] K.S. Chung, I.H. Hutchinson, B. LaBombard and R.W. COM. Phys. Fluids B 1 (1989) 2229. 1121 C. Boucher, C. MacLatchy, G. LeClair and J.L. Lachambre, in these Proceedings, J. Nucl. Mater. 176 L 177 (1990). [13] J.H. Rogers, J.S. DeGroot, Z. Abou-AssaIeh, J.P. Matte, T.W. Johnston and M.D. Rosen, Phys. FIuids Bl (1989) 741. f14] Z. Abou-Assaleh, R. Marchand, J.P.Matte, T.W. Johnston and K.J. Parbhakar, Contrib. Plasma Phys. 30 (1989) 37. [15] M. Hudis and L.M. Lidsky, J. Appl. Phys. 41 (1970) 5011. (161 R.C. Bissell, P.C. Johnson and P.C. Stangeby, Phys. Fluids Bl (1989) 1133.