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A mechanical device for enhancing the halo density in the TMX-U tandem mirror
264
Journal of Nuclear Materials 121 (1984) 264-270 North-Holland. Amsterdam
A MECHANICAL DEVICE FOR ENHANCING THE HALO DENSITY IN THE TMX-U TANDEM MIRROR W.L. HSU Sandia National Laboratories, Livermore, California 94550, USA
W.L. BARR and T.C. SIMONEN Lawrence LivemoreNational Laboratory. Livermvre, Cal&wnia 94550, USA
The halo recycler, a mechanical device similar to pump limiters used in tokamaks, is studied as a means of enhancing the halo plasma density in the Tandem Mirror Experiment Upgrade (TMX-U). The recycler structure consists of an annular chamber at each end of the tandem mirror device where the halo plasma is collected. The halo plasma density is increased by recycling the halo ions as they are neutralized by the collector plate. With sufficient power fed into the halo electrons, the recycler can sustain an upstream electron temperature of 30 eV for effective halo shielding while maintaining a low temperature of 5 eV near the collector plate to reduce sputtering. A power flow model has shown that the required power for heating the halo is low enough to make the halo recycler a practical concept.
1. Introduction In tandem mirror devices such as TMX-U [l] and MFTF-B [2], the plasma consists of three main axial regions: the center cell is bounded on each end by an end cell, beyond which is the end fan (fig. 1). The main fusion power in a mirror Kactor is supplied from the center cell region. The hot ions in the plasma core are confined from axial end loss by electrostatic potentials in the end cells which are supported by sloshing ions and enhanced by localized electron cyclotron resonance heating. The un~nf~~ edge plasma (halo) ions flow into the end fan and are removed by vacuum pumping. The neutral pressure in the end fan must be kept low to reduce the axial power loss [3]. Ahhough the ha10 plasma does not contribute to the fusion power, it increases the plasma energy confinement time by shielding the core plasma from the influx of background neutrals [4,5]. When hydrogen molecules impinge on the plasma, Franck-Condon neutral atoms are produced by molecular dissociation. If the halo is not sufficiently dense and hot, these neutral atoms can penetrate into the core plasma and charge-exchange
~22-3115/84/$03.~ 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
with the hot ions. In the end cells, the sloshing density could be sufficiently reduced to prevent
ion
the formation of an endplugging potential. The presence of halo shielding was inferred on the ZXIIB experiments (61. Hot plasma buildup was experimentally observed, whereas modelling by radial buildup codes predicted a decaying plasma if the halo plasma were not present. In ThfX-U, the effects of plasma pumping were observed [7]. The halo was also measured by Langmuir probes and found to have T, - 15 eV and no - 2 x 10” cme3 (83. As will be discussed below, these parameters are not sufficient for shielding. In this paper a halo recycler for enhancing the halo density in TMX-U
is described.
2. Halo reeyeler The halo recycler consists of an enclosed annular collector chamber, at each end of TMX-U, that closely surrounds the end fan plasma (see fig. 2). The edge plasma that flows into the annular chamber is defined to be the halo. This scheme is similar to the recycler B.V.
265
W.L. Hsu et al. / Mechanical device for enhancing halo density
VENTED PLATE
CORE PLASMA 0
Fig. 2. Schematic diagram of the halo recycler located in the end fan.
Fig. 1. tihematic diagram of TMX-U. Depicted are the plasma, the neutral beams, and the magnetic coils.
being designed for MARS (Mirror Advanced Reactor Study) [9], which is patterned after the pump limiters used in tokamaks [lo-131. The recycler is separated into two regions by a vented plate; on the upstream side is the channel region and on the downstream side is the pumping plenum. The vented plate has holes that allow only a small fraction of the plasma flux to flow into the pumping plenum while most of the plasma flux is neutralized on the vented plate. The role of the vented
plate is to provide some control over the recycling of the particle flux in the channel region. The halo plasma density in the channel is high while the electron temperature is low due to the power expended in ionizing and heating the recycled gas. The plasma flux to the vented plate is many times larger than the total particle throughput and the ions, on the average, are recycled many times before being pumped. This mode of operation has been observed in tokamak divertor experiments on ASDEX [14], PDX [15], and DIII [16,17]. The condition of high recycling characterizes a situation in which the plasma flow is subsonic (except near the vented plate) with a velocity that is much lower than in the case of low recycling (i.e. in the absence of a recyler) (181.
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W. L Hsu et al. / Mechanical device for enhancing halo density
Since the total particle flow (xv) in the halo should remain unchanged, a reduction of the flow velocity should result in the enhancement of the halo density. By changing the dimensions of the holes, which would vary the amount of‘recycling, the halo plasma density can be controlled. Particle balance in the pumping plenum gives: (nJ2)CJa
= Q + ( n0/4)V,Auf.
(I)
The left hand side gives the rate that ions enter the holes whose combined area is a fraction a: of the vented plate cross sectional area A. Q (molecules/s) is the gas throughput. The last term in the equation gives the flow of gas from the plenum, with density no, to the channel region. The mean molecular speed is Vs, and f is a correction factor in the conductivity of the holes for gas. For circular holes of diameter D and length L, f = l/(1 + 3L/4D). Eq. (1) can be rearranged as: xe =
@Q/aA + @U/WC,.
(2)
Since no (or the pressure p,,) in the plenum is determined by the gas throughput Q and the pumping speed S ( p0 = ZQ/S), eq. (2) shows that the halo density adjacent to the vented plate can be controlled by both a and f. If there are many holes, the vented plate can also be used to control the radial profile of the halo by allowing different a! or f at different parts of the plate.
3. Halo !&ieldll The role of the halo is to shield hot core ions from the influx of cold neutral gas. The shielding effect is accomplished by ionzing the neutral particles which are then diverted to the end fan along the near-axial field lines in mirror devices. The necessary halo parameters for achieving a given level of gas attenuation was calculated by a neutral transport code [19] which accounts for all of the major ionization, dissociation, and chargeexchange processes. The code requires given radial profiles of plasma density, electron and ion temperature, and calculates the steady state neutral density and deposition profiles. In fig. 3 the halo line density is shown as a function of electron temperature (assuming Ti = Te) to reach a given attenuation factor. The attenuation factor is de fined as the ratio of the total neutral density at the halo-vacuum interface to the neutral density at the core plasma-halo interface. The results do not depend strongly on the ion temperature since Ti mainly affects the energy of the charge-exchanged neutrals which is a
10’2
L 0
20
40 T, (eV)
60
go
Fig. 3. The required halo line density as a function of electron temperature necessary to reach a given neutral gas attenuation factor. The assumptions are ri = T, and that the plasma is
cylindrically symmetrical.
small fraction of the total neutral density (see the discussion in section 5). The piasma geometry is taken to be cylindrically symmetrical and to extend axially to infinity. When Te is low the attenuation increases sharply with the electron temperature but then reaches a plateau at T, 2 40 eV. This effect reflects the dependence of the electron ionization rate coefficient for hydrogen on T,. The attenuation factor also rises with increasing halo line density. These results show that the desired halo shielding effect can be produced by varying the halo line density while fixing the halo electron temperature in the range of 30-40 eV. From fig. 3, a halo line density /n,dl= 1.5 X 1013 cm-* and T, = 30 eV will attenuate the gas density 50 fold.
4. Power flow In the channel region the electron temperature is substantially reduced from the upstream value because of energy expended in interacting with the the recycled gas. A major issue regarding the practicality of a shielding halo is whether the power necessary for sustaining the large temperature gradient along the halo plasma is within an acceptable limit. In the region where the electron temperature gradient scale length is greater than the electron scattering mean free path, d In T,/ds > l/X,, heat transport is mainly by thermal conduction
W.L. Hsu et al. / Mechanical device for enhancing halo density
along the magnetic field. At steady state, the electron temperature Te as a function of distance s along the field line from the midplane is given by: -d/ds(kA(s)T,5’2dTJds)=P,(s).
(3)
Here, the thermal conductivity is K = kT’/* and k = 2100 W/m. (eV) ‘I*; A(s) is the cross-secional area of the halo flux tube which, from magnetic flux + conservation, is given by A = #/B; P, is the net power input to the halo electrons per unit length and P = lP,ds is the total net power. This equation is integrated numerically subject to the boundary conditions T,(O) and T,(L), where s = 0 defines the midplane of the center cell and s = L the location of the vented plate. It can be derived from eq. (3) that T, (0)“’
= T,(L)“*
+(7/2k+)jP,(s)
B(s)
ds.
(4)
Because of the 7/2 power dependence, the power necessary to support the electron temperature gradient is insensitive to T.(L) if T,(L) < T,(O)/2, and a reasonable estimate of the power required to maintain a given T,(O) can be obtained without knowing the details of the interactions in the chamber. The calculated halo electron temperature profile along the axis of TMX-U is shown in fig. 4. P = 430 kW was found necessary to sustain T,(O) = 30 eV. The calculated power is much smaller than might have been
261
necessary because A(s) is small where T, is large and Te is small where A(s) is large. The mean free path for electron scattering is given by X, = 9.7 x lO”T~*/n,. In a halo plasma where ttc = 2 x lo’* cme3 and T = 30 eV, X, = 4 m. Since the axial length of TMX-U is’ = 18 m we are at the limit where the assumption of thermal conduction becomes marginal. At higher electron temperatures a convective flow model must be used. An earlier calculation assuming thermal convection [S] showed that in a halo with jn,dl = 1.5 x 10” cm-* and T, = 30 eV the axial power loss is comparable to the power flow determined from eq. (4). However, at higher T, thermal convection results in a substantially lower Rower level. The source of power into the halo can result from radial heat transport or direct heating from auxiliary sources. Fast ions trapped in the halo from neutral beams transfer their energy to the electrons via collisions. In addition, halo electrons can be directly heated by ECRH and ICRH. In tandem mirror reactors alpha particles whose orbits interesect the halo supply most of the heating. The total power injected into TMX-U is approximately 3 MW (2.4 MW from neutral beams, 0.2 MW from ECRH and 0.2 MW from ICRH). The 430 kW necessary for heating the halo plasma is a small fraction of the available power and therefore would not pose an unreasonable requirement.
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10
Z (m) Fig. 4. The magnetic field B and the calculated halo T. along the axial length, I, of TMX-U. Power into the TMX-U halo electrons = 430 kW.
W.L., Hsu et al. / Mechanical deuice /or enhancing halo density
268
5. PartIde flow
In this section we estimate the ion flow, Q, along the halo plasma into the recycler. This particle throughput must eventually be removed by the recycler vacuum pumping system. From eq. (2), for a given a and f the required neutral pressure in the pumping plenum can then be determined. To a first order of approximation, the halo plasma flow is assumed axial and at steady state must be equal to the ionization rate of neutrals in this region. The gas pumped by the TMX-U halo was estimated using the neutral transport code discussed in section 2. Numerical calculations were performed for three plasma regions: the gas box, the center cell, and the end cells. The gas box is located at the transition region between the center cell and the end cell where the magnetic flux surface is highly elliptical. Calculations in this region account for the trapping of gas that
f i’o;-\
was injected for fueling the plasma. The center cell and the end cells have large surface areas; calculations in these regions account for the trapping of the background gas. The plasma radius is 26 cm at the midplane of the center cell and the halo extends from 18-26 cm. By following the magnetic flux surface, the halo thickness maps to 1.8-2.6 cm on the minor axis of the elliptical gas box plasma and 14-20 cm at the circular midplane of the end cell. Because of the large ellipticity, the plasma in the gas box was approximated as a slab to determine gas deposition. The plasma density profile was assumed to be ne = 4 X lo’* exp( -(x/2.58)*) cme3, with x(cm) as the distance out from the midplane of the slab (see fig. 5a). Electron and ion temperatures were assumed equal and given by T, = 300 exp( -(x/1.27)*) eV. These profiles were chosen such that when mapped to the end cell midplane, the halo
II
-a
-...*. *.l.
“s
0. ‘.
-300
s -200
II-
‘.
al
*.
‘.
*. ‘.
*.
*.
a. *-.* *...
lo”
I 0
0.5
1
1.5
X (cm)
T, *. -.....* 2
0 2.5
0
0.5
1
1.5
X
2
2.5
(cm)
X (cm) Fig. 5. (a) The electron temperature and density profile assumed for the gas trapping calculations. x is the distance out from the midplane of of the plasma slab at the gas box. The halo plasma extends from 1.8 to 2.6 cm. (b) The calculated neutral density profile along X. (c) The calculated net rate of iosn deposited in the plasma as a function of X.
W. L Hsu et al. / Mechanical
line density and the average halo electron temperature would satisfy the conditions prescribed in section 3. Total gas feed to the gas box during typical TMX-U operation is 90 Torr l/s. Figs. 5b and SC show the calculated neutral density (molecular, Franck-Condon, and charge-exchange) and the net ion source as a function of x. Near the edge of the plasma, the total neutral density is dominated by molecular gas. However, at x < 1.2 cm the Franck-Condon component becomes dominant because the Franck-Condon neutrals are more energetic than the room temperature molecular particles and therefore are less likely to be attenuated by the plasma. Fig. 5b shows that the total neutral density attenuation across the halo in the gas box region is a factor of 10, much less than the factor of 50 that would result at the center and the end cells. The ion source profile, shown in fig. SC, has a peak at 1.8 cm. The source drops sharply at large x, as the electron temperature drops below the ionization threshold. At x closer to the center the source also drops, although less drastically, because of the decreasing neutral density. Integrating the ion source over the halo region and assuming that equal amounts flow to each end of the device gives 4.3 x 10” ions/s per end. In the center cell the background gas pressure results in 15.5 Torr l/s of molecular gas impinging at the plasma surface. By mapping the electron temperature and density profiles from the gas box plasma to the center cell and using the version of the neutral transport code for cylindrical geometry the center cell region was estimated to contribute 1.3 x lo*’ ions/s per end to the halo. Since the total plasma surface area in the end cell differs by less than 10% from that of the center cell and the background gas pressures are essential equal, it was assumed that the end cell gave the same contribution as the center cell. The total ion source is therefore = 7 x 10” ions/s per end, or Q = 3.5 x lo*’ molecules/s per end (11 Torr l/s) to be pumped by the recycler vacuum pump. The axial electric field is expected to be small in the halo plasma and the flow is subsonic (see the discussion just before eq. (1)) therefore, the plasma pressure would be roughly constant constant along the field lines. Then the assumed T,(O) = 30 eV and n,(O) = 2 x lo’* cmw3 imply that n,(L) = 1.2 x lOI cmm3 if T,(L) = 5 eV. Inserting n,(L), T,(L), and Q into eq. (2), expressing no in term of pressure, and assuming the ions are H+, we obtain: 1 = (4.7 X 10e3/a)
+ O.llp,(mTorr)f.
(5)
For the case of TMX-U, eq. (5) shows that unless a is very small this parameter has little influence on the overall recycling and pof becomes the controlling
device for enhancing halo density
269
parameter. Practical design and heat removal considerations lead to vented plates with a < 0.1 and f< 0.5. If we assume a = 0.02 and f= 0.5 this implies the plenum pressure must be = 14 mTorr to give the desired n,(L).
6. Summary In this paper, a halo recycler is proposed for enhancing the density of the halo plasma in the TMX-U tandem mirror. The recycler is an annular chamber at each end of the mirror device that scrapes the halo plasma and is similar to pump limiters and divertors used in tokamaks. ‘Ihe recycler is operated in a high recycling mode and also has the advantage of reducing the erosion of the end plate. The molecular throughput in the halo of TMX-U is 11 Torr l/s per end. TO generate high recyling, the recycler is operated using a vented plate with a plenum pressure = 14 mTorr. With approximately 500 kW of heating the halo can attenuate the neutral gas density by a factor of 50. Before the halo recycler can be implmented in TMXU, many issues must be better understood. In TMX-U, the end fan typically operates at a background pressure of 5 x 10e6 Torr. Because of high recycling the gas pressure in the channel region is expected to be high, the resulting pressure gradient must be supported by halo plasma pumping. This condition would determine the channel length which must be short when compared to the length of the end fan. It is also important to determine whether localized cooling of the gas box plasma by the fueling gas would substantially affect the electron temperature and the power flow calculation.
Acknowledgement The authors wish to thank Dr. D.P. Grubb for his helpful comments. This work was supported by the US Department of Energy.
References
PI T.C. Simonen, S.L. Allen, T.A. Casper et al., Phys. Rev. Letters 50 (1983) 1668.
PI D.E. Baldwin and B.G. Logan, Eds., Physics Basis for an Axicell Design for the End Plugs of MFTF-B, UCID-19359 (1982). 131 G.D. Porter, Nucl. Fusion 22 (1982) 1279. [41 A.H. Futch, Bull. Am. Phys. Sot. 26 (1980) 878. 151 T.C. Simonen, A.H. Futch, W.L. Hsu et al., Bull. Am. Phys. Sot. 27 (1982) 999.
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W. L. Hsu et al. / Mechanical device
[6] B.W. StaIIard, F.H. Coensgen, W.F. Cummins et al., in
[7] [8] [9]
[lo] [ll] [12]
Proc. Intern. Symp. on Plasma Wall Interaction, Jiilich (Pergamon, 1976) p. 63. W.L. Pickles, MO. CaIderon, MR. Carter et al., J. Vacuum Sci. Technol. Al (1983) 1288. W.L. Hsu, W.R. Wampler, T.J. Orzechowski et al., Bull. Am. Phys. Sot. 27 (1982) 997. G.A. Carbon, D.E. Baldwin, W.L. Barr et al., Mirror Advanced Reactor Study (MARS) End Plasma Technology Development, Am. Nut. Sot. 5th Topical Meeting on Technology of Fusion Energy, Knoxville, TN (1983). R. Jacobsen Nucl. Fusion 22 (1982) 277. P. Mioduszewski, J. Nucl. Mater. lllBr112 (1982) 253. S. TaImadge, R.W. COM, A.K. Prinja et al., Nucl. Fusion 22 (1982) 1369.
forenhancing
halo density
[13] R.W. COM, S.P. Grotz, A.K. Prinja et al., in: Proc. 10th Symp. on Fusion Technology (SOFT) (1983) 497. [14] W. EngeIhardt, G. Becker, D. Behringer et al., J. Nucl. Mater. 1118112 (1982) 337. [15] R.J. Fonck, M. Bell, K. Bol et al., J. Nucl. Mater. 1118112 (1982) 343. [16] M.A. Mahdavi, C.J. Armentrout, F.P. Blau et al., J. Nucl. Mater. lllBt112 (1982) 355. [17] M. Shimada, M. Nagami, K. Ioki et al., J. Nucl. Mater. 111&112 (1982) 362. [18] D.E. Post, D.B. Heifetz and M. Petravic, J. Nucl. Mater. lllBr112 (1982) 383. (191 G.E. Gryukowski and J.M. Gilmore, Buildup Studies of a Tandem Mirror Reactor With Inboard Thermal Barrier, Lawrence Livermore National Laboratory Report UCRL84233,198O.
Journal of Nuclear Materials 121 (1984) 264-270 North-Holland. Amsterdam
A MECHANICAL DEVICE FOR ENHANCING THE HALO DENSITY IN THE TMX-U TANDEM MIRROR W.L. HSU Sandia National Laboratories, Livermore, California 94550, USA
W.L. BARR and T.C. SIMONEN Lawrence LivemoreNational Laboratory. Livermvre, Cal&wnia 94550, USA
The halo recycler, a mechanical device similar to pump limiters used in tokamaks, is studied as a means of enhancing the halo plasma density in the Tandem Mirror Experiment Upgrade (TMX-U). The recycler structure consists of an annular chamber at each end of the tandem mirror device where the halo plasma is collected. The halo plasma density is increased by recycling the halo ions as they are neutralized by the collector plate. With sufficient power fed into the halo electrons, the recycler can sustain an upstream electron temperature of 30 eV for effective halo shielding while maintaining a low temperature of 5 eV near the collector plate to reduce sputtering. A power flow model has shown that the required power for heating the halo is low enough to make the halo recycler a practical concept.
1. Introduction In tandem mirror devices such as TMX-U [l] and MFTF-B [2], the plasma consists of three main axial regions: the center cell is bounded on each end by an end cell, beyond which is the end fan (fig. 1). The main fusion power in a mirror Kactor is supplied from the center cell region. The hot ions in the plasma core are confined from axial end loss by electrostatic potentials in the end cells which are supported by sloshing ions and enhanced by localized electron cyclotron resonance heating. The un~nf~~ edge plasma (halo) ions flow into the end fan and are removed by vacuum pumping. The neutral pressure in the end fan must be kept low to reduce the axial power loss [3]. Ahhough the ha10 plasma does not contribute to the fusion power, it increases the plasma energy confinement time by shielding the core plasma from the influx of background neutrals [4,5]. When hydrogen molecules impinge on the plasma, Franck-Condon neutral atoms are produced by molecular dissociation. If the halo is not sufficiently dense and hot, these neutral atoms can penetrate into the core plasma and charge-exchange
~22-3115/84/$03.~ 0 Elsevier Science Publishers (North-Holland Physics Publishing Division)
with the hot ions. In the end cells, the sloshing density could be sufficiently reduced to prevent
ion
the formation of an endplugging potential. The presence of halo shielding was inferred on the ZXIIB experiments (61. Hot plasma buildup was experimentally observed, whereas modelling by radial buildup codes predicted a decaying plasma if the halo plasma were not present. In ThfX-U, the effects of plasma pumping were observed [7]. The halo was also measured by Langmuir probes and found to have T, - 15 eV and no - 2 x 10” cme3 (83. As will be discussed below, these parameters are not sufficient for shielding. In this paper a halo recycler for enhancing the halo density in TMX-U
is described.
2. Halo reeyeler The halo recycler consists of an enclosed annular collector chamber, at each end of TMX-U, that closely surrounds the end fan plasma (see fig. 2). The edge plasma that flows into the annular chamber is defined to be the halo. This scheme is similar to the recycler B.V.
265
W.L. Hsu et al. / Mechanical device for enhancing halo density
VENTED PLATE
CORE PLASMA 0
Fig. 2. Schematic diagram of the halo recycler located in the end fan.
Fig. 1. tihematic diagram of TMX-U. Depicted are the plasma, the neutral beams, and the magnetic coils.
being designed for MARS (Mirror Advanced Reactor Study) [9], which is patterned after the pump limiters used in tokamaks [lo-131. The recycler is separated into two regions by a vented plate; on the upstream side is the channel region and on the downstream side is the pumping plenum. The vented plate has holes that allow only a small fraction of the plasma flux to flow into the pumping plenum while most of the plasma flux is neutralized on the vented plate. The role of the vented
plate is to provide some control over the recycling of the particle flux in the channel region. The halo plasma density in the channel is high while the electron temperature is low due to the power expended in ionizing and heating the recycled gas. The plasma flux to the vented plate is many times larger than the total particle throughput and the ions, on the average, are recycled many times before being pumped. This mode of operation has been observed in tokamak divertor experiments on ASDEX [14], PDX [15], and DIII [16,17]. The condition of high recycling characterizes a situation in which the plasma flow is subsonic (except near the vented plate) with a velocity that is much lower than in the case of low recycling (i.e. in the absence of a recyler) (181.
266
W. L Hsu et al. / Mechanical device for enhancing halo density
Since the total particle flow (xv) in the halo should remain unchanged, a reduction of the flow velocity should result in the enhancement of the halo density. By changing the dimensions of the holes, which would vary the amount of‘recycling, the halo plasma density can be controlled. Particle balance in the pumping plenum gives: (nJ2)CJa
= Q + ( n0/4)V,Auf.
(I)
The left hand side gives the rate that ions enter the holes whose combined area is a fraction a: of the vented plate cross sectional area A. Q (molecules/s) is the gas throughput. The last term in the equation gives the flow of gas from the plenum, with density no, to the channel region. The mean molecular speed is Vs, and f is a correction factor in the conductivity of the holes for gas. For circular holes of diameter D and length L, f = l/(1 + 3L/4D). Eq. (1) can be rearranged as: xe =
@Q/aA + @U/WC,.
(2)
Since no (or the pressure p,,) in the plenum is determined by the gas throughput Q and the pumping speed S ( p0 = ZQ/S), eq. (2) shows that the halo density adjacent to the vented plate can be controlled by both a and f. If there are many holes, the vented plate can also be used to control the radial profile of the halo by allowing different a! or f at different parts of the plate.
3. Halo !&ieldll The role of the halo is to shield hot core ions from the influx of cold neutral gas. The shielding effect is accomplished by ionzing the neutral particles which are then diverted to the end fan along the near-axial field lines in mirror devices. The necessary halo parameters for achieving a given level of gas attenuation was calculated by a neutral transport code [19] which accounts for all of the major ionization, dissociation, and chargeexchange processes. The code requires given radial profiles of plasma density, electron and ion temperature, and calculates the steady state neutral density and deposition profiles. In fig. 3 the halo line density is shown as a function of electron temperature (assuming Ti = Te) to reach a given attenuation factor. The attenuation factor is de fined as the ratio of the total neutral density at the halo-vacuum interface to the neutral density at the core plasma-halo interface. The results do not depend strongly on the ion temperature since Ti mainly affects the energy of the charge-exchanged neutrals which is a
10’2
L 0
20
40 T, (eV)
60
go
Fig. 3. The required halo line density as a function of electron temperature necessary to reach a given neutral gas attenuation factor. The assumptions are ri = T, and that the plasma is
cylindrically symmetrical.
small fraction of the total neutral density (see the discussion in section 5). The piasma geometry is taken to be cylindrically symmetrical and to extend axially to infinity. When Te is low the attenuation increases sharply with the electron temperature but then reaches a plateau at T, 2 40 eV. This effect reflects the dependence of the electron ionization rate coefficient for hydrogen on T,. The attenuation factor also rises with increasing halo line density. These results show that the desired halo shielding effect can be produced by varying the halo line density while fixing the halo electron temperature in the range of 30-40 eV. From fig. 3, a halo line density /n,dl= 1.5 X 1013 cm-* and T, = 30 eV will attenuate the gas density 50 fold.
4. Power flow In the channel region the electron temperature is substantially reduced from the upstream value because of energy expended in interacting with the the recycled gas. A major issue regarding the practicality of a shielding halo is whether the power necessary for sustaining the large temperature gradient along the halo plasma is within an acceptable limit. In the region where the electron temperature gradient scale length is greater than the electron scattering mean free path, d In T,/ds > l/X,, heat transport is mainly by thermal conduction
W.L. Hsu et al. / Mechanical device for enhancing halo density
along the magnetic field. At steady state, the electron temperature Te as a function of distance s along the field line from the midplane is given by: -d/ds(kA(s)T,5’2dTJds)=P,(s).
(3)
Here, the thermal conductivity is K = kT’/* and k = 2100 W/m. (eV) ‘I*; A(s) is the cross-secional area of the halo flux tube which, from magnetic flux + conservation, is given by A = #/B; P, is the net power input to the halo electrons per unit length and P = lP,ds is the total net power. This equation is integrated numerically subject to the boundary conditions T,(O) and T,(L), where s = 0 defines the midplane of the center cell and s = L the location of the vented plate. It can be derived from eq. (3) that T, (0)“’
= T,(L)“*
+(7/2k+)jP,(s)
B(s)
ds.
(4)
Because of the 7/2 power dependence, the power necessary to support the electron temperature gradient is insensitive to T.(L) if T,(L) < T,(O)/2, and a reasonable estimate of the power required to maintain a given T,(O) can be obtained without knowing the details of the interactions in the chamber. The calculated halo electron temperature profile along the axis of TMX-U is shown in fig. 4. P = 430 kW was found necessary to sustain T,(O) = 30 eV. The calculated power is much smaller than might have been
261
necessary because A(s) is small where T, is large and Te is small where A(s) is large. The mean free path for electron scattering is given by X, = 9.7 x lO”T~*/n,. In a halo plasma where ttc = 2 x lo’* cme3 and T = 30 eV, X, = 4 m. Since the axial length of TMX-U is’ = 18 m we are at the limit where the assumption of thermal conduction becomes marginal. At higher electron temperatures a convective flow model must be used. An earlier calculation assuming thermal convection [S] showed that in a halo with jn,dl = 1.5 x 10” cm-* and T, = 30 eV the axial power loss is comparable to the power flow determined from eq. (4). However, at higher T, thermal convection results in a substantially lower Rower level. The source of power into the halo can result from radial heat transport or direct heating from auxiliary sources. Fast ions trapped in the halo from neutral beams transfer their energy to the electrons via collisions. In addition, halo electrons can be directly heated by ECRH and ICRH. In tandem mirror reactors alpha particles whose orbits interesect the halo supply most of the heating. The total power injected into TMX-U is approximately 3 MW (2.4 MW from neutral beams, 0.2 MW from ECRH and 0.2 MW from ICRH). The 430 kW necessary for heating the halo plasma is a small fraction of the available power and therefore would not pose an unreasonable requirement.
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8
10
Z (m) Fig. 4. The magnetic field B and the calculated halo T. along the axial length, I, of TMX-U. Power into the TMX-U halo electrons = 430 kW.
W.L., Hsu et al. / Mechanical deuice /or enhancing halo density
268
5. PartIde flow
In this section we estimate the ion flow, Q, along the halo plasma into the recycler. This particle throughput must eventually be removed by the recycler vacuum pumping system. From eq. (2), for a given a and f the required neutral pressure in the pumping plenum can then be determined. To a first order of approximation, the halo plasma flow is assumed axial and at steady state must be equal to the ionization rate of neutrals in this region. The gas pumped by the TMX-U halo was estimated using the neutral transport code discussed in section 2. Numerical calculations were performed for three plasma regions: the gas box, the center cell, and the end cells. The gas box is located at the transition region between the center cell and the end cell where the magnetic flux surface is highly elliptical. Calculations in this region account for the trapping of gas that
f i’o;-\
was injected for fueling the plasma. The center cell and the end cells have large surface areas; calculations in these regions account for the trapping of the background gas. The plasma radius is 26 cm at the midplane of the center cell and the halo extends from 18-26 cm. By following the magnetic flux surface, the halo thickness maps to 1.8-2.6 cm on the minor axis of the elliptical gas box plasma and 14-20 cm at the circular midplane of the end cell. Because of the large ellipticity, the plasma in the gas box was approximated as a slab to determine gas deposition. The plasma density profile was assumed to be ne = 4 X lo’* exp( -(x/2.58)*) cme3, with x(cm) as the distance out from the midplane of the slab (see fig. 5a). Electron and ion temperatures were assumed equal and given by T, = 300 exp( -(x/1.27)*) eV. These profiles were chosen such that when mapped to the end cell midplane, the halo
II
-a
-...*. *.l.
“s
0. ‘.
-300
s -200
II-
‘.
al
*.
‘.
*. ‘.
*.
*.
a. *-.* *...
lo”
I 0
0.5
1
1.5
X (cm)
T, *. -.....* 2
0 2.5
0
0.5
1
1.5
X
2
2.5
(cm)
X (cm) Fig. 5. (a) The electron temperature and density profile assumed for the gas trapping calculations. x is the distance out from the midplane of of the plasma slab at the gas box. The halo plasma extends from 1.8 to 2.6 cm. (b) The calculated neutral density profile along X. (c) The calculated net rate of iosn deposited in the plasma as a function of X.
W. L Hsu et al. / Mechanical
line density and the average halo electron temperature would satisfy the conditions prescribed in section 3. Total gas feed to the gas box during typical TMX-U operation is 90 Torr l/s. Figs. 5b and SC show the calculated neutral density (molecular, Franck-Condon, and charge-exchange) and the net ion source as a function of x. Near the edge of the plasma, the total neutral density is dominated by molecular gas. However, at x < 1.2 cm the Franck-Condon component becomes dominant because the Franck-Condon neutrals are more energetic than the room temperature molecular particles and therefore are less likely to be attenuated by the plasma. Fig. 5b shows that the total neutral density attenuation across the halo in the gas box region is a factor of 10, much less than the factor of 50 that would result at the center and the end cells. The ion source profile, shown in fig. SC, has a peak at 1.8 cm. The source drops sharply at large x, as the electron temperature drops below the ionization threshold. At x closer to the center the source also drops, although less drastically, because of the decreasing neutral density. Integrating the ion source over the halo region and assuming that equal amounts flow to each end of the device gives 4.3 x 10” ions/s per end. In the center cell the background gas pressure results in 15.5 Torr l/s of molecular gas impinging at the plasma surface. By mapping the electron temperature and density profiles from the gas box plasma to the center cell and using the version of the neutral transport code for cylindrical geometry the center cell region was estimated to contribute 1.3 x lo*’ ions/s per end to the halo. Since the total plasma surface area in the end cell differs by less than 10% from that of the center cell and the background gas pressures are essential equal, it was assumed that the end cell gave the same contribution as the center cell. The total ion source is therefore = 7 x 10” ions/s per end, or Q = 3.5 x lo*’ molecules/s per end (11 Torr l/s) to be pumped by the recycler vacuum pump. The axial electric field is expected to be small in the halo plasma and the flow is subsonic (see the discussion just before eq. (1)) therefore, the plasma pressure would be roughly constant constant along the field lines. Then the assumed T,(O) = 30 eV and n,(O) = 2 x lo’* cmw3 imply that n,(L) = 1.2 x lOI cmm3 if T,(L) = 5 eV. Inserting n,(L), T,(L), and Q into eq. (2), expressing no in term of pressure, and assuming the ions are H+, we obtain: 1 = (4.7 X 10e3/a)
+ O.llp,(mTorr)f.
(5)
For the case of TMX-U, eq. (5) shows that unless a is very small this parameter has little influence on the overall recycling and pof becomes the controlling
device for enhancing halo density
269
parameter. Practical design and heat removal considerations lead to vented plates with a < 0.1 and f< 0.5. If we assume a = 0.02 and f= 0.5 this implies the plenum pressure must be = 14 mTorr to give the desired n,(L).
6. Summary In this paper, a halo recycler is proposed for enhancing the density of the halo plasma in the TMX-U tandem mirror. The recycler is an annular chamber at each end of the mirror device that scrapes the halo plasma and is similar to pump limiters and divertors used in tokamaks. ‘Ihe recycler is operated in a high recycling mode and also has the advantage of reducing the erosion of the end plate. The molecular throughput in the halo of TMX-U is 11 Torr l/s per end. TO generate high recyling, the recycler is operated using a vented plate with a plenum pressure = 14 mTorr. With approximately 500 kW of heating the halo can attenuate the neutral gas density by a factor of 50. Before the halo recycler can be implmented in TMXU, many issues must be better understood. In TMX-U, the end fan typically operates at a background pressure of 5 x 10e6 Torr. Because of high recycling the gas pressure in the channel region is expected to be high, the resulting pressure gradient must be supported by halo plasma pumping. This condition would determine the channel length which must be short when compared to the length of the end fan. It is also important to determine whether localized cooling of the gas box plasma by the fueling gas would substantially affect the electron temperature and the power flow calculation.
Acknowledgement The authors wish to thank Dr. D.P. Grubb for his helpful comments. This work was supported by the US Department of Energy.
References
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forenhancing
halo density
[13] R.W. COM, S.P. Grotz, A.K. Prinja et al., in: Proc. 10th Symp. on Fusion Technology (SOFT) (1983) 497. [14] W. EngeIhardt, G. Becker, D. Behringer et al., J. Nucl. Mater. 1118112 (1982) 337. [15] R.J. Fonck, M. Bell, K. Bol et al., J. Nucl. Mater. 1118112 (1982) 343. [16] M.A. Mahdavi, C.J. Armentrout, F.P. Blau et al., J. Nucl. Mater. lllBt112 (1982) 355. [17] M. Shimada, M. Nagami, K. Ioki et al., J. Nucl. Mater. 111&112 (1982) 362. [18] D.E. Post, D.B. Heifetz and M. Petravic, J. Nucl. Mater. lllBr112 (1982) 383. (191 G.E. Gryukowski and J.M. Gilmore, Buildup Studies of a Tandem Mirror Reactor With Inboard Thermal Barrier, Lawrence Livermore National Laboratory Report UCRL84233,198O.