Impact of several reactor features on TF coil design for TPSS

A significant driver of machine size in previous designs was the amount of nuclear shielding placed between the blanket and the toroidal field (TF) coils to minimize the radiation heating and damage in these critical components. Of course the total amount of shielding is not arbitrary; it certainly must adequately suppress radiation outside the plant. However, if all of this shielding were contained inside the TF coils, several parameters (coil size and weight, maximum field at the windings, stored energy, etc.) would become inordinately large. Reducing the amount of shielding inside the TF coils and allowing the radiation load to climb to less ''conventional'' levels could pay big benefits in reducing the machine size, so long as the damage and heat load remain tolerable. Recent studies indicate that superconducting windings in TF coils can accept much higher heat loads than have been previously considered and simultaneously can be designed with higher than conventional current densities. The purpose of the present exercise is to probe the limits of acceptable radiation levels in relation to winding pack current densities in the TF coils for reactor relevant designs.


INTRODUCTION
Past studies that have tried to project the appearance of future •fusion reactors have produced designs that were unattractive because o-f their high capital cost, which was due mainly to their large size. In current studies, much effort is being expended to find ways to minimize machine sUe and complexity in the hope that the final designs will prove less expensive. A significant driver of machine size in previous designs was the amount of nuclear shielding placed between the blanket and the toroidal field <TF) coils to minimise the radiation heating and damage in these critical components. Of course the total amount of shielding is not arbitrary; it certainly must adequately suppress radiation outside the plant. However, if all of this shielding mere contained inside the TF coils, several parameters (coil size and weight, maximum field at the windings, stared energy, etc.) would become inordinately large.
Reducing the amount of shielding inside the TF coils and allowing the radiation load to climb to less "conventional" levels could pay big benefits in reducing the machine size, so long as the damage and heat load remain tolerable. Recent studies 1 -3 indicate that superconducting windings in TF coils can accept much higher heat loads than have been previously considered and simultaneously can be designed with higher than conventional current densities. The purpose of the present exercise is to probe the limits of acceptable radiation levels in relation to winding pack current densities in the TF coils -for reactor relevant designs.

BASELINE RADIATION LOAD
A very aggressive level of radiation will be examined in this exercise. In essence, we pose the following question: "Suppose an insulating material can be found that will survive 10 ia rads absorbed over the life of the machine, which is assumed to be 40 full power years (fpy); can the other consequences of this level Df radiation, namely 7 mW-cm~3 peat; heat load in the winding pack, 4 :; 10 =o n-cm -= fast neutron fluence, and 0.2 dpa damage to the copper stabilizer of the conductor, be tolerated?" Some immediate consequences of this scenario can be noted. Figure 1 gives part of the evidence suggesting that the none of the A15 compound superconductors will survive neutron fluences greater than ~10 1B n-cm~=. NbTi conductors probably will be useable at these levels; however, we shall see that this presents a non-trivial problem for heat removal because of the much lower critical temperature T e of this alloy compared to the A15 compounds. The result is lower attainable maximum fields.
Force cooled conductors will be stipulated in this study bWKp active cooling will be needed to handle thB high peak heat^^Q^Jyeind W rffr DISTRIBUTE CF THIS K-SL'MEuT IS £"-• -: -a because cable-in-conduit, force-cooled conductors are expected to suffer much less degradation of stability due to radiation damage to the capper stabilizer. But in this type conductor, some temperature margin between inlet helium temperature and the current sharing temperature of the superconductor must be used in removing the heat and some must be maintained to stabilize the conductor against perturbations that may be imposed during operation of the magnet. It will be shown that maximum field of around 6 T, with quite reasonable winding pack current density, can be supported while maintaining adequate stability and the ability to protect the coils in the event of a quench to end of the machine life.

BASELINE TF CONFIGURATION
Several machine configurations of interest for the TPSS were suggested by D. A. Ehst. 3 The version having approximately 6 T field at the coil case (6.21 T at the windings) is characterised by the parameters listed in Table 1. More detail must be added to this list subject to various constraints and performance characteristics.
The number of coils in the TF set affects field ripple at the outer plasma edge, machine access, ease of assembly and disassembly, and <to some extent) protection. To illustrate the effect of the number of coils on field ripple, a winding pack current density J B .»=K = 60 A-mm"" 55 and a winding build of 0.2 m was assumed, and the calculations in Fig. 2 were performed. For 16 coils with the assumed winding geometry, the ripple is 4.4 '/. peak-to-peak.
The number of coils has the strangest influence, but spreading the windings might be expected to reduce the ripple somewhat. To get a feel for the magnitude of this effect, an additional 16 coil essample was calculated. In this case, the same 0.2 m winding build was used, but Op. = i< was reduced to 40 A-mm" 2 and the winding spread laterally to compensate. Figure 3 shows a comparison of the assumed winding shapes and lists the corresponding field ripple values. From Fig. 2 it is apparent that -if field ripple no higher than 2 -3 7. can be tolerated, there may be no fewer than IS coils, unless other means suppress.!oft techniques are used (e.g. shimming with appropriately placed ferromagnetic inserts).

WINDING PACK DESIGN
Particular features of the winding pack are often a matter of designer's choice. A successful design results when the strong features of a particular type of design sire emphasised and the wealfeatures compensated. We begin this design with a cable-in-conduit conductor (CICC). The sheath provides strong containment of the helium coolant and til so adds structure at the source of the electromagnetic forces. There are benefits for, maximiaing the overall current;." density of a winding pack based on this type of conductor if the sheath is used ef f ecti vel y in these roles. If it is not used effectively, it becomes a penalty to the obtainable pack current denstiy.
The CICC also allows for solid insulation between turns of conductor and thus the opportunity for higher allowable turn-to-turn and terminal voltages. It is not possible to fully optimize the fractions of steel and insulation in the winding pack without detailed knowledge of the mechanical loads, internal pressures, fault conditions, etc., but experience from previous designs where inanufacturabi1ity, tensile load sharing, and support of centering leads by the conductor sheath were primary considerations suggests that 20 -25 "/. of the winding pack should consist of steel and 15 -20 '/. insulation. We choose f'» t ".i = 22 X and f'i".ui<cii>n = 15 '/. for this study. The remaining 63 V., consisting of helium, superconductor, and copper stabilizer (aluminum has been shown to be inferior in a high radiation environment*), must be tailored to the requirements of heat removal, protection, and stability.
Heat removal-Heat, is removed in a CICC by introducing single phase He at some temperature Tin and forcing it through the conductor at a sufficient flow rate that the ma;;imum temperature in the flowpath does not compromise the stability required. Df course the flow cannot be increased without limit because fractional losses become significant, and any further increase in flow gives an increase in the maximum temperature in the flowpath.*•" The alternative is shorter, more numerous flowpaths with the consequence of more complex manifolding for injection and removal of the helium. Boad advantage can be taken of the high heat capacity of helium in the pressure range just above the critical pressure, e.g. in the range from about 300 -500 kPa, both for steady heat removal and for stabilization. 1 Shorter channels that allow for sufficient flow, but with low enough pressure drop ta stay in this range over an entire flowpath, are an attractive design option.
To test our ability to adequately remove the heat, same assumptions must be made about the distribution of heat in the windings. First, even with shielding of uniform thickness between the plasma and the circumference of the TF coils, the circumferential distribution of heat will not be uniform. This is because the outboard legs of the TF coils represent only a fraction of the total cross section intercepting the radiation of the outer plasma surface and because they &rB further from the plasma than are the inboard legs. The combination of effects should reduce the radiation heat load at the midplane of an outboard TF coil leg by 1/10 when compared to the maximum at the midplane of the inboard leg. Second, calculations with "typical" materials of a winding pack suggest that heating rates should fall off exponentially with depth into the pack with a characteristic <e-folding) depth of 9 -10 cm.* These assumptions can be combined in the following simple form for an approximate distribution of heating in a TF coil that will be useful •for estimating purposes: q tr.e) = q eKp£-<r -R>/0.0'?5:K sinte/2) + (1/10)C 1 -sin(e/2)33 M n ' ^ma>: ^ where R is the equivalent inner radius of a "dee" coil topologically deformed into a circle, and the angle 6 is measured from a radius through the midplane of the outer leg.
From this distribution, we estimate that the average heat load into a turn of conductor in the innermost layer is <& > = 0.67 q s 4.7 kW/m 0 ^n max Later, when a determination of the useable winding pack current density has been made, and the winding pack dimensions have been set, we can use the same distribution function to obtain an appro;;imation of the total radiation heat load per coil. However, of more immediate interest is whether the average heat load per turn on the inner layer of the winding can be accomodated. Using the approximate techniques of ref. 1, it can be shown that this load can be absorbed with a temperature rise of < 0.4 K in that turn by appropriate manifolding to provide the required He flow. The conductor must be rather "open", however, and a minimum void fraction of 40 V. in the cable space of the CICC is suggested to preclude too much pressure loss.
Stabi1itv-At a particular current density and field, the stability margin provided by a CICC can be expressed in the form where S M » is the effective volumetric heat capacity of the helium between the initial bulk fluid temperature Tt, and the current sharing temperature T" of the superconductor. The ratio of the helium fraction f H -to conductor fraction f cor ,d in the cable space merely refers the sudden absorbed energy that, will just quench the conductcr to a unit volume of conductor. The above relation is essentially a statement of experimental observation that, to first order, the stability of a CICC is derived from the heat capacity of the interstitial helium over the temperature range that the conductor is superconducting.^ Th<2 temperature dependence of the critical current density of a superconductor at the operating field is sufficiently linear over the range cf interest that it can be fully represented far our purposes by the intercepts J e o(B) and T = (B). The above can then be cast in the dimensionless form, where J is the current density inside the cable space of the CICC and feu is the fraction of copper in the conductor strands (note that J". E k = 0.63 J far the fractions of steel and insulation assumed).
In this form, the dimensionless stability parameter ^ h has the properties of the coolant factored out, leaving only those parameters describing the conductor and the operating conditions.
Note that the above relation does not contain the resistivity of the copper stabilizer since, to first order at least, the stability margin is observed to be independent of it." Rather, at a given current density, the conductor design offering the maximum stability is established by a trade off between adding more superconductor and adding mors helium. The amount of superconductor of course depends on the amount of copper contained in the conductor strands (for reasons other than direct stabilization). The optimum trade off thus depends an this fraction of capper, as can be seen by examining contours of A h in the (f cundji T(3(.| ) plane. A typical mapping is shown in Fig. 4 with the locus of optimum f = t,r>a for fi^ed fc.-There are Df course limits, to the amount of copper that can be used.
Minimum copper fraction-The processing of NbTi into practical superconducting wire requires a minimum amount of copper to be codrawn with it. The limit is not absolute, but very few manufacturers regularly make good wire with less than 50 "/. copper. We will take this number as a minimum for this study, recognising that other considerations will probably call for higher fractions anyway.
Effect of damage to copper stabilizer-The proposed level of radiation will cause an increase in the residual resistivity of the copper matri:; according to a relation of the following form: . where /3 0 includes the effects of radiation damage.
Limiting current-The limiting current density in a CICC is the value below which full stability is available even with initially stagnant helium inside, 11 and as such may be viewed as a good indicator that heat transfer from the cable to the helium is good, even without being augmented by net flaw. Therefore, choosing a conductor configuration for which the limiting current density Jim exceeds the design value for the cable space current density J amounts to choosing a design that is not limited by heat transfer. Towards the end-of-life, as capper damage accumulates to reduce J un , the lass will be offset by the helium flow already required for heat removal. In Fig. 5, contours of the stability parameter have been overlaid with contours of Jn. = J for both initial and end-of-li-fe stabiliser resistivities. In the present study, we will observe the constraints on conductor configuration (i.e. f" nd and f cu ) due to the former and ignore those due tD the latter.
Protection-There are two major considered when providing for the p event of a quench: maintaining a sa conduit and maintaining a safe maxi conductor. An experimentally based the former depends strongly on dist To facilitate removal of the radiat necessarily be short, and high quen problem. Maximum hot spot temperat and will in fact be the dominant li current density for the present cas consequences that must be rotection of a CICC coil in t!ie fe maximum pressure inside the mum hot spot temperature of the , worst-case prediction shows that ance between flow connections. 113 ion heat loads, that distance will ch pressure should not be a severe ure during a quench is more crucial tnitation on the winding pack e.
The unper limit to the cable space current density in terms of the allowed maximum hot-spot temperature can be determined from the following expression: where Pi and CA are the density and heat capacity, respectively, of a particular component (helium, copper, or NbTi) of the CICC and ^cu is the electrical resistivity of the copper in the conductor. The dump time constant T is given simply by where E. is the stored energy per TF coil, V^ is the dump voltage across the terminals of an individual coil, and l" p is the operating current. Experiments simulating a fully quenched CICC 13 have shown that the initial density of the helium and the constant volume heat capacity of the helium lessentially constant and approximately equal to 3.1 kJ-ffg-**K -1 ) are the appropriate choices for the values in the first term of the above equation (as indicated).
We are free now to make several choices that are important to our estimation of the protection limit tD J. The values we choose for T m »", V.J, and I<, c reflect our personal assessments of the current state-of-the-art and future trends in the technologies impacted by these choices. Selecting T n " x 100 K ensures that differential thermal expansion of the coil components in the event of a quench will be negligible. A maximum coil terminal voltage Vc K 5 kV should be accomodated easily by a CICC design that provides solid insulation devoid of helium between conductor turns. And coil current I =p x 30 fcrt will ease the protection problem without penalizing the design with a too high refrigeration load (in comparison to that from the radiation heating) or an intractably large and di.f f icul t-to-wi nd conductor '.especially if the operating current density can be kept high). These choices are all conservative in that thay can all be pushed higher by innovative development (translate-research dollars', but first let us examine the consequences of these choices. In Fig. 6, the contours of J = J pr at are overlayed on contours of the stability parameter and the other limits already discussed. Ths lower corresponds to undamaged copper (i.e. RRR = 100 and magnetoresistance appropriate to the operating field), the ne>:t corresponds to copper damage of 0,005 dpa (1 fpy operation), and th<? highest to 0.2 dpa (40 fpy). With the design philosophy of selecting the conductor configuration giving the maximum stability consistent wiLh all other limits and constraints, the conductor d&sign proceeds as follows: Select a trial value of J and produce a mapping of the stability parameter such as that in Fig. 6.
Move from the upper rightto the lower left along the locus of optimum f ean4 (increasing stability) until the contour defining some constraint is met. Move down along this constraint contour so long as stability continues to increase or until another constraint is met. Then move down along the newt contour. Eventually, either a maximum available stability or the minimum copp&r fraction will be reached. If the resulting stability margin is higher than needed, a higher value of J can be chosen and the selection process repeated.
This selection process is easy to automate and Figs. 7, S, and 9 show the results of varying the cable space current density J and extracting the corresponding values a-F feu, •?«=""*, and Ah.
The resultant copper -fraction remains acceptable aver the entire range examined. However, each trajectory eventually exceeds the maximum allowed conductor fraction (remember, we had decided to maintain 40 '/. void to alleviate heat removal). And a minimum acceptable stability parameter has also been passed (we have somewhat arbitrarily chosen h = 0.066 corresponding to a stability margin of 300 mJ-cm -3 of conductor).
As might be expected, the trajectory in each case corresponding to the highest copper damage gives the lowest allowable current density. The lowest limit to cable space current density by this design methodology is J = 59 A-mm -3 (J pJ «" w = 37 A-mm -= ) corresponding to the intersection of the limit on f==r.d and the trajectory for a copper damage of 0.2 dpa. It can be seen by inspection that the portion of the trajectcry at the intersection corresponds to points on the boundary for J = Jprec. The same is true far the trajectory far capper damage of 0.005 dpa <but not for the undamaged copper trajectory). Thus we see that for the levels of radiation being examined in this study, the winding pack current density is simultaneously being limited by considerations of heat removal and protection. Stability and minimum copper fraction are not primary constraints. Table 2 lists the important TF coil and conductor characteristics obtained from this study. The following general conclusions can be made:

SUMMARY AND CONCLUSIONS
The fast neutron fluence of 4 >; lO 30 n-crn -31 precludes the use of Nb 3 Sn and other A15 superconductors, and may preclude the consideration of fields much higher than 6 T. At the "6 T" level considered here, accepting 7 mW-crn"" 3 radiation heating appears workable even with NbTi .
A decision to anneal out the copper damage at 1 fpy intervals should allow the pack current density to be about 15 7. higher.
The minimum number of cDils based on acceptable field ripple appears to be IS unless alternate ripple reduction techniques are found.
Even with IS coils, the stored energy per coil, together with the anticipated radiation damage to the copper, makes coil protection a critical issue in setting the winding pack current density. 9             DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or use fulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any spe cific commercial product, process, or service by trade name, trademark, manufac turer, or otherwise does not necessarily constitute or imply its endorsement, recom mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.