scoping studies for net

Nuclear Engineering and Design/Fusion 4 (1987) 247-264 247 North-Holland, Amsterdam

S C O P I N G S T U D I E S F O R N E T

K. B O R R A S S

The NET Team, c/o Max-Planck.lnstitut fl~r Plasmaphysik, D-8046 Garching Fed. Rep. Germany

Received 5 June 1986

Scoping studies for NET using the SUPERCOIL system code are described. Capital cost optimized devices satisfying constraints imposed on stresses/strains, fields, access, etc. are compared. The main objectives are to determine what impact the main design characteristics, performance objectives and underlying plasma physics assumptions have on the parameters and cost of NET. A complete picture for choosing the main parameters of NET is developed and illustrated by the main NET study points used during the conceptual design phase.

I. Introduction

"NET aims to produce a plasma with reactor-like parameters (i.e. full ignition, extended burn pulse and adequate power density) and with machine parameters and a configuration which could be safely extrapolated to DEMO. NET will adopt as far as possible reactor- relevant technologies and be capable of performing engineering testing for the development of the DEMO blanket/f irst wall" [1]. These general objectives are reflected by the following features common to all systems considered in this study:

Design characteristics

single-null/double-null divertor configuration superconducting coils breeding blanket

Objectives

ignition margin >/1 fluence -- 3 MW y m -2 breeding ratio R = 0.8 burn pulse duration (provided inductively) >/200 s

Physics assumptions

plasma safety factor qt = 2.1 average elongation >t 1.6 maximum ripple 1.5%

In this paper we give a review of the scoping studies performed for NET during the period spring 1983 to

spring 1985. During these studies many different aspects were considered, reflecting the ongoing discussions and the progress made in the conceptual design work, but nevertheless the work proceeded in essentially three major phases:

In the first phase the impact of various design characteristics was studied, while the objectives of the machines and the underlying physical assumptions were fixed. The results of this phase are mainly reported in section 2. At the end of this phase a concept for the main design features including the overall system integration concept had evolved which has remained basi- call), unchanged since then.

In the second phase emphasis was placed on the impact of the various performance objectives (fluence, burn time, ignition margin), the main design characteristics and the underlying physical assumptions being kept fixed. These results are reported in section 3.

Int he third phase the impact of different underlying physical assumptions (beta scaling, confinement scaling, q, plasma shape) was studied for now fixed performance objectives and design characteristics.

Such a decoupling of different problem areas re- quires that the results in one area do not critically depend on those specifications kept fixed. That this assumption was indeed justified was not at all obvious at the beginning and its validation is ultimately a result of the whole study. So, for instance, it is by no means clear that the overall system integration (in particular, the sector removal) can be made essentially independent of the underlying physical assumptions.

We proceed in the usual way by specifying reference

0167-899x /87 /$03 .50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publ ishing Division)

248 K. Borrass / Scoping studies for NET

systems which are used as a starting point for the sensitivity studies. All calculations are performed with the SUPERCOIL system code [2]. SUPERCOIL choo- ses from the infinite set of possible designs of a tokamak the one which has prescribed design characteristics and performance parameters and is in addition minimized with respect to cost. When one of the input parameters is changed from its reference value in order to study the sensitivity with respect to this particular parameter, a new optimized system is evaluated for this modified value, the remaining input being kept fixed. We thus compare machines identical in their engineering characteristics and performance parameters except for the one quantity under consideration. The philoso- phy of SUPERCOIL is outlined in ref. [2], and it is supposed that the reader is familiar with it. In this study the main emphasis is placed on single-null divertor configurations.

At the beginning of the NET conceptual design studies a workable reference parameter set was needed in order to serve as a framework for the more detailed engineering design. At that time no detailed component studies had been done and one had to rely to some degree on best guesses for certain data required as input in the system code (blanket thickness and attenuation lengths, for instance). When more detailed information was available, slight iteration proved appropriate. Fur- ther need for the investigation of different study points came from the scoping studies themselves and particularly reflected the evolution in the knowledge of beta limits and confinement in auxiliary-heated tokamaks during the past few years. As a consequence, different reference systems were used in the scoping studies. Even though this inevitably leads to a slight inconsistency of the material, we found it appropriate to present it in its original form. The two main reference systems, which were also the two main NET study points, are described in the Appendix.

A similar problem arises with respect to costing. Costing has been continuously improved during the past two years and, as a consequence, slightly different cost models were used during the scoping studies. As a general rule one can say that in cases where NET-III is used as reference system costing is based on the SCAN 1 cost code [3], representing the best cost basis at present available within the NET team. In all cases where NET-II is the reference system a less evolved cost model was used. Both models agree satisfactorily but generally SCAN 1 predicts a somewhat weaker dependence of cost on machine size.

Uncertainties in costing may affect our conclusions in three different ways: Besides entering directly into

statements on absolute and relative cost, the particular model may influence the choice of the optimized parameter sets. The latter point is discussed in section 5.2 with the main conclusion that, for the class of systems considered in this study, the optimized parameter sets are rather independent of the particular figure of merit. Furthermore, relative costing is in general less critical than absolute costing. In this paper we do not give any absolute cost figures and therefore the details of costing need not be a major concern.

All units are inks units except where otherwise stated. Symbols used in tables are not always explicitly ex- plained. A full description can be found in tables 1 and 2 of the Appendix.

2. Impact of various design characteristics

2.1. Impact of different blanket concepts

A high degree of tritium self-supply is a prerequisite for any high-fluence device. The high tritium breeding ratio required calls for an inboard breeding blanket. A typical example of a machine having an outboard breeding blanket only is INTOR. Table 1 gives a re-evaluation of INTOR II-A [4] by SUPERCOIL (third column). Provision of an inboard blanket in a system which is otherwise specified like INTOR II-A leads to the system NET-I (second column). A modest increase of the linear dimensions relative to INTOR II-A is observed. The shielding effect of the inboard blanket reduces the inboard shield thickness. This partly compensates for the space requirements of the inboard blanket. The direct capital cost increases by roughly 3% over the INTOR value. The situation is even more favourable if the saved tritium cost is also taken into account. The increase of complexity, on the other hand, may very well have an impact on the availability of the system, the estimation of which is, however, beyond the scope of this study.

2.2. The minimum shield concept

The NET scoping studies were strongly guided by the intention of reducing the machine cost at a given performance. Potential to make a machine more compact is offered by the so-called "minimum shield concept", which means that no more shield is placed inside the TF coil bore than is actually needed for the protec- tion of the coils. It differs from the approach (e.g. INTOR), where additional outboard and penetration shields (0.55 m and 0.25 m, respectively, in INTOR) are provided in order to allow "hands-on operation" 24 h after shut-down.

K. Borrass / Scoping studies for NET 249

Table 1 Selective list of data for the NET-II, NET-I and INTOR II-A systems. The INTOR data were obtained by modelling INTOR II-A with the SUPERCOIL code.

NET-II NET-I INTOR II-A

a (m) 1.34 1.25 1.2 plasma minor radius R 0 (m) 5.18 5.36 5.19 plasma major radius B t (T) 4.88 5.35 5.50 field on axis Ip (MA) 7.15 6.59 6.46 plasma current

d (m) 0.8 1.5 1.5 axial access gap g (m) 0.19 0.26 0.31 empty vertical space A R (m) 0.33 0.57 0.72 empty radial space ( (%) 1.50 1.49 1.18 field ripple at boundary N 16 12 12 number of TF coils

B m (T) 10.1 10.7 10.7 maximum toroidal field R l (m) 2.19 2.30 2.27 TF coil inboard leg radius R 2 (m) 8.60 9.64 9.59 TF coil outboard leg radius A (m) 0.629 0.784 0.791 TF coil radial thickness E m GJ 18.8 30.3 30.0 stored magnetic energy j (MA/m 2) 15.5 13.2 13.2 TF coil current density

DBS 1 (m) 0.25 0.25 0.0 inboard blanket thickness DBs 2 (m) 0.50 0.50 0.50 outboard blanket thickness D (m) 0.536 0.620 0.775 inboard shield thickness D z (m) 0.387 1.02 1.03 outboard shield thickness D D (m) 0.496 0.715 0.706 penetration shield thickness Win t (MWy/m 2) 2.0 6.5 6.5 neutron fluence

(/)c / q~Nzr-x 0.69 1. relative capital cost

With in the frame of a model for beta and confinement the p lasma dimensions are essentially de termined by the p lasma performance objectives. Given these, the posi t ion of the o u t e r c o i l legs and hence the overall

~ - - ~ - - . . ~ vertical build / ~ up constraint

| ~ \ v v / ~ Y / ; - ~ . ~ \ \ \ r a d i a l build ~ : ' ~ L L ~ _ _ _ a ~ I ~ u P constraint

~ . ~ ~ . maintenance ~ c o n s t r o i n t

access constraint Fig. 1. Schematic illustration of the peripheral constraints (here

for a segmentation which is N times).

machine size are then mainly determined by the most severe of the following five constraints ("per iphera l constraints" , see fig. 1):

(i) Ripple const ra int (ii) Access condi t ion (characterized by a min imum

value of the axial bore of a penetra t ion hole for heating, refuelling, etc.)

(iii) Sector removal condi t ion (characterized by the re- qui rement that a torus segment can be moved through two adjacent coils)

(iv) Radial bui ld-up constra int (v) Vertical bui ld-up constraint .

Clearly, the omission of the addi t ional shield relaxes the radial build-up and access constraints, but it is not clear whether the other three constraints allow full use to be made of this relaxation. The S U P E R C O I L results on this point can be summarized as follows:

The space that is gained compared to the I N T O R approach by the ommission of the extra shield can be fully used to reduce the machine size, provided that

(i) the coil number is allowed to increase to 16, (ii) the min imum value allowed for the axial width of a

penet ra t ion hole is 0.8 m,


z ~ c= z ~ ,=,~ ,=,,- '===~ ~ .=...=.. i = ~ . . . . == .==.e ~ z = = ~ g_. ~ ~ ~ ~ 9 -

I:':". ::):!

me.t,1 " : R1 = Z.lgl u = 0.15 (SAPS)

RO • 5.179

Fig. 2. Radial build-up of the NET-II system.

been essentially confirmed for all NET study points considered so far. In particular, the radial and vertical build-up constraints are always nearly met, while the sector removal condition slightly dominates. No further increase of the coil number is required in order to meet the ripple condition. The access condition, of course, is relaxed if one goes to larger machines such as NET-Ill.

The minimum shield concept does not exclude "hands-on operation" in principle. Additional shield can be placed outside the TF coils, allowing "hands-on operation" in the whole torus hall except on the TF coil outboard legs. Whether this is really a restriction is not obvious in the light of the fact that the TF coil inboard legs are inaccessible to "hands-on operation" anyway.

(iii) the segmentation is at least 2 N times (at least 2 torus segments per coil).

The impact of the minimum shield concept is illustrated by columns 1 and 2 of table 1. NET-II and NET-I are specified in exactly the same way except that the minimum shield concept was applied for NET-II while the INTOR concept was applied for NET-I.

As expected the plasma major radius remains practically unaffected, while the outboard (centre line) coil radius R 2 is reduced by 1 m. This is the net effect of various changes in the radial build-up as is illustrated by figs. 2 and 3. The capital cost reduction is close to 30%.

More detailed inspection shows that NET-II is sin- gular in the sense that all peripheral constraints are nearly met. A further reduction of R 2 would require the simultaneous relaxation of all peripheral constraints, which, apart from minor corrections, is inconceivable. In this sense NET-II is, within the class of systems under consideration, the most compact machine to meet the underlying plasma performance objectives and design characteristics. It is pointed out that this result has

. . . . . . . c ~ "

I . . . . . . . . . I I i:: : : " . ; : ' : ' . i ~i" "~;;'::

R1,Z.Z97 u • 015 (GAPS)

RQ,S,3S7

RZ • 9,54~

Fig. 3. Radial build-up of the NET-Ill system.

3. Impact of performance objectives

3.1. Variation of the fluence

No definite figure for the necessary and desirable fluence can be given at presented and the reference values suffer from a certain arbitrariness. Fig. 4 shows the relative direct capital cost versus fluence, with NET- III taken as the reference system. The sensitivity is rather weak. Even though the analysis is limited to the impact of the shield thickness variation and does not include other aspects such as breeding requirements, availability, reliability etc., it indicates that there is some room for flexibility in the fluence design value.

3.2. Variation of the OH flux swing

The required flux swing V~ determines the size of the OH transformer (core constraint). In the code we use

1.0S -

1.

0.95

0.90

01.1 0.2 d.s 1 2 ; ;0. Wint I M W ¥ 1 m 2 ]

Fig. 4. Normal ized capital cost versus fluence. N E T - I I I is taken as the reference system.


the normalized flux f = Vs//LpIp. In the case of inductive current drive a value f > 1 is required to compensate for the restrictive flux consumption during start-up and burn. For the burning plasma Lp /Rp- - 103 s holds and thus any increase of f by 0.1 would enhance the burn time % by = 100 s. Considering, on the other hand, non-inductive current drive, f can be reduced and one even has f = 0 if the current is built up and maintained entirely noninductively. The sensitivity to variations of f is thus related to the following two questions: (i) What is the impact of an increase of r b in the case

of inductive current drive? (i.i) What is gained in terms of size and cost if the core

constraint is relaxed by non-inductive current drive? Any increase of Cb relaxes the fatigue problem.

Inclusion of this effect is at present beyond the scope of the model. In the case of RF current drive additional equipment may be required. Its possible cost impact is also ignored here. Finally, any increase of cb over its reference value would increase the duty cycle.

Fig. 5 shows the normalized (to the reference system value) capital cost versus the normalized flux f. NET-III is taken as reference system. An increase of f from 1.75 to 2.75, corresponding to an increase of % of approximately 1000 s, enhances the direct capital cost by about 10%. If f decreases, ~ e / ~ ° (0 indicates reference system values) smoothly saturates to a limit which is reached when f = 1.75 holds. The reference value of f = 1.7 was chosen to be close to this threshold. For values of f below this limit the core constraint is no longer effective and the device parameters become independent of f. The resulting system represents a "real" optimum in the sense that it is unconstraint from further shiqnking. (See also the discussion at the end of section 5.2.) For values of f above the threshold the core constraint becomes effective and any increase of f

I

, ad

1.l-

1.1 ]

tll-

0.9i

0B-

0.7

J

is i ;s i s 1 Fig. 5. Normalized capital cost versus normalized volt-seconds

f. NET-III is taken as the reference system.

leads to an increase of the overall machine size. The relatively weak dependence on f in the right branch of fig. 5 is related to the following phenomena: Decreasing f , for instance, relaxes the core constraint. This leads to a lower aspect ratio. A decreasing aspect ratio enhances, for a given field on axis, the field B m at the coils as well as the ratio R 2 / R 1. Both effects enhance the tensile stress in the TF coil. In a system which is tensile stress limited this has to balanced by an increase of the coil thickness, which in turn counteracts the beneficial effect of the aspect ratio reduction.

3.3. Variation of the ignition margin

For a next-generation device a sufficient ignition margin is one of the main performance objectives and hence the sensitivity with rpsect to variations of the ignition margin should be considered in this section. It is found, however, that information on this subject is a natural by-product of the analysis of section 4. We therefore refer to this section, in particular to subsection 4.1.

4. Impact of physical assumptions

4.1. Impact of the assumptions on beta and confinement

4.1.1. Impact of various models for beta and confinement on the parameters and cost of NET-H

Physical assumptions in the evaluation of next-generation devices enter mainly via the models for confinement and critical beta. The following models are compared here: (for a discussion of the various models see ref. [5] and the literature cited there, notations see below.) Confinement:

INTOR-ALCATOR: ~'E = 5.0 X lO-Zl~ea2S, (1)

a version of

NEO ALCATOR: T E = 7.0 x lO-22~eaR2oql/2sl/2, (2)

ASDEX H-MODE: ~'E = 1.67 × lO-7Ips 1/2. (3)

Beta:

Ip[MA] = g aB----S-' (4)

INTOR:g = 5.8, (5)

TROYON: g = 2.9. (6)


In eqs. (1) to (6) ~'E is the total energy confinement time, ~e is the line average electron density, a is the plasma minor radius, R 0 is the plasma major radius, lp is the plasma current, ql is the current safety factor (see eq. (14) below), s is the elongation and B t is the field on axis.

It is not claimed that any of the confinement models might actually apply to next-generation devices. They exhibit, however, a representative spectrum of different scaling characteristics and absolute values for ~'E.

The type of scaling assumed for fit is now generally accepted and is supported by ideal MHD theory and experiment [5]. The two values for the coefficient represent the previous optimistic assumptions made for IN- TOR and the more pessimistic current theoretical pre- dictions (Troyon).

The assumptions on confinement and beta mainly influence the ignition capability and wall load. The ignition margin C ( = a-heating during burn/ideal losses (i.e. without additional los channels for burn control)) is used to characterize the ignition capability. We further confine ourselves to systems for which the neutron wall load Nn does not exceed a certain minimum value N rain (somewhat arbitrarily = 1 M W / m 2 in the following).

When comparing the different models we want to distinguish, if possible, between the impact of the difference in scaling on the one hand and the impact of the different absolute values of *E and fit on the other hand. To this end we vary the ignition margin for all combinations of models enlisted above. One would ex- pect that the whole series of parameter sets generated in this way is essentially determined by the type of scaling of r E and fit, while the position of a particular system within the series is determined by the absolute values of 'r E and fit.

Tables 2 to 7 give the result. The system NET-II (having an ignition margin of C = 1.25 for INTOR-ALCATOR confinement and INTOR beta assumptions (see table 1)) is taken as reference system. Clearly, the system size increases with the ignition margin.

In order to make the impact of different scaling more obvious we use the representation given in figs. 6 to 8. They represent part of the information contained in tables 2 to 4 in that a selective set of parameters is given versus Ip (the choice of the plasma current as label being arbitrary). The solid lines giving a (plasma minor radius), A (plasma aspect ratio), B t (field on axis) and R 2 (outer coil radius) are of particular impor- tance. These quantities, together with Iv or equivalently qi, essentially characterize (within the frame of the other specifications of the machine) the whole tokamak system and therefore all major components of the device. Figs. 6 to 8 show that the pattern given by the solid lines is the same, irrespective of the underlying scaling law. We mention without explicit demonstration that this also remains valid for the Troyon beta model.

This result, if generalized, can be stated as follows: For given qI ("current q"), plasma shape and engineering specifications there exists a "Universal Series" of parameter sets which can be labelled by a single parameter such as Ip or a. Though individual sets correspond in general to different plasma performance (C) if different physical assumptions axe made, the whole series is the same, irrespective of the underlying physical models. Another way of saying this is that the sets under consideration are, except for this one degree of freedom, completely determined by qi, the plasma and engineer- hag constraints.

It is useful to put into a more explicit form the

Table 2 NET-II parameters versus ignition margin C; ~E: INTOR-ALCATOR, fit: INTOR.

C 1.~ 1.25 2.~ 3.~ 4.~ 5.~

a (m) 1.29 1.33 1.43 1.53 1.61 1.69 R 0 (m) 4.98 5.16 5.59 6.04 6.39 6.71 A 3.85 3.86 3.91 3.95 3.96 3.98 B t (T) 4.68 4.97 5.34 5.74 6.02 (~.23 fit (%) 6.23 6.21 6.14 6.08 6.06 6.04 Ip (MA) 6.67 7.15 8.28 9.43 10.4 11.2

N 16 16 16 16 16 16 Brn (T) 9.92 10.1 10.6 10.9 11.2 11.3 R 2 (m) 8.43 8.60 9.23 9.90 10.43 10.91

Pf (MW) 473 612 1061 1718 2427 3184 N n (MW/m 2) 1.00 1.22 1.83 2.58 3.28 3.93

K. Borrass / Scoping studies for NET

Table 3 NET-II parameters versus ignition margin C; "rE: NEO-ALCATOR, fit: INTOR.

253

C 4.25 5.00 10 15 20 25

a (m) 1.32 1.31 1.44 1.53 1.60 1.66 R o (m) 5.04 5.12 5.67 6.05 6.35 6.60 A 3.83 3.91 3.94 3.95 3.96 3.97 B t (T) 4.70 4.92 5.45 5.75 5.98 6.16 fit (70) 6.27 6.14 6.09 6.08 6.06 6.04 Ip (MA) 6.85 6.98 8.44 9.47 10.3 10.9

N 16 16 16 16 16 16 B m (T) 9.93 10.2 10.7 10.9 11.1 11.3 R 2 (m) 8.48 8.58 9.35 9.92 10.37 10.74 "

Pr (MW) 508 586 1165 1745 2318 2888 N, ( M W / m ~) 1.05 1.19 1.97 2.61 3.17 3.68

Table 4 NET-II parameters versus ignition margin C; 're: ASDEX, fit: INTOR.

C 1.00 1.25 1.50 1.75 2.00

a (m) 1.36 1.43 1.51 1.57 1.63 R o (m) 5.28 5.61 5.93 6.20 6.48 A 3.89 3.93 3.93 3.96 3.96 B t (T) 5.06 5.40 5.63 5.88 6.06 fit (%) 6.16 6.10 6.10 6.06 6.06 lp (MA) 7.47 8.30 9.15 9.85 10.6

N 16 16 16 16 16 B m (T) 10.3 10.6 10.8 11.1 11.2 R 2 (m) 8.77 9.27 9.74 10.14 10.55

Pr (MW) 735 1094 1531 2023 2599 N, ( M W / m 2) 1.41 1.88 2.37 2.90 3.42

Table 5 NET-II parameters versus ignition margin C; rE: INTOR-AL- CATOR, fit: TROYON.

Table 6 NET-II parameters versus ignition margin C; rE: NEO AL- CATOR, fit: TROYON.

a (m) 1.72 1.76 1.86 a (m) 1.71 1.83 1.67 R o (m) 6.86 7.08 7.54 Ro (m) 6.87 7.34 7.93 A 3.99 4.01 4.02 A 4.01 4.02 4.05 B t (T) 6.33 6.49 6.77 Bt (T) 6.39 6.65 7.00 fit (%) 2.93 2.92 2.91 fit (%) 2.92 2.91 2.89 I v (MA) 11.5 12.1 13.4 Ip (MA) 11.6 12.8 14.3

N 16 16 16 N 16 16 16 B m (T) 11.4 11.5 11.8 B m (T) 11.5 11.7 12.0 R z (m) 11.25 11.46 12.15 R2 (m) 11.15 11.86 12.74

Pr (MW) 846 1007 1431 Pf (MW) 8.65 1237 1837 N n ( M W / m 2) 1.01 1.13 1.43 N, ( M W / m 2) 1.03 1.29 1.67

C 1.3 1.5 2.0 C 7.00 I0.0 15.0


Table 7 NET-II parameters versus ignition margin C; "rE: ASDEX, fit: TROYON.

C 1.15 1.25 1.5

a (m) 1.72 1.75 1.87 R o (m) 6.83 7.04 7.50 A 3.98 4.02 4.02 B, (T) 6.33 6.49 6.76 #, (%) 2.94 2.91 2.91 lp (MA) 11.5 12.0 13.3

N 16 16 16 B m (T) 11.4 11.6 11.8 R 2 (m) 11.09 11.41 12.10

Pf (MW) 842 989 1403 N, (MW/m 2 ) 1.00 1.12 1.41

2 - A

A Bt Rz C T] [ml

! 5 -

& - 8 - -

- - Z O -

- 1 4 -

7 -

1 5 -

- 1 7 -

5- 6- -

- io- IO-

5- - 8 -

5 -

3 - t ,- 5 -

I -

o

1.5 R2

C

| .ooo...ooo°OOO.°*°'***°'°°°°°°°*°°° I I I I I I I I 6 8 10 12

Ip [HAl

Fig. 6. a, A, B,, R 2 , and C versus Ip for the series of parameter sets generated by variation of C. INTOR-Alcator confinement and the INTOR beta model are used. NET-II is

taken as the reference system.

0 A B t R z [m] [T] [m]

1.5

I -

2 - 4 - 8 - -

- 14-

7 -

- 12-

. 5 - 6 - -

- I0-

5 -

8 -

3 - 4 - 6 -

25-

?0-

15-

iO-

5 -

I -

;C / /

j l - - - - - - j - / ' A /

/ 1 /

/ / Q

Rz

/ /

/ /

I I I ,I I I I I 6 8 I0 IZ

Ip[MA]

Fig. 7. a, A, B t , R 2 , and C versus I v for the series of parameter sets generated by variation of C. NEO-Alcator confinement and the INTOR beta model are used. NET-II is


correlation existing between the key parameters a, A, B,, ql and R 2 within the "Universa l Series". Taking a as the independent variable, we then have

ql = constl ( = 2.1) (7)

by definition. F rom tables 2 to 7 we also find that the following relations are approximately fulfilled within

the "Universa l Series":

A C a ) = const 2 , (8)

R o ( a ) - const3, (9)

and

R 2 ( a ) - R o ( , , ) R 2 ( a ) = const4, (10)

where const 2 -- 3.9, const 3 = 0.95 and const 4 = 0.39. These relations are useful for drawing certain general


o

[ml

2-

1.5

A t I R z ] [T] [m]

ZS-

4- e--I -t

20-

it,-q 7.,~

15-

5- 6-~

10-4 I0-

5- 8 -

5-

3- I,- 6-

i

A

Q

RZ

...................... C

I I I I I I I I 6 8 I0 IZ

lp [HA]

Fig. 8. a, A, B t, R2, and C versus lp for the series of parameter sets generated by variation of C. ASDEX H-mode confinement and the INTOR beta model are used. NET-II is


conclusions but they are rather crude approximations and at present purely plienomenological.

4.1.2. Evaluation of the "Universal Series" for NET-I l l We now also give an evaluation of the "Universal

Series" defined by the reference system NET- I l l (see the Appendix). Table 8 gives the results. One again finds that eqs. (8), (9), (10) are satisfied, but with const 2 = 3.9, const 3 = 0.87 and const 4 = 0.4. These values are again found to be insensitive to changes of the underlying scaling laws. Since NET-II and NET-I l l have equal ql and similar plasma shape, the slight difference to those of section 4.1.1 is indicative of the impact of the different design characteristics of the two reference systems (blanket thickness, fluence, central support cylinder).

4.2. Impact of q I and plasma shape

In the preceding section the "Universal Series" of parameter sets was identified and shown to be independent of the underlying scaling laws for I" E and fit- In these studies q and the plasma-shaping parameters were kept fixed and the question arises how the "Universal Series" is affected by these parameters.

The question of the inipact of q and the plasma shape has gained additional significance through the present situation with respect to critical beta and confinement. At present best guesses of the maximum beta in a tokamak predict a scaling according to eq. (4) with g = 3.5 ("experimental l imit" [5]). Compared with previous assumptions ( INTOR g = 5.8), this constitutes a considerable deterioration. The favourable scaling of fl with Ip has led to the speculation that the overall impact of this deterioration may be overcome by going to lower q a n d / o r higher plasma elongation. This idea gains further weight by the observation that one also has I" E - Ip in non-ohmic discharges.

Table 8 NET-Ill parameters versus ignition margin C; rE: ASDEX H-mode (Gruber), fit: experim, limit.

C 1.5 2.0 2.5 3.2 4.0 5.0

a (m) 1.45 1.49 1.57 1.65 1.76 1.88 R 0 (m) 5.64 5.91 6.18 6.50 6.87 7.30 A 3.88 3.95 3.94 3.92 3.91 3.89 B t (T) 4.83 5.26 5.48 5.73 5.92 6.11 fit (7o) 3.84 3.76 3.77 3.79 3.81 3.82 Ip (MA) 7.71 8.45 9.27 10.3 11.3 12.5

N 16 16 16 16 16 16 B m (T) 11.0 11.5 11.6 11.9 11.9 12.0 R 2 (m) 9.49 9.85 10.3 10.8 11.4 12.1

Pt (MW) 260 387 529 748 1026 1409 Nn (MW/m 2) 0.42 0.59 0.73 0.94 1.16 1.41 ~c/~e ° 0.72 0.81 0.89 1.0 1.13 1.28


In what follows, the impact of variation of q and elongation s on the parameters and cost of N E T is studied and compared with the impact of a variation of g in eq. (4). The reference system NET- I l l is used for this study. In agreement with the Appendix, the beta model is one given by eq. (4) with g = 3.5 and the ASDEX H-mode type scaling as proposed by Gruber

[51

"rE= Clp[MA]R o (11)

with c = 0.103 is adopted for confinement. It is representative of a variety of confinement models showing beneficial scaling with Ip and size but no deterioration with injected power and differs from the one used in section 4.1.1 essentially through the assumed R 0 dependence.

As far as the variation of q is concerned, one has to take into account the well-known operational limit

% >~ 2, (12)

where

1 dlB, (13) q~ = ~ ~ RBp

is the usual M H D q. If q is prescribed, eq. (13) constitutes a constraint which depends on the details of the equilibrium and is difficult to give in explicit form, as is desirable for use in a system code. Furthermore, in the case of divertor configurations, this being the case of prime interest at present, Bp vanishes at the stagna- tion point and % ( a ) is no longer defined at all. In order to overcome this difficulty, we use the usual current q (if not otherwise stated it is always the boundary value that is meant):

1 Bt ~ d l p 2'n" Bta 2 K 2 (14)

PO IpRo ' ql = 2,n" R o ~ d l p B p

where

~ dlp

K= 2 ¢r-----a" (15)

is a purely geometrical quantity. We approximate the upper / lower plasma shape by an ellipse having elongation sl/2 and triangularity Yl/2, respectively:

R l l 2 = R o + a cos(O + Yl/2 sin v~), (16)

Z1/2 = sl/2a sin #. (17)

Generally one has ql < %, the ratio % / q l depending on the shaping parameters sl, s2, Yl, "Y2, the poloidal fl and profiles. Though ql is well defined in all cases and relatively easy to handle, the connection with the constraint eq. (12) is somewhat vague. For our purpose it is, however, sufficient to know that in a limiter configuration having the mean shaping parameters of the reference system, % = 2 corresponds roughly to qt --" 1.5. To take into account the condition eq. (12), we therefore confine the range of varaitin of ql to q~ >/1.5.

4.2.1. lmpact of ql on the parameters of NET-111 Table 9 gives the key parameters of the three systems

having ql = 1.5 (extreme lower end), qt = 2.1 (reference case) and qx = 2.9 (extreme upper end) to illustrate the impact of variation of q on the parameters of NET. All three systems show the main features of the universal series for NET- I l l in that eqs. (8) to (10) are approximately fulfilled with the constants of section 4.1.2. Thus the correlation between a, A, B, and R 2 existing within the "Universa l Series" is insensitive to qv

4.2.2. Impact of q l, g and C on the cost of NET-I I I We now consider for a fixed plasma configuration

the impact of q~ on cost and compare it with the impact of g and C.

Fig. 9 gives the normalized capital cost 4~c/4) ° versus g/gO, C / C o and q l /q ° (0 indicates reference system values). An increase of g from 3.5 (experimental limit to 5.8 ( INTOR) results in a cost reduction of roughly 15%. The same reduction could be obtained by going from q~ = 2.1 to 1.7, the latter value corresponding to approximately % = 2.2 for the shaping parameters of the reference system (kept fixed here). The value ql = 1.7

Table 9 NET-Ill parameters versus qt

ql 1.5 2.1 2.9

a (m) 1.52 1.65 1.98 R 0 (m) 6.11 6.50 7.76 A 4.01 3.92 3.91 B t (T) 4.88 5.73 6.29 /3 t (%) 5.19 3.79 2.76 Ip (MA) 11.0 10.3 9.83

N 16 16 16 B m (T) 10.3 11.9 12.0 R 2 (m) 10.1 10.8 12.7

V s (Vs) 285 280 319 N, (MW/m z) 0.85 0.94 0.88 ~c/e~ ° 0.84 1.0 1.22


1.6-

1.4

1.2

1.0'

0 . 8 -

0 . 6

(I) c

E

ql

X

I I I I I I I 0.2 0.6 1.0 1.4

I I I I 1.0 2.0 3.2 4.0

I I I =- 1 . 8

c., g ql ) p---

so 60 [

I I I I I I 5.8 4.6 4 3.5 2.9 2.5

INTOR Fxp. l imit Troyon f I I I r I I r

1.5 1.7 1.9 2.1 23 25 2.7 29 ql

Fig. 9. Normalized capital cost ff~c/ff~ ° of NET-III versus C, g and ql-

would probably constitute the extreme end of low q operation.

Fig. 9 indicates that ~c depends approximately on C, g and ql through the combination Cg-lq~. This is even more true of the machine parameters, as is ex- hibited by table 10, where the main parameters of three systems having equal Cg-lq 2, but different C, g and

q~, are given. This becomes plausible if one takes into account that the ignition condition for the scaling laws, eqs. (4) and (11), has the form

cg-lq~ KaB4a2 A (18)

Table 10 NET-III parameters for different C, g and ql at fixed Cg- Iq~

g = 5.8 C = 2 q, = 1.63

a (m) 1.49 1.49 1.55 R o (m) 5.83 5.90 6.19 A 3.91 3.95 3.99 B t (T) 5.17 5.26 5.08 /~, (%) 6.31 3.76 4.80 lp (MA) 8.42 8.45 10.8

N 16 16 16 B m (T) 11.5 11.5 10.7 R 2 (m) 9.76 9.85 10.2

258 K. Borrass / Scoping studies for N E T

C, g and q~ affect the system not only via the ignition condition but also via the required OH flux (q~), the cost of the PF system (ql) and the cost for heating and tritium handling, both of which are related to the a-par- ticle power (g, C). A more detailed inspection, however, shows that these dependences are weak.

This result can be extended to other physical assumptions. In the case of I N T O R - A L C A T O R confinement one has, for instance, instead of eq. (18)

Cg-2q~ K6B: a2 A2 (19)

The impact of g is now stronger and a reduction of qx from 2.1 to 1.3 would be required in order to compensate for the deterioration of beta from g = 5.8 to g = 3.5. This estimation is confirmed by explicit code calculations.

Using A = const, and B ° t / R o = const., one obtains from eqs. (18) and (19)

C g - l q 2 - a 5, (20)

and

Cg-2q~ - a 6, (21)

respectively. An immediate consequence of eqs. (20) and (21) and the above remarks is that it is also true that the capital cost, for fixed ~, is determined by a. As the capital cost depends much more weakly on a than a 6, this explains why the impact of Cg-2q~ on cost is comparatively weak.

With eq. (9) we obtain for the critical density pre- dicted by the Hugill limit [5]

n H - 1 / q ~ . (22)

Assuming a constant burn temperature, we obtain for the working density at the critical beta

Bt 2 a 2 C°4g°-._...~ 6 n~ - f l tB 2 - g q-T - g ql qO.2 ' (23)

where we assume fixed shape and use eqs. (8) and (9) and eq. (20). Thus we have

q0.2

ni l~he q~g O.6cO. 4 . (24)

In the reference system NET-I I I we have n H / n ~ = 0.5 if q~, is used in the Hugill limit expression. Eq. (24) indicates that the impact of g is relatively weak. The beneficial q dependence could be taken as an additional argument for low q operation.

4.2.3. Impact o f p lasma shape As far as the impact of the plasma shape is con-

cerned, the main interest is quantification of the benefit from increased elongation. In the reference system we have a single-null configuration with an upper / lower elongation of 1.4/1.9 (in S U P E R C O I L a single null is always assumed to be situated in the lower half), corresponding to a mean value of 1.65. A specific situation is given by the fact that an increase of the mean value naturally leads to double-null configurations. Because of this jump of the configuration it is more appropriate to consider distinct cases instead of doing a continuous parameter variation. Three u p / d o w n symmetr ic double-null configurations with s 2 = s~ = 1.9, 2.0 and 2.1 are considered and compared with the reference system.

The type of plasma configuration is strongly corre- lated with other design characteristics, in particular the blanket concept and sector removal concep t . We assume that the blanket and sector removal specified for the reference system (tubular blanket concept, one inboard, two outboard modules per coil, axial thickness ratio of two neighbouring outboard sectors 0.6/0.4, oblique removal) can be adopted here. This implies the assumption that in the double-null configuration the second chamber need not be pumped. Any blanket configuration allowing pumping of both chambers is likely to be much less favourable. In this sense our calculations are an optimistic estimation of the benefit of increased elongation.

Table 11 NET-Ill parameters versus elongation (double-null configurations; s l = s 2 = s ) . ~¢/~0 ° is the capital cost normalized to NET-III. The bracket values are lowercost estimates of extra- elongated coil shape solutions, also normalized to NET-III.

s 1.9 2.0 2.1

a (m) 1.60 1.65 1.37 R o (m) 6.42 6.41 6.14 A 4.00 3.89 4.48 B t (T) 5.52 5.14 5.84 fit (%) 3.75 4.07 3.72 lp (MA) 11.3 12.1 10.6

N 16 16 16 B m (T) 11.4 10.8 11.7 R 2 (m) 10.6 10.8 10.4

A R (m) 0.44 0.66 0.66

~ c / ~ ° 0.98 0.95 0.92 [0.981 [0.951 [0.88]


The elongation s is treated as the only independent shaping parameter. For a given value of s the triangu- laxity is essentially determined by the requirement of minimum ampere-turns in the PF coils and vertical stability considerations. It has to be rather high in highly elongated systems. A value of y~ = Tz = 0.5, based on a preliminary analysis, was taken in all three cases.

In table 11 the key parameters for the three cases s = 1.9, 2.0 and 2.1 are given. The first system fits well into the conditions of the universal series. For the more elongated cases, A, Bt /R o and (R E - R 0 ) / R 2 differ somewhat more from, respectively, const2, const 3 and const4, given in the previous section. This can be attri- buted to the fact that for s/> 2 the position of the outer coil leg is determined by the vertical build-up constraint. For smaller elongations the sector removal condition or the radial build-up constraint axe dominant. It is pointed out that the cost minimum is very flat around the third case with respect to variation of the aspect ratio. The case with A = 4 would thus practically constitute an equivalent solution.

In table 11 we also give the normalized capital cost for the three cases under discussion. Even for s = 2.1 the cost benefit is less than 10~. Up to s = 1.9 there is no gain at all, since the benefit from the improved plasma performance is compensated by the detrimental effect of the additional space needed for the second divertor chamber.

At present the treatment of highly elongated systems is hampered by the fact that SUPERCOIL is limited to pure-tension D-shaped coils. In cases where the radial build-up constraint is effective one might try to go to more strongly elongated coils in order to avoid empty space in the outboard region of the machine. Even though this case cannot be treated in a proper way we can given a lower cost estimate for such a solution, which is obtained by ignoring the vertical build-up constraint in SUPERCOIL. The corresponding values are given in brackets in table 11. As can be seen, the beneficial impact of extra coil elongation is moderate.

5. Misce l laneous topics

5.1. Sensitivity to deviations from the optimum

Within the SUPERCOIL code a unique solution of the model equations is obtained by requiring that a figure of merit, typically the cost, be minimized. In this section we study the vicinity of the optimum. We are particularly interested in specifying the range within which the cost of the system is not significantly en-

hanced over its minimum value. If this region of approximately cost equivalent systems is not too small one has the possibility to take into account additional requirements which are qualitative or difficult to quantify, without having to pay for it.

In order to obtain non-fully-optimized solutions, we can specify at least one of the generally self-consistently determined grid parameters (a, A, D, A, Bt, N) ap- pearing in the SUPERCOIL code [2]. The deviations of the cost from the minimum axe the higher the more of these quantities are fixed at a value different from the optimum value. Since we want to confine ourselves to small cost deviations, it suffices to consider situations where only one of these quantities is fixed at a prescribed value, while the others remain self-consistently determined. The role of the shielding thickness D and coil thickness A is in a certain sense trivial. For values lower than the optimum values typically constraints are violated and no solution exists. For values larger than the optimum values the shield and the coils are unneces- sarily thick and the system blows up in a trivial way. As to the remaining free parameters, the situation is greatly simplified in that (as a matter of experience) fixing any of the parameters (a, A, B~) and applying the optimi- zation procedure determines the same hypersurface in the full parameter space. Hence it suffices to study cb versus ouly one of these parameters.

Fig. 10 shows Oc/O ° versus the aspect ratio A, with NET-II taken as reference system. The bends, as ex- hibited in fig. 10, typically occur when one constraint becomes dominant over another one. In our case there is competition between the ripple and the access conditions which repeats periodically with the coil number.

In the range covered by fig. 10 one observes in good

I

1.1-

1.0-

N • 16 N • 16 N • 14 ,U, O

ccess domin, access domin. ' pie domin. ~ ripple domin.

I

0.9 30 31s 41o 41s sio A

Fig. 10. Relative capital cost versus the aspect ratio in the vicinity of the optimum. NET-II is taken as the reference

system.


approximation

Aa °s = const, (25)

and

Bt a = const. (26)

Thus we have low aspect ratio, low field, large minor radius systems at the left, and high aspect ratio, high field, small minor radius systems at the right end of the range considered in fig. 10. Ro is nearly constant. In fig. 10 the (a , R0, Bt) vector is given for two extreme cases.

As was pointed out in section 4.2.2, the Hugill density limit is typically exceeded in the machines under consideration. We now briefly discuss whether the freedom in choosing A can be used to bridge this gap. F rom n e - ~ t B 2 t - B2t/A (note that qi is fixed now), nrt - Bt/Ro and eq. (26) we get

Bt A 1 nH/n e const. (27)

Ro B2t aB t

Changing the machine parameters in the way discussed in this section is thus not a means to relax the density limit problem.

5.2. Impact of the figure of merit on the optimum

In table 12 we give the main parameters of four systems having identical input specifications except that different figures of merit were used for the optimiza- tion. Besides the capital cost ~c, we use the stored TF energy Era, the outboard centre line coil radius R 2 and the " tokamak volume" Vto k (volume of the smallest cylinder enveloping the TF coil system). The latter two parameters can be considered as a measure of the compactness of a tokamak. The reference system (sec-

ond column) is close to but not identical to NET-II . The following observations can be made from table

12: The cost of all four systems is very similar. The differences of the other three figures of meri t ( E m, R 2, Vtok) are more pronounced but still relatively small. While the plasma major radius R 0 is nearly constant, the aspect ratio A (and consequently a) and the field on axis B t vary considerably. One finds that low A, high a is combined with low B t and vice versa. Comparison with section 5.1 indicates that the four systems lie on the hypersurface defined in section 5.1. The particular choice of the figure of merit has thus little impact on the solution, apart from a possible shift in the flat region around the opt imum found in section 5.1. Taking parameter sets in this region as equivalent, one can say that there is practically no impact of the figure of merit on the choice of the optimum. This is of course only true if the figure of merit is reasonable in the sense that pure enlargement of the machine generally leads to an increase of the figure of merit.

Care is also required when extrapolating these observations to devices of different type. In fact, if ~c is the figure of merit a real opt imum exists with parameters close to the reference system even if f = 0 (see section 3.2). The maximum TF field of this solution is close to 12 T. If R 2 or Vto k are the figures of merit, the core constraint or a l imitation of the maximum TF field close to 12 T prevent the system from shrinking. The result of table 12 thus depends on the fact that for the devices under consideration the cost opt imum is close to the boundary in parameter space established by the core constraint a n d / o r a 12 T limit for B m. A different situation would be given in systems without core constraint (non-inductive current drive) and advanced TF magnets (maximum TF field exceeding 12 T). They will be considered in a separate paper [6].

Table 12 Impact of the figure of merit on the optimum

Figure of merit Em q~c R 2 Vtok

a (m) 1.51 1.24 1.00 0.89 A 3.34 3.90 4.73 4.94 R 0 (m) 5.05 4.84 4.78 4.87 B t (T) 4.27 5.09 6.23 6.43 N 18 16 14 14 B m (T) 9.22 11.0 12.4 12.4 •

Em GJ 17.3 19.9 25.6 26.7 ff~c / ff~c ° 1.03 1. 1.08 1.12 R 2 (m) 8.86 8.27 8.11 8.17 ~ok (m 3 ) 2440 2040 1840 1830

plasma minor radius plasma aspect ratio plasma major radius field on axis number of coils maximum toroidal field

stored magnetic energy relative capital cost outer coil radius tokamak volume


6. Summary and discussion

Scoping studies for NET were performed, with particular attention being paid to the impact of various design characteristics and performance objectives on the parameters and cost. The role of physical uncertainties was studied by comparing a variety of underlying physical models.

Combining the minimum shield concept with appropriate solutions for access, sector removal and number of coils greatly reduces the size and cost. An inboard blanket has a relatively mild impact on the size and capital cost.

The well-known result that the machine parameters and capital cost depend very slightly on the fluence was confirmed. There is also a surprisingly weak dependence of capital cost on the normalized volt-seconds f = V J L p l p . This limits the cost benefit of current drive but also offers the possibility of designing the machine with some flexibility in the OH flux. This weak dependence was confirmed in a wide range (0~<f~ 3, the latter value corresponding to %/> 2000 s).

Physical assumptions enter into the evaluation of next-generation tokamaks via the models for confinement and beta, the plasma shape and the value adopted for the safety factor. It was shown that the series of parameter sets which is obtained when a machine is evaluated for different values of the ignition margin, but fixed models for I" E and fit, fixed value for qi and fixed plasma shape, is independent of the underlying scaling relations for ¢ E and fit ("Universal Series"). Thus, irrespective of the scaling adopted, there exists, for given ql and shape, a correlation between the main parameters of a tokamak (a, A, Bt, RE) and a particular set can be labelled by one of these parameters, such as the plasma minor radius a (or any parameter which is a function of these parameters, such as Ip, if ql and plasma shape are fixed). Apart from this one degree of freedom, the sets under discussion are completely determined by engineering constraints, the ql value and the plasma shape. A variation of qx leaves the correlation between a, A, B t and R2 essentially unchanged. Similar insensitivity is observed with respect to a moderate increase of the elongation. In all cases one has A = 4 and Bt , /R o = 1[T/m].

The impact of qi on cost was evaluated and compared with the cost impact of the coefficient g in the beta scaling. The impact of g is weak. A decrease of g from 5.8 (INTOR) to 3.5 (experimental limit) results in a cost increase of about 15~. A decrease of qx from 2.1

(reference value) to 1.7 (corresponding to q~= 2.2) would compensate for this increase, if confinement follows the H-regime scaling, but in the light of the relatively small absolute gain one has to balance carefully the gain against the increased risk of low-q operation.

The cost benefit of increased elongation is limited by the inevitable jump to double-null configurations for average elongations exceeding s ~ 1.8. Up to s ~ 1.9 there is practically no cost reduction, while for s = 2.1 it still remains below 10%. Thus, from the cost point of view, there is no strong incentive to go to lower ql or highly elongated double-null configurations.

With specifications adopted for the shape and q~, only the machine size is still free to be chosen. A number of considerations, contradictory in tendency, are relevant in this context. Among these are:

1. The absolute machine cost. 2. The requirement that on the basis of present best

guesses for ~'E and fit the machine should have sufficient ignition margin and the wall load should be reactor-relevant.

3. The requirement that NET should b e based on physical assumptions which would make extrapo- lation from JET not too large.

The study point NET-III was chosen as being representative of the largest conceivable machine in the light of the enlisted requirements. NET-II, on the other hand, if the same plasma physics assumptions as for NET-I l l are made, is close to marginal ignition and thus estab- lishes a lower limit as far as size is concerned. The potential candidates for NET are thus the devices lying within the "Universal Series" between NET-II and NET-III. As outlined in the study the devices under consideration show, within the frame of the assumptions made, maximum compactness. Nevertheless the detailed design studies have indicated that some space Can be saved as compared with the reference system in the critical inboard region of the machine by being less conservative with respect to, for instance, the thermal insulation thickness, gaps etc. A slight reduction of the ignition margin might also be acceptable. This would then lead to a study point somewhat smaller than NET-Il l . An additional decrease in (radial) machine dimension is obtained by going to highly elongated double-null configurations [7].

A similar analysis has been performed for demonstration (DEMO) and commercial tokamak reactors (FCTR) in Ref. [8]. Despite the considerable extrapola- tion the essential features of NET-like devices are found to be preserved in this parameter range.


Appendix: Description of reference systems

In this Appendix e give a more detailed description of the two study points NET-II and NET-I l l which are used as reference systems in this study. NET-II was the first parameter set studied in detail. It was established before any detailed component studies had started. In- stead of presenting the original NET-II parameter set which was actually used for the scoping studies, we give rather the NET-II.2 parameter set, which evolved by minor iterations of some engineering specifications (blanket and shield attenuation lengths, blanket thick- nesses, no bucking cylinder). The difference between the NET-II and NET-II .2 parameters is small. On the ohter hand the NET-II.2 and NET-III(2) systems have identical engineering specifications and illustrate the impact of the different underlying plasma physics assumptions. We emphasise that for NET-II.2 the INTOR plasma physics assumptions were adopted. NET-II .2 thus il- lustrates the impact of the novel system integration concept and engineering solutions developed for NET. In this paper we do not distinguish between NET-II and NET-II.2.

NET-III was chosen as the second main study point on the basis of the results given in section 4. It was considered as the extreme upper end in the "Universal Series" still representing a realistic possibility. It is consistent with reduced fl limits as found in present experiments and confinement in H-mode type discharges.

Tables A.1 and A.2 give an extensive list of parameters including the main design characteristics and physical assumptions. Note, however, that in this representation we do not distinguish between prescribed input quantities and evaluated parameters.

Table AI: Reference system NET-II

Plasma

Plasma minor radius (a) 1.368 (m) Plasma major radius (R0) 5.194 (m) Plasma aspect ratio (A) 3.798 Upper plasma elongation (s2) 1.400 Lower plasma elongation (s 1) 1.900 Upper triangularity (82) 0.1000 Lower triangularity (St) 0.4000 Field on chamber axis (Bt) 4.932 (T) Plasma current (Ip) 7.548 (MA) Safety factor (current q)

at boundary (ql) 2.100 Toroidal beta (burn, average) (/~) 6.320 (%) Toroidal beta (useful part) (~t) 4.703 (%)

Table A1 (continued)

Poloidal beta (tip) Average ion temperature (T i ) D-T-density (volume average)

(//f) Electron density (volume

average)(~e) Ignition margin (C) Peak (~-power (P,,) Peak fusion power (Pr) mean neutron wall load

(N.) Peak inboard wall load

(equatorial plane) ( Nn 1 ) Peak outboard wall load

(equatorial plane) (N 2) Tritium consumption (to) Neutron fluence ( Win t) Integral burn time (~'tot)

Blanket and shield

2.252 10.00 (keV)

1.321 x10 z° (m -3)

1.454 x 1020 (m -3) 1.250 124.2 (IvlW) 621.1 (MAV)

1.205 (MW/m 2 )

1.225 (MW/m 2)

2.292 (MW/m 2) 8.668×104 (g) 2.996 (MWy/m 2 ) 78.45 x 106 (s)

Inboard blanket thickness (DB1) Inboard blanket inverse attenu-

ation length (hi) Outboard blanket thickness ( D a2) Outboard blanket inverse attenu-

ation length (~, 2 ) Top/bottom blanket thickness (DBt) Inboard shield thickness (D) Outboard shield thickness (Dz) Penetration shield thickness (DD) Shield inverse attenuation length (hs) Vessel thickness (u) Peak ,/-dose rate at TF coils (qy) Peak heat deposition in TF coils (Q n) Peak neutron fluence at TF coils (¢Pn)

Toroidal field system

0.3500 (m)

4.810 (m- 1 ) 0.6500 (m)

4.850 (m- t ) 0.3500 (m) 0.6836 (m) 0.5888 (m) 0.5653 (m) 15.50 (m- l) 0.1200 (m) 1.983 X 108 (rad) 79.37 (W/m 3) 1.983 X 10 zl (n /m 2)

Number of coils (N) Field ripple at plasma boundary

(peak to average) (() maximum field (Bin) Coil radial thickness (A) Coil axial thickness (Ath) Inboard centre line radius (R 1) Outboard centre line radius (R 2) Half vertical bore (h) Stored energy (Era) Average tensile stress (o) Thickness of the coil casing (B) Thermal insulation.thickness (8) Strain in the winding (() Average current density in the

winding (jw) Conductor current (It) Total mass of the TF coils (GT)

i6.00

1.334 (%) 11.53 (T) 0.7203 (m) 0.8671 (m) 1.862 (m) 8.930 (m) 4.976 (m) 25.86 (G J) 179.8 (MPa) 0.5000 x 10 -1 (m) 1.000 x 10- l (m) 11.19X10 -4

16.31 (MA/m 2) 19.21 (k.A) 2.404 × 103 (to)



Poloidal field system and OH system

Current sum of the PF coils (El) 101.9 (MA) Radius weighted current sum (~,RI) 366.3 (MAm) Total weight of PF coils (Gp) 1102. (to) Outer radius of solenoid ( R~H ) 1.452 (m) Thickness of the solenoid (A t) 0.3020 (m) OH-field (Bot.t) 9.215 (T) Winding average current density in

the solenoid (JoH) 24.28 (MA/m 2)

Further specifications

Physics assumptions "r E = 5.0X 10 -21 nea2Seff(S, m -3, m)

1 fit = 0.315 - - A q/serf

Blanket Tubular blanket concept Oblique removal Two sectors per coil;

axial thickness ratio Breeding material Neutron multiplier Structural material Coolant Coolant pressure Coolant temperature (inlet/outlet) Breeding ratio Maximum temperature of structure Maximum temperature of breeder

Shield Inner shield/reflector Outer shield

0.6 : 0.4 17Li83Pb Pb 316 SS H20 8 MPa 240/280°C 1.15 450°C 400°C

90%316SS/10% H20 75% borated 316SS/

25% H20 0.25 m Inner shield thickness

Outer shield thickness (inboard/outboard) 0.43/0.34 m

Toroidal field coils Bath cooling Conductor Nb 3 Sn Stabilizer Cu

Poloidal field coils Conductor NbTi Stabilizer Cu

Table A2: Reference system NET-III

Plasma

Plasma minor radius ( a ) 1.644 (m) Plasma major radius (R0) 6.493 (m)


Plasma aspect ratio (A) Upper plasma elongation (s2) Lower plasma elongation (s D Upper triangularity (82) Lower triangularity (81) Field on chamber axis ( B t ) Plasma current (Ip) Safety factor (current q) at

boundary (ql) Toroidal beta (burn, average) (/~) Toroidal beta (useful part) (~°t) Poloidal beta (tip) Average ion temperature (~) D-T-density (volume average) (~ r) Electron density (volume

average) (ff~) Ignition margin (C) Peak a-power (P,) Peak fusion power (Pt) Mean neutron wall load (N,) Peak inboard wall load

(equatorial plane) (Nn l) Peak outboard wall load

(equatorial plane) (N 2) Tritium consumption (t c ) Neutron fluence ( Win t) Integral burn time (ztot)

Blanket and shield

3.949 1.400 1.900 0.1000 0.4000 5.772 (T) 10.21 (MA)

2.100 3.766 (%) 2.803 (%) 1.451 10.00 (keV) 1.079,1020 (m -3)

1.187 × 1020 (m -3) 3.200 149.6 (MW) 747.8 (MW) 0.9479 (MW/m 2)

0.9576 (MW/m 2)

1.794 (MW/m 2) 13.26;<104 (g) 2.996 (MWy/m 2 ) 99.69 × 106 (s)

Inboard blanket thickness ( Dai ) Inboard blanket inverse attenu-

ation length (~'l) Outboard blanket thickness (DB2) Outboard blanket inverse attenu-

ation length (h 2) Top/bottom blanket thickness (DBt)

Inboard shield thickness (D) Outboard shield thickness (Dz) Penetration shield thickness (Do) Shield inverse attenuation length (hs) Vessel thickness (u) Peak "t-dose rate at TF coils ('/'v) Peak heat deposition in TF coils (Qa) Peak neutron fluence at TF coils (%)

Toroidal field system

0.3500 (m)

4.810 (m- 1) 0.6500 (m)

4.850 (m -1) 0.3500 (m)

0.6832 (m) 0.5884 (m) 0.5410 (m) 15.50 (m- l) 0.1200 (m) 1.995 × 10 s (rad) 62.85 (W/m 3) 1.995 × 1021 (n/m 2)

Number of coils (N) Field ripple at plasma boundary

(peak to average) (c) Maximum field (Bin) Coil radial thickness ( A ) Coil axial thickness (A th) Inboard centre line radius (R 1 ) Outboard centre line radius ( R 2) Half vertical bore (h)

16.00

1.450 (%) 11.92 (T) 0.9232 (m) 1.227 (m) 2.684 (m) 10.80 (m) 5.366 (m)



Stored energy (Era) Average tensile stress (o) Thickness of the coil casing (B) Thermal insulation thickness (8) Strain in the winding (() Average current density in the

winding (jw) Conductor current Ic) Total mass of the TF coils (GT)

Poloidal field system and OH system

52.26 (OJ) 179.9 (MPa) 0.5000 x 10-1 (m) 1 . 0 0 0 X 10 - 1 ( m )

10.92 × 10- 4

12.64 (MA/m 2) 29.33 (kA) 4.627 X 103 (to)

Current sum of the PF coils (]El) Radius weighted current sum (ERI) Total weight of PF coils (Gp) Outer radius of solenoid (R ~3H) Thickness of the solenoid (A t) OH-field ( Boll ) Winding average current density

in the solenoid (JoH)

Further specifications

116.1 (IvL,~) 490.8 (MAm) 1476. (to) 2.172 (m) 0.3873 (m) 9.043 (T)

18.58 (MA/m 2)

Physics assumptions r E = 0.103 .IpR 0 (s, MA, m)

---7--1(2 ql 21r Bla 2 r2 ' K= ~dl flt=O'175Aqt' ~0 lpRo 2*ra

R e f e r e n c e s

[1] R. Toschi, Objectives and features of the Next European Torus Project, 6th Topical Meeting on the Technology of Fusion Energy, San Francisco, 1985.

[2] K. Borrass and M. SiSll, SUPERCOIL: A model for the computational design of tokamaks, Nucl. Engrg. Des./Fu- sion 4 (1986) 21-35.

[3] W.R. Spears, to be published. [4] INTOR, International Tokamak Reactor, Phase IIA, Part

I, IAEA, Vienna 1983, STI/PUP/638 ISBN 92-0-131283-0. [5] INTOR Phase II-A, Second Part, Critical Issues, European

Contributions to the INTOR Phase II-A Workshop, Group F (Physics), Vol. IV.

[6] K. Borrass, Impact of the TF coil performance on cost and compactness of next-generation tokamaks, 14th Sym- posium on Fusion Technology, SOFT, Avignon, 1986, paper G0.04.

[7] Next European Torus, Status Report December 1985, NET Report No. 51.

[8] W.R. Spears, DEMO&FCTR Parameters, NET Report No. 41, EURFU/XII-361/85/41.

Further specifications as for reference system NET-H

scoping studies for net

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