plasma and neutral dynamics in a simulated tokamak gas...

Plasma and neutral dynamics in a simulated tokamak gas target divertor L Schmitz B. Merriman,a)sb) L. Blush, R. Lehmer, R. W. Conn,a)sb) R. Doerner,a)Tb) Al GrossmHn,a)*b) and F. Najmabadia)“) Institute of Plasma and Fusion Research, University of California, Los Angeles, Los Angeles, California 90095I597

(Received 1 February 1995; accepted 14 April 1995)

A stationary, detached ionization front is observed in an experimentally simulated divertor plasma (nG3X 1019 mW3, kT,G20 eV) interacting with a hydrogen gas target. with a neutral hydrogen density, n0=2X 10Z1 me3, the electron temperature at the simulated divertor target is reduced to kTe tigrt w 2.5 eV. Up to 97% of the ele&on heat flux (G7 MW/m’) is dissipated by dissociation and ionization losses and hydrogen line radiation. The plasma pressure is observed to peak near the ionization front, and a plasma flow reversal is observed in the region of reversed pressure gradient. Classical momentum flow parallel to the magnetic field and anomalous cross-field particle transport are found. The plasma flow is strongly damped by ion-neutral collisions and is subsonic. Numerical results from a one-and-one-half dimensional (1 $D) coupled plasma-neutral fluid model (incorporating radial particle transpo& recycling, and neutral gas injection) agree well with the experimental data, and indicate that the’ electron heat flow is classical and well described by a harmonic flux limit. The scale length of the parallel plasma pressure gradient in a gas target is found to depend on the neutral density, the electron coefficient. 0 1995 American Institute of Physics.

I. INTRODUCTION

The achievement of controlled fusion in a tokamak reactor necessitates the continuous, controlled removal of charged fusion products (energetic a particles) to avoid buildup of helium ash and fuel dilution. In next generation tokamaks, such as the proposed International Thermonuclear Experimental Reactor (ITER), the a-particle power is pro- jected to be greater than 240 MW.’ A poloidal magnetic divertor configuration2 is envisioned in order to avoid excessive fuel dilution and deflect the particle and heat efflux from the plasma core toward a separate divertor region. The power flux into the divertor is expected to reach values in excess of 150 MW/m2 in future tokamaks such as ITER. This power would be deposited within a localized region (Ars5 cm) around the magnetic separatrix onto a material divertor target, leading to excessive thermal loading, ion sputtering, and impurity release. Co&o1 of the divertor heat 16ad and target plate erosion is therefore critical for the achievement of long pulse and steady-state tokamak operation. High recycling’ and gas target c@ertors4-7 have been proposed to achieve a reduced electron temperature and sheath potential at the divertor target. While a substantial reduction of the divertor electron temperature and power loading has been demonstrated in a high recycling divertor configuration (in the Doublet-III tokamak, for example8), the plasma pressure fe- mains nearly constant along the niagnetic field in this regime since a low divertor electron temperature is offset by a corresponding increase in plasma density. In a high recycling

B)Also at the Fusion Energy Research Program, University of California, San Diego, La Jolla, California 92093-0417.

b)Also at the Mechanical Engineering Division, University of California, San Dieio, La Jolla, California 92093-0417.

‘)Also at the ElectricaI and Computei Engineering Department, University of California, San Diego, La Jolla, California 92093-0417.

temperature, and the cross-field diffusion

divertor, the maximum power dissipated by deuterium and impurity line radiation may be limited to 50% of the core power efflux, depending on the edge plasma density and on the impurity species and concentrations in the divertor plasma.9~‘0 This fraction of radiated power will be inadequate for ITER or reactor conditions. Also, the radiation layer is typically localized in the immediate vicinity of the target plate in a high recycling divertor and a large portion of the radiated power is still deposited onto the target rather than di&ibuted over a large surface area at the sidewalls of the divertor chamber.

In contrast, a simultaneous decrease of electron temperature and density toward the target is envisioned in the gas target regime.6*7 If the parallel plasma momentum can be dissipated in the divertor, the plasma pressure need not be constant along the magnetic field. Momentum damping can be induced by ion-neutral collisions, if the neutral density inside the plasma is sufficiently high and the neutrals effectively deposit momentum onto the sidewalls of the divertor chamber before being reionized.” A necessary condition for momentum removal is that the neutral ionization mean-free path be comparable to or larger than the radial extent of the divertor plasma. Thus, the prerequisite for accessing the gas target regime is a low electron temperature near the divertor target, making the plasma transparent to neutrals. Strong volumetric energy losses in the boundary plasma or the divertor region are therefore required to reduce the divertor electron temperature sufficiently. In principle, the power flow into the divertor may be redistributed over a large surface area through various mechanisms, such as hydrogenic, or impurity line radiation, by recombination radiation or by atomic collisions, such as charge exchange. A substantial reduction of the electron temperature in the presence of strong neutral gas injection has first been demonstrated in linear plasma facilities, simulating the plasma conditions in a tok-

Phys. Plasmas 2 (8), August 1995 1070-664X/95/2(8)/3081/14/$6.00 0 1995 American Institute of Physics 3081 Downloaded 30 Aug 2002 to 132.239.190.78. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/pop/popcr.jsp

amak divertor.5”2-‘4 More recently, a reduced target electron temperature and strongly reduced heat flux to the divertor target have been observed during divertor gas puffing and/or impurity gas injection in the Doublet III-D (DIII-D) tokamak,i5 in the Joint European Torus (JET),16 and in the Alcator C-Mod tokamak.17 Plasma detachment from the divertor strike point during divertor gas puffing has been observed at heating power levels of up to 22 MW, and is attributed to a combination of impurity and hydrogen line radiation and radial plasma momentum loss by ion-neutral collisions.‘6

In this paper, we present a systematic study of the particle, momentum, and heat flow in a hydrogen plasma interacting with a hydrogen gas target. Experimental results are compared with calculations from a one-and-one-half- dimensional (1 j-D) coupled plasma/neutral fluid model. The plasma density, electron temperature, and the ratio of the ion gyroradius to the plasma radius, Pilrc, are similar to present- day tokamak divertor plasma parameters. The peak parallel eIectron heat flux (qeZG7 MW/m*) is comparable to the poloidal electron heat flux in present day tokamak diverters, however, the ion temperature, the ion heat flux, and the magnetic field (B,~0.17 T) are much lower.

The paper is organized as follows: in Sec. II, the experimental setup and the diagnostics in the PISCES-A linear plasma device are described. In Sec. III, the 1 i-D fluid model used to interpret the experimental data is presented. In Sec. IV, the measured and calculated plasma parameters profiles along the magnetic field are discussed. In Sec. V, the momentum balance parallel to the magnetic field is examined. We present radial profiles of the plasma parameters and the parallel plasma flow velocity in Sec. VI, and examine radial particle transport in Sec. VII. Plasma detachment in hydrogen and argon gas targets is discussed in Chap. VIII, and the parallel pressure gradient scale length is calculated and compared to experimental data. A summary of the results and conclusions are presented in Sec. IX.

II. EXPERIMENTAL SETUP

The experiments are carried out in the PISCES-A linear plasma device (Fig. l).” The plasma is created in a reflex arc configuration using a hot lanthanum hexaboride cathode, resulting in source plasma densities of 5X1017 mw3Sn S 1 X 10” mw3 and source electron temperatures kT,s20 eV (kT,=2 eV). A water-cooled, cylindrical copper anode is used. Typical discharge voltages in hydrogen are 90 VCU,~ 150 V, while the discharge current is 15 AG,< 150 A. A circular tube, made of anodized aluminum (length L=O.9 m, inner radius r,=2.25 cm) is located at a distance of 0.55 m from the source to simulate a closed “slot-type” divertor channel. The axial magnetic field B, is generated by two sets of coils. The magnetic field can be varied in the range 0.03 TsB:=GO. 1 T in the plasma source region and 0.04 TGBZG0.19 T in the “divertor” region. Unless other- wise indicated, the measurements described here were carried out for B; = 5.6 X 10M2 T in the plasma source region and B, =0.17 T in the “divertor” region. Hydrogen gas can be admitted at the plasma source and/or through a gas feed located near the center of the target plate (z=O). The neutral

3082 Phys. Plasmas, Vol. 2, No. 8, August 1995

Pump Gas Feed

FIG. 1. Experimental setup and diagnostics for the PISCES gas target divertor simulation experiments.

pressure is monitored by baratron and ionization gauges at various axial positions. A water-cooled, axially movable, plane Langmuir probe is employed to measure the plasma density and electron temperature profiles parallel to the magnetic field. This probe has also been constructed as a calo- rimeter so it can be used to record the parallel plasma heat flux to the target. A fast scanning probe provides radial profiles of plasma density, floating, and space potential (via an emissive filament) at various axial positions. Mach probes (consisting of a pair of mechanically insulated Langmuir probe tips facing the plasma source and the target) are used to determine the parallel plasma flow speed from the upstream/downstream ratio of the ion saturation currents using the Hutchinson model.” The atomic and molecuIar hydrogen densities are determined from absolutely calibrated H, line emission intensities and neutral pressure measurements (using the photon yield per ionization event*‘-** and the measured radial plasma density and electron temperature profiles), as discussed in detail in the Appendix.

III. 1 $D FLUID MODEL

A fully implicit one-and-one-half-dimensional (1 i-D) coupled plasma/neutral fluid model is employed to interpret the experimentally measured plasma profiles parallel to the magnetic field. The plasma particle, momentum, and electron heat flux equation? are solved along to the magnetic field on a 200 cell grid. The model is called a “‘1 f-D” model since radial plasma transport, sidewall recycling, and gas injection are included as source or sink rates depending on the axial coordinate only. Neutral diffusion equations for atomic and molecular hydrogen are empIoyed. The equations solved in the model are

i-2 f+nn,((rdissVth,e}tot-n fk+ (11 1

Schmitz et aL

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D, =-t.U$ZV(Y&+Vi*)-WliYlV T;ZI (2)

I

=- Ei,,nn,( gionv th,&) - C Ejnnrn(aeu dj

-3 y (kT,-kTi)-Q,,, i

(3)

(4)

(5)

The plasma, atomic, and molecular hydrogen densities are denoted, respectively, by n, n2,, and n, . Particle sources due to hydrogen ionization and dissociation are included.24T25 The rate coefficient for ionization of atomic hydrogen is ( (+ionvth,e) and the total dissociation rate coefficient is l ~~issv e,&. In the dissociation term, f+ (kT,) is the fraction of H2 molecules ionized into Hf, thus resulting in 2 ff ions. a6 Cross-field particle transport is included as a sink term depending on the axial location, and is assumed to be diffusion dominated, with a diffusion coefficient D,., as described in more detail in Sec. VII. A Bessel profile is assumed for the radial plasma density distribution with the radial diffusion scale length h,=rd2.405. In the plasma momentum equation (2), the electron mass has been neglected compared to the ion mass. The parallel plasma flow speed is designated by u, and Iii is the parallel ion viscosity.23 Here VCX = (Ucxuh,i)na is the momentum loss rate due to resonant charge exchange,‘4 and Yin = 0.5((ri,,U*,i)na + 0.667(~,v&n, is the momentum loss rate due to elastic ion-atom and ion-molecule collisions.“7,2s As discussed in Sec. V, we use a rate coefficient for elastic ion-molecule collisions ( cimu *,i), which is larger by a factor of 2, as compared to recent theoretical calculations.28 In this model, the parallel neutral velocity is assumed to be small compared to the plasma velocity and is neglected (the neutral diffusion approximation).

In the electron heat flux equation (3), the terms on the left-hand side describe the convective energy Ilow and the electron heat conduction. If the electron-electron collisional mean-free path is comparable to or larger than the temperature gradient scale length, electron heat conduction is bound by the flux limit qf= Eql, where ql= (2/m,r)“2n(kT,)3’2 is the free-streaming limit, and E is the flux limit factor (typically, E is taken to be in the range 0.2-0.5). In order to allow for a continuous transition between the collisional and colli- sionless regimes, we employ a harmonic flux limit formula- tion and write the electron heat flux as qez= qsqf/(qs+ qf), where qr= -3.2n(kT,lm.v,,)dkT,/dz is the classical Spitzer heat flux. The first term on the right-hand side of Eq.

(3) describes ionization and radiation losses. (Where EiDn is the electron energy loss per ionization event, including excitation losses. Here Eion is a function of the local electron temperature and density. ;35,29) The electron energy Iosses due to the various dissociation reactions are described by the second term.24 The third and fourth terms describe the collisional energy transfer from electrons to ions and neutrals.

In the neutral diffusion equations (4) and (5), D, and D, are the atomic and molecular diffusion coefficients, taking into account neutral particle collisions as well as collisions between neutrals and plasma ions [Da= kT,lm,( v,,,+ v&, Dm=kT,Jm,(~,,, + v,,!j, where T, and T, are the atomic and moIecular temperatures, and m, , m,, and v designate the appropriate masses and momentum loss rates]. We typically assume kT, = 1 .O eV for atomic hydrogen and kT,,,=O. 1 eV for molecular hydrogen. Neutral recycling at the target and at the radial boundary is included into the source terms S, and S, . These terms also include the pumping of neutrals in front of the divertor tube, as well as molecular hydrogen injection either in the plasma source region or at the target.

In solving Eqs. (l)-(S), the plasma density, electron temperature, and the derivative of the flow speed (duldz=O) are prescribed in front of the divertor tube at z = 1 m. Sheath boundary conditions are used at the target (z=O):

v(O)=c,(O), (6)

~u(O)n(O)kT,(O>+q,,(O)=n(O)c,(O)ykT,(O), (7)

where Eq. (6) corresponds to the Bohm sheath criterion and C,=[(kT,+kTi)/mi] iI2 is the ion sound speed. The heat flux through the sheath is equated to the total electron heat flux in Eq. (7). The ion heat tlux is neglected since kT,~kT, . Here y is the sheath heat transmission factor (we use y=6 since kT$kT, in our experiment). In the neutral diffusion equations, the molecular and atomic fluxes are prescribed at the target. These fluxes have contributions both from plasma recycling and from the molecular hydrogen injection through the target:

+- Rdl -fH)n(O)c,jO)+SH?(O), (8) Z=O

D, 2 “RTfdO)C,(O). z=O

Here, RT is the target recycling coefficient (typically, we use R,=O.99), and f u is the fraction of ions recycled in the form of atomic hydrogen.30 Two additional boundary conditions are chosen in the plasma source region (z = z,) corresponding to the gradient of the experimentally determined neutral density profiles:

dn, dn, dZ

=c,, x =c,. z=z, z=zs

IV. PLASMA AND NEUTRAL DYNAMICS PARALLEL TO THE MAGNETIC FIELD

Figure 2 shows measured axial profiles of the plasma density and the electron temperature with and without gas injection through the target. Without target gas injection, the

Phys. Plasmas, Vol. 2, No. 8, August 1995 Schmitz et a/. 3083


z (ml

0' I 0.2 0.4 0.6 0.8 1.0

= b-0

o pO(z=O) = 0.21 Pa n PO@=0) = 3.7 Pa 0 Po(z=O) - 10 Pa l Po(z=o) = 24 Pa

0.2 0.4 0.6 0.8 1.0

= (ml

FIG. 2. Measured axial profiles of the plasma density (a), the electron temperature (b). and the neutral hydrogen pressure (c) with and without target gas injection (B:=0.17 T). The neutral hydrogen pressure at the target P,(z=O) is indicated for each case. The case P, (0)=0.21 Pa is the case without target gas injection.

electron temperature is observed to decrease from 21 to roughly 11 eV in the upper half (nearest the plasma source) of the divertor tube. This temperature decline is mainly due to the energy loss associated with inelastic electron-neutral collisions inside the tube. The neutral pressure is increased due to plasma recycling off the target and the tube sidewalls. The plasma density increases inside the tube because recycled neutrals are reionized rather than escaping through the pumping port located in the plasma source region. This regime bears similarity to the high recycling divertor regime in a tokamak, where a reduced target electron temperature is offset by an increased plasma density due to neutral recycling off the divertor target and subsequent reionization.

3084 Phys. Plasmas, Vol. 2, No. 8, August 1995

With an increasing gas injection rate resulting in higher target neutral pressures, the target electron temperature is reduced substantially due to dissociation, radiation, and ionization energy losses. An “ionization front” develops, characterized by a pronounced local maximum in the plasma density at the location where significant dissociation and ionization of the injected neutrals occurs (kT,-5 eV). The maximum plasma density increases substantially with increasing gas injection rate St+ reaching 3X1019 rnv3 for St.+ = 0.3 Pa m3/s. Simultaneously, the target electron temperature is reduced to kT,=2.5 eV. The ionization front separates the region of warm plasma (kT,>5 eV) from the cold, neutral dominated plasma near the target. For sufficiently high target neutral pressure, the plasma “detaches” from the target. With increasing target neutral pressure and plasma density, the gas conductance of the divertor tube is reduced significantly, and the neutral gas is compressed in the target region [Fig. 2(c)].

We have used the 14-D fluid model to analyze two of the cases presented in Fig. 2. Figure 3 shows a comparison of measured and calculated profiles along the magnetic field for the case without target gas injection. Neutral hydrogen is only admitted at the plasma source resulting in a neutral pressure of 6X10-* Pa in that region. The electron energy measured in front of the divertor tube near the plasma source (z =0.95 m) is about 21 eV, with a small fraction of energetic primary electrons (aehlnG3%; Uehe 100 eV). We would expect the plasma pressure, P = n(kT, + kTi), to be roughly constant along the magnetic field if no net particle source were present inside the divertor tube. However, the atomic and molecular neutral densities increase toward the divertor target due to plasma recycling on the target and on the sidewalls of the divertor tube [Figs. 3(e) and 3(f)]. Therefore, the plasma source rate peaks inside the tube, and, correspondingly, the plasma pressure exhibits a maximum. [Fig. 3(c)].

To model the data, we employ a distributed gas injection profile peaking in the plasma source region and rapidly ta- pering off into the divertor tube in order to account for the finite neutral conductance of the tube. The difference between the measured and the calculated density profile [Fig. 3(a)] may be partially due to the difference between the measured and the calculated plasma flow speed [Fig. 3(d)]. The calculated plasma density is lower than the experimentally measured density, since the parallel particle loss to the target is larger in the model calculation, due to the larger calculated flow speed, The discrepancy between the measured and calculated magnitude of the axial plasma flow speed may be due to two-dimensional effects (for example, the radial shear viscosity and/or a finite neutral velocity directed oppositely to the plasma flow) not taken into account in the 14-D fluid model. Also, it cannot be excluded that there is some hydrogen desorption from the tube sidewalls, locally increasing the particle source and the plasma density inside the tube. The simulation results suggest a reversal of the parallel plasma flow in the region of reversed pressure gradient (~20.75 m) [Fig. 3(d)]. Experimentally, it is unclear whether the pressure gradient is reversed for 2>0.5 m due to the large error bars, but reversed plasma flow is indeed observed at z=O.95 m,

Schmitz et al.


- 1.5 “E i

(a)

co‘ 1.0

~G;\

72 &iii~ 0

y 0.5 qi

03)

“E 0.2 is co z 0.1 z

0.0 0.0 0.2 0.4 0.6

= b-9 0.6 1.0

FIG. 3. Axial profiles of (a) plasma density, (b) electron temperature, (c) plasma pressure P and neutral pressure PO, (d) plasma flow velocity, atomic and molecular neutral densities n, , (e) and n, (f) and radiated power QR (gj without target gas injection. A comparison of experimental data (symbols) with modeling results (lines) is shown. In (c), the measured plasma and neutral pressures are indicated by cIosed and open circles, respectively. The calculated plasma and neutral pressures are depicted by the solid and dashed line, respectively. The dotted line indicates the sum of the calculated plasma and neutral pressures.

The plasma momentum balance will be discussed in more detail in Sec. V.

The modeling results indicate that the electron heat flow is strongly flux-limited, and depends only weakly on the electron temperature gradient (the electron-electron colli-

Phys. Plasmas, Vol. 2, No. 8, August 1995

sional mean-free path is larger than the axial plasma length due to the low plasma density). In the modeling calculations, the flux limit coefficient providing the best fit to the measured electron temperature profile is ~=0.2. The dissociation rate and, correspondingly, the atomic hydrogen density, are overestimated in the modeling calculation since radial profile effects are neglected and the dissociation rate is calculated based on the central electron temperature and density, rather than the values averaged over the plasma cross section [Fig. 3(e)]. A good match is obtained for the molecular hydrogen density [Fig. 3(f)]. The discrepancy in the radiated power at z=O.43 m may be due to energetic neutrals reaching the bolometer element [Fig. 3(g)]. It is unlikely that impurity radiation is important since we have not been able to detect significant impurity line emission from materials in contact with the plasma (A1203, LaB,, Cu). From the l&D model, the electron heat flux on axis into the divertor tube is calculated to be 0.5 MWIm’, while the calculated target heat flux is 0.13 MW/m2 (for comparison, the measured heat flux to the target on axis is 0.18 MW/m”). The balance is taken up by dissociation losses (58%‘of the input power), ionization loss (3.6%), and hydrogen line radiation losses (12%). It should be noted that this power balance is calculated from a 14-D model, neglecting radial profile effects. Therefore, it is strictly valid on axis (r=O) and does not reelect the global plasma power balance. Considering the intrinsic limitations of the 1$-D model, there is acceptable agreement between calculated and measured proliles.

Figure 4 shows a comparison of experimental and modeling results for a case with strong neutral hydrogen injection through the target [Su,(O) w 0.3 Pa m3/s]. The neutral hydrogen pressure at the plasma source is kept below 0.15 Pa in order to maintain a high electron temperature in the source region. Strong target gas injection results in the formation of a stationary, “detached” ionization front at z-0.3 m [Figs. 4(a) and 4(b)]. The parallel electron heat flux and the electron temperature decrease dramatically due to large dissociation, ionization, and radiation losses in the divertor channel. In the case shown, the calculated parallel peak electron heat flux in front of the divertor tube (z= 1 m) is 7 MW/m2. The target electron temperature is reduced to 2.5 eV, and the measured peak heat flux to the target (Y=O, z=O) is reduced to 0.22 MW/m2 or 3% of the peak heat flux at the tube entrance.

The measured plasma pressure peaks at z =0.45 m in the vicinity of the ionization front. A reversed pressure gradient is observed between the pressure peak and the plasma source [Fig. 4(c)]. The measured plasma flow speed parallel to the magnetic field is locally reversed in this region, as shown in Fig. 4(d). On the opposite side of the ionization front, the plasma pressure decreases strongly toward the target. The modeling results suggest that the plasma pressure decreases due to two separate effects: the parallel plasma momentum is collisionally dissipated, and the plasma density is reduced due to large radial particle loss. Momentum loss arises from ion-neutral collisions which are frequent near the target due to the high molecular and atomic neutral densities. The neutral particles, in turn, deposit momentum on the sidewalls of the divertor tube since the mean-free paths for hydrogen ion-

Schmitz et a/. 3085


0.0 I I I I -0.5 I-- (4

_ 102’ Q % 2 1020 f

4-L

2 10’9 f i c i 10’6

- 75 20

I 15 (D z 10 2 5

L 1 (9)

I 0

0.0 0.2 0.4 0.6 z 0-N

0.8 1.0

FIG. 4. Axial profiles of plasma parameters with strong target gas injection [SH,(0) = 0.3 Pa m3/s]. For an explanation of the other symbols, refer to the caption for Fig. 3.

ization and dissociation are larger than the plasma radius in this region. In Fig. 4(d), the modeling results clearly show that the flow velocity decreases toward the target (except in the presheath region at zCO.1 m). As will be shown in Sets. VII and VIII, the radial particle loss dominates the parallel plasma flow to the target, causing a strong reduction of the plasma density. It should be pointed out that volume recombination does not contribute to charged particle loss in this experiment. since the volume recombination rate at kT,a2.5

eV and ~263XlO’~ me3 is negligible compared to the observed radial particle loss rate.24’25

The target neutral pressure is smaller than the peak plasma pressure by a factor of less than 2. Therefore, we can state that the peak plasma pressure is approximately balanced by the neutral hydrogen pressure at the target. This result differs from our earlier observations in a pure argon plasma, where detachment was achieved for P,(Z=O)eP,+Pi*” This difference is discussed in more detail in Sec. VIII and is primarily due to the fact that the plasma flow speed is smaller in argon as compared to hydrogen due to the reduced ion sound speed, while the radial particle loss is larger than in hydrogen for our experimental conditions.

Figures 4(e) and 4(f) show the atomic and molecular hydrogen neutral densities. The molecular hydrogen injected at the target is partially dissociated, and the dissociation rate increases rapidly with electron temperature. The atomic hydrogen density peaks at about .z=O.25 m, and, simultaneously, the molecular hydrogen density decreases. For 2>0.2.5 m, both atomic and molecular density decrease substantially due to ionization and dissociation. The radiated power is evaluated from bolometer measurements at z =0.17 m and z,=O.43 m. The modeling results suggest that the line emission power peaks in the vicinity of the ionization front [z=O.3 m, Fig. 4(g)], since the atomic hydrogen distribution peaks here. The gas conductance of the divertor tube with and without plasma was evaluated from the pressure difference between the tube entrance and the target region. In the presence of plasma, the conductance is found to be reduced by a factor of 8 due to “plasma plugging.”

In modeling this case, molecular hydrogen is injected only at the target corresponding to the experimental situation. The modeling results suggest that the electrons are partially flux limited near the tube entrance (~=0.5), while the heat flux is mainly diffusive in the high-density region (~~0.5 m). The parallel electron heat flux on axis is reduced by 97% due to hydrogen line radiation (50%), dissociation losses (25%), and ionization loss (deposited as recombination energy onto the sidewalls by radial charged particle transport, 22%). As mentioned earlier, the power balance presented is strictly valid on axis (r=O). Between the pIasma source and the ionization front, the particle flux and the convected electron heat flux are directed oppositely to the conducted electron heat flux. The convected electron heat flux, however, is less than 10% of the conducted heat flux.

Considering the limitations of a 1 f-D model, the simulation results match the experimental data quite well. Differ- ences between the calculated and measured flow reversal point are due to the different peaking position of the plasma pressure. Above the flow reversal point, the measured Mach number is much smaller than the calculated one. This discrepancy can again be attributed to radial profile effects not taken into account in the l&D model. The experimentally measured molecular hydrogen density is much higher than the calculated density for z>O.4 m due to the penetration of moIecular hydrogen toward the plasma source in the low- density plasma at the radial periphery of the tube (radial density profiles are discussed in Sec. VI>. Due to the higher

3086 Phys. Plasmas, Vol. 2, No. 8, August 1995 Schmitz et al.


(4 . ’ . ’ . ’ ’ .

-0.3 -0.2 -0.1 0.0 0.1 0.2 0.3

M calculated

0.8

-0.8 -0.8 -0.4 0.0 0.4 0.8

&$ (n kT,) + 0.71$& kT,(IO-*V/m)

m PO (DO) d 0.21 Pa

q PO (z=O) = 3.7 Pa

0 PO @SO) = 6.6 Pa

0 PO (~0) = 24 Pa

FIG. 5. (a) Measured Mach number on axis (r=O) versus the Mach number calculated from Eq. (11); (b) measured parallel electric tield versus the electric field calculated from Eq. (12). The data is taken at four different target neutral pressures P,(O), as indicated.

molecular hydrogen density, stronger damping of the parallel flow by ion-neutral collisions, and thus a lower Mach number is observed in the experiment.

V. PLASMA MOMENTUM BALANCE

The parallel Mach number can be obtained from the steady-state momentum equation. We neglect the convective derivative and the ion viscosity, since these terms are small, except in the immediate vicinity of the plasma sheath at the target. The pressure gradient force is then balanced by the collisional drag force due to ion-neutral collisions. The Mach number is proportional to the parallel gradient of the plasma pressure, divided by the momentum loss rate:

1 M= -5 [n(kT,+kT~)].

lYZ$ZC~( Vex-t Vi”) dZ (11)

Figure 5(a) shows the Mach number evaluated from Mach probe data plotted versus the Mach number calculated from Eq. (ll), using the experimentally measured pressure gradient and plasma and neutral densities. The collision rate coefficients for resonant charge exchange and elastic collisions with atomic hydrogen are given in Refs. 24 and 27. For elastic ion-molecule collisions, a rate coefficient (q&J = 2 x 1o-8 cm31s is used in order to achieve

good agreement with the experimentally measured Mach number. This rate coefficient is twice as large as the rate coefficient calculated recently.” Figure 5(a) clearly demon- strates that the plasma pressure gradient is balanced by the ion friction forces due to elastic ion-neutial and charge exchange collisions over a large range of neutral densities.

The parallel electric field in the plasma can be evaluated from the electron momentum balance equation (neglecting the electron mass compared to the ion mass.):23

E;=---=(nk~,)-0.71 ffkT.. 02)

The first term on the right-hand side of the equation represents the electron pressure gradient force, while the second term represents the electron thermal force.. Experimentally, the electric field E, is obtained from the measured plasma potential, deduced from the inflection point of the swept probe characteristics (by extrapolating the exponentially increasing electron current). Figure 5(b) shows that the measured electric field corresponds, within experimental error, to the value obtained from Eq. (12), using the experimentally measured electron pressure and electron temperature gradi- ents.

VI. RADIAL PLASMA PROFILES

Figure 6 shows the measured radial electron temperature profiles at 2=0.43 m. Without target gas injection, the electron temperature profile is peaked on axis, and the electron temperature at the plasma periphery is about one-half the central temperature [Fig. 6(a)]. Dissociation, ionization, and line radiation losses are more effective at the plasma center than at the plasma periphery due to the higher electron temperature and reaction rate coefficients. Therefore, with increasing target neutral pressure, the electron temperature reduction is more pronounced, relatively, in the plasma center than at the periphery. As a result, the electron temperature profile is observed to broaden in the vicinity of the ionization front with increasing target neutral pressure [Figs. 6(b) and 6641.

The corresponding radial density profiles are presented in Fig. 7. In our experiment, the- cathode radius (3 cm) is somewhat larger than the radius of the divertor tube (ro=2.25 cm). Also, in a reflex arc discharge at low neutral pressure, plasma electrons are lost to the cathode preferen- tially on axis, since the radial plasma potential profile is a well and the sheath poten’tial is lowest on axis.3*mThe combination of these two effects tends to produce a fairly broad density profile at low pressure. With increasing neutral pressure, the plasma potential on axis increases due to the increased cross-field ion mobility.31 The sheath potential and the plasma electron loss to the cathode become more uniform radially, and the density on axis increases. Also, the electron heat flow is lower at the plasma periphery due to the lower electron temperature and parallel temperature gradient, and incoming neutrals are ionized farther away from the target. We expect therefore that the ionization front forms a conical surface. As a result of the two effects discussed here, the radial density profile at 2=0.43 m becomes more peaked as the neutral pressure is increased.



15 Tt (a)

cg IO 3

m !G 5

m

f i

0 -3 -2 -1 0 1 2 3

r (cm)

0’ I -3 -2 -1 0 1 2 3

r (cm)

6

0 -3 -2 -1 0 1 2 3

r (cm)

FIG. 6. Radial profiles of the electron temperature for z, =0.43 m; (a) without target gas injection [Pa(O)=O.21 Pa]; (b) with moderate target gas injection [S”,(O) = 0.04 Pa m3/s, P,(O)=3.7 Pa]; and (c) with strong target gas injection [SHZ(0) = 0.08 Pa m3/s, P,(O)= IO Pa]. The lines are parabolic fits to the data.

Radial profiles of the parallel plasma flow velocity, u ( I-), are obtained from Mach probe data taken at z =0.17, 0.43, 0.65, and 0.95 m. Figure 8(a) shows a comparison of the radial Mach number profiles measured at z=O.43 m and z=O.65 m for the case without target gas injection. At z=O.43 m, the parallel plasma pressure gradient is positive [see Fig. 3(d)], and the flow is directed toward the target (in the negative z direction). The plasma flow clearly has a two- dimensional structure and is largest at the plasma center since the parallel pressure gradient is largest there. At z=O.65 m, the flow is reversed in the outer region of the plasma column. This is likely to be due to the fact that the parallel pressure gradient is locally reversed at this radius. For comparison, results with strong gas injection are shown in Fig. 8(b). At z=O.43 m, the plasma pressure gradient is positive and the plasma is observed to flow toward the target [see Fig. 4(d)]. At z =0.65 m, however, the pressure gradient is negative and the flow is reversed across the entire plasma column. The flow reversal is always more pronounced near the radial boundary, possibly because neutrals streaming to-

I’S ‘- I * ,” I - ‘. * I ’ ‘,

- 24Pa - - 14Pa : - 5.8 Pa 1 ‘-0. 3.5 Pa . - 1.3 Pa 1 - 0.21 Pa 1

0.0 0.5 1.0 1.5 2.0

r (cm)

FIG. 7. Radial profiles of the plasma density with and without target gas injection (z =0.43 mf. The neutral pressure at the target PO(O) is indicated for each profile. The case P,,(O) =0.21 Pa is the case without target gas injection.

ward the plasma source impart momentum to the ions at large radii, where the plasma density is locally lower than the neutral density. A similar radial structure in the parallel plasma flow velocity has previously been observed in the bundle divertor of the DITE tokamak with strong gas injection.32

-0.1 -

d2F.""""~""""~' (4 i

0.0 0.5 1 .o 1.5 2.0

r (cm>

0.5 1.0 1.5 r b-4

FIG. 8. Radial profiles of the measured parallel Mach number for r =0.43 m and z =0.65 m; (a) without target gas injection [Pa(O)=O.21 Pa]; (b) with strong target gas injection [S”,(O) = 0.08 Pa m/s, P,(O)= 10 Pa].



0 B = 0.04 T

e B = 0.08 T 0 B=O.l7T

0’ * ’ ’ ’ 0. 1 2 3

na +nm (102’m”)

FIG. 9. Radial plasma diffusion coefficient (evaluated from measurements of the H, line emission intensity and the neutral hydrogen pressure) versus the sum of the atomic and molecular hydrogen densities, no=n,+ n, , for three different values of the axial magnetic field B. The data is taken at z=O.43 m and normalized to kT,=lO eV. Also indicated is the offset-linear scaling used to fit the experimental data [Eq. (13)].

FIG. 10. Radial plasma diffusion coefficient evaluated from measurements of the H, line intensity and the neutral hydrogen pressure, in comparison to the classical diffusion coefficient D,, and the Bohm coefficient DBohm (B,=O.17 T). Here D,, is evaluated for kT= kT,+ kTi (lo+2 eV) and for kT= kTi (2 eV).

VII. RADIAL PLASMA TRANSPORT

cross-field electron transport31 The diffusion coefficient is often found to be on the order of the Bohm diffusion coefficient,

Radial particle losses have been calculated from the ionization source in the plasma. The ionization rate is estimated from measurements of the absolute H, emission line intensity, as described in more detail in the Appendix. The H, line emission intensity, radially integrated over the plasma diameter, has been measured at an axial distance z=O.43 m from the target for this purpose. The divergence of the parallel flux is small at this location, and the local radial particle loss rate approximately equals the local plasma source rate. In order to evaluate the scaling of ~the radial particle transport, we have measured the H, intensity as a function of neutral hydrogen density and magnetic field, and subsequently calculated the radial plasma loss rate. If we assume that the radial plasma loss is diffusive, the equivalent diffusion coefficient is given by D,, = y,,,AT . The calculation of the radial particle loss rate from the line-integrated H, intensity is described in the Appendix. In Fig. 9, the diffusion coefficient evaluated in this way is plotted versus the sum of the atomic and molecular hydrogen densities at z =0.43 m. The data has been normalized to kT,= 10 eV in order to eliminate the dependence on electron temperature. The data suggests that the diffusion coefficient, in the range of neutral densities examined, follows an offset-linear scaling with neutral density and does not depend sensitively on the magnetic field. The scaling providing the best fit to the experimental data is given by

D 1 kT,

Bohm=~ z’

At sufficiently high neutral density, the classical ambipolar diffusion coefficient DC1 due to ion-neutral collisions can exceed the Bohm coefficient. Here DC1 is given by

D cl

=kT( vcxf vin> 2 9

miwci

D,=[~+p(~,f~,JlkTe, 03)

where ~=0.45 m*/s eV, ~=9.17XlO-*~ m5/s eV, kT, is in eV, and D, is in m21s.

since in our experiment (v,.,+ ~,J2/o$~l. In classical ambipolar radial diffusion, kT=(kT,+ kTi), since the ions are accelerated by a radial electric field directed outward. In a reflex arc discharge, however, the plasma potential exhibits a radial well and the radial electric field is directed toward the plasma center. Therefore, we would expect the ambipolar diffusion coefficient to be proportional to kTi rather than kT, if the cross-field ion mobility is negligible, and smaller still if the ion mobility is important and the radial electric field impedes cross-field ion transport. Figure 10 shows a comparison of the experimentally determined diffusion coefficient with the Bohm diffusion coefficient and the classical diffusion coefficient evaluated both for kT=kTi and kT= (kT, + kT,). Although numerically similar to the Bohm coefficient at low neutral density, De+, does not scale like the Bohm coefficient. Here D,, increases with neutral density and becomes larger than both the Bohm coefficient and the classical diffusion coefficient (and does not scale as either l/B or l/B*). Near the divertor target, where the neutral density can reach 1021 md3, Dexp can exceed the Bohm coefficient by a factor of 20.

Next we compare the experimentally determined diffusion coefficient to the Bohm diffusion coefficient and the classical diffusion coefficient due to ion-neutral collisions (classical diffusion due to Coulomb collisions is negligibly small). In a reflex arc discharge, we expect large anomalous

VIII. PLASMA DETACHMENT

We are now in a position to relate the experimentally observed decrease of the plasma pressure in the gas target region to the dissipation of plasma momentum by ion- neutral collisions and to the radial particle loss. Figure 11(a)

Phys. Plasmas, Vol. 2, No. 8, August 1995 Schmitz et a/.

IO

3 G- !z d 1

0.1

. kq-t ‘--g=P-‘l-- /-*

/-- ..*-

/--

_..+* *-

._/- ..-*

_./ *.+

/.-* _.a-.

/.-* *./.

#/

_ ,....-* . ..---

B=O.l7T

1 kT,=lOeV

na +nm (1020m’)

0 - --_

DW D Bohm D d (IO+2 ev) Dcl(2.54

(14)

3089


<no>(m9)

(W

ena>

P cLE .

P e 2

<nn>(ma)

FIG. 11. Ratio of the plasma density (a) and electron temperature (b) at the target (:=O) to the corresponding quantity in front of the neutralizer tube (z=O.95 m) versus the neutral density averaged over the gas target region (OC; d cmax); (cl ratio of the plasma pressure at the target (z=O) to the maximum plasma pressure P,, (z,,). Data for hydrogen and argon plasmas are included. The data is taken on axis (r=O). The lines are guides to the eye.

shows the ratio of the plasma density measured at the target to the source plasma density as a function of the average neutral density (no) in the “gas target” region (zQ,,,). For hydrogen, (Q) = (n,) + (n,}. We have included data obtained in a pure argon plasma interacting with an argon gas target. Axial profiles of the plasma parameters for an argon plasma with argon gas injection have been discussed in an earlier paper.” The argon neutral density was obtained from measurements of the neutral pressure and the neutral argon temperature (0.2 eV, as measured by a Fabry-Perot etalon). The peak electron heat flux (r=O, z=O.95 m) is in the range 1 MW/m*Gq,,G7 MW/m* for the dataset presented here. For both hydrogen and argon, the target plasma density increases initially with increasing neutral density, reminiscent of the high recycling divertor regime. The plasma pressure at the target is similar to the source plasma pressure in this regime [Fig. 1 l(c) J. Note that in hydrogen, the target electron temperature is about one-half the source temperature, even without target gas injection [Fig. 11(b)]. The pIasma density

in hydrogen is substantially lower than in argon, and the electron heat transport is strongly flux-limited in hydrogen, as discussed earlier. Therefore, the electron heat flux is de- coupled from the parallel temperature gradient, and a substantial parallel temperature gradient is maintained even for relatively moderate energy loss in the divertor channel (Fig. 3). Beyond a certain threshold in neutral density, both the plasma density and the electron temperature decrease rapidly, and the plasma pressure is no longer constant along the magnetic field. We define as “detachment” a situation where the target plasma pressure is less than 10% of the source plasma pressure. In argon, the neutral density threshold for detachment is abserved to be substantially lower than in hydrogen [Fig. 11 (c)l.

To illustrate how plasma detachment occurs in our experiment, we make some simplifying assumptions. The convective derivative and the ion viscosity are neglected, as compared to the friction force in the plasma momentum equation. For this calculation, the electron temperature is assumed to be independent of position in the gas target region, and the neutral densities (atomic and molecular) are assumed constant in this region. It then follows that the cross-tieId diffusion coefficient and the ionization and ion-neutral collision rates are independent of position as well. The steady- state continuity and momentum equations are

D, +2 f+n,(adissuth,e)tot- ‘j;2- p*

1

$P=-mi (Vcx+i&)+ i

D , s;T **, I I (171

where P = n (k Ti f k T,) is the total plasma pressure. Differ- entiating Eq. (17) with respect to the axial coordinate z, we obtain

-I 82

dz2 P. (18)

Substituting this result into Eq. (16) and solving for P, we obtain

p = pmaxe(z - %lu.~~~, 09)

where zmax is the location of the pressure peak, P max =P(z,,,,) is the pressure maximum, and

- 2 f fnnt(ahissuth.~)t~t (20)

is the parallel pressure gradient scale length. A comparison of the experimentally measured pressure

gradient scale length with this result is hampered by the fact that the electron temperature and neutral density are typically not constant in the gas target region, and the pressure decay is not exponential over the entire gas target region, However, we have obtained reasonable agreement of the measured and

3090 Phys. Plasmas, Vol. 2, No. 8, August 1995 Schmifz et a/+


c no> (lO*O mm3)

FIG. 12. Comparison of measured and calculated pressure gradient scale lengths XL versus the neutral density in the gas target region (OSzgz,d for hydrogen and argon plasmas. The lines are guides to the eye.

calculated pressure gradient scale length in cases where the temperature and neutral density variations are small (Fig. 12). Here, we have used the cross-field diffusion coefficient D derived earlier and the neutral densities determined frz H, line intensity and pressure measurements. For argon, the cross-field diffusion coefficient was determined experimentally in a similar manner than for hydrogen (equating the local ionization rate at the flow stagnation point to the local particle loss rate). For an identical neutral density and electron temperature, the diffusion coefficient was found to be about three times larger in argon than in hydrogen. The rate coefficient for ion-neutral collisions in argon is determined primarily by resonant charge exchange at the neutral temperatures under consideration (kTo+=0.2 eV).33 Here, we use a cross section uCx=6X lo-l5 cm”.34 The ion temperature in argon was found to be kTy0.5 eV, and we obtain (U&*,J = 9.3 x lo-lo cm3/s. From Fig. 12, it is obvious that the neutral density required for detachment in a pure argon plasma is smaller by a factor of 3-4, as compared to a hydrogen plasma. It is obvious from Eq. (20) that detachment can only occur if the the electron energy loss is sufficiently large, since X, depends strongly on the electron temperature.

It is instructive to calculate the number of collisions required for momentum dissipation in the gas target region. For argon, the number of ion-neutral collisions in the gas target region between the ionization front (z = zmax), and the target (z=O) is given by

(211

The analogous expression for hydrogen includes elastic collisions with atomic and molecular neutrals. Figure 13 dem- onstrates that, for a given pressure reduction factor, the number of ion-neutral collisions is much larger (by about a factor of 15) in hydrogen than in an argon plasma. This difference is due to the fact that the parallel plasma flow is slower in argon as compared to hydrogen due to the lower

10’ 0 Ar++Ar l H++H,

N

FIG. 13. Ratio of plasma pressure at the target P(0) to the maximum plasma pressure P(z-) versus the number N of ion-neutral collisions in the gas target region (O~z.~z,,& The lines are guides to the eye. .

ion sound speed, while cross-field particle loss is larger due to the larger -diffusion coefficient. Also, in argon, the dissipation of parallel momentum loss by cross-field plasma diffusion is comparable to the momentum dissipation by ion- neutral collisions, thus increasing the total momentum loss. The radial ion loss time is much smaller than the parallel ion transit time to the target both in hydrogen and argon, so that ions are continually lost to the sidewall by diffusion and replenished by neutral recycling and subsequent ionization.

IX. DISCUSSION AND CONCLUSIONS

We have demonstrated that a stationary ionization front can be maintained in a plasma interacting with a high-density neutral gas layer. In particular, we observe that the plasma pressure is not constant along the magnetic field, but exhibits a local maximum in the vicinity of the ionization front. The plasma flow locally stagnates in the vicinity of the ionization front, and subsonic reversed flow is observed in the region of reversed pressure gradient. In a pure hydrogen plasma, the maximum plasma pressure is approximately balanced by the neutral pressure at the target. Plasma detachment from the target in our experiment is due to two effects: On the one hand, the parallel plasma momentum is effectively dissipated by ion-neutral collisions in the presence of a sufficiently high neutral density. The momentum taken up by the neutrals is subsequently dissipated in wall collisions. On the other hand, the radial particle loss causes a strong decrease of the plasma density toward the target. We wish to point out that the fluid code does not predict plasma detachment if the friction force between ions and neutrals is excluded, con- firming the role of momentum dissipation by ion-neutral collisions. The momentum and heat flow are found to be classical, while the radial particle transport is strongly anomalous and exceeds Bohm diffusion and/or classical diffusion due to ion-neutral collisions. The electron heat flow is given by the classical (Spitzer) heat conductivity and can be adequately described by a harmonic flux limit. Hydrogen line radiation, dissociation, and ionization all contribute substantially. to the dissipation of the electron heat llux. The maximum radiative fraction observed on axis (r=O) is 50%. However, an additional 47% of the electron power flux is



dissipated by neutral dissociation and ionization. The energy lost in ionization processes is transported radially to the sidewalls of the divertor tube by charged particles in the form of recombination energy.

The PISCES-A plas-ma exhibits strong low-frequency fluctuations (G/n ~0.5, e @kT,s 1). The frequency spectrum and the characteristic wavelengths are similar to a typical tokamak boundary plasma (1 kHz<e~/2ns200 kHz, e~/fl,,~O.l, 100 m-‘<k0<500 m-r, k~Jpi~O.1, where o is the fluctuation frequency, ~,i is the ion cyclotron frequency, k, is the poloidal wave number, and pi is the ion gyroradius). The fluctuations are strongest near the radial plasma boundary. A conventional radiative instability is not likely in hydrogen since the radiation rate increases monotonically with electron temperature in the temperature range under consideration. While it is likely that the anomalous radial particle loss observed in the experiment is due to fluctuation-induced transport, preliminary analysis of the power spectra indicates that it is not simply due to quasicoherent fluctuations and an associated time-averaged radial particle flux. The ionization front remains axially localized (no “burnthrough” of hot plasma to the target is observed}, while the plasma density and potential locally fluctuate. The macroscopic stability of the ionization front may be due to the high collisionality and the strong dissipation of plasma momentum by ion-neutral collisions.

The observation of a flow reversal raises the question of whether core fueling control can be accomplished in a tokamak gas target divertor. Control of the core plasma density requires particle exhaust through the divertor and is incom- patible with a flow reversal at the divertor throat. Also, plasma and neutral sputtering from the sidewalls of the divertor channel and subsequent impurity transport to the main plasma region is a serious concern. The flow reversal in our experiment, however, is a consequence of strong target gas fueling. Continuous target gas fueling and a reversed plasma flow may be avoided in a tokamak, if a regime governed by volume recombination can be accessed.35s36 Very high plasma density and low electron temperature (kT,S 1 eV, n a 1021 m-3)24.25 are required for the volume recombination rate to be comparable to the ionization rate and for recombination radiation to dissipate a large fraction of the incident power. Further research is required to determine the viability of this approach and the stability of the plasma/neutral inter- face under these conditions. A potential disadvantage of this regime is that the neutral density at the target may reach values of 1021-1022 rnb3 35*36 while a neutral density of less than 10” mm3 may have ;o be maintained at the main plasma boundary in order to access regimes of enhanced core confinement [i.e., high confinement mode (H mode)]. The required pressure drop between the divertor and the main plasma region therefore may be prohibitively large. Tight baffling of the divertor plasma would be required, and the erosion resulting from the proximity of the plasma to the sidewall of the divertor channel may be intolerably large for low-2 wall materials.37

Potentially, a major fraction of the core exhaust power can be dissipated by trace impurity radiation. While it is not easily possible to achieve divertor radiative fractions in ex-

cess of 50% in a high recycling divertor regime, we do not expect the same limitation in a gaseous divertor regime, where the plasma is detached from the target and/or the plasma pressure is not constant along the magnetic field. impurity radiation is known to be important in the detached or low divertor temperature regimes recently observed in tokamak plasmas.‘5-‘7 There is direct evidence that the neutral hydrogen (or deuterium) pressure in the divertor region is much lower than the plasma pressure in these experiments. Experiments in PISCES-A have also demonstrated plasma

detachment for Po( 0) 4 P, + Pi in pure argon plasmas due to the high level of argon line radiation 10~s.‘~ The neutral hydrogen density required to dissipate the plasma momentum in the presence of substantial impurity radiation is moderate compared to the neutral density, which would be required in a (pure hydrogen) volume recombination scenario. Extend- ing our 11-D modeling calculations to a device such as ITER with a core exhaust power of 100-200 MW, we find from our fluid model that a moderate impurity fraction (-2% in the case of argon) in the divertor plasma may produce detachment or a very low electron temperature at the target.36 The calculated neutral hydrogen density at the target is less than 10” rnw3 f m this case, which is moderate compared to what would be required in the volume recombination scenario, and more reasonable with regard to divertor baffling requirements. However, core plasma purity and fuel dilution are of concern if even small fractions of high-Z impurities need to be maintained at the plasma boundary or in the divertor. Also, the radiation energy loss can locally exceed the heat flow aIong the fieId lines for relatively low impurity concentrations, producing either localized stationary MARFEs or radiative instabilities and relaxation oscillations and making control of the boundary symmetry and divertor conditions more difficult.38,3g These instabilities are most likely in a temperature range where the impurity radiation rate QR decreases with electron temperature (aQ,ldkT,<O). In spite of these potential problems, a dissipative divertor relying on medium-Z or high-2 trace impurity radiation may still be the most attractive scenario for divertor power exhaust in next generation tokamaks.

ACKNOWLEDGMENTS

We greatly acknowledge the technical support of the experimental work in the PISCES-A facility by T. Sketchley, L. Chousal, P. Luong, J. Latchum, G. Gunner, M. Srinivasan, S. Keller, and the PISCES team.

This research is supported by the U.S. Department of Energy under Grants No. DE-FG03-86ER-52134 and No. DE-FG03-86ER-52130.

APPENDIX: CALCULATION OF THE ATOMIC AND MOLECULAR HYDROGEN DENSITY

Here, we describe the evaluation of the atomic and molecular neutral hydrogen densities and the local particle loss rate from H, line intensity measurements and neutral pressure measurements. We first discuss the processes generating H, radiation. In a tokamak, H, line emission is primarily generated by electron impact excitation of Franck-Condon



or charge exchange atoms.20 In addition, dissociative excitation of Ha and dissociative recombination of HZ+ can play a role. Most of these processes result in Franck-Condon atoms with a substantial kinetic energy (32.5 eV). The corresponding H, emission therefore would show significant Doppler broadening. Through one particular reaction channel, dissociative excitation of Hz can also produce product atoms with a mean energy of 0.3 eV.20,21,24 Depending on the local plasma density, the Doppler broadening of the H, line in PISCES-A indicates temperatures of 0.25-0.4 eV for the emitting neutral atom. A high-energy tail, if present at all, was found to be weaker by at least a factor of 50, as compared to the slow group in PISCES-A. This indicates that the vast majority of photons in PISCES-A originate from dissociative excitation, resulting in low-energy atoms. The main reason for this is that the time of flight of dissociated Franck-Condon atoms to the wall of the divertor tube is shorter than the excitation time to the third level. Franck- Condon atoms in the ground and first excited states are therefore very likely to recombine into H2 before further excitation can occur.

The absolute H, line emission density, integrated radially over the plasma diameter, is measured with a 1.35 m Czerny-Turner monochromator at four different axial loca- tions (z=O.17, 0.43, 0.65, and 0.95 m). Since the radiation originates from dissociative excitation of molecules, the molecular hydrogen density can be deduced with the knowledge of the radial plasma density and electron temperature profiles. If we assume that the molecular hydrogen density is radially uniform, the result is

1 xFl c 0

ZHII ds.

Here, rl/(O,z) is the photon yield per dissociated molecule for the particular dissociation channel considered,20-22 and F, is the form factor

For high plasma density [n(0,zj>1019 m-j), the dissociation mean-free path for H, can be smaller than the plasma radius, making the plasma partially opaque to H,. We then approxi- mate the radial Ha density profile by a zeroth-order modified Bessel function:

%(r>z) =%(ro ,z> ~O{r[n(Z)(adissu*,e)(Z)l~m(Z)11’2}

~o{~or~(Z)(~dissU*,@~(Z)~~,(Z)l~~Z}. (A3)

Here, n(z) and ( cdissUth,J(zj are the density and dissociation rate averaged over the plasma cross section. This expression yields another form factor that can be easily incorpo- rated into Eq. (Al).

The atomic neutral density is evaluated from neutral pressure measurements with the knowledge of the molecular density. The ionization mean-free path for Franck-Condon atoms is larger than the plasma radius in our experiment, so

that the atomic hydrogen density is radially uniform. To calculate n,(zj, we need to know the molecular and atomic neutral temperatures. From the linewidth measurement of hydrogen molecular lines, we estimate that kT,=O.l eV. While there is no direct measurement of the atomic hydrogen temperature, the best agreement between experimental and calculated parallel profiles of the pIasma parameters was obtained for kT, = 1 eV. This temperature is somewhat below the Franck-Condon energy, which is reasonable, since there is some cooling of hydrogen atoms by collisions with molecular hydrogen. We therefore use this value in calculating the atomic hydrogen density. The atomic hydrogen pressure is obtained by subtracting the molecular pressure P,(r, ,z) = n,(ro ,z)kT, from the total neutral pressure Po(ro ,z) measured at the wall of the divertor tube:

Pa(z)=PO(rO,z)-P,(rO,z).

The atomic neutral density is then given by

h44)

; P,(z) %(Z) = -zk-. (-45)

The plasma source rate can now be obtained by integrat- ing the contributions from molecular and atomic hydrogen over the cross section of the divertor tube:

27r ‘0 S,(zj = II 0 0

CnRZ(r~z)n(r~Z)2 f+tr,Z)((T&sUfh,e )(rA

+no(Z)lt(Y,Z)(~iionUt~,~)(T,Z)IT &- de. (-46)

Here, ft is the fraction of molecular hydrogen dissociated into Ht. The direct ionization of atomic hydrogen typically accounts only for lo%-25% of the total Ht source rate, The radial particle loss rate equals the source rate if the parallel plasma flux is sufficiently small to be neglected. We can then write

%ssfZ) = S,(z)

jzrrJzn(r,z)r dr de’

where v toss(z) is the radial particle loss rate.

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