redeposition—status and implications for fusion design

Fusion Engineering and Design 60 (2002) 515– 526 www.elsevier.com/locate/fusengdes

Modeling of sputtering erosion/redeposition —status and implications for fusion design Jeffrey N. Brooks * Argonne National Laboratory, 9700 South Cass A6enue, Argonne, IL 60439, USA

Abstract This paper reviews sputtering erosion/redeposition modeling for plasma facing surfaces. Basics of the WBC Monte Carlo impurity transport code are described. An example analysis is shown for erosion of a liquid tin fusion reactor divertor. Multiyear erosion studies of candidate divertor and first wall coating materials (Li, Be, C, W, etc.) are summarized—showing generally serious erosion concerns for low-Z solid materials, and encouraging results for high-Z materials and liquid divertor surfaces. Future goals are discussed, e.g. for supercomputer modeling. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Erosion/redeposition; Sputtering; WBC code; Lithium; Tin; Tritium co-deposition

1. Introduction A critical issue for magnetic fusion reactors is sputtering of plasma facing surfaces by plasma ions and neutrals. There are three concerns: 1. Erosion of plasma facing components (divertor, first wall, limiter). 2. Tritium codeposition in growing redeposited surface layers. 3. Contamination of the core plasma from sputtered material. Sputtering erosion helps to determine the component lifetime. Tritium codeposition affects tritium inventory and reactor operations (downtime needed for tritium removal from codeposited areas). Plasma contamination affects the available * Tel.: +1-630-252-4830; fax: +1-630-252-3250. E-mail address: [email protected] (J.N. Brooks).

core plasma fuel density and fusion power. Key design choices are: “ Plasma facing material, i.e. low- or high-Z metals (Be, W), metals vs. carbon, liquid materials (Li, Sn, etc.), and possibly compounds (SiC). “ Component design, e.g. limiter or divertor geometry, power loading. “ Plasma edge regime —to the extent controllable —e.g. radiative edge plasma via addition of neon, high recycling plasma with low to moderate vacuum pumping. Erosion/redeposition modeling and analysis emerged as a separate discipline at the time of the Starfire commercial fusion reactor study [1] about 20 years ago. It has since been developed, by this author and others, and used for numerous design studies and to explain experimental results. This includes erosion/redeposition analysis for the IN-

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TOR [2 –4], ITER [5– 10], FIRE [11] design studies, TEXTOR [12,13], TFTR [14– 17], JET [18,19], DIII-D [20– 24], ASDEX-U [25] tokamaks, and the PISCES arc discharge device [26,27]. The models have been successfully tested and validated, for many but not all regimes and materials, a notable exception being carbon in a detached tokamak plasma. The most detailed validations have been done for DIII-D, ASDEXU, and PISCES using removable material probes with good plasma diagnostics. An early review of erosion/redeposition modeling is given in Ref. [28]. A review focusing on implications for near-term ITER-type devices is contained in Ref. [29]. A review focusing on tritium codeposition modeling is given in Ref. [30]. There are numerous reviews of the underlying sputtering process, e.g. [31] and as contained in Ref. [29]. The purpose of this paper is to provide a brief review—for the general Fusion Engineering Design reader— of methods for modeling erosion/redeposition, conclusions reached after multiyear analysis of numerous devices, and outstanding research areas. The companion paper of Hassanein [32] covers disruption erosion, which together with sputtering erosion largely determines the component surface lifetime. The paper of Rognlien and Rensink [33] discusses edge plasma calculations including plasma solutions used for erosion/redeposition analysis. Finally, the paper of Nygren [34] discusses design implications of plasma facing material choices.

plasma parameters, and material properties, is generally necessary for accurate computations. This is not an area where ‘scoping’ or parametric type models typically work well. The two basic modeling approaches are computation of self-consistent sputtered impurity transport via: (a) deterministic/integral-equation method i.e. REDEP code [2–4]; and (b) Monte Carlo method e.g. WBC code [28,35]. These codes use single-particle, trace impurity content, kinetic treatment, with either sub-gyro-orbit (WBC) or gyro-orbit-average (REDEP) treatment. Other Monte Carlo codes in use include BBQ [36], LIM [37], DIVIMP [38], and ERO [39]. The current approach with REDEP and WBC remains basically the same as discussed in Ref. [28] with advances— from data and theory— implemented in sub-models, particularly for carbon chemical sputtering (yields, hydrocarbon transport), liquid surface sputtering, mixed-material effects, atomic and molecular processes, tritium trapping fractions (e.g. in pure and oxygen-containing beryllium), and detached plasma regime parameters. Also, with availability of fast inexpensive workstations the trend is to use more Monte Carlo analysis, which while 1–2 orders of magnitude slower, is more detailed and incorporates more processes. In this paper we focus on Monte Carlo modeling.

3. Monte Carlo sputtered particle transport model (WBC code) 2. Model overview Sputtering erosion is governed by the erosion/ redeposition process whereby sputtered surface atoms can be redeposited on the surface after ionization and transport in the plasma. The net erosion rate depends on the difference between sputtering and redeposition. The net rate is typically an order of magnitude lower than the gross rate and depends on a fine balance between the erosion/redeposition processes. Due to this fine balance very careful attention to modeling detailed plasma impurity transport processes,

The level of description is three-dimensional, fully kinetic, sub-gyro-orbit motion of a sputtered particle in a fixed background D–T plasma. The code contains about a 100 submodels for surface geometry, magnetic and electric fields, plasma parameters (density, temperature, sound-speed, etc.), plasma deuterium, tritium, and helium ion and neutral fluxes, sputtering coefficients and sputtered velocity distributions, atomic and molecular processes, surface temperature-dependent tritium codeposition, and related phenomena.

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3.1. Single-particle equation of motion The motion of a sputtered particle is given by Newton’s law with Lorentz force and collisional terms: m

)

dVa (Vb = q(Eb +Vb xBb ) + , dt (t collisions

(1)

for particle velocity Vb (x, y, z, t), mass m, charge q(t), electric field Eb , and magnetic field Bb . A particle (atom for most materials, atom or hydrocarbon molecule for carbon) is launched from the surface at a point (x0, y0, z0) with initial conditions: Vb (x0, y0, z0, 0)= Vb 0,

(2)

q(0) = 0.

(3)

Initial velocity Vb 0 is randomly selected from a distribution given by a sputtering code or by an analytical model such as a random collision cascade distribution or thermal distribution. The launch point (x0, y0, z0) is randomly selected based on the incident plasma particle fluxes (D + , T+, D0, T0, etc.) and the respective sputtering coefficients.

3.2. Charge state The particle charge is determined by Monte Carlo, where the probability of changing charge state in a time interval Dt is: p =1 − exp

 

− Dt , ~

(4)

where ~ is the time constant for the relevant charge-changing processes. For a particle subject to electron impact ionization and recombination only, the time constant is: ~=

1 , Ne[Ž|6i,k + Ž|6r,k ]

(5)

where Ž|6i,k is the rate coefficient for electron impact ionization from the k to k +1 charge state, Ž|6r,k  is the rate coefficient for recombination from the k to k −1 state, and Ne is the plasma electron density. (In most cases recombination is negligible for near-surface transport of sputtered

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impurities. Recombination is important for impurities traversing the entire scrape-off-layer (SOL), for instance material flowing from the wall to the divertor.) Analogous terms are used to model other charge-changing processes, where applicable, such as impurity-hydrogen charge exchange. If it is determined that some process occurs in the time interval, than the process that occurs is determined by further Monte Carlo selection. For the above example, given that either ionization or recombination occurs, the probability of ionization is given by: Pi =

Ž|6i,k  . [Ž|6i,k + Ž|6r,k ]

(6)

3.3. Collisions Collision terms for Eq. (1) cover neutral and charged impurity particle collisions with background plasma ions and plasma neutrals. For impurity ion collisions with the plasma ions the code uses the Fokker Plank treatment. This covers parallel friction of single-particle impurity ions with the background D–T plasma flowing along the (total) magnetic field lines, parallel velocity diffusion, and perpendicular velocity diffusion, where the change of velocity in a time interval due to collisions is given by: D6par collisions = ŽD6parDt 9 ŽD6 2parDt,

(7)

D6perp collisions = 9 ŽD6

(8)

2 perp

Dt,

where ŽD6par is the parallel friction rate of change; ŽD6 2par, parallel velocity diffusion coefficient; ŽD6 2perp, perpendicular velocity diffusion coefficient and where the plus and minus terms are chosen randomly per the Monte Carlo method. The collision coefficients have been derived for an arbitrary mass impurity particle in a D–T Maxwellian plasma, by Terry [40] via an extension of the Braginskii method [41]. The Braginskii method is for a disparate mass approximation (high ratio of impurity mass to D–T mass), and the Terry extension is for arbitrary impurity mass. The collision terms depend in general on background plasma electron and ion temperatures and temperature gradients, ion and electron densities,

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and fluid velocity and velocity gradient. So-called thermal forces and viscosity terms are included. Bohm (anomalous) diffusion is also modeled. For most edge plasmas, near-surface ( 0 – 5 cm) plasma gradients are small which simplifies collision terms. Collisions with plasma neutrals are computed by a somewhat different method as follows: an impurity particle collides with a randomly selected background plasma particle (atom, ion, molecule). The background particle selection is based on its respective velocity distribution (e.g. thermal distribution for D2 molecules). The change in velocity of the impurity particle due to elastic scattering with the plasma particle, given a scattering angle in the center-of-mass frame, is computed using the Takizuka and Abe formulation [42]. Collision cross sections/scattering angles from a variety of sources are used, as discussed further in the references.

3.4. Sheath The near-surface electric field consists generally of the sheath field, and possibly a pre-sheath and a radial field. For most divertor and limiter geometries, the sheath in WBC is modeled [35] by the dual potential structure found in studies [43– 45] of highly oblique ( 85 – 89 °C from the normal) magnetic field geometry. In the WBC model the sheath potential varies in the direction ‘z’ normal to the surface as: ƒ(z) =ƒ1 exp(− z/2uD) + ƒ2 exp( − z/RD – T). (9) This comprises a ‘Debye sheath’ with width of about six Debye lengths (uD) of order 10 mm containing about 25% of the potential drop, and a ‘magnetic sheath’ of width about three times the D –T ion gyroradius (RD – T,) of order 1 mm containing about 75% of the potential drop. The total sheath potential is ƒ1 +ƒ2 :3kTe for pre-sheath electron temperature Te. The potential also varies in the ‘x–y’ plane parallel to the surface per variations in plasma parameters. Related models such as electron density variation in the sheath are described in Ref. [35].

The sheath region is typically critical for the transport of sputtered heavy metals such as tungsten, or for thermally emitted chemically sputtered hydrocarbons, where the emitted velocity is small and material can be ionized in the (magnetic) sheath. Such ionization causes immediate redeposition due to strong electric field acceleration of the impurity ion back to the surface. Even for most cases— with ionization outside the sheath— the sheath is still highly important to erosion/redeposition because of the effect on selfsputtering of the high sheath energy acquired by redepositing ions, for both singly charged and higher charge states. The sheath also affects the angle of incidence of redeposited ions, average elevation angles for typical plasma conditions being  45° from the normal for redeposited light ions (Be, C) and  20–30° for heavy ions (Mo, W). On a related subject, the sheath has been found to be critical to the transport of e6aporated surface material, this being a major non-sputtering plasma–surface-interaction area of analysis for liquid surface erosion [44,45].

3.5. Chemically sputtered carbon Chemical sputtering of carbon is unique because instead of just atoms and ions, numerous hydrocarbon molecules and radicals are involved, with an extensive number of processes involving proton impact and electron impact ionization, dissociation, and recombination. The same basic Monte Carlo approach is used but with much more complexity. [9,18] describe current hydrocarbon modeling in WBC. Briefly, chemically sputtered molecules are launched from the surface as CH4, C2H2, C2H4, C2H6, and C3H6. In the plasma, 34 particle species are tracked, ranging from C, C+, CH, CH+, CH2, CH+ 2 , etc. up to C3H6 and C3H+ 6 . A total of 134 reactions for carbon and hydrocarbons are currently modeled.

3.6. Code output and numerical issues The WBC code tracks the fate of each sputtered particle. A redeposited particle can stick, backscatter (reflect, desorb) and/or self-sputter

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and this is determined by energy- and material-dependent models. A particle history is terminated upon sticking to a surface. A particle leaving the near-surface region can be tracked in detail by WBC if needed, or can be treated by simplified kinetic models, or can be tracked via coupling to a different code such as a fluid plasma code. The latter case has been done, for example, via off-line input of WBC-derived boundary conditions to the UEDGE fluid code [33,46]. Real-time coupling of these codes is also possible but not yet implemented in practice. The number of computed particle histories varies from about a thousand to several million depending on the problem and the desired output such as experimental data to be compared with. Computation times (e.g. on Sun ULTRA SPARC™ workstation) vary from several minutes to about 10 h. After computing all particle histories, the code calculates the total sputtered impurity flux to the various regions, the gross and net erosion rates, and the tritium codeposition in regions of net growth. Also computed— depending on the problem—are impurity neutral and ion densities and photon emission. As with Monte Carlo calculations in general, considerable effort is typically required to rigorously input specific geometries such as photon viewing cone in an experiment, along with related models e.g. photon efficiency for a particular ion. Fig. 1 shows an example of WBC computed sputtered particle trajectories. This is from analysis [23] for the DIII-D/DiMES-71 experiment involving a  5 cm diameter probe containing small metallic films of beryllium and tungsten, exposed to the divertor plasma. A typical particle trajectory exhibits the following behavior: (a) an essentially straight line motion of the sputtered atom (there is a small effect of impurity-atom– plasma elastic collisions for this plasma regime); (b) once the particle is ionized, a complex gyro-orbit motion due to the magnetic field, impurity-ion– plasma collisions, and possibly ionization into higher charge states; (c) high probe-redeposition of tungsten due to short ionization distances, collisional friction with the sound-speed-flowing plasma and strong sheath field acceleration; (d) low probe-redeposition of beryllium but redeposi-

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tion (not-shown) occurring elsewhere on the divertor.

4. Model validation Erosion/redeposition analyses and validation efforts have been conducted and/or are in progress on all major tokamaks, and on some laboratory facilities. The above-mentioned DIII-D work has been the most extensive, using DiMES divertor test probes with removable inserts containing various beryllium, lithium, carbon, vanadium, molybdenum, and tungsten samples exposed to different edge plasma conditions. Code/data comparison for DIII-D [20–24], for ELM’ing and ELM-free attached plasmas, shows generally good agreement for erosion profiles, photon emission, and core plasma contamination by sputtering. In study [23], for instance, the following are REDEP/WBC-predicted/measured values of several parameters: “ Peak net carbon erosion rate (DiMES-79 experiment) 3.7/3.4 nm s − 1. “ Beryllium photon emission (DiMES-71) 2.8× 1016/3.3× 1016 s − 1 m − 2 sr − 1. “ Molybdenum ‘downstream’ e-folding redeposition distance (DiMES-70) 3.2/3.5 mm. Code/data comparisons have also shown good agreement for other devices. Thus, there is reasonable confidence in the predictive value of the erosion codes, for the regimes and materials studied. An exception is a rather puzzling code/data discrepancy for vanadium redeposition distances in the DiMES experiments [23] which has defied various attempts to explain it. Carbon performance in a tokamak detached plasma regime is currently being modeled for DIII-D experiments [24], and also for MARK-II divertor operation in JET [19]. As discussed in Refs. [19,29] unexpectedly high tritium codeposition observed in JET provides some evidence for phenomena such as anomalous carbon impurity drift and/or higher chemical sputtering yields possibly due to poorly bonded redeposited surfaces. On a positive note for carbon, simulations of PISCES experiments of transport of chemically sputtered carbon in low temperature plasmas (1–4 eV) have shown a good

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match to data [27]. In particular, the data trend of CD penetration into the plasma decreasing much less than linearly with increasing electron density and the data trend of extreme sensitivity of the D/XB parameter to the electron density, is reproduced by the modeling. 5. Liquid tin analysis Flowing liquid surfaces (Li, Ga, Sn, Sn– Li, etc.) are being studied by the U.S. fusion program Advanced Limiter-Divertor Plasma Facing-Systems (ALPS) project [47] (limiters/divertor systems) and Advanced Power Extraction (APEX) project [48] (first wall systems). Liquid plasma facing surfaces could eliminate both disruption and sputtering erosion concerns, and may be able to handle higher steady-state heat loads. Erosion/redeposition is one of many issues under analysis for ALPS/APEX. An initial erosion/redeposition study of lithium, tin– lithium, and flibe divertor surfaces [46] appears encouraging, showing finite self-sputtering, low plasma contamination, and low tritium codeposition. Liquid tin has lower vapor pressure than these materials and hence would permit higher evaporation-limited surface temperature operation. For this reason, and to illustrate aspects of erosion/redeposition modeling for this paper, we performed an initial erosion analysis for a conceptual liquid tin divertor. We apply the WBC code to a liquid tin surface for the divertor design of the ARIES-AT conceptual tokamak fusion reactor study [49]. Near-surface plasma parameters (0– 5 cm from the plate) are supplied by a UEDGE 2-D plasma fluid code solution for the tilted divertor plate [33]. The plasma temperature for this high-recycle solution varies from several eV at the strike point to about 60 eV away from the strike point. Other inputs to WBC are sputtering coefficients for D, T, on tin from TRIM-SP code calculations [50], self-sputtering coefficients from VFTRIM-3D calculations [51], and electron impact ionization rate coefficients for tin from the ADAS database [52]. The analysis uses one million launched particle histories including self-sputtering. For a flowing liquid, there is no net erosion. The key erosion/redeposition issue is whether the sput-

Table 1 Summary of erosion/redeposition parameters from WBC Monte Carlo impurity transport code simulation for the ARIES-AT tokamak reactor divertor with a liquid tin surface Parameter

Value

Mean-free-path for sputtered atom ionization (normal to surface) Transit timea (ionization-to-redeposition) Charge statea Elevation angle of incidencea (from normal) Energya Fraction of sputtering due to D–T sputtering Fraction of sputtering due to self-sputtering Redeposition fraction Fraction of sputtered tin escaping the near-surface region (0–5 cm)

1.5 mm 9.2 (25) ms 2.0 (1.2) 22 (14°) 273 (257) eV 0.58 0.42 0.9991 0.0009

a Average value and (standard deviation) for redeposited ions.

tered tin has acceptably low contamination of the plasma including an obvious requirement for no runaway self-sputtering. Low contamination is, in fact, predicted. Fig. 2 shows the 3-D profile of tin ion density (summed over all charge states) in the near-surface region. (This is computed using the track length estimator method applied to the ion portion of all particle histories.) The tin ion density is always small compared with D–T density (see Ref. [33]) and declines very quickly away from the plate. Essentially no sputtered tin enters the SOL and core plasma. This is due to short mean-freepaths for ionization of sputtered tin, and high redeposition of tin ions due to collisions with the incoming plasma. In summary, the results show finite self-sputtering, very high confinement of sputtered tin near the divertor, and negligible core plasma contamination by sputtering. A liquid tin divertor thus looks promising from the erosion/redeposition standpoint. Analysis is ongoing on other issues including elevated surface temperature effects on sputtering. Of course, numerous other issues starting with MHD issues are critical to the feasibility of liquid metal surfaces and this is under evaluation in the ALPS project. Table 1 lists a number of erosion/redeposition parameters from the tin analysis. These parameters

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Fig. 1. Typical WBC code computed beryllium and tungsten sputtered particle trajectories for the DIII-D/DiMES 71 experiment. The red circle denotes the DiMES probe  5 cm diameter boundary. From Ref. [23] used with permission. Fig. 2. WBC Monte Carlo code erosion/redeposition analysis of a liquid tin divertor. For ARIES-AT plasma with divertor surface at Z =0. Sn ion density in the near-surface region.

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are of relevance internally to the calculation, such as for computing sputtering yields, and are of interest in elucidating the overall situation. For example, the average impurity ion transit time of 9 ms is small compared with the time scale for certain other processes such as recombination and Bohm diffusion. Also, as shown by the high transit time standard deviation, there are significant supraaverage particles in the distribution.

6. Erosion/redeposition results for fusion tokamak reactors

6.1. Di6ertor materials Table 2 summarizes erosion/redeposition modeling results for divertor plasma facing materials

from a variety of studies spanning about a 20-year period. These studies use a range of divertor designs, plasma edge conditions, and evolving models of sputter yields, tritium trapping rates, atomic and molecular models, and other models. In spite of model differences, these and other studies show fairly consistent results, the key findings being as follows: (1) Net sputtering erosion rates on the divertor will be high for low-Z materials, i.e. carbon or beryllium. Because of low duty-factors, however, carbon or beryllium may be acceptable for nearterm devices. They will not be feasible target surfaces for a demonstration or commercial reactor due to erosion, for example, where a 1 cm thick Be coating would last about 1 week.

Table 2 Performance summary of candidate tokamak divertor surface materials based on composite of erosion/redeposition studies Material

Beryllium

Carbon

Erosion: peak ratea, (gross) net, nm s−1 (0–500), 0–20

(50–350), 5–40

Vanadium

(0–60), 0–10

Molybdenum Tungsten

(0–45), 0 (0–2), 0–0.003

Lithiumb

Tin–lithiumb

Tinb

(130), 0

(1000), 0

(70), 0

Comments

Major issue is sputtering erosion. Marginally acceptable for near-term device with low duty-factor. Not acceptable for commercial reactor (except for unlikely fully-detached plasma). Need more data on tritium codeposition, role of oxygen on same. Major issue is sputtering erosion and tritium codeposition (typical rates 0.01 gT s−1). Marginally acceptable for near-term device with proper choice of plasma edge regime. Not acceptable for commercial reactor. Chemical sputtering with detached plasma and redeposited surface properties are key uncertainties. Limited analysis. Lifetime performance likely to be midway between low-Z materials (Be, C) and high-Z (W). Could be attractive for several reasons (e.g. low activation). Could ‘self-pump’ helium [54] with plasma V pellet injection. More analysis needed. Limited analysis. Niobium performance similar. Sputtering performance excellent for Te550 eV. Long erosion lifetime with essentially zero plasma contamination. Appears promising. May improve core plasma physics via trapping of hydrogen isotopes [46]. Helium trapping needs to be determined. PMI issues to be resolved (for all liquids) include surface temperature limits on evaporation, temperature-dependent self-sputtering yields. Appears promising. High gross erosion due to high lithium sputtering and high D–T flux, but low plasma contamination due to high redeposition. Issues include lithium surface segregation, overall surface composition. Advantage, if any, over pure lithium or pure tin needs to be determined. Flibe may behave similarly. Appears promising. High surface temperature limit (1500 °C) possible. Gallium should behave similarly.

For solid materials typical results for expected plasma edge regimes varying from detached plasma (Te1–3 eV), semi-detached plasma (Te1–30 eV) to high-recycle plasma (Te10–50 eV). For liquid materials high-recycle regime for tin–lithium and tin, low-recycle regime (200 eV) for lithium. Liquid net erosion rate is zero due to flow. b Liquid surface. a

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(2) A tungsten divertor coating greatly reduces both gross and net sputtering erosion for most edge plasmas (i.e. with Te 575 eV). Plasma con-tamination by sputtering is negligible due to low gross erosion and very high local redeposition. From the standpoint of sputtering erosion alone tungsten appears to be a near-perfect divertor material. Non-sputtering issues including disruption response, thermal and mechanical performance, activation, tritium implantation/retention, are also issues for tungsten (and other materials), e.g. as discussed in detail in Ref. [53]. However, the superior erosion performance of tungsten is a major design advantage. (3) Tritium codeposition in carbon is a serious issue for even near-term devices, requiring the development of adequate techniques for periodically removing substantial amounts of tritium (e.g. 10 gT for a 1000 s pulse) from codeposited growth areas of the divertor and other regions. Tritium codeposition in beryllium should be less than for carbon but may still be non-trivial, with more H/Be trapping data needed. Tritium codeposition is probably insignificant for other materials due to low erosion/growth rates and/or low tritium trapping fractions. (4) As discussed above, a liquid surface divertor is promising. (5) Plasma contamination from divertor sputtering does not appear to be a serious concern for any material due to high local redeposition occurring at least somewhere on the divertor. Predicted plasma contamination fractions (ratio of plate-sputtered material to D–T core plasma density) vary from order 0.01 to 1% for lithium, beryllium, and carbon, to essentially zero for medium and high-Z materials. The exception would be where a self-sputtering runaway occurs, such runaway likely causing a plasma disruption. Runaway can occur if the plasma is hot enough — even for low-Z materials due to oblique incidence of redeposited ions. The exact boundaries of acceptable operation are uncertain due to lack of data on oblique incidence self-sputtering yields and on certain mixed-material effects, particularly the reduction of self-sputtering yields in low-Z materials due to dilution from surface hydrogen isotope content. There appears, in any event, to be adequate margin in the selection/

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control of an edge plasma regime to avoid self-sputtering runaway for all materials. (6) Considerable data and further analysis are needed for certain materials/conditions such as carbon chemical sputtering at low energies and high fluxes, atomic and molecular cross sections for chemically sputtered hydrocarbons, sputtering properties of redeposited and mixed materials, and oxygen-dependent hydrogen isotope codeposition ratios in beryllium. For liquid surfaces, data and analysis are needed on sputtering properties at high surface temperatures. Other less-studied materials like vanadium could offer good design choices, including the ability to ‘self-pump’ helium [54], but these materials need more analysis.

6.2. First wall materials The first wall is mainly sputtered by charge-exchange D–T atoms arising from the recycling of D–T ions hitting adjacent divertor and/or limiter surfaces, and possibly by charge exchange from plasma refueling via gas puffing. In detached or semi-detached plasma regimes, a high flux of hydrogen isotope molecules (D2 etc.) may also impinge on the wall [7]. There can be an ion flux as well, usually smaller than the charge-exchange flux, depending on the plasma edge-to-wall distance, and depending on how magnetic field lines intersect the wall. There is generally low redeposition on the wall due to the field line structure, i.e. field lines containing newly ionized impurity particles likely do not intersect the wall, and also due to the lower density plasma at the wall which permits sputtered atoms to travel relatively far from the wall before being ionized. In this case the only process causing redeposition on the wall is diffusion across field lines, which is a weak process. Major erosion/redeposition issues for first wall materials are the net erosion rate/coating-lifetime and the transfer of sputtered material from the wall to both the plasma and divertor. Material transported to the divertor affects tritium codeposition in areas of growth and also sputtering properties of the possibly mixed-material surface formed on the divertor and adjacent areas. Modeling of first wall erosion/redeposition is conceptually similar to that for the divertor with differences in detail, including a much stronger

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focus on the input of detailed neutral flux calculations. Such charge exchange information, for example, has been supplied from DEGAS+ Monte Carlo neutrals code calculations [7– 9]. An uncertainty for wall calculations, regarding any ion sputtering, is the existence and structure of a sheath, this depending on exact magnetic field/ wall geometry. Another difference between wall and divertor erosion modeling is that instead of the relatively small (5 cm from the plate) nearsurface region typically critical for divertor calculations, wall-to-divertor and wall-to-plasma impurity transport generally involve the entire SOL region. Processes such as diffusion, recombination, and radiation are typically much more important to impurity transport in the entire SOL than the divertor (or limiter) near-surface region— this due to the long distances and hence long transport times involved. For the same reason, computations of wall-to-divertor and wall-toplasma transport are usually done with poorer statistics than pure divertor calculations. Also, due to the increased dependence on plasma transport processes in the SOL, and related uncertainties, e.g. in values of diffusion coefficients, modeling of wall sputtered transport is more uncertain than divertor-sputtered impurity transport. Notwithstanding these differences, erosion/redeposition modeling leads to fairly similar conclusions about material choices for both the wall and divertor, at least for solid materials. Erosion of a beryllium or carbon first wall, e.g. see Ref. [8], is probably tolerable for near-term devices but too high for later high duty-factor machines. Tritium codeposition in wall-sputtered carbon depositing on the divertor or adjacent areas is a serious concern for even near-term devices [8]. Tritium codeposition is a lesser problem for wall-sputtered beryllium but may still be significant [8]. There is limited analysis of higher Z walls (Fe, V, W) but these show generally favorable performance particularly with high-recycling or detached plasma edge regimes. There can be a concern about plasma contamination by wall charge-exchange sputtering e.g. [55]. However, for low to moderate edge plasma temperatures, there may be almost no wall sputtering of tungsten due

to charge exchange atom energies being below the sputtering threshold. The absence of a sheath effect on charge exchange impingement energy is a help here. Iron sputtering and plasma contamination, i.e. for a bare stainless steel wall could likewise be acceptable, thus eliminating the need for a wall coating. Erosion of liquid walls has received recent study [48,56–58]. Here, the major issue seems to be contamination of the SOL and core plasma by evaporating material and not by sputtering. The wall is much less tolerant of evaporation than the divertor. Divertor evaporated material is strongly redeposited due to in-sheath ionization of the slow-moving evaporated atoms and subsequent very strong transport to the surface via the sheath electric fields, and in addition, near-surface ionization and redeposition of any non-sheath ionized surface material by the strongly-flowing incoming plasma [45,59]. These effects are largely or completely absent at the wall. Due largely to vapor pressure differences, analysis [56–58] suggests that liquid lithium, tin–lithium, and flibe are unacceptable for wall use (evaporating impurities overly contaminate plasma), but liquid tin is acceptable, from the plasma contamination standpoint.

6.3. Miscellaneous applications There has been some erosion/redeposition modeling for other plasma facing components such as a startup limiter for ITER. For this specialized application high-Z materials are not a good choice due to high plasma contamination by sputtering. This differs from the divertor situation because limiter-sputtered material can directly enter the edge plasma rather than having to traverse a SOL. Beryllium appears to be a good choice for this application. There has been some analysis of compounds. A key concern appears to be maintenance of surface stoichiometry in the face of different net erosion rates of the compound elements. There has been some analysis of doped materials, e.g. 8% silicon doped carbon [9] which may offer reduced chemical erosion yields. These doped materials appear to have some promise, with erosion/redeposition issues generally similar to compounds.

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7. Future work

8. Conclusions

Most of the limitations of erosion/redeposition modeling come from sub-models, particularly for the near-surface plasma, and not from the underlying impurity transport models themselves. In particular, the erosion code predictions can be no better than the input plasma solution. Unlike existing machines where measurements of nearsurface plasma conditions are often available, we must use code-computed plasma solutions of varying degrees of speculation for reactor design analysis. Detached and/or semi-detached plasma regimes, while promising because of reduced heat load, tend to involve highly uncertain physics and analysis of these regimes needs much further work. Other key uncertainties exist as described above for chemically sputtered carbon and redeposited material properties in general. Modeling work with the next generation of faster computers will likely involve kinetic-model computation of mixed-material surface evolution, more use of molecular dynamic simulations for computing impurity sticking/reflection, and integrated coupling of these and other codes, for sheath dynamics, plasma core, SOL, etc. to erosion/redeposition codes. Some specific goals for future erosion/redeposition modeling are: “ Supercomputer implementation of the REDEP/WBC code package. Parallel processing on teraflop machines, with a factor of 100– 1000 speedup would permit new capabilities such as rigorous large-scale wall/divertor material coupling analysis. “ Real-time coupling of the impurity transport codes to a molecular dynamics code for selfconsistent calculations of particle/surface reflection/emission. “ Real-time coupling to plasma SOL and core codes for complete, integrated, predictive capability. “ Improved understanding of detached-plasma carbon erosion and transport, e.g. to explain JET high tritium codeposition. Improved liquid metal and other material models. Another goal is to use the modeling capability for non-fusion applications: e.g. plasma-assisted semiconductor manufacturing.

Erosion/redeposition modeling grew out of early fusion reactor design studies and has been a vital part of the plasma– surface-interaction analysis of major design studies and existing devices. Modeling is done with specialized codes, such as the WBC Monte Carlo code, for kinetic-level impurity sputtering and transport from and around plasma facing surfaces. The codes contain extensive sub-models for plasma parameters, impurity-plasma collisions, sheath physics, sputtering, reflection and codeposition material properties, and atomic and molecular processes. The erosion codes are generally well validated to the available experimental data. Much remains to be done including work with advanced materialevolution models, chemically sputtered carbon, liquid surfaces, semi-detached plasmas, and largescale, real-time coupling of erosion/redeposition codes to plasma codes and other codes using supercomputers. Modeling results generally show serious erosion problems with the future use of low-Z plasma facing materials. For near-term devices the choice of materials requires a trade-off assessment against the favorable properties of these materials such as the high temperature capability of carbon and the lack of melting during disruptions. HighZ materials work very well in terms of sputtering erosion for a divertor, and probably the first wall. Tungsten appears to be a near-ideal divertor coating material— from the sputtering erosion standpoint— for all but high temperature plasma edge regimes. Initial erosion analysis for liquid-surface divertor materials is promising, showing non-runaway self-sputtering, low plasma contamination, and low tritium codeposition, for the plasma regimes analyzed and using the existing sputtering database.

Acknowledgements Work supported by U.S. Department of Energy, Office of Fusion Energy.

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References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

[11]

[12] [13] [14] [15] [16] [17]

[18] [19]

[20] [21] [22]

[23] [24] [25] [26]

[27] [28]

M. Abdou, et al., Nucl. Eng. Des. 63 (1981) 199. J.N. Brooks, J. Nucl. Mater. 111 –112 (1982) 457. J.N. Brooks, Nucl. Tech./Fus. 4 (1983) 33. J.N. Brooks, R.F. Mattas, A.M. Hassanein, M.I. Baskes, J. Nucl. Mater. 128 –129 (1984) 400. J.N. Brooks, Fus. Technol. 18 (1990) 239. J.N. Brooks, D.N. Ruzic, D.B. Hayden, R.B. Turkot Jr., J. Nucl. Mater. 220 –222 (1995) 269. J.N. Brooks, R. Causey, G. Federici, D.N. Ruzic, J. Nucl. Mater. 241 – 243 (1997) 294. J.N. Brooks, D.N. Ruzic, D.B. Hayden, Fus. Eng. Des. 37 (1997) 455. J.N. Brooks, D. Alman, G. Federici, D.N. Ruzic, D.G. Whyte, J. Nucl. Mater. 266 –269 (1999) 58. G. Federici, J.N. Brooks, D.P. Coster, G. Janeschitz, A. Kukushkin, A. Loarte, H.D. Pacher, J. Stober, C.H. Wu, J. Nucl. Mater. 290 –293 (2001) 260. M. Ulrickson, J.N. Brooks, D.E. Driemeyer, A. Hassanein, C.E. Kessel, T. Rognlien, J.C. Wesley, D.M. Meade, Fus. Eng. Des. 58 –59 (2001) 907. R.T. McGrath, G.L. Doyle, J.N. Brooks, A.E. Pontau, G.J. Thomas, J. Nucl. Mater. 145 – 147 (1987) 660. A. Kirschner, A. Huber, B. Phillips, A. Pospiesczyk, P. Wienhold, J. Winter, J. Nucl. Mater. 290 –293 (2001) 238. J.N. Brooks, D.K. Brice, A.B. DeWald, R.T. McGrath, J. Nucl. Mater. 162 – 164 (1989) 363. R.T. McGrath, J.N. Brooks, J. Nucl. Mater. 162 –164 (1989) 350. T.Q. Hua, J.N. Brooks, J. Nucl. Mater. 196 –198 (1992) 514. C. Skinner, J.T. Hogan, J.N. Brooks, W. Blanchard, R.V. Budny, J. Hosea, D. Mueller, A. Nagy, D.P. Stotler, J. Nucl. Mater. 266 – 269 (1999) 940. D.A. Alman, D.N. Ruzic, J.N. Brooks, Phys. Plasmas 7 (2000) 1421. J.P. Coad, N. Bekris, J.D. Elder, S.K. Erents, D.E. Hole, K.D. Lawson, G.F. Matthews, R.-D. Penzhorn, P.C. Stangeby, J. Nucl. Mater. 290 –293 (2001) 224. C.P.C. Wong, et al., J. Nucl. Mater. 196 – 198 (1992) 871. T.Q. Hua, J.N. Brooks, J. Nucl. Mater. 220 –222 (1995) 342. D.G. Whyte, J.N. Brooks, C.P.C. Wong, W.P. West, R. Bastasz, W.R. Wampler, J.I. Rubenstein, J. Nucl. Mater. 341 – 243 (1997) 660. J.N. Brooks, D.G. Whyte, Nucl. Fus. 39 (1999) 525. D.G. Whyte, et al., J. Nucl. Mater. 266 – 269 (1999) 67. D. Naujoks, J. Roth, K. Krieger, G. Lieder, M. Laux, J. Nucl. Mater. 210 (1994) 43. M.J. Khandagle, Y. Hirooka, R.W. Conn, J.N. Brooks, A. Hassanein, R.B. Turkot Jr., J. Nucl. Mater. 207 (1993) 116. D.G. Whyte, G.R. Tynan, R.P. Doerner, J.N. Brooks, Nucl. Fus. 41 (2001) 47. J.N. Brooks, in: R.K. Janev, H.W. Darwin (Eds.), Atomic and Plasma-Material Interaction Processes in Controlled

[29] [30]

[31]

[32] [33] [34] [35] [36]

[37] [38] [39] [40] [41]

[42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57]

[58]

[59]

Thermonuclear Fusion, Elsevier Science Publishers BV, Amsterdam, 1993, p. 403. G. Federici et al., Nucl. Fus. 41 (2001) 1967. J.N. Brooks, Recent progress in tritium codeposition modeling, 9th Advanced Research Workshop on Hydrogen Isotope Recycling at Plasma-Facing Materials in Fusion Reactors, Argonne IL 2000, proceedings to be published. W. Eckstein, J. Bohdansky, J. Roth, Physical sputtering, atomic and plasma-material inter-action data for fusion, vol. 1, Supplement to Nucl. Fus., IAEA, Vienna, 1991, p. 51. A. Hassanein, this issue. T.D. Rognlien, M.E. Rensink, this issue. R. Nygren, this issue. J.N. Brooks, Phys. Fluids 8 (1990) 1858. J. Hogan, C.C. Klepper, J. Harris, et al., Proc. 16th Inter. Conf. on Fusion Energy, Montreal, 1966, IAEA, Vienna, vol. 2, 1997, p. 625. P. Stangeby, Contrib. Plasma Phys. 28 (1998) 507. P.C. Stangeby, J.D. Elder, J. Nucl. Mater. 196 – 198 (1992) 258. D. Naujoks, R. Behrish, J.P. Coad, L. deKock, Nucl. Fus. 33 (1993) 581. W.K. Terry, Phys. Fluids B 2 (1990) 1944. S.I. Braginskii, Reviews of plasma physics, in: M.A. Leontovich (Ed.), (Consultants Bureau, New York, 1965), vol. 1, p. 205. T. Takizuka, H. Abe, J. Comp. Phys. 25 (1977) 205. R. Chodura, Phys. Fluids 25 (1982) 1628. T.Q. Hua, J.N. Brooks, Phys. Fluids B 11 (1994) 3607. J.N. Brooks, D. Naujoks, Phys. Plasmas 7 (2000) 2565. J.N. Brooks, T.D. Rognlien, D.N. Ruzic, J.P. Allain, J. Nucl. Mater. 290 – 293 (2001) 185. R.F. Mattas, et al., Fus. Eng. Des. 49 – 50 (2000) 127. M.A. Abdou, et al., Fus. Eng. Des. 54 (2001) 181. A.R. Raffray et al., Fus. Tech. 39 (2001) 429. R. Bastasz, SNL, W. Eckstein IPP/Garching, personal communication, 2000. J.P. Allain, D.N. Ruzic, UIUC, personal communication, 2000. The Originating Developer of ADAS is the JET Joint Undertaking. Y. Hirooka, et al., J. Nucl. Mater. 196 – 198 (1992) 149. J.N. Brooks, R.F. Mattas, J. Nucl. Mater. 121 (1984) 392. J.N. Brooks, J. Nucl. Mater. 145 – 147 (1987) 837. T.D. Rognlien, M.E. Rensink, J. Nucl. Mater. 290 – 293 (2001) 312. R.W. Moir, M.E. Rensink, T.D. Rognlien, 18th IAEA Fusion Energy Conf., Sorrento, paper IAEA-CN77FTP2/07 (IAEA, Vienna, 2001), IAEA-CSP-8/C ISSN 1562 – 4153. T.D. Rognlien, M.E. Rensink, Edge-plasma properties in liquid-wall environments, PET conference Helsinki 2001, Contrib. Plasma Phys., to be published. D. Naujoks, J.N. Brooks, J. Nucl. Mater. 290 – 293 (2001) 1123.