NUCLEAR ANALYSIS OF A TOKAMAK EXPERIMENTAL POWER REACTOR KEYWORDS: tokamak-typereac- CONCEPTUAL DESIGN tors, design, specifications, neu- tron reactions, breeding blankets, shielding. first wall, wall loading, hlIOHAhlED A. ABDOU and JUNGCHUNG JUNG heating, spa rial distribution ,.I rgo~rtrc,Vuiio~cul Lrrhoraior,v. Apl)liztl P/'lr)..ric.rDii.itiotr Y7lJO Solrill (urs ;lvc,~rr~c~.:lrporrtrc8. tllr~rois 60J.IY .

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power-producing tokamak will play a major role in the U.S. tokamak reactor development program. Detailed nreclear tit~alysisof a referetlce con- The EPR is projected to begin operation in the cepticul desi,<.n ,for (i tokaltlnk experimetital poiver mid to late 1980's. From 1975 to 1976, conceptual reacto). (EPR) is p)-csctited. The refererice EPR design studies for EPR were performed at Argonne lrtis ti 6.2.i-n7 it1ti.jot- r(it1irts atit1 t[ ?.l-ttl ijrinor National Laboratory (.4NL) (Refs. 1 and 2), General rcitli/cs cir-crtlnr pla.s,tra ~c.itlr n tiut?iintrl t~clctron Atomic and Oak Ridge National Lab- 11 (.!/I loatIit1,y qi 0.,i 111 IIr/)tl 2. ,4 O..?S-t?l-//rick hl(iti- oratory ."" These studies were intended to define kct of sttiinless steel sitrrolctlds a stnitzless-steel the characteristics and requirements for an EPR r-ric~tltttr ~,essel. The itzner slricld consists of within the context of the general objectives and stteitlless steel tit~tl B,C ant1 is 0.58 717 thick. Tire schedule of the current U.S. program. In Ref. 7, 0.97-ttl -(/rick o!etev sllielrl et7rplo~,sletitf ,?lor-far. the various options and trade-offs in the nuclear s ltcitlless steel. atld ,:.vnplrite. Tlle ncitt rotiics re- design of the blanket/shield for the EPR were sults iti /he ,firs/tc~ill nrirl blanket r4tirysi,ytli,ficantly investigated. Here a detailed neutronics analysis 111 tlre poluidcil tlirection elite to (01 olitictlrtl shift in is presented for one complete system, the ANL- Ilie tlcre/er-iictn-tritilo?r ~ieictrotz sortrce tlistrihrr/ion EPR conceptual design.' ' The analysis includes titztl tlre' toroirlnl cro-clcitlerc. Tlie in,iinite c?litzder an investigation of important nuclear aspects not trppro.uit?lation ot~erestitt7tites resputzsc mtes it1 previously addressed, such as the effects of the first ic,trll conlparetl ~c.itll toroitlal ,q-eort7etry toroidal seometry and major penetrations on the c~ilc!tliitiot~s.?;elel val hennl litzes, r,clc1iicnr tlitcls. nuclear performance of the EPR. !itit1 other petictra/ions oi tilt, hlatlket trtztf huliz The ANL-EPR (Ref. 2) is a tokanlak with a siriclti vepr-escnt lnr,ye (-0.6- to 1.0-ti!? ct-oss 6.25-m major radius and a 2.1-m minor radius scc.liot7) streci7uitlg ptitlls for neictrotzs (old )-enlei-re circular plasma. The design basis performance special sliielriin,y. .A special 0.75-tti -thick ntztzrriar objective of the AXL-EPR is to operate for 10 yr sllieltl s~ivi..oitnris tile tlelttrnl beczn~ ciltct (r,fter it with a plant capacity factor of 50';. The plant exits irottl tiit, brilk sllirltl ntld estetzris heyotzd the capacity factor is defined as the product of the to)-oiticil fielti coil ntld oict to tlre heani itljecfors. .-I plasma duty cycle (75';) and plant availability ptzeut?ltiticnll:~operntetl n-lol.able slrieitl plug, opetz- (67';). The important characteristics oi the ANL- iri,q L~ICYI~Z,;'tlle plit?7pdozcrr phase atid c1ositr.q dlcvin,<. EPR relevant to this paper are shown in Table I. the plasttln burtr , is selected as the principcil The toroidal magnetic field is provided by 16 tiesi~71optiott for silieldin*q the er!acuatiore ducts. cryostatically stable NbTi superconducting toroi- dal field (TF) coils. Cryostatically stable NbTi superconducting ohmic heating (OH) and equilib- rium field (EF) coils are located external to the TF coils. I. INTRODUCTION Neutronics and photonics analyses play a major role in defining a technically sound design for the An experimental power reactor (EPR) that blanket/shield system. The remainder of this demons!r-,tcs the technological feasibility of a paper is devoted to the fiuclear analysis of the Abdou and Jung ANALYSIS OF A TOKAMAK

TABLE I threshold for radiation damage, and the Major Features of the ANLEPR intolerable consequences of virtually all major failure modes in the TF coils. Major radius, m 6.25 A study of the radiation effects on components Minor plasma (circular) radius, m 2.1 of superconducting magnets as well as a trade-off First wall radius ,. m 2.4 Design basis operating life, yr 10 study of 'the conflicting requirements for an EPR Nominal power during bun, MW 400 resulted in the definition of the following primary Plant capacity factor, '?& 50 magnet protection criteria: 1. Maximum radiation-induced resistivity in - crease in the copper stabilizer of the supercon- ducting TF coils should be <3 X lo-' S2-cm (0.3 ANL-EPR reference design and is organized as pS2 -mm) for a maximum magnetic field of 8 T and follows. The primary design criteria and con- <1.5 x lo-' S2 -cm (0.15 p~ -mm) for a maximum straints are discussed in Sec. 11. In Sec. 111, field of 10 T during the longest time period be- nuclear systems for the EPR reference design are tween scheduled magnet anneals. described and the calculational models are ex- plained. Section IV is devoted to an investigation 2. Maximum tolerable decrease (due to irradi- of the toroidal geometry effects in' the reference ation) in the crifical current 'density of the NbTi design. The neutronics effects in the blanket, bulk superconductor during the longest time period shield, and TF coils are presehted in Secs. V, VI, between scheduled magnet anneals is <5% of the and VII. The important effects of major penetra- pre-irradiation value. tions and nuclear design of their special shields 3. Maximum local energy deposition in the are discussed in Sec. VIII. The radioactivity and conductor matrix by nuclear radiation must not afterheat in the reference design are considered exceed lo-= w/cm3 (1 kw/m3) at full reactor in Sec. IX. We conclude with a summary in power. Sec. X. 4. The total nuclear heating in all TF coils should be small compared to other heat sources that contribute to the refrigeration power require- ments. The primary function of the blanket is to 5. The total radiation dose to all cryogenic convert and possibly multiply the kinetic energy of coil insulators must be kept at a level that permits fusion neutrons and secondary gamma rays into all these insulators to function properly for the heat at sufficiently high power density so that magnet lifetime (-log rads for the aromatic base thermal-energy retrieval and conversion to elec- epoxies). tricity with a reasonably high efficiency is fea- sible. This requirement of high power density The foundations for these design criteria are implies the use of efficient attenuating materials discussed in detail in Ref. 7. However, a brief that, in turn, leads to a relatively small overall clarifying discussion is in order. Radiation dam- blbket thickness. age studies on normal and super conductors at 4 K The blanket/shield system is required to -reduce indicate that the increase in the resistivity of the the radiation level in all reactor components to a normal conductor, used as the stabilizer, and the permissible level. The most. critical of these decrease in the critical current density of the components are the superconducting TF coils. superconductor can be recovered by annealing at Protection of these coils is also the most difficult near room temperature. Therefore, criteria 1 in view of: and 2 above are set for only the time span between magnet anneals. Since inorganic insulators that 1. space restrictions in the high magnetic field are resistant to radiation damage are too brittle region between the plasma and the interior to be useful in TF coils, organic insulators have portion of the D-shaped magnet to be used.' As discussed later in this section, 2. the presence of many large-size penetrations radiation damage to organic insulators is irre- on the top, bottom, and outer side of the versible. In addition, any replacement of the coil plasma, which greatly enhance radiation insulation is almost impossible, and exchange of streaming to the TF coils the coils themselves is very expensive. There- fore, criterion 5 requires that the m;udmum 3. the stringent magnet protection criteria that radiation dose tolerated in the coil insulation be result from low operating temperature, low based on the magnet lifetime. Data on radiation

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK damage to organic insulators at 4 K do not exist. Again, this calls for efficient attenuating materials In view of this situation and until more experi- for the penetration shield. mental results are available, extrapolation of Since the bulk shield is not efficient in pro- available data at higher temperatures has led to tecting the TF coils from neutrons and gamma-ray the tentative choice of an epoxy coil-insulation streaming through penetrations, the following de - set with an aromatic-type curing agent, reinforced sign criteria were adopted: with Fiberglas, and filled with granular alumina. 1. For a given material composition, the di- A total integrated radiation dose of lo9 to 10'' rad mensions of the bulk shield should be kept to the may be tolerable for these epoxy composites. minimum that is sufficient to protect the TF coils One of the major constraints on the blanket/ in regions far away from the penetrations, i.e., in shield system in EPR is a severe restriction on complete absence of any penetration effects. space in the high-magnetic-field region on the inside of the torus between the plasma and the 2. The penetration shield must completely vertical segment of the D-shaped TF coils. To offset the penetration effects at the TF coils; i.e., conserve on space in this critical region without the penetration shield must reduce the maximum violating the magnet protection criteria discussed radiation level at the TF coil to that in the absence above, a combination of materials that is very of penetrations. effective in attenuating neutrons and secondary 3. The penetration shield must also extend far gamma rays must be used on the inner side of the enough to protect auxiliary systems external to torus. Unfortunately, such materials are generally the TF coils that are affected by penetration- more expensive and result in significantly more assisted streaming. neutron-induced activation than the less efficient attenuators. However, because of the relatively In the pres'ence of an abundance of high-energy small volume of the inner shield (5 to 10% of the neutrons, activation of many of the reactor com- total), the increase in material cost, if kept mod- ponents is unavoidable, and the consequences erate, can be more than offset by a net reduction must be factored into the design. Construction of in the overall reactor cost resulting from a sub- all components of an EPR from low-activity stantial reduction in reactor size and/or a more materials, such that contact maintenance is fea- than compensating increase in the reactor power sible everywhere in the system in a short time output. after shutdown, is not possible at present. For Since the vertical and horizontal bores of the example, employing aluminum as the supporting D-shaped TF coils can be increased without large structure and stabilizer in superconducting mag- cost penalty, there can be more space on the top, nets requires resolving a considerable number of bottom, and outer side of the plasma than is avail- technological and economic problems. The use of able on the inside. Thus, the shield in these graphite blanket and A1-B4C shield on the inner regions can, in principle, be constructed with side of the torus results in a large size reactor materials that meet many other desirable criteria, with an added cost that outweighs the benefits of such as reduced cost and induced activation, but contact maintenance. Thus, remote maintenance still provide adequate protection of the TF coils has to be planned in EPR design. and auxiliary equipment. However, the EPR, as However, there are two goals concerning in- well as future tokamaks, requires that the blanket/ duced activation that are achievable for EPR and shield system accommodate major penetrations, were included as design criteria for the present including those for vacuum pumping, neutral beam EPR design. These are: and/or radio-frequency (rf) heating, diagnostics, and maintenance access. Many of these penetra- 1. The total inventory of radioactive materials tions represent large open regions (some -0,6 to should be kept to a minimum in cases where there 1 m2 in cross-sectional area), which extend from are no serious conflicts with other critical design the first wall, directly visible to the plasma criteria. This is aimed at reducing the inventory of materials that will require provision for long- neutrons, radially outward through the blanket/ term storage at disposal time. shield, and between the TF coils. Since these penetrations are numerous and large, they can be 2. The biological dose in the space inside the accommodated only on the top, bottom, and outer reactor building and external to the torus and regions of the shield. As discussed later, the bulk magnets should be reduced to a level that permits magnet shield can do very little to attenuate controlled personnel access to this region within radiation streaming through these penetrations; a reasonably short time (-24 h) after shutdown. a special penetration shield has to be provided. Since the walls of the reactor building, which also The penetrations and their special shield create a serve as the biological shield during operation, space problem inside and between the TF coils. are -1.5 m thick, there is a substantial savings Abdou and Jung ANALYSIS OF A TOKAMAK

on remote maintenance equipment cost and repair TF coils was purposely included in the design for time if personnel access to the reactor building is reasons that are discussed later. Because of the feasible. complexity of the gqometric details required to describe the penetration shield, its description is deferred to Sec. VIII, which is devoted to the Ill. DESCRIPTION OF THE NUCLEAR SYSTEMS FOR penetration analysis. THE EPR: REFERENCE DESIGN AND Neutron and photon transport calculations for CALCULATIONAL MODELS the nuclear analyses were carried out in one-, two-, and three-dimensional geometries. One- and For the purposes of nuclear analysis, the two-dimensional geometries were calculated by blanketjshield system can be classified into the the S, method with the ANISN (Ref. 8), DOT following subsystems: (a) first-wall assembly, (Ref. 9), and TWOTRAN (Ref. 10) codes. The (b) blanket, (c) bulk shield, and (d) penetration continuous energy VIM Monte Carlo code" was shield. Figure 1 shows a schematic cross section employed to treat the three-dimensional geom- of the reactor. Many of the engineering details etries. The S,, calculations were carried out with are omitted from this figure. The bulk shield 100 energy groups for the neutrons and 43 energy circumscribes the blanket and' consists of the groups for the gamma rays with cross sections inner, top, bottom, and outer shield. Since the generated from ENDF/B. Response functions bulk shield is essentially the same in the last were generated with MACK (Ref. 12) from ENDF/B three regions, these regions are referred to (Ref. 13). collectively as the outer shield unless a need for Nuclear analysis for the EPR blanket/shield distinction arises. Tables I1 and 111 show the requires multidimensional calculations to treat dimensions and material compositions of the first the following effects: wall, blanket, and bulk shield for the inner and 1. the presence of major penetrations outer regions, respectively, at the midplane. The stainless-steel assembly that forms the 2. the toroidal geometry first wall, with internal coolant passages, is 3. the nonsymmetry of the shield that can be idealized as a uniform 4-cm (40-mm)-thick stain- seen in a vertical cross section of the ANL- less-steel region that has a 240-cm (2.4-m) inner EPR design (Fig. 1). minor radius and has the coolant passages homog- enized. The blanket is symmetric and consists of The penetrations require three-dimensional cal- a 28-cm (280-mm)-thick region of stainless steel culations, but the other two effects can be analyzed with space provided for coolant. The inner shield by adaptation of a two-dimensional model to handle consists of a 58-cm (0.58-m)-thick region contain- toroidal geometry as well as any nonsymmetry in ' ing alternating layers of stainless steel and boron the vertical cross section. A solution accurate

' carbide in an optimized configuration to produce everywhere in the system requires full three- maximum attenuation of neutrons and secondary dimensional geometric modeling, since it is not gamma rays. The two sides of the inner/outer possible to Pompletely isolate the major individual shield interface form a 50-deg angle at the plasma effects listed above. At present, prediction of center. The outer bulk shield is 97 cm (0.97 m) neutron and photon transport effects in three thick and consists of 15 cm (150 mm) of graphite dimensions is feasible only with the Monte Carlo with 1% natural boron, 65 cni (0.65 m) of lead method. Because of the statistical nature of the mortar, 8 cm (80 mm) of stainless steel, and method, obtaining a reasonably accurate solution 9 cm (90 mm) of aluminum. The composition everywhere in a complicated large-size geqmetry and atom densities of lead mortar are shown in with deep radiation penetration is too expensive at Table IV. The major constituents of lead mortar present. Since the ANL-EPR blanket/shield is are hydrogen, oxygen, boron, carbon, and lead, toroidally axisymmetric, all the effects except all of which have no significant long-term activa- those for penetrations can be reasonably accounted tion. Lead mortar can withstand heat conditions for in a two-dimensional model. The approach up to -150°C. While the graphite is not as used for the nuclear analysis here is effective in neutron and gamma-ray attenuation as lead mortar, graphite is employed at the outer 1. application of two-dimensional calculations to predict the gross behavior of the neu- perimeter of the blanket to ensure a sufficiently tronics and photonics effects away from the low power density in the lead mortar. Zones 19 penetrations through 27 in Table I1 and Zones 26 through 40 in Table I11 represent a reasonable idealization of 2. application of three-dimensional calculations the TI? coil assembly. The aluminum structure in with geometric modeling that includes the the exterior regions of the outer shield and the penetrations and the penetration shield to

NLICLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and lung ANALYSIS OF; A 'I'OKAMAK

1 r METRE, SCALE-

Fig. 1. The EPR blanketlshield layout.

NUCLEAR TECHNOLOGY VOL. 35 MID-AUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

TABLE I1 Dimensions and Material Compositions of the EPR Inner Blanket/~hieldit the Midplane

Outer Major Outer Minor Radiusa ~adius~ Thickness (cm) (cm) (cm) Material Density Zone (mm + 10) (mm + 10) (mm + 10) Composition Factor 210 Plasma 240 Vacuum Stainless steel Stainless steel (+ coolant) Stainless steel i Stainless steel Vacuuin

Stainless steel Boron carbide Stainless steel Boron carbide Stainless steel Boron carbide Stainless steel Boron carbide Stainless steel

TF coil Dewar (Al) Vacuum, liquid nitrogen tubing, and superinsulation Thermal shield (Al) Vacuum (+ super- insulator) TF coil bobbin (SS?

( TF coil (449 SS + 4lr{ Cu + i 3% NbTi + 12: He)

Support cylinder (SS) OH coil (40'3 SS + 289 Cu + Z NbTi + 30q He) a~~inimumdistance in midplane from the center of the torus to the outer boundary of the zone. b~istancealong the minor radius from the center of the plasma to the outer boundary of the zone. 'Stainless steel.

analyze the effects in penetration regions tion IV is devoted to an accurate treatment of the and to superimpose the penetration effects toroidal geometry effects. Sections V and VI on the gross behavior predicted by two- present the gross behavior of the neutronics and dimensional calculations. photonics effects in the blanket and bulk shield away from the penetration regions. Since the The rest of this paper is organized as follows criterion for the local penetration shield was to with respect to the calculational models. Sec- reduce the radiation level at the TF coils to that

56 NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST I977 Abdou and Jung ANALYSIS OF A TOKAMAK

TABLE 111 Dimensions and Material Compositions of the EPR Outer Blanket-Bulk Shield at the Midplane.

Outer Major Outer Minor Radiusa ~adius~ Thickness (cm) (cm) (cm) Material Density Zone (mm t 10) (mm t 10) (mm + 10) Composition Factor

210 Plasma 240 Vacuum Stainless steel SSC (+ coolant) Stainless steel 1 Stainless steel 1 Vacuum I Stainless steel 1 Graphite (1%B) I Stainless steel

Lead mortar

Aluminum Aluminum 1 Free space (Vacuum) TF coil Dewar (Al) Vacuum, liquid nitrogen tubing, and superinsulation Thermal shield (Al) Vacuum (+ super- insulation) TF coil bobbin (SS)

TF coil (44% SS + 41% Cu + I 3% NbTi + 12% He) Helium bath (liquid + gas) TF coil bobbin (SS) Vacuum + superinsu- lation Thermal shield (Al) Vacuum, liquid nitrogen tubing, and superinsulation TF coil Dewar (Al) aMinimum distance in midplane from the center of the torus to the outer boundary of the zone. b~istancealong the minor radius from the center of the plasma to the outer boundary of the zone. '~tainlesssteel.

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

TABLE IV Composition and Atom Densities of Lead Mortar*

Atom Density Composition (lon atom/cm3) Element (wt? ) (loa atom/m3)

Hydrogen 2.4 3.6 Oxygen 3.3 0.3 Boron 5 .O 0.7 Carbon 15.2 1.9 Lead 73.6 0.5 Others 0.5 ---

*The composition selected liere corresponds to Chem- tree product CT-1-6-82-5 with a physicaI density of 2.5 g/cm3 (2.5 hlg/m3). I 1 ~OROIDALAXIS Fig. 2. A schematic reference of toroidaI geometry. in %the absence of penetrations, the neutronics effects in the TF coils given in Sec. VII are nearly the same (except for small variations) in coordinates. The new program was then used to the absence of penetrations as in the presence of calculate the neutronics effects in the reference fully shielded penetrations. The analyses of pene- design. trations, penetration shield, and penetration effects It was found in the course of this work that the on the nuclear performance of the blanket and bulk local neutronics effects in the first wall and shield given in Sec. VIII are derived from three- blanket are far more sensitive to the spatial dimensional calculations. Additional relevant in- distribution of the deuterium-tritium (D-T) neutron formation on calculational methods is given in the source strength as affected by the toroidal geom- appropriate sections. etry and the magnetohydrodynamic (MHD) equilib- rium plasma distribution of the plasma than they are to the local toroidal curvature in the first wall IV. TOROIDAL GEOMETRY EFFECTS IN THE and blanket. Therefore, a neutron source distri- REFERENCE DESIGN bution was derived from the MHD equilibrium The neutron transport equation can be solved in plasma distribution of the reference case plasma analyzed in Ref. 2. This source distribution is an axisymmetric toroidal, system (see Fig. 2) using two approaches: shown in Fig. 3 as a function of the major radius R for - several values of Z = constant = Z,, 1. two-dimensional geometrical model in (R,Z) where Z represents the elevation from the mid- cylindrical representation with the poloidal plane along the poloidal axis. An isomeric view of axis as the axis of the cylinder and R as the this source distribution is also shown in Fig. 4. major radius The neutron source strength per unit volume, 2. two-dimensional geometrical model in (r,~) S(R.Z,), peaks inside the plasma region and de- representation with r as the minor radius creases steadily until it reaches zero at R = and X the poloidal angle, provided the toroi- RO * .?/tan X. Note that the major radius at the dal curvature is properly accounted for in torus centerline Ro is 625 cm (6.25 m) and the the transport operator. plasma radius is 210 cm (2.1 m). The peak of S(R,O), i.e., at midplane, occurs at R = 686 = Ro + The first method has at least one drawback, EO with EO defined as the plasma shift. The peak particularly for circular tokamaks. Currently S, of S(R,Z,) occurs at a smaller shift as Z, is codes employ a rectangular spatial mesh that increased. cannot yield a' sufficiently adequate representation This reference neutron source distribution was of the geometry, particularly the first wall, with a used in (r,X) toroidal geometry calculations. The reasonable number of mesh points. The second neutron wall loading as a function of the poloidal (T,X) approach is very useful in overcoming this angle X is shown as curve a in Fig. 5. The difficulty. Therefore, the TWOTRAN program10 neutron wall loading is used here in its normal was modified according to the formulation pre- definition15 as the product of the D-T neutron sented in Ref. 14 to solve the transport equation in current in the direction of the normal to the first axisymmetric toroidal geometry with the cross wall times the energy (14.06 MeV) of a D-T section of the torus represented in the (r,x) neutron. Curve b in Fig. 5 represents the neutron

NllrI FAR TFCHNnI O(;Y VOI 35 MID-AIIGIIST 1977 MAJOR RADIUS, R, incm (mm + 10)

Fig. 3. Sourcc strength S(R. Z). of the D-T neutrons in the plasma region as a fi~nctionof major radius at several values of Z.

REFERENCE SOURCE ,/- NOMINAL __----- _--- UNIFORM /

Fig. 5. Variation of the neutron wall loading with the polbidal angle x for three cases: (a) neutron source distribution as derived from the MHD equilibria in the reference plasma calculations, (b) uniform neutron source dis- Fig. 4. Isomeric veiw of the D-T neutron source strength in tribution, and (c) the nominal case of a uniform source the EPR plasma region. distribution in an infinite cylinder approximation.

wall loading when the toroidal geometry calcula- the toroidal magnetic axis and the volumetric tions are made with a volumetric neutron source neutron source constant in the plasma region. The distribution that is uniform (constant) throughout three cases are normalized such that the tbtal the plasma region. The third line, curve C, in number of D-T neutrons emitted from the plasma this figure is for a nominal case widely used in per unit time is the same. In other words, a fhced the literature, a one-dimensional infinite-cylinder thermonuclear power for the reactor is taken as approximation with the cylinder axis representing the basis for normalization. Thus, the neutron Abd,ou and lung ANALYSIS OF A TOKAMAK wall loading, 0.5 MW/~',in the nominal case also represents the mean neutron wall loading in all cases, independent of any assumption about the - c NOMINAL volumetric neutron source distribution. This mean neutron wall loading is the average of the neutron - --+---UNIFORM SOURCE\. wall loading over the inner surface area of the I\--< first wall, or it is simply equal to the thermo- - I nuclear neutron power divided by the first wall /' area. - 'REFERENCE SOURCE Some important observations can be made from / / the results in Fig. 5. For the reference case, - neutron wall loading P,. varies from -0.56 Mw/rn2 / at the outermost point (X = 0 deg) to -0.4 Mw/rn2 at the innermost point (X = 180 deg). The maxi- mum neutron wall loading is 12% above the mean and 40% above the minimum. .The uniform source distribution, however, results in only <8% varia- X, deg tion in P, around the mean. Thus, the neutronics Fig. 6. Variation of the helium production rate within the effects are strongly dependent on the form of the first 10 mm of the first wall with the poloidal ahgle volumetric neutron source distribution. This im- X. plies a strong correlation between the nuclear performance of the first wall/blanket/shield and the plasma spatial characteristics. These calcu- lations of the neutron wall loading are consistent with the work of Chapin and which ex- rice,'^ NOMINAL amined the behavior of the uncollided fluxes and currents in toroidal systems. Figures 6 and 7 show the variation of the rates - 10.0 /-- of helium production and atomic displacements I- / within the first 1 cm (10 mm) of the first wall / with the poloidal angle X for the same three cases / of Fig. 5. For curve a, where the neutron source /REFERENCE SOURCE .(D / n distribution is derived from the plasma spatial T1 / distribution, the helium production is maximum at 9 .O / X = 0 deg (outermost), and decreases montonically as x is increased until it reaches a minimum at X = 180 deg (innermost). The maximum to mini- mum ratio is -1.3. The uniform source distribu- tion, on the other hand, shows a helium production that is maximum near the top of the torus and higher in the inner region than on the outside. The helium production for the nominal case of the Fig. 7. Variation of atomic displacements within the first infinite cylinder approximation is also shown in 10 mm of the first wall with the poloidal angle X. Fig. 6. An important conclusion to be drawn from the results in Figs. 6 and 7 and from comparing the results for other response rates is that the based on S6. Since these calculations are inher - infinite cylinder approximation with a uniform ently expensive, a systematic evaluation of the volumetric source overestimates the reaction convergence was not possible. Therefore, only rates at all points of the first wall. Thus, earlier the convergence of the first energy group (13.5 to results7'17 based on this one-dimensional model 15 MeV) was examined. The results show some represent conservative estimates of the radiation interesting trends. For the reference source damage indicators in the first wall, as far as the case, the dependence of the first wall neutron flu maximum rates of gas production and atomic on X retains the general features of being highest displacements are concerned. at X = 0 and monotonically decreasing as X is It is important to note the convergence of the increased. The convergence is most difficult at toroidal geometry calculations with the order of the innermost point (X = 180 deg) with the differ - S, approximation. The results in Figs. 6 and 7 for ence between S6 and SIB results of -8%. The cases of uniform and reference sources were convergence of the neutron flux in the first energy

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ASALYSIS OF A TOKAMAK group at the first wall for the case of the uniform important characteristics compared with the uni- source is rapid near X = 0 with a maximum error form source distribution. The reference source is of Sg of -2%. On the other hand, the convergence peaked inside the plasma and drops rather rapidly near X = 150 to 180 deg is slow with a difference to zero at the plasma boundary. Moreover, the of -10% between the SG and S3, results. The de- peak occurs at the horizontal midplane and is pendence of the neutron flux on X retains the shifted toward the outer part of the torus. The general feature of having a maximum near the top "peaking" effect alone causes a reduction in the of the torus (X = 90 deg) as the order of S, is number of incident neutrons close to the tangent of increased. However, the neutron flux at X = the first wall and, hence, a reduction in the 180 deg decreases as the order of S, is increased. reaction rates in the first wall compared with the While the SG results show the neutron flux at the uniform source. 18 The geometric shift of the first wall is higher at X = 180 deg than that at source peak causes. the total number of neutrons X = 0, the S32 results show the reverse is true. crossing a unit area of the first wall to increase The results in Figs. 5, 6, and 7 can be explained at the outer part of the torus and decrease on the by a detailed analysis of the angular fluxes and the inner side of the torus. collision probabilities at all points in the first The neutronics calculations in toroidal geom- wall for all cases considered. However, the fact etry show several important considerations that that the reaction rates at the first wall calculated need to be accounted for in a tokamak reactor in the toroidal geometry representation are lower design. Among these are the variations of the than those predicted by the infinite cylinder angular flux with position around the first wall approximation with a constant volumetric neutron surface. Figures 6 and 7 show that the rate of gas source can be explained qualitatively as follows: production and atomic displacement in the first the collision probability of a neutron incident on wall vary with the poloidal angle X. Variation of the first wall generally increases as the angle of radiation damage effects with position in a struc- incidence, 6 (see Fig. 2), to the first wall is in- tural member is undesirable. ~ifferentialswell- creased, i.e., neutrons incident at a direction ing, for example, may create large stresses. -lose to the tangent (6 = 90 deg) to the wall have a Note, however, that the largest rate of poloidal grzater probability for inducing a reaction in the variation in the neutronics effects is <~.l%/cm wall than neutrons incident near the normal (6 = along the minor circumference of the first wall, 0 deg) to the wall. In the infinite cylinder approx- compared with a typical variation due to attenua- imation with a volumetric neutron source, the tion of >10%/cm radially outward. Thus, although angular flux is peaked (actually singular) at the the poloidal variations are significant enough that tangent direction parallel to the cylinder axis. In they should be considered in the radiation damage the toroidal geometry representation, the angular and stress analyses, they do not appear to intro- flux is zero for 6 > Omax,where 8max depends on duce any new major difficulties into the first wall the poloidal angle X, the neutron source distribu- design. tion, and the characteristics of the torus. The Figures 8 and 9, respectively, show the rates of maximum angle of incidence, Omax, is <80 deg at atomic displacements and helium and hydrogen X = 0 deg. It increases slowly but is <90 deg at production for the reference design as functions of all points on the outer part of the torus. At the depth in the blanket for two directions defined by inner side of the torus where Omax can reach X = 4 and 176 deg. These results show that the 90 deg, the angular flux is still higher1' at small 8 radial attenuation varies slightly with X. Since the since the flux near 6 - 90 deg does not cover the length of a minor circumference increases with entire range of angle $I (see Fig. 21, while it depth in the blanket, the rate of change of poloidal covers all values of $I for small 6. This explains variations of the reaction rates along a minor qualitatively two effects: circumference decreases radially outward in the 1. Reaction rates on the outer side of the torus blanket. Thus, the toroidal geometry effects are with uniform and reference source distribu- more pronounced at the first wall than in the tions are lower than the reaction rates deeper regions of the blanket. predicted in the infinite cylinder approxima- The results presented here show that the tion, although the neutron current to the wall toroidal geometry effects are significant and is lower in the latter case. should be accounted for in the detailed EPR design in all relevant technical areas such as thermal 2. Reaction rates in the toroidal geometry, hydraulic, stress, and radiation damage. At this uniform source case have maxima near the stage of EPR design, however, it is desirable to top of the torus. use a representative average over each minor The volumetric neutron source distribution circumference to reduce the large effort involved derived from the reference plasma case has two in design analyses of the full toroidal geometry. Abdou and Jung ANALYSlS OF A TOKAMAK

3OGEN HELIUM 1 oO

0 0 5 10 15 20 25 30 DISTANCE FROM FIRST WALL, cm (mm + 10) DISTANCE FROM FIRST WALL, cm (mm + 10) Fig. 9. Helium and hydrogen production as functions of Fig. 8. Atomic displacement as a function of distance from distance from the first wall in the reference EPR the first wall in the reference EPR design (reference design (reference source) at x = 4 deg and x = 176 deg. source) at x = 4 deg and x = 176 deg.

TABLE V On the other hand, the use of averaged parameters Rates of Helium and Hydrogen Production in may not be acceptable as a design basis in many Several Low-Z Coating Materials critical areas (e.g., radiation damage effects in the first wall), which are more affected by the appm/ (~~-yr/m') maximum than by the average. The neutronics Helium Hydrogen and photonics effects derived from the infinite cylinder approximation with a uniform volumetric Beryllium 3 110 51 neutron source distribution are more conservative oro on^ 70 130 5 34 in this regard. Therefore, this latter case is 'Carbon 2 241 --- taken as the reference design base for the re- Be0 2 018 7 2 mainder of the nuclear design analysis. BezC 2 820 34 B~C~ 56 550 427

V. NEUTRONICS EFFECTS IN THE FIRST WALL a~oronwith natural isotopic enrichment (19.8% '% and AND BLANKET 80.s "B).

To reduce the deleterious effects of plasma contamination by wall-sputtered impurities, it was two critical parameters (helium and hydrogen ~roposedthat the first wall be coated on the inside production rates) in several low-z materials with a very thin layer of low-Z material. The applied as a coating on the inside of the first wall coating will not affect the neutron and gamma-ray of the EPR reference design. Note from this table flues to any appreciable degree, but it is in- that the hydrogen production rate is <2% of the teresting to compare the nuclear performance for helium production rate. The helium production is the various coating candidates. Table V compares highest in boron and BIC,with >99% of the helium

62 NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK produced by 'OB. At this high rate of (n,a) reac- and 530 and 215 appm/(M~-yr/m2)for hydrogen tion, the 'OB is burned up at the rate of 30% per and helium production, respectively. The helium- MW-yr/mz, with a corresponding reduction in the and hydrogen-production rates decrease by about helium production rate in boron and boron carbide. an order of magnitude in 13 cm (130 mm), while The high rate of helium production in a boron the atomic displacements decrease at a much coating can be significantly reduced by using boron slower rate. The ratio of the rates of helium that is largely depleted in 'OB. Note that the helium production rate in a boron-containing coat- ing can be reduced by more than an order of magnitude by placing a strong 1ow:energy neutron absorber, e.g., 6~i,behind the first wall. Figure 10 shows the spatial (radial) distribution of nuclear heating in the first wall and blanket of the reference design for a neutron wall loading of 0.5 Mw/mZ. The maximum nuclear heating is 5.8 w/cm3 (5.8 Mw/rn3) in the first wall and 3.5 w/cm3 (3.5 Mw/rn3) in the blanket; it drops to 0.3 w/cm3 (0.3 Mw/rn3) at the outer boundary of the blanket. The total recoverable energy per fusion reaction, including the 3.5-MeV a, is 18.3 MeV, -40% of which deposited in the first wall assembly in the absence of penetrations. - Figure 11' shows the atomic displacement in I I I I I I stainless steel as a function of position in the first b 5 10 15 20 25 30 wall and blanket. A 40-eV displacement energy DISTANCE FROM FI RST WALL, cm (mm t 10) was assumed for stainless steel. The spatial Fig. I I. Spatial distribution of atomic displacement in the distribution of the helium and hydrogen production EPR first wall and blanket. rates in the stainless steel are shown in Fig. 12. The maximum values in the first wall are 11 dpa/(Mw-yr/mz) for the atomic displacement, L- I I I I I 1: - - -

- - -

-

- He / dpa - -

I I I I I I

0 5 10 15 20 25 30 DISTANCE FROM FIRST WALL, cm (mm + 10) DISTANCE FROM FIRST WALL, cm (mm + 10) Fig.- 12. Spatial distribution of helium and hydrogen produc- Fig. 10. Spatial distribution of nuclear heating in the EPR tion rates in the EPR first wall and blanket. Also first wall and blanket for a neutron wall loading of shown is the spatial dependence oi helium-todpa 0.5 MW/m2. ratio.

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 63 Ahdou and Jung ANALYSIS 01- A 1-OKAMAK production to atomic displacements is also shown the presence of a significant amount of boron in in Fig. 12 with some small variations omitted for lead mortar, most of the low-energy neutrons clarity of the graph. Note that across the 4-cm transmitted from nkighboring regions are absorbed (40-mm)-thick first wall assembly, helium pro- in the first few centimetres of lead mortar with an duction decreases by a factor of -2.5 and the exothermic 'OB(~,*) reaction. This causes a atomic displacements decrease by only a factor of maximum heating rate in lead mortar of -0.2 -1.5, causing the helium-to-displacements per w/cm3 (0.2 MW/~~),which drops to -0.02 within atom (dpa) ratio to vary by -60% across the wall. 8 cm (80 mm) and to -8 X w/cm3 in an Thus, in addition to being relatively high, all the additional 55-cm (0.55-m) lead mortar. In the significant radiation damage indicators exhibit a midregion of lead mortar, where the number of significant spatial dependence. low-energy neutrons is small, gamma-ray heating (mostly from absorption in lead) is comparable with neutron heating. VI. NEU'TRONICS ANALYSIS OF THE BULK SHIELD The rate of nuclear heating in the midplane in the inner bulk shield is shown in Fig. 14. Nuclear Figure 13 shows the spatial distribution of heating in the stainless -steel innermost region is nuclear heating rates in the outer shield for a -0.2 w/cm3 (0.2 Mw/m3) but rises to 1.4 w/cm3 neutron wall loading of 0.5 Mw/rn2. The maximum (1.4 Mw/rn3) in B4C. The minimum nuclear heat- heating rate at the inner structural steel ring is ing in the inner shield is w/cm3 (100 w/m3). -0.3 w/cm3 (0.3 Mw/rn3). This value drops The nuclear heating rate per unit volume in boron across 23 cm (230 mm) of stainless steel and car- carbide is a factor of -6 higher than in the bon (1% boron) to -0.04 w/cmS (40 kw/m3). As neighboring stainless -steel regions. The thermal expected, neutron heating is dominant in graphite, conductivity is lower for B4C than for stainless while the absorption of secondary gamma rays steel; however, no severe difficulties arise in the contributes the greatest part of nuclear heating design of the heat transfer systems because B4C in stainless steel. Nuclear heating in lead mortar can be operated at much higher temperatures than exhibits a rather interesting behavior. Because of stainless steel. In the absence of penetrations,

\\ 10'- - -.\ . '. L lo2 - - ' ..

10' - - \

12- TOTAL HEATING

------NEUTRON HEATING \ ----- GAMMA-RAY HEATING'\\, \' \. -5 clo5 I I I I I \\ lo 40 60 80 100 120 30 40 50 60 70 80 90 DISTANCE FROM FIRST WALL, cm (mm +- 10) DISTANCE FROM FIRST WALL, crn (mm -:-10) Fig. 13. Spatial disrrihution of I~catingrates ill tllc EI'R outcr Fig. 14. Spatial distrihtrtio~lol' licati~lgrates in thc. tl'K inner ,llicld for a ncutron wall loading of 0.5 MW/n12. sllicld for a ~lcutrorltrall loading ol'0.5 MW/n12. Ahdou and Jung ASALYSIS 01: A 'IOKAhlAK

-7% of the reactor (nominal) thermal power is efficient in attenuating nuclear radiation than the generated in the shield. The penetrations cause stainless-steel-B4C composition employed in the this fraction to be increased by an additional few inner shield. However, the total attenuation pro- percent. vided by the outer shield is significantly better The helium and tritium production in boron than that provided by the inner shield because of a carbide is of concern. Table VI presents the much larger shield thickness on the outside. rates of helium and tritium production in boron From the viewpoint of magnet protection, the carbide in the reference design. The maximum outer shield can be replaced with the same ma- tritium production in boron carbide is 0.36 appm/ terial composition (stainless steel-B4C) and di- (MW -yr/m2). This level of tritium production mensions used for the inner shield. This would does not present any serious problems. Moreover, have the advantage of providing more access space tritium diffusion in boron carbide is expected to outboard of the shield if such space were needed be very slow, particularly at the low operating for other purposes. However, there are two temperature of the shield. The spatial dependence strong reasons that led to the selection of the of the helium- and hydrogen-production rates in reference design. First, the graphite/lead mor- stainless steel and B.IC in the inner shield is tar/aluminum combination has no significant long- presented in Fig. 15. The maximum helium- and term activation, in sharp contrast with stainless . hydrogen-production rates in stainless steel are steel. Since the volume of the outer shield is 1 and 4 appm/(MW-yr/n?), respectively, and are >90% of the total shield volume, this leads to a more than two orders of magnitude less than those significant reduction in the total inventory of in the first wall. About 70%of the hydrogen pro- radioisotopes that require special provision for duced in the B4C is tritium. The helium-produc- long-term storage at disposal time. Moreover, it tion rate in the innermost layer of B,C is 1390 is possible in the current design to pefmit con- appm/(~~-yr/m'),a significantly high value. trolled personnel access into the reactor building Thus, the use of boron carbide with -92% theo- retical density is planned to accomnlodate the anticipated swelling and to accelerate helium diffusion. The helium production in B,C decreases rapidly inside the shield as the low-energy neu- trons are captured in the preceding layers of B4C. The outer shield material composition is less \

TABLE VI

Helium and Tritium Production Rates in Boron Carbide in the AN L- EPR Inner Shield

- 2 Distance from First Wall appm! (RIW-yr/m) (cm) (mm + 10) Ilelium Tritium

36 1390 3.6a (-1) 38 508 3.0 (-1) 40 368 2.4 (-1)

51 121 4.8 (-2) 53 55 4.0 (-2) 55 35 3.2 (-2)

67 10 5.7 (-3) 69 4.2 4.8 (-3) 7 1 2.4 3.9 (-3) 30 40 50 60 70 80 90 73 1.6 3.1 (-3) DISTANCE FROM FIRST WALL, cm (mm + 10) Fig. 15. Spa!ial distribution of hzliurn and hydrogen pro- (-4) 85 0.5 5.3 duction rates in the inner shield (iri ;tlic midplane) 87 0.2 4.5 (-4) of the EPR design. (The 10-2 shown on the curves 89 0.1 3.6 (-4) for helium production in B,C is to indicate that th~. actual values were multiplied by a factor of lo-' for a3.6 (-1) should be read as 3.6 x lo-', etc. plotting.)

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

within 24 h after shutdown for repair and inspec- of position within the homogenized composition of tion. The second reason is based on economic the magnet. The maximum nuclear heating is considerations. At present, boron carbide with -2.5 X w/cmS (25 w/m3), which is much less 95% density costslg >I20 $/kg. A demand for than the joule lokses for which the conductor must large quantities (-0.5 million kg) could possibly be designed. The heating rate decreases with an reduce the B4C price by a factor of 2. Other exponential attenuation coefficient of -0.1 3 cm-' material costs are typically 2.7, 3, and 3.5 $/kg (13 m-I). The total nuclear energy deposition in for stainless steel, carbon (1% boron), and lead the bobbin and winding of the 16 magnets is 1.5 kW. mortar,20 respectively. Thus, for the reference The refrigeration power requirements will depend design, the inner shield costs -4 million dollars greatly on whether this thermal load -would be and the outer shield costs -6 million dollars with removed at 3 or 4 K, with the lower temperature a total material cost of -10 million dollars. If requiring -1% of the plant electrical power out- the reference design were changed to include a put. The magnitude of nuclear heating, however, symmetric shield of stainless steel-B4C, the ma- is much less than the eddy current heating due to terial cost would be -30 million dollars. pulsed fields. One of the most important effects of radiation in the superconducting magnet is the increase in V11. NEUTRONICS EFFECTS IN TF COlLS resistivity of the normal conductor used as the stabilizing material. In previous work,' available The maximum radiation effects in the TF coils experimental results from 4 K irradiation were of the reference design occur in the inner (verti- used to derive a correlation between radiation- a cal) segment at midplane. The neutronics effects induced resistivity p, and the number of atomic in this segment are presented here. displacements. For copper, this correlation is Figure 16 shows nuclear heating as a function

where d is the number of displacements with an assumed displacement energy for copper of 40 eV. The value of p, calculated from this correlation may have a 10 to 20% uncertainty due to scatter in experimental data, a comparable uncertainty due to harder neutron spectrum in the EPR than in experiments, and uncertainties in energy depen- dence of the displacement cross sections. The level of atomic displacement is also affected by uncertainties in neutron cross sections of ma- terials in the shield. The cumulative effects of these uniertainties were not evaluated yet. How- ever, a 5% change in the "effective" mean-free- path of neutrons in the blanket/shield can easily lead to more than a factor of 2 change in the radiation level at the magnet. Figure 17 shows the variations of dpa and p, with depth within the windings of the TF coils. The maximum p, is 6 X lo-' S2-cm (60 nS2.mm) after irradiation for an integral neutron wall loading of 1 MW-yr/m2. Thus, the reactor can be operated up to 2.5 MW-yr/m2 before the design GAMMA-RAY HEATING I --- I value of 1.5 x lo-' 52 -cm (0.15 pS2. mm) allowed in the TF coil conductor is reached. The reactor could be operated continuously at 0.5 MW/~~for lo9 1 I I I I I I 5 yr before magnet warm-up would be needed. 0 10 20 30 40 50 60 70 This period can be doubled if operation is only DEPTH IN TF COIL, em (mm4 10) at 50% capacity factor. However, it should be Fig. 16. Spatial distribution of nuclear heating in the inner strongly emphasized that the uncertainties in segment of the EPR TF coil (in the midplane) for a calculating p, are great at present and a more neutron wall loading of 0.5 MW/m2. frequent annealing schedule should be planned in

NUCLEAR TECHNOLOGY VOI.. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A 'I'OKAMAR

DEPTH IN TF COIL, cm (mm t 10) Fig. 17. Atomic displacements and radiation-induced resistivity (p,) in copper (stabili~cr)as a function of depth within the inner segment of thc TF coils after reactor opera- tion for an integral wall loading of 1 MW-yr/m2.

TOTALDOSE 8.4 the conceptual design. Note from Fig. 17 that p, ----- NEUTRON DOSE decreases by an order of magnitude in -25 cm --- GAMMA-RAY DOSE (250 mm). Beyond that the change in the conductor width to accommodate7 the radiation-induced re- lo4 1 I I I I I I 1 sistivity is very small. 0 10 20 30 40 50 60 70 The TF coils employ a variety of organic DEPTH IN TF COIL, cm (mm + 10) thermal and electric insulators. In the tempera- Fig. 18. Dose absorbed in Mylar and epoxy (with aroliiatl~,- ture range from 3 to 4.2 K, there is a paucity of type curing agent) il~s~~latorsas a fun~.tionof Jclltll irradiation data on the properties of these ma- within the inner seg~nentof the IF coil. terials." Extrapolation of data accumulated at higher temperaturesz2 led to a choice of aromatic base epoxies for the magnet insulators. The is -9 x lo7 rad/(~w-~r/m'),which is -40 lower radiation dose at which their mechanical, and r than that in aromatic -based epoxy. However, perhaps dielectric, properties are seriously de- irradiation experiments on Mylar at 77 K showed2' graded is not known at low temperatures, but it severe effects on its mechanical properties at may be in the range of 10' to 10" rad. Figure 18 lo8 rad. Thus, the Mylar could only be used up to shows the absorbed dose in the aromatic base 1 Mw-yr/m2 in the EPR design. epoxy (C10H1302) as a function of position inside the conductor windings of the TF coil. The maxi- mum dose to the epoxy inside the conductor is VIII. NUCLEAR DESIGN OF LOCAL SHIELOS FOR 1.4 x 10' rad/(Mw-yr/m2). Thus, the aromatic- MAJOR PENETRATIONS based epoxy could probably be operated up to more than 10 MW-yr/m2. Although an integral The EPR, as well as future tokamak fusion wall loading of 10 MW-yr, n~'is greater than a reactors, will require provision for several types reasonably optimistic estimate of the lifetime for of access regions into the plasma chamber through the EPR, irradiation experiments at 3 to 4.2 K on the blanket, shield as clearly seen from the EPR organic insulators are nevertheless needed to plan view given in Fig. 19. Penetrations such as provide a more reliable estimate of the tolerable those for vacuum pumping and neutral bean1 andjor radiation dose in insulators. radio-frequency heating represent 1a r g e void Also shown in Fig. 18 is the radiation dose to regions that greatly enhan4e neutron and ganlnla- Mylar (Clo~&,), another possible candidate for ray streaming into regions external to the blanket1 insulators. The maximum absorbed dose in Mylar shield. The effects of these penetrations were

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 67

Ahtlou alitl June ANALYSIS Ol- A I OKAMAK not treated in any previous conceptual design 1. Since the torus consists of 16 segments that studies; however, the sizes and locations of these are essentially identical, only one segment needs penetrations indicate their impact on reactor to be analyzed. The segment is defined as the design would be significantly large. This was entire reactor region bounded by two planes that confirmed by a detailed study of the penetrations intersect at the poloidal axis (see Fig. 2); each in EPR. The study also indicated that these plane divides a TF magnet into two symmetric penetrations and their special shield must be halves. A periodic boundary condition is applied treated as an integral part of the design. at both planes. During the course of this study, the penetrations 2. To avoid explicit toroidal calculations on and their shield were considered in trade-off penetration analysis, the toroidal curvature was studies for the EPR conceptual design. Detailed ignored, but the dimensions of the segment were neutronics analyses of various penetration sizes adjusted to produce correct volumes and spacing and geometric orientations, as well as various of regions in the neighborhood of the beam ducts. approaches for shielding against major penetration The effect of toroidal curvature on local fluxes is effects, are given in another paper.23 In this small as shown in' Sec. IV. However, toroidal section, gross penetration effects and prominent geometry causes the spacing between the TF features of the penetration shield adopted for the magnets to vary from almost zero at the inside to reference design are described. a few metres on the outside. To account for the The study mainly focused on large vacuum correct relative positions of the penetrations, ducts required for vacuum pumping and neutral penetration shield, and magnets, spacing between beam injection. These ducts are -0.6 to 1 m2 in the TF magnets at midplane, where the beam ducts cross-sectional area and extend from the first are located, was employed. Note the outward wall (directly visible to the plasma neutrons), shifting of the magnetic flux surfaces, which radially through the blanket/shield, and outward causes an outward shift of the plasma neutron to the exterior of the TF coils (see Fig. 19). Two source strength, increases radiation st reaming vacuum pumping ducts are located between each through the neutral beam ducts compared with the pair of the 16 TF coils, one at the top and one at uniform source case. the bottom of the torus. A neutral beam duct is located between each pair of TF coils, centered 3. Since the exact position of the beam axis about the midplane with its axis almost tangential relative to the toroidal axis cannot be reproduced to the major magnetic axis. Vacuum pumping and in the geometric model discussed above, a 35-deg neutral beam injection ducts are comparable in inclination angle, Oh (see Fig. 20), was employed. size and share many common features of radiation Studies presented in Ref. 23 show the results streaming from unshielded ducts. However, the given in this section are not overly sensitive to approach for shielding adopted for the reference this assumption because of many counteracting design is different for the two systems because of and compensating effects when Ob is varied. the substantial difference in functional require- ments of the evacuation and plasma-heating sys- Figure 20 shows the geometric representation tems. The two systems are discussed separately in the neighborhood of the beam ducts in the below. In the rest of this subsection, the blanket reference design. An orthogonal coordinate sys- and bulk shield are collectively referred to as the tem (x,y,z) is also shown in the figure. The r axis bulk shield except in those instances where a is taken along the toroidal magnetic axis, x is the distinction needs to be made. minor parameter in the midplane, and j, represents the elevation from the midplane. The bulk shield VII1.A. Shielding of Neutral Beam Ducts is essentially the same as that of the outer blanket/shield system described in Table 111. The Neutronics analysis was carried out using a beam duct is represented as a cylindrical void three -dimensional geometric model with the con - region with 85-cm (850-mm) diameter. The r.,, tinuous energy VIM Monte Carlo code." These parameter shown in the figure is 45 cnl (450 nlm) calculations a r e inherently machine-time and and represents a half -width of a TF magnet. A TF man -time consuming, making a thorough three - magnet cross section in the x-y plane has a dimensional analysis of the full reactor geometry D shape. very costly. Therefore, a somewhat simplified Table VII shows the neutron fluxes normalized three -dimensional geometric model that is less to a neutron wall loading of 1 MW, m' at several costly but incorporates the basic features of the key locations for three cases. Case 1 represents reactor geometry and accounts for all first-order a design similar to that in Fig. 20, but in the effects of penetrations was developed as follows complete absence of bean1 ducts: i.e., the bulk (see Fig. 20): shield is solid and continuous everywhere. Case 2

I U It IIOLO VOL. 3.F $111)-AU<;US'I 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

I PLASMA

Fig. 20. Schematic of geometry representation for analysis of neutral beam penetrations and their shield.

is for the design in the presence of beam ducts, flux) or leakage value in Table VII is the statistical but without any provision for penetration shielding. error as estimated by the VIM code. Region 25 Case 3 is described shortly. The neutron fluxes, represents a disk whose radius is equal to that of g, given in Table VII represent averages over the beam duct and is 5 cm (50 mm) thick with the geometric regions whose numbers are used as center of the disk located at the intersection of the subscripts for $I. Regions 18, 19, 28, and 29 are beam axis with the outermost toroidal surface that inside the TF coils. Regions 18 and 28 constitute touches the outer corners of the TF magnet as the first 5-cm (50-mm)-thick zone in the TF shown in Fig: 20. coils with region 18 extending from y = -100 to The values of the neutron fluxes for Case 1 +I00 cm and region 28 spanning the rest of the y represent a maximum radiation level at the TF values. Thus, region 18 is closer to the beam coils that meets the magnet protection criteria duct and is more affected by radiation streaming defined in Sec. 11. The presence of the unshielded than region 28. Regions 19 and 29 correspond, beam duct causes the radiation level at the TF respectively, to regions 18 and 28 except they coils to increase by a factor >600. Note that this represent the second 5-cm (50-mm) depth in the factor is a strong function of the design, as shown TF magnets; i.e., r = r, + 5 to 7, + 10 cm (r,= in Ref. 23. For example, if the graphite and lead 7, + 50 to r, + 100 mm), where 7m is the inner- mortar in the bulk shield are replaced with a much most radius of the magnet [r = (x2 + y2)l"]. better attenuating composition, the radiation levels The percentage value (in parentheses below each at the TF coils will drop substantially for Case 1,

70 NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

TABLE VII surrounded by a shield capable of reducing the Total Neutron Fluxes in TF Coils and Beam Ducts radiation level in the component to a tolerable level. (Normalized to a neutron wall loading of 1 MW/~'for three cases: (1) no penetrations, (2) unshielded 3. Bulk shield extension-The bulk shield can neutral beam ducts, and (3) partial shield be extended into and between the TF coils, and to of neutral beam ducts.) the outside as necessary. Case 1 Case 2 Case 3 4. Local (exterior) penetration shield-Each penetration is surrounded as it emerges from the 85 cm 85 cm Beam duct diameter 0.0 (0.85 m) (0.85 m) bulk shield by an appropriate shield sufficient to reduce the radiation level at the TF coils, and all Penetration shield thickness 50 cm other equipment located in the reactor building, to (0.5 m) (50% SSa + 50% B4C) --- 0.0 a permissible level. h The shield plug is the easiest to define in terms 61s 1.5 (9f 9.4 (11) 6.1 (10) (+25%) (ill%) (+25%) of nuclear requirements, since it needs the same 1.1 (9) 8.2 (11) 4.0 (10) dimensions as the penetration itself, and it can be 61gd (+26%) (*15%) (+2fi) of a composition similar to that of the bulk shield. The most important advantage of the movable 1.5 (9) 1.5 (11) 4.8 (10) $28' (+25%) (44%) (*31%) shield plug in contrast to all other approaches is that it completely eliminates the penetration 1.1 (9) 8.5 (11) 3.2 (10) &sf effects and restores the effectiveness of the bulk (+26%) (*20%) (dl%) shield. It also requires the smallest inventory of 1.5 (9) 1.3 (13) 1.1 (13) shielding materials of the four options. The &sg (+25%) (+15%) (+I 1%) movable shield plug approach is not practical, Neutron leakage per 7.7 (-6) 1.3 (-2) 4.2 (-3) however, for the neutral beam ducts for several DT neutron (+lfiY (*5%) (*a) reasons: "stainless steel. 1. The tokamak EPR may have to be operated b$18 = average flux in the TF coil region [(r = r,, r, + 5), in a beam-driven mode, either to offset subignition (y = -100, loo)]. '1.5 (9) should be read as 1.5 X lo9, etc. confinement or to prolong burn pulses. In this dQ)19 = average flux in the TF coil region [(r = r, + 5, r, + case, the beam duct cannot be closed at the time lo), (y = -100, loo)]. of plasma burn. '&B = average flux within the first 5 cm of the TF coil. f&, = average flux within the second 5 cm of the TF coil. 2. During the plasma heating phase, the neutral g&, = neutron flux in the beam duct at a location in the im- beam is injected for a finite period of time (-6 s mediate exterior of the TF coil. in the reference design) and the fusion power increases steadily. The total energy of the neu- trons emitted during the beam injection phase depends on the characteristics of the design, but but only slightly in the presence of the unshielded it is generally significant and represents -5% of void ducts. Also note that the void penetrations the total fusion energy during the burn phase in cause a significant fraction of the high energy the EPR reference d e s i g n. Thus, radiation neutrons to reach the TF coils and the exterior streaming during the plasma heating phase when regions. In any event, an efficient shielding the shield plug cannot be used is high and cannot scheme is always required to protect against radiation streaming from void penetrations. be tolerated. The same problem arises when the There are several shielding schemes to protect beam is used to extend the burn pulse. reactor components external to the bulk shield 3. The neutral beam ducts have to provide a from enhanced radiation streaming caused by straight-through path from the neutralizer to the large-size penetrations. These are: plasma chamber. Thus, the mechanical move- 1. Movable shield plug-If the functional re- ments of the shield plug to close the neutral beam duct involve rotational as well as displacement quirements of a penetration permit that penetration movements. This involves time delay in closing to be closed during the plasma burn, then a shield the beam duct with the plasma already in the plug can be moved (mechanically) at the beginning ignition phase. Moreover, complicated patterns of of each pulse to completely close the penetration movements for placing the shield plug inside the region embedded in the bulk shield. beam duct magnify the risk of failure that is 2. Local component shield-Reactor compo- always associated with mechanical movements of nents affected by radiation streaming can be massive weights on a short time scale. Ahdou ant1 Jung ASALI'SIS OF A TOKAIl.4K

The local component shield approach can be shield surrounds the beam duct and extends from rejected as the primary approach on the grounds the outer surface of the bulk shield to the outer of large volumes of reactor components that have surface that touches the outermost corners of the to be shielded. This approach, however, is a TF coils. This shield is sufficient to protect the useful supplement for some small-size equipment TF coils, but not the reactor components and that is overly sensitive to nuclear radiation. auxiliary systems located in the reactor building The simple extension of the bulk shield is not external to the TF coils, as is discussed shortly. efficient, as demonstrated in Ref. 23. It requires The stainless-steel-B4C mixture is relatively a much larger inventory of materials than needed expensive and has the disadvantage of strong for the local penetration shield for the same neutron-induced activation in stainless steel. This efficiency of radiation attenuation. composition is used here, however, because of its The local penetration shield is adopted here as high attenuation efficiency to conserve space and the principal approach for shielding against the keep the necessary extension of the D-shaped TF the radiation streaming effects of neutral beam coils to a moderate level. Among other things, ducts in the reference design. As shown in future work on these penetration problems should Fig. 20, each neutral beam duct is completely involve an additional effort to optimize the geo- surrounded as it emerges from the bulk shield by metric shape of the penetration shield. an effective combination of shielding materials. Two important parameters in Table VII are the The dimensions and material composition for this neutron flux in region 25, Ozs, and the neutron local penetration shield are examined next. leakage per D-T neutron, Lo, for the three cases Case 3 in Table VII is the same as Case 2, described earlier (see Fig. 20). The presence of previously discussed, but a partial penetration the neutral beam duct causes the neutron flux at shield is provided. This penetration shield con- the beam axis (as it leaves the outermost surface sists of 50% stainless steel + 50% B4C. It is a enclosing the TF magnets) to increase from cylindrical region that completely surrounds the 1.5 x lo9 to 1.3 X 1013 n/cm2 s (1.3 X 1014 n/m2. s) cylindrical beam duct and excludes the bulk shield for a neutron wall loading of 1 MW/~'. The and TF coils wherever an interface occurs. The presence of the beam duct shield does not signifi- 0.d. of the penetration shield in Case 3 is 187 cm cantly reduce the magnitude of the neutron flux (1.87 m), providing a net shield thickness of 50 cm along the beam duct, although the average neutron (0.5 m). In Case 3, particles crossing the outer energy is somewhat reduced. Note that although toroidal surface touching the outermost corners neutrons traveling in the beam duct can strike the of the TF coils were counted in the leakage term shield on the sides of the duct, many neutrons shown in Table VII. Comparing Cases 3 and 1 in also scatter into the duct where they can travel a Table VII shows that the 50-cm (0.5-m)-thick long path before they make another collision on penetration shield is not sufficient, but brings the the side shield further down the duct. Thus, the maximum neutron fluxes in the TF coils down to population of the neutrons in the duct remains within a factor of 40 from the maximum permis- significantly high, which implies the following: sible flux at the TF coils, in addition to reducing the average energy of the neutrons. A character- 1. The penetration shield has to be extended istic of the Monte Carlo method is that as the for long distances to protect components and shield thickness is increased, i.e., the shield equipment located on the sides of the beam duct. attenuation is improved, the cost of determining However, the thickness can be reduced as one the radiation level external to the shield increases moves radially out parallel to the axis of the beam dramatically if the same statistical accuracy is to duct, because of the geometric attenuation and be maintained. As shown in Ref. 23, reasonable softening of the neutron spectrum. results can be obtained if the radiation field at the 2. A significant fraction of the neutrons will outer surface of the partial penetration shield is travel down the beam duct and strike the objects used as input to deterministic S, calculations to at the outer end of this duct. In this case, the define additional shielding requirements. This objects are the components located inside the approach shows that the penetration shield thick- chamber of the beam injector. ness has to be increased to -75 cm (0.75 m) to reduce the maximum neutron flux in the TF coils The chamber of a beam injector (see Fig. 19) to the tolerable level. is large in size, typically with a 1000-m3 volume Thus, the penetration shield for the neutral and a 600-mZ surface area. Besides possible beam duct is specified as 75 cm (0.75 m) thick, initiation of hot spots on the structural walls of the first 65 cm (0.65 m) is a 50% stainless steel + this chamber, the components located inside the 50% B4C composition, followed by 5-cm lead and chamber can be affected by nuclear radiation; an additional 5-cm (0.05-m) aluminum alloy. This e.g., the crysorption panels and bending magnets.

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

The analysis of neutrons and photons inside the the horizontal axis represents the distance x-xu, in large-size neutral injector chamber was not Fig. 21 with x, = 240 cm (2.4 m). From this carried out in detail because of the high computa- figure, note that the beam duct serves as a tional cost involved. However, it is believed that secondary neutron source that redistributes the the potential problems involved here must be neutrons and increases their population signifi- investigated. Approximate calculations based on cantly in the deeper regions of the blanket and the total neutron leakage to the neutral injector bulk shield. At an 80-cm (0.8-m) depth into the chambers show that nuclear heating at the cryo- blanket/shield, the total neutron flux in the vicinity sorption panel possibly can exceed 0.01 w/cm3 of the penetrations is -3 orders of magnitude (10 kw/m3), and that the absorbed dose in the higher than at points located on the same toroidal epoxy insulator located in the bending magnet may surface but -100 cm (1 m) away from the beam be >lo" rad/(~~-yr/m2). walls. The neutronics effects in the beam duct wall, Thus, even for an axisymmetric blanket/shield, blanket, and shield regions adjacent to the beam the presence of penetrations causes spatial varia- ducts were also considered. Figure 21 shows the tions in the toroidal direction that are stronger total neutron flux as a function of depth within the near the penetrations and that increase radially blanket and bulk shield for two cases. The first outward. These effects must be accounted for in case is in the absence of penetration effects; i.e., thermal-hydraulic, stress, and radiation damage in regions far away from penetration near the analyses. Figure 22 shows neutron heating in the lower boundary of Fig. 20. The second case is for water coolant as a function of distance from the flux at a surface surrounding the beam duct and is first wall at three concentric cylindrical surfaces. located 5 cm (50 mm) away. In this latter case, The first surface, a, is the wall of the beam duct; the second surface, 6, is located 10 cm (100 mm) outward from the beam duct wall; the third surface, c, is 30 cm (300 mm) away from the beam

loe 0 20 40 60 80 100 120 130 0 20 40 60 80 100 120 DISTANCE FROM FIRST WALL, cm (mm + 10) DISTANCE FROM FIRST WALL, cm (mm + 10) Fig. 22. Neutron heating in the water coollant as a function of Fig. 2 1. Total neutron flux (normalized to a neutron wall depth in the blanketlshield for three locations with loading of I MW/m2) as a function of depth within respect to the neutral beam duct: (a) at the wall of the the blanket and bulk shield at two locations: (a) beam duct, (b) 0.1 In from the wall of the beam a radial line far removed from penetration effects, duct, and (c) 0.3 m from the wall of the beam duct. and (b) a surface parallel to the walls of the neutral (Results normalized to 0.5 MW/rnp neutron wall load- beam duct and 5 cm away. ing.)

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 wall. Neutron heating in the water coolant at the inner edge (at the first wall) of the beam duct wall is -5 W, cm3 (5 hlw/n13) for aneutron wall loading of 0.5 hlW, nl'. This value drops by a factor of 10 along the entire length of the beam wall inside the blanket -bulk shield. For comparison, neutron heating in the water coolant in regions far re- moved from the beam ducts varies from 5 w/cm3 (5 ll~/rn~)at the first wall to 0.4 w/cn13 (0.4 MW,m3) at the outer perimeter of the blanket to W, cm3 (100 w/n13) near the outer surface of the bulk shield. Figure 22 shows that the heating rates in regions surrounding the penetra- tion are significantly increased by penetration- assisted streaming of nuclear radiation. Thus, the -20-cnl (200-mm)-thick region in the bulk shield- ing surrounding the beam duct requires an efficient heat removal system similar to that of the blanket. Furthermore, the material composition of this region cannot be a low-temperature material such - WITH PENETRATION SHIELD as lead mortar and must be constructed of ma- terials that can withstand high heating conditions 10-2 such as those enlployed in the.blanket. Note that 0 20 40 60 80 100 120 I30 the neutron population is increased near the outer DISTANCE FROM FIRST WALL, cm (rnrn +lo) region of the bulk shield, in the absence of the penetration shield, by those neutrons streaming Fig. 23. Atomic displacement in stainless steel as a function of depth in the blanket/shield for three locations with out of the beam duct and backscattered into the rcspect to the neutral beam duct: (a) at the wall of bulk shield by external components. This effect the beam duct, (b) 0.1 m from the wall of the beam is also shown in Fig. 22. Note here that the duct, and (c) 0.3 m from the wall of the beam duct. results in Fig. 22, as well as those in Fig. 23, were derived from a combination of three-dimen- sional Monte Carlo and two-dimensional S, calcu- lations to obtain detailed spatial-distributions. V111.B. Shielding the Evacuation Ducts Figure 23 is similar to Fig. 22 except that the dpa in stainless steel is the response rate of In the reference EPR design, there are 32 interest here. The spatial variation of the dpa evacuation (vacuum pumping) ducts that are ap- exhibits essentially the same general behavior proximately cylindrical, each with a 95-cm (0.95- discussed above for water heating. Of particular m)-diam wall. They are located at the top and concern here, however, is radiation damage to the bottom of the torus, each equally spaced between a walls of the neutral beam duct as well as the walls pair of TF coils. of any vacuum duct that cannot be completely These evacuation ducts are larger in size and closed during the plasma burn. These walls must number than the neutral beam ducts. Radiation satisfy the same requirements as those on the streaming through these evacuation ducts was first wall; i.e., they must guarantee structural studied and it is similar in many respects to the integrity and maintain the vacuum integrity of the case of the neutral beams, except for some dif- plasma chamber. The radiation damage indi- ferences due to size and orientation of the ducts. cators, dpa, and gas production rates near the Although the spacing between the TF coils at the inner end of the duct walls are essentially the top and bottom of the torus is tight, the functional same as in the first wall. Moreover, they drop requirements of the evacuation ducts permit mod - along the duct wall by -l%/cm. In addition to the erate bends in the duct, which would make the considerable radiation damage at the inner part of design of an adequate exterior penetration shield the duct walls, variations in dpa and gas production feasible. This shield, however, would cost -10 rate, as well as fluctuations in the temperature million dollars for the reference design and would along the wall, aggravate the radiation damage and occupy most of the space on the top and bottom of can create relatively large stresses in this struc- the torus as well as the space between the TF tural member. The inner surfaces of these walls coils. The exterior duct shield would introduce may also have to be coated with a low-Z material many other disadvantages similar to those dis- to minimize plasma contamination. cussed for the neutral beam penetration shield.

74 NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

Since the evacuation ducts can be completely The maximum radioactivity occurs in the stain- closed during the.plasma burn, the concept of a less-steel first wall. Table VIII shows the specific movable shield plug was adopted as the principal radioactivity in the innermost region of the first design option. The movable shield plug can, in wall in units of disintegration per s/cm3 (m3) after principle, be constructed with materials and di- a 2-yr operation with a neutron wall loading of mensions such that when it is moved to close an 0.5 MW/~'. In the first few minutes after shut- evacuation duct, the blanket and bulk shield become down, the radioactivity is dominated by 55~e 5 1 continuous. However, there must be a finite (T112 = 2.6 yr), 56~n(T1/2 = 2.58 h), Cr (TI/, = clearance between the shield plug and the evacua- 27.8 day), and 58~o(T1/2 = 71.3 day). Except for tion duct that can provide possible streaming paths 56~n,the radioactivity from these isotopes re- for radiations. Therefore, the shielding plug cross mains dominant during the first few weeks after section should be varied in steps with correspond- shutdown. At long times, the main isotopes are 63 ing change in the evacuation duct as shown in Ni = 92 yr), 59~i = 8 X lo4 yr), and Fig. 24. 53~n = 2 X lo6 yr). . A crude but useful indication of the biological effects of the various radionuclides is provided by IX. RADIOACTIVITY, AFTERHEAT, AND BIOLOGICAL DOSE the Biological Hazard Potential (BHP). The BHP is defined as the amount of air required per kW Calculations of radioactive inventories, after - of thermal power to dilute the radioactive isotope heat, and biological hazard potential provide im- to its maximum permissible concentration. The portant information for the safety analysis and BHP for the reference design is shown in Fig. 25 environmental impact questions. The biological as a function of time after shutdown following a dose at many key locations during operation and 2-yr operation. The maximum permissible con- after shutdown is important for planning mainte- centration (MPC) values in the TK3 programz4 nance and repair services. This section presents library used in these calculations are taken from such information for the reference design. U.S. Atomic Energy Commission Rules, Title 10, These calculations are based on the neutron Part 20. At shutdown, the BHP is 800 km2/kw(th) radiation field as characterized in previous sec - with about one-third of this value coming from the tions. The concentrations of the radionuclides 4-cm (40-mm)-thick first wall. The greatest from the transmutation chains were calculated contribution to BHP comes from 54~n(25%), 57~i with the TK3 program.24 The transport of decay (25%), 5a~~(17%), 60~o(lo%), 56~n(5%), and gamma rays was determined with a series of 56~e(4%). one-dimensional geometric models serving as Figure 26 shows the afterheat as a function of idealization of the nuclear systems of the refer- time after shutdown following a 2-yr operation. ence EPR. The average energies of the /3 parti- The afterheat expressed as a percentage of the cles were calculated according to the method reactor thermal operating power is also fairly described in Ref. 12. independent of the neutron wall loading in the Figure 25 shows the radioactivity in units of range 0.1 to 5 Mw/m2. At shutdown, the decay Ci/MW(th) as a function of time after shutdown heat is -2.506 of the operating thermal power. following a 2-yr operation. The level of neutron- This value drops by only -20% during the first induced activation at shutdown is 3.5 MCi/MW(th) few minutes that are crucial to emergency cooling. [I30 PBq/Mw(th)] and decreases by only a factor However, the percentage afterheat here is about of 4 during a cool-down period of 1 yr, then drops one-third that in a fission reactor. Moreover, the much more rapidly at later times. More than 99% maximum power density in the EPR reference of this activity comes from the first wall and design was shown in Sec. V to be -6 w/cn13 blanket that constitute a 32-cm (320-mm)-thick (6 MW/~~),which is about a factor of 10 lower region of stainless steel surrounding the plasma. than the power density in a light water reactor and The level of radioactivity builds up fast during a factor of 100 lower than that in a fast breeder operation and reaches a significant level in a few reactor. hours and a near steady-state level in a few days. The biological dose that would be received by a Note that the level of radioactivity expressed here human being at many key locations in the reactor in ci/MW(th) [~q/M~(th)]is a factor of -3 higher is extremely important for the design and planning than in reactors employing lithium blankets with of maintenance and repair operations, as well as only 5 to 10% stainless-steel structure such as classifying the various areas for control of human UWMAK-I1 (Ref. 25). It was also found that the access. During operation, the biological dose in Ci/MW(th) are fairly independent of the neutron regions external to the TF coils is -10" mrem/h, wall loading when the latter is in the range of which is too high to permit access to the inside of 0.1 to 5 MW/~'. the reactor building for any reasonable length of

NUCLEAR TECHNOLOGY VOL. 35 MID-AUGUST 1977 Ahdou and June ANALYSIS OF A TOKAMAK

EF COILS OH COILS 1 a STAINLESS STEEL ma qRAPHlTE (1% BORON) SCALE BORON CARBIDE (BaC). . = LEAD MORTAR w STAINLESS STEEL OR ALUMINUM

Fig. 24. A vertical cross section for the blanketlshield schematically showing the movable shield plug for the evacuation ducts.

76 NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK

X. SUMMARY

The nuclear design of the blanket/shield system for a reference EPR conceptual design was pre- sented. The reference EPR is a tokamak with a 6.25-m major radius and a 2.1-m minor radius circular plasma. Surrounding the plasma is a stainless-steel vacuum vessel with detachable beryllium-coated cooling panels. A 0.28-m-thick blanket of stainless steel surrounds the vacuum vessel. The bulk shield on the inner side of the torus is 0.58 m thick and is constructed of alternating layers of stainless steel and B4C to achieve high radiation attenuation in a limited space. The bulk shield 'on the top, bottom, and outer side of the torus is 0.97 m thick with lead mortar as the principal shielding material. Q 102 -=- A two-dimensional S, program was modified to 2 5 1 10 11 1 solve the neutron transport equation in axisym- min min 1 h day week month 10 yr 100 yr = metric toroidal systems. The program was used - to calculate the toroidal effects in the reference 10' I 10-3 design. Neutronics results in the first wall and 10' lo2 103 104 105 lo6 lo7 loe 109 1ol0 blanket were found to be far more sensitive to the TIME AFTER SHUTDOWN, s spatial distribution of the DT neutron source strength as affected by the toroidal geometry and Fig. 2. Kadioactivity and biological hu~ard potential as a f~~nc.tionof time aftcr shutdown following a 2-yr the MHD equilibrium of the plasma than they are operation. to the local toroidal curvature in the first wall and blanket. Although the poloidal variations in the neutronics results due to toroidal geometry are significant enough that they should be accounted for in a detailed design, these variations do not time. The primary containment, also serving as appear to introduce any new major difficulties the wall of the reactor building and as the bio- into the first wall and blanket design. Another logical shield, is 1.5-m-thick ordinary concrete, significant finding is that the first-wall response which reduces the biological dose outside the rates are overestimated in the infinite cylinder reactor building to -1 mrem/h. approximation compared with values obtained The biological dose after shutdown in the from toroidal geometry calculations. reactor building at the exterior of the outer shield Beryllium represents a strong candidate for a is of particular concern. As indicated earlier, low-Z coating on the inner side of the first wall. remote maintenance is required for all service Boron is another good possibility if it is largely operations on components inside the first wall and depleted in 'OB. For a mean neutron wall loading blanket. However, substantial savings on time and of 0.5 MW/~',the maximum nuclear heating rates cost of these operations can be made if they are are 5.8, 3.5, and 0.3 w/cm3 (5.8, 3.5, and 0.3 directed from a central platform inside the reactor Mw/m3) in the first wall, blanket, and bulk shield building rather than from the outside. The bio- regions far removed from penetrations, respec- logical dose exterior to the TF coils is the most tively. The maximum values of the radiation difficult to calculate because of the presence of damage indicators in the first wall are 11 dpaj many major penetrations and the large-size neu- (MW-yr/m2)for atomic displacement, and 530 and tral beam injectors that represent potentially 2 15 appm/(Mw -yr/m" for hydrogen and helium large sources of induced activation. In the com- production, respectively. The maximum radia- plete absence of penetrations and beam injectors, tion-induced resistivity in the copper stabilizer the biological dose is -2 mrem/h at 24 h after of the TF coils is 6 x lo-' R -cm (60 nR. mm) shutdown. To keep the biological dose to this after irradiation for an integral neutron wall value in the presence of the penetrations and loading of 1 M~-~r/m'.The reactor can be injectors, full shielding of the penetrations as operated up to 2.5 Mw-~r/rn' before the design described in the preceding section is required. value of 1.5 x lo-' 52 -cm (0.15 10.mm) allowed Moreover, a shield has to surround all walls of in the TF coil conductor is reached. The TF the neutral beam injectors. coils employ a variety of organic thermal and Ahdou and Jung ANALYSIS~t A TOKAMAK

TABLE VIlI Specific Radioactivity in the First \Val1 loisintegration per r/cn,3 ([3q/mm3 x lo3) after a 2-yr operation with a neutron wall loading of 0.5 ~ll;/~',]

I Time After Shutdown

Nuclide Half- Life 0 1 min 10 min lh 1 day I \reek I yr 10 yr 100 yr

55F e 2.6 yr 4.5 (11)~ 4.5 1 4.5 (11) 4.5 (11) 4.5 (11) 4.5 (11) 3.5 (11) 3.2 (10) 1.2 (0) 51~r 27,8day 2.1 (11) 2.1(11) 2.1 (11) 2.1(11) 2.0(11) I.7(11) 2.3(7) 9.1 (10) 9.1 (10) 8.9 (10) 54nIn 303 day 9.1 (10) 9.1 (10) 9.1 (10) 3.9 (10) 2.0 (7) 57Co 270 day 4.2 (I()\ 4.2 (10) 4.2 (10) 4.2 (10) 4.2 (10) 4.2 (101 1.7 (10) 3.6 (6) 60 Co 5.26 yr 1.0 (10) 1.0 (10) 1.0 (10) 1.0 (10) 1.0 (10) 1.0 (10) 9.0 (9) 2.7 (9) 1.9 (4) 60mCo 10.5 min 2.8 (10) 2.6 (10) 1.4 (10) 5.2 (8) 1.3 (0) 1.3 (11) 8 58~~71.3 day 1.3 (11) 1.3 (11) 1.3 (11) 1.3 (11) 1.2 (11) 3 (91 41 (-5) 56 hln 2.58 h 3.6 (11) 3.5 (11) 3.4 (11) 2.7 (11) 5.5 (8) 7.3 (-91 52~ 3.7 min 5.9 (10) 4.9 (10) 9.2 (9) 9.0 (5) "AI 2.3 min 1.8 (10) 1.3 (10) 8.7 (8) 2.5 (2) 63~i 92 yr 7.3 (7) 7.3 (7) 7.3 (7) 7.3 (7) 7.3 (7) 7.3 (7) 7.2 (7) 6.8 W) 3.4 (7) 8.1 (4) 8.1 (4) 8.1 (4) 8.1 (4) 8.1 (4) 8.1 (4) 5gNi 8 Yr 8.1 (4) 8.1 (4) 8.1 (4) 53fi 2 106yr 1.2 (4) 1.2 (4) 1.2 (4) 1.2 (4) 1.2 (4) 1.2 (4) 1.2 (4) 1.2 (4) 1.2 (4) Total 1.4 (1%) 1.4 (12) 1.3 (12) 1.2 (12) 9.3 (11) 8.9 (11) 4.2 11) 3.4 (10) 3.4 (7)

a4.5 (11) should be read as 4.5 '' 10"1 etc.

electrical insulators. There is a lack of irradia- tion data on these insulators at cryogenic temper- atures. Irradiation experiments at 3 to 4 K on organic experiments are needed. Extrapolation of data accumulated at high temperatures led to a choice of aromatic base epoxies for the magnet insulators. The maximum absorbed dose in the insulators is 1.4 Y 10' rad/(~~-~r/m'). The level of neutron-induced activation in the EPR is 3.5 x lo6 Ci/MW(th) (130 PB~/MW(~~)]and decreases by a factor of 4 one year after shutdown and more rapidly for longer times. At shutdown, the decay heat is 2.5% of operating power and only drops -20% during the first few minutes that are crucial to emergency cooling. Multidimensional neutronics calculations were carried out for the major penetrations in the EPR. The study resulted in defining a multiple penetra- tion shielding system that varies from one pene- tration to the other according to the size, orientation, and functional requirements of each penetration. For the evacuation (vacuum ~umping) ducts, a movable shield plug pneumatically oper- ated, opening during the pumpdown phase, and closing during the plasma burn, seems to present the least challenging design problems at present. Radiation streaming from the neutral beam ducts poses one of the most difficult problems in penetration shielding. A local penetration shield that completely surrounds the beam duct as it emerges from the bulk shield is the only viable shielding option. The TF magnet protection Cri- ~i~.26. Afterheat a func,ioll of time after shutdown fol- lowing a 2-yr operation. teria are satisfied by a local shield whose thick-

78 NUCLEAR TECHNOLOGY vOL. 35 MID-AUGUST 1977 Abdou and Jung ANALYSIS OF A TOKAMAK ness is comparable to the diameter of a cylindrical I I. E. M. GELBARD and R. E. PRAEL, "Monte Carlo Work at beam duct and extends from the outer boundary Argonne National Laboratory," Proc. NEACRP Mtg. Monte of the bulk shield to between the TF coils. This Carlo Study Group, ANL-75-2, Argonne National Laboratory (1974); see also, R. E. PRAEL and L. J. MILTON, "A User's imposes severe constraints on the minimum Manual for the Monte Carlo Code VIM." FRA-TM-84, Argonne spacing between the TF coils. To protect other National Laboratory Internal Memorandum (I 976). auxiliary systems located outside the TF coils, this beam duct shield needs to be extended further 12. M. A. ABDOU. C. W. MAYNARD. and R. Q. WRIGHT, (but can be tapered off in proportion with the "MACK: A Computer Program to Calculate Neutron Energy Release Parameters and Multigroup Neutron Reaction Cross reduction in the radiation level) to the chambers Sections from Nuclear Data in ENDF Format," UWFDM-37 and of the beam injectors. Inside these chambers, ORNL-TM-3994, University of Wisconsin and Oak Ridge Na- nuclear heating in the cryosorption panel is -0.01 tional Laboratory ( 1973). w/cm3 (10 kw/m3), and the absorbed dose in the bending magnet insulator is 10" rad/(MW-yr/ 13. D. GARBER. C.DUNFORD. and S. PEARLSTEIN, "Data - Formats and Procedures for the Evaluated Nuclear Data File, m2). This level of radiation in the beam injectors ENDF," BNL-NCS-50496 (ENDF 102), Brookhaven National is high and should be factored into any comparative Laboratory, (Oct. 1975); sec also, TID-4500, Division of Tech- assessment of various plasma heating methods. nical Information, U.S. Energy Research and Development Administration.

ACKNOWLEDGMENTS 14. J. JUNG. "Finite Difference Equations for Transport Equa- tion in Toroidal Geometry," Nucl. Sci. Eng., 60, 74 ( 1976). This work was carried out as part of the EPR conceptual design studies at ANL. The authors thank T. Y. Sung of tllc IS. M. A. ABDOU. "Calculational Methods for Nuclear Heating University of Wisconsin for assistancc with some of the radio- and Neutronics and Photonics Design for CTR Blankets and activity calculations. Shields," PhD Thesis, 74-8981, University Microfilms Inc.; This research was supported by the U.S. Energy Research and also issued as UWFDM-66 and UWFDM-67, Nuclear Engineering Development Administration. Department, University of Wisconsin (1973).

REFERENCES 16. D. L. CHAPIN and W. G. PRICE. Jr., "A Comparison of 1. W. M. STACEY, Jr. et al., "Tokamak txperimental Power the D-T Neutron Wall Load Distributions in Several Tokamak ?eactor Studies," ANLJCTR-75-2, Argonnr National Laboratory Fusion Reactor Designs," MATT-1 186, Plasma Physics Labora- (June 1975). tory. Princeton University ( 1975).

2. W. M. STACEY, Jr., et al., "Tokamak Experimental Power 17. M. A. ABDOU and R. W. CONN. "A Comparative Study of Reactor Conceptual Design," ANL/CTR-76-3, Argonne National Several Fusion Reactor Blanket Designs," Nttcl. Sci t'ng.. 55, Laboratory (Aug. 1976). 256 (1974).

3. GAC Fusion Engineering Staff, "E~perimentalPower Reac- 18. M. A. ABDOU and C. W. MAYNARD. "Neutron Source tor Conceptual Design Sti~dy,"General Atomic Company (July Geometry Effects on Fusion Reactor Blankets," Trans. Am. 1975). Nrrcl. Soc.. 15, 34 ( 1972).

4. C. C. BAKER et al., "Experimental Power Reactor Concep- 19. NEIL N. AULT. Norton Company, Private Communication tual Design Study-Final Report for the Period July 1, 1974 ( 1975). Through June 30, 1976,"GA-A14000, General Atomic Cornpany ( 1976). 20. WILLIAM CORNELIUS HALL. Chemtree Corporation, Privatc Communication (1976). 5. M. ROBERTS et al., "Oak Ridge Tokamak Experimental Power Reactor Study Scoping Report," Oak Ridge National 21. C. A. M. VAN DER KLEIN, "The Organic Insulation in Laboratory (Aug. 1975). Fusion Reactor Magnet Systems," RCH-240, Reactor Centrum Nederland (Dec. 1975). 6. M. ROBERTS et al., "Oak Ridge Tokamak Experimental Power Reactor Studies-1976," ORNL-TM-5572, Oak Ridge 22. H. BRECHNA, "Effect of Nuclear Radiation on Organic National Laboratory (1976). Materials: Specifically Magnet Insulation in High-Energy Acceler- ators," SLAC-40, Stanford Linear Accelerator Center (Mar. 7. MOHAMED A. ABDOU, "Nuclear Design of the Blanket/ 1965). Shield System for a Tokamak Experimental Power Reactor," Nucl. Technol.. 29, 7 (1976). 23. M. A. ABDOU rt al.. "Multidimensional Neutronics Analysis 8. W. ENGLE, Jr., "A Users Manual for ANISN," K-1693. Oak of Major Penetrations in Tokamaks," Proc. 2nd Topl. Mtg. Ridge Gaseous Diffusion Plant (1967). Tech?~ologyof Cotltrolled Nuclear Fusion, Richland, Washington (Sep. 1976). 9. W. A. RHOADES and F. R. MYNATT, "The DOT Ill Two Dimensional Discrete Ordinates Transport Code," ORNL-TM- 24. T. Y. SUNG and W. F. VOGELSANG. 'TK3: A Program to 4280, Oak Ridge National Laboratory (1973). Calculate Radioactivity and Afterheat in Fusion Reactors," to be published as a University of Wisconsin FDM report. 10. K. D. LATHROP and F. W. BRINKLEY, "TWOTRAN SPHERE: A FORTRAN Program to Solve the MultigroupTrans- 25. B. BADGER et al., "UWMAK-11, A Conceptual Tokamak port Equation in Two-Dimensional Spherical Geometry," Power Reactor Design," UWFDM-I 12, University of Wisconsin LA-4567, Los Alamos Scientific Laboratory ( 1970). Report (Oct. 1975).

NUCLEAR TECHNOLOGY VOL. 35 MIDAUGUST 1977