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COIL DESIGN FOR HELIAC, A HELICAL AXIS STELLARATOR
P. Materna, P. Heitzenroeder, K. Lee
To cite this version:
P. Materna, P. Heitzenroeder, K. Lee. COIL DESIGN FOR HELIAC, A HELICAL AXIS STELLARATOR. Journal de Physique Colloques, 1984, 45 (C1), pp.C1-181-C1-184.
�10.1051/jphyscol:1984137�. �jpa-00223692�
JOURNAL DE PHYSIQUE
Colloque C l , suppl6ment a u n o 1, Tome 45, janvier 1984 page C l - 1 8 1
C O I L DESIGN FOR HELIAC, A H E L I C A L A X I S STELLARATOR
P. Materna, P. Heitzenroeder and K.L. Lee
Princeton University, Plasma Physics Laboratory, Princeton, New Jersey 08544, U.S.A.
R6sum6 - On d 6 c r i t un s t e l l a r a t o r 2 a x e h 6 l i c o ? d a l ( H s l i a c ) pour l e c o n f i - nement de plasma B B6ta 6lev6. On p r s s e n t e un p r o j e t p r s l i m i n a i r e e t l ' a n a l y s e des f o r c e s e t c o n t r a i n t e s .
A b s t r a c t - A proposed H e l i c a l A x i s S t e l l a r a t o r ( H e l i a c ) f o r H i g h - B e t a plasma confinement i s d e s c r i b e d . A p r e l i m i n a r y d e s i g n and a n a l y s i s o f l o a d s and s t r e s s e s i s presented.
The h e l i c a l a x i s s t e l l a r a t o r ( H e l i a c ) i s a m a g n e t i c c o n f i g u r a t i o n f o r plasma confinement which o f f e r s t h e p o s s i b i l i t y o f s t a b l e h i g h - b e t a s t e a d y - s t a t e o p e r a t i o n . The plasma has a bean-shaped c r o s s - s e c t i o n w h i c h s p i r a l s as i t goes around t h e major c i r c u m f e r e n c e . The HX-1, a h e l i a c o f 1.5 m m a j o r r a d i u s , i s a proposed embodiment o f t h e c o n f i g u r a t i o n .
The o v e r a l l arrangement o f t h e machine i s shown i n F i g . 1. It c o n t a i n s t o r o i d a l f i e l d (TF) c o i l s , as i n a tokamak, b u t t h e arrangement o f t h e s e c o i l s i s n o t c i r c u l a r l y symmetric. R a t h e r , t h e c e n t e r s o f t h e t o r o i d a l f i e l d c o i l s d e s c r i b e a h e l i x around t h e p o l o i d a l f i e l d (PF) c o r e . I n t h e proposed HX-1, t h e m a j o r c i rcumference around t h e machine c o n t a i n s t h r e e p e r i o d s . The p o l o i d a l f i e l d c o r e i s a c i r c u l a r c o i l which l i n k s t h e t o r o i d a l f i e l d c o i l s . There i s l i t t l e o r no plasma c u r r e n t , b u t a s m a l l o h m i c - h e a t i n g s o l e n o i d i s p r o v i d e d f o r i n i t i a t i o n o f plasma.
F i n a l l y , a u n i f o r m v e r t i c a l f i e l d i s p r o v i d e d by a s e t o f e x t e r n a l c o i l s . I n HX-1, t h e vacuum vessel f o l l o w s a h e l i c a l p a t h t h r o u g h t h e b o r e o f t h e TF c o i l s . I n g e n e r a l , t h e c o i l system i s s i m p l e r t h a n t h a t o f a tokamak w i t h t h e p o s s i b l e e x c e p t i o n o f t h e i n t e r l o c k i n g f e a t u r e o f t h e p o l o i d a l f i e l d core. I n comparison w i t h o t h e r s t e l l a r a t o r s , t h e h e l i a c c o n f i g u r a t i o n can b e produced u s i n g o n l y c i r c u l a r c o i l s , which a r e c o n s i d e r a b l y s i m p l e r t h a n t h e h e l i c a l c o i l s r e q u i r e d by most o t h e r s t e l l a r a t o r s .
The i n t e r a c t i o n o f t h e PF and TF c o i l s i n a H e l i a c produces m a g n e t i c s u r f a c e s w h i c h a r e bean-shaped and w h i c h a l s o have a m a g n e t i c w e l l ( l o c a l minimum i n m a g n e t i c f i e 1 d magnitude) l o c a t e d w i t h i n t h e plasma c r o s s - s e c t i o n . These t w o f e a t u r e s combine t o g i v e a p r e d i c t e d l i m i t o f 10% t o 20% f o r b e t a ( t h e r a t i o o f plasma p r e s s u r e t o magnetic p r e s s u r e ) . T h i s i s s u b s t a n i a l l y l a r g e r t h a n t h e b e t a l i m i t f o r present-day tokamaks and s t e l l a r a t o r s , and would be an i m p o r t a n t advantage t o w a r d a p r a c t i c a l r e a c t o r .
OVERALL PARAMETERS
The major parameters o f t h e proposed HX-1 machine a r e g i v e n i n T a b l e 1. One o f t h e b a s i c assumptions i n t h i s d e s i g n was t h a t t h e machine would use t o r o i d a l f i e l d c o i l s which a l r e a d y e x i s t f r o m an e a r l i e r machine a t t h e P r i n c e t o n Plasma P h y s i c s L a b o r a t o r y . T h e i r i n s i d e r a d i u s i s 0.56 m. The average m a j o r r a d i u s o f HX-l i s 1.47 m, and t h e average t o r o i d a l f i e l d i s 1.1 T. T h i s t o r o i d a l f i e l d i s r e l a t i v e l y low compared t o e x i s t i n g plasma c o n f i n e m e n t e x p e r i m e n t s , b u t i t i s a s s o c i a t e d w i t h t h e goal o f e x p l o r i n g h i g h b e t a plasma regimes. Four d i f f e r e n t c u r r e n t s a r e used i n
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984137
Cl-182 JOURNAL DE PHYSIQUE
F i g . 3 : Loads o n T o r o i d a l F i e l d C o i l s
R A D \ A L e- ; LOADS
TABLE 1: PARAMETERS OF HX-1 OVERALL MACHINE PARAMETERS
Averaae M a i o r Radius l m l -. ~.
~ i n i m i m ~ a j o r ~ a d i u s , ' ~ i a s m a A x i s (m) 1.2025 Maximum M a i o r Radius. Plasma A x i s (m) 1.8377 Aspect ~ a t i o
Average T o r o i d a l F i e l d ( T e s l a ) Number o f F i e l d P e r i o d s
i n M a j o r Circumference 3
Pulse l e n g t h , equiv. square wave ( s e c ) 1.5
R e p e t i t i o n t i m e (sec). 180
TOROIDAL FIELD COILS
I n s i d e Radius o f C o i l ( m e t e r ) 0.56 O u t s i d e Radius o f C o i l ( m e t e r ) 0.725 Number o f C o i l s
Turns p e r C o i l C o i l C u r r e n t s :
11, 18, 19, 116, 117, 124, ( k A ) 37.5 12, 17, 110, 115, 117, 123, (kA) 33.1 13, 16, Ill, 114, 119, 122, (kA) 28.8 14. 15. 112. 113. 120. I 2 1 (kA) 26.9
~ o t a l NI ( ~ e ~ a - ~ m p e r e l i u r n s ) ' ' 7.578 Number o f C o o l a n t P a t h s p e r C o i l 2
Peak Temperature ('C) 85.
POLOIDAL FIELD CORE
M a j o r Radius ( m e t e r ) 1.46875
M i n o r Radius: (main body of t o r u s ) ( m ) 0.305 ( j o i n t r e g i o n s o n l y ) (m) 0.387
Number of Turns 24
C u r r e n t ( K i l o - A m o e r e l 37.5 T o t a l NI ' ( ~ e g a - ~ m p e r i - ~ u r n s ) 0.9
Conductor S i z e 73mm X 16.7 mm
Water h o l e dimensions 15.9 mm X 6.4 mm Number o f C o o l a n t P a t h s 2
Peak Temperature ('C) 42.
OHMIC HEATING COILS
: T o t a l Turns: 100
Mean C o i l Radius (m) 0.4
O v e r a l l S o l e n o i d L e n g t h (m) 2.
C u r r e n t (Kilo-Ampere) 11
System Maximum V o l t - S e c 0.2
Cbpper S i z e (Square); H o l e Dia. 15.2 mm; 6.4 lmm VERTICAL FIELD COILS
Turns
C u r r e n t ( K i l o - A m ~ e r e )
T o t a l NI ' (~ega-~mpere- urns ) 0 i 3 3 6 U n i f o r m F i e l d ( T e s l a ) -.0653 Copper S i z e ( S q u a r e ) ; H o l e D i a . 11.1 mm; 6.0 mm
. -
Fig 4 : Loads on Poloidal Field
Core ( kN/m. ) I
Fig. 2 : D e t a i l s of Poloidal Field Core and S p j i c e J o i n t
d i f f e r e n t TF c o i l s so t h a t t h e plasma sees a p p r o x i m a t e l y t h e same t o r o i d a l f i e l d d e s p i t e t h e f a c t t h a t t h e m a j o r r a d i u s o f t h e c e n t e r o f t h e plasma changes as t h e plasma s p i r a l s . The maximum c u r r e n t i n a t o r o i d a l f i e l d c o i l i s 37.5 kA. Although t h e He1 i a c c o n f i g u r a t i o n i s capable o f s t e a d y - s t a t e plasma confinement, t h e HX-1 i s designed t o o p e r a t e on a p u l s e d b a s i s because o f thermal l i m i t a t i o n s o f t h e e x i s t i n g t o r o i d a l f i e l d c o i l s . These c o i l s a r e s h a r p l y shaved a t t h e nose, a f e a t u r e n o t r e q u i r e d f o r He1 i a c .
Each t o r o i d a l f i e l d c o i l i s s u p p o r t e d a t t h r e e l o c a t i o n s : a t a l i n e s u p p o r t (column) a l l a l o n g t h e nose, and a t s u p p o r t pads near t h e t o p and bottom o f each c o i l . The column s u p p o r t a t t h e c o i l nose extends f r o m a l o w e r s h e l f t o an upper s h e l f , w h i c h a r e connected t o each o t h e r by d i a g o n a l braces i n a manner s i m i l a r t o t h e t o r q u e frame o f many tokamaks. The ohmic h e a t i n g s o l e n o i d and t h e v e r t i c a l f i e l d c o i l s a r e c o n v e n t i o n a l copper c o i l s w i t h t h e parameters g i v e n i n Table 1. The p r i m a r y plasma h e a t i n g method i n HX-1 i s n e u t r a l beams.
POLOIDAL FIELD CORE DESIGN
The major d e s i g n r e q u i r e m e n t s of t h e p o l o i d a l f i e l d c o r e a r e t h a t i t i n t e r l o c k s t h e t o r o i d a l f i e l d c o i l s , and t h a t i t must be surrounded by a vacuum-tiqht s t a i n l e s s s t e e l l i n e r . The i n t e r i o c k i n g f e a t u r e r e q u i r e s e i t h e r d w o u n d - i n - p r i c e c o r e o r a c o r e w i t h a j o i n t i n it. Wind-in-place schemes were c o n s i d e r e d u s i n g p r e - i n s u l a t e d w a t e r - c o o l e d c a b l e - t y p e conductors, b u t were r e j e c t e d because o f space l i m i t a t i o n s and t h e d i f f i c u l t y o f f a b r i c a t i n g t h e l i n e r around a wound-in-place core.
The s e l e c t e d method uses a p r e - f a b r i c a t e d c o r e s p l i t i n t o 180' s e c t o r s t o p e r m i t i n s t a l l a t i o n w i t h i n t h e b o r e o f t h e vacuum vessel. Each s e c t o r w i l l be p o t t e d w i t h epoxy i n s i d e a 1.5 mm t h i c k s t a i n l e s s s t e e l vacuum l i n e r . The r e l a t i v e l y t h i c k l i n e r i s p e r m i t t e d because t h e H e l i a c does n o t r e q u i r e c u r r e n t induced i n t h e plasma by t h e ohmic h e a t i n g c o i l . The i n d i v i d u a l t u r n h a l v e s w i l l be j o i n e d by m a t i n g sawtooth faced, s c a r f j o i n t s s i m i l a r t o t h o s e w h i c h have been used s u c c e s s f u l l y i n t h e ASDEX Tokamak f o r s e v e r a l y e a r s now. T h i s t y p e o f j o i n t i s compact and i t c a r r i e s b o t h c o o l a n t and c u r r e n t and t r a n s m i t s t e n s i l e loads. The use o f such a demountable j o i n t r e q u i r e s t h a t a l l t u r n s be a c c e s s i b l e from t h e e x t e r i o r , i.e., a t w o - l a y e r winding. I n o r d e r t o e f f i c i e n t l y f i l l t h e c i r c u l a r c o r e w i t h a 12 t u r n X 2 t u r n w i n d i n g bundle, t h e c o n d u c t o r must be e l o n g a t e d w i t h a r a c e t r a c k - shaped c o o l a n t hole. The j o i n t r e g i o n causes a bulge i n t h e e x t e r i o r o f t h e core, b u t t h i s i s acceptable. D e t a i l s o f t h e c o r e a r e shown i n F i g . 2.
POLOIDAL FIELD CORE MANUFACTURING AND MACHINE ASSEMBLY
The c o r e l i n e r i s made o f two h a l f - t o r u s e s spun of 1.5 mm t h i c k t y p e 305 s t a i n l e s s s t e e l and c u t i n t o segments t o f i t t h e c o r e halves. The j o i n t r e g i o n s o f t h e l i n e r a r e s l i g h t l y l a r g e r . The copper w i n d i n g i s h a l f - h a r d e x t r u d e d A l l o y CDA- 102 copper, w i t h t h e t u r n ha1 ves b e i n g s t r e t c h - f o r m e d t o m i n i m i z e " k e y s t o n i n g " o f t h e c r o s s - s e c t i o n . A l l t u r n - t o - t u r n and l a y e r - t o - l a y e r t r a n s i t i o n s a r e h y d r a u l i c a l l y die-formed. The i n d i v i d u a l c o n d u c t o r s a r e i n s u l a t e d w i t h M y l a r t a p e and f i b e r g l a s s tape. A f t e r t h e c o i l t u r n segments a r e s t a c k e d and p o s i t i o n e d , t h e b u n d l e i s i n s u l a t e d w i t h f i b e r g l a s s tape. T h i s assembiy i s p l a c e d i n s i d e t h e l i n e r and vacuum-pressure impregnated w i t h epoxy o f t h e same f o r m u l a t i o n use t o f a b r i c a t e t h e TFTR p o l o i d a l f i e l d c o i l s . A f t e r t h e epoxy i s cured, t h e j o i n t ends, j o i n t t e e t h and 0 - r i n g grooves a r e m i l l e d i n t h e ends o f each c o r e h a l f . D u r i n g machine assembly, t h e t o r o i d a l f i e l d c o i l s and vacuum vessel s e c t o r s a r e assembled i n t o two 180' a r c s w i t h a c o r e h a l f r o t a t e d i n t o each a r c . These a r e t h e n b r o u g h t t o g e t h e r w i t h t h e c o r e h a l v e s t o u c h i n g b u t t h e vacuum vessel h a l v e s s l i g h t l y d i s p l a c e d sideways. T h i s gap i n t h e vacuum vessel p r o v i d e s room f o r assembly o f t h e s p l i c e j o i n t . F i n a l l y , t h e vacuum vessel i s closed.
LOAD DEFINITION
The l o a d s on t h e TF c o i l s a r e g i v e n i n F i g . 3 f o r one o f t h e t h r e e p e r i o d s i n t h e h e l i x . Numerical v a l u e s a r e l a b e l e d f o r t h e l a r g e r magnitudes o f each load.
The t o r o i d a l f i e l d c o i l s e x p e r i e n c e r a d i a l l y i n w a r d ( c e n t e r i n g ) f o r c e s and o v e r t u r n i n g moments as i n a tokamak, b u t t h e y a l s o e x p e r i e n c e n e t v e r t i c a l loads, n e t l a t e r a l loads, and moments around t h e v e r t i c a l a x i s o f t h e c o i l . The l a t t e r occur because o f t h e o s c i l l a t i o n i n t h e l o c a t i o n s o f t h e t o r o i d a l f i e l d c o i l s , and because o f t h e d i f f e r e n t c u r r e n t s i n d i f f e r e n t t o r o i d a l f i e l d c o i l s . The
Cl-184 JOURNAL BE PHYSIQUE
l o a d s on t h e p o l o i d a l f i e l d c o r e a r e g i v e n i n F i g . 4. The v e r t i c a l l o a d s produce c y c l i c a l o u t - o f - p l a c e bending, and t h e r a d i a l l o a d s a c t t o bend t h e c o r e i n - p l a n e i n t o a t r i a n g u l a r shape. The maximum r a d i a l l o a d i s 2.4 t i m e s as l a r g e as t h e maximum v e r t i c a l load.
STRESS ANALYSIS:
The s t r e s s e s i n t h e machine s t r u c t u r e and t h e t o r o i d a l f i e l d c o i l s a r e found t o be g e n e r a l l y low. I n t h e t o r o i d a l f i e l d s c o i l s t h e maximum combined hoop and bending s t r e s s i s 45 MPa (6.5 k s i ) . I n t h e machine s t r u c t u r e t h e s t r e s s l e v e l s a r e l e s s t h a n 70 MPa ( 1 0 k s i ) . The machine s t r u c t u r a l d e s i g n i s d e f l e c t i o n - l i m i t e d r a t h e r t h e s t r e s s - l i m i t e d . The w o r s t case d e f l e c t i o n s o f p o i n t s on t h e TF c o i l s and p e d e s t a l s a r e .38 mm (15 m i l s ) t o .51 mm (20 m i l s ) i f t h e s t r u c t u r e i s made o f s t a i n l e s s s t e e l .
S t r e s s a n a l y s i s o f t h e p o l o i d a l f i e l d c o r e i s i m p o r t a n t m a i n l y because o f t h e t e e t h used i n t h e demountable j o i n t . These t e e t h i n t r o d u c e a s t r e s s c o n c e n t r a t i o n f a c t o r o f a p p r o x i m a t e l y 5 ( d e f i n e d as s t r e s s a t t h e r o o t o f t h e t e e t h d i v i d e d by average t e n s i l e s t r e s s i n t h e nearby w i n d i n g ) . The s t r e s s e s i n t h e p o l o i d a l f i e l d c o r e a r e p r i m a r i l y bending s t r e s s e s . I n t h e ASDEX OH c o i l s , t h e nominal hoop s t r e s s away f r o m t h e j o i n t was 24.8 MPa (3.6 k s i ) , and f a t i g u e t e s t i n g t o 500,000 c y c l e s was done a t 37.2 MPa (5.3 k s i ) w i t h no adverse e f f e c t s . Thus, t h e d e s i g n f o r H e l i a c must l i m i t s t r e s s e s i n t h e p o l o i d a l f i e l d c o r e t o v a l u e s i n t h i s range.
Two s e t s o f assumptions s t r o n g l y i n f l u e n c e t h e s t r e s s e s c a l c u l a t e d i n t h e core: t h e bonding c o n d i t i o n s between t h e copper and t h e i n s u l a t i o n , and t h e l o a d s u p p o r t c o n d i t i o n s . The assumption used f o r t h e bonding was c o n s e r v a t i v e b u t n o t c o m p l e t e l y p e s s i m i s t i c , i.e., p a r t i a l s l i p p a g e between t u r n s . Supports were assumed t o have t h e s t i f f n e s s o f t h e o v e r a l l machine s t r u c t u r e f o r l o a d s a l o n g t h e i r l e n g t h , b u t no s t i f f n e s s f o r l o a d s i n o t h e r d i r e c t i o n s o r f o r moments i n any d i r e c t i o n . I n a l l cases t h e s u p p o r t s connect t o t h e c o r e f r o m t h e s i d e away from t h e plasma.Three d i f f e r e n t s u p p o r t arrangements were assumed. F o r t h e case o f t h e s i x v e r t i c a l supports, t h e peak s t r e s s i s 76 MPa ( 1 1 k s i ) . For t h e case o f t h e s i x r a d i a l supports, t h e peak s t r e s s i s 5 1 MPa (7.4 k s i ) . The l o w e s t peak s t r e s s , 26 MPa (3.8 k s i ) , i s o b t a i n e d w i t h 12 s u p p o r t s , i.e. b o t h s e t s o f s u p p o r t s used i n t h e p r e v i o u s two examples. The s p l i c e s occupy a l a r g e enough a n g l e t h a t some p a r t s o f them w i l l p r o b a b l y be i n peak s t r e s s regions. The t e n t a t i v e c o n c l u s i o n i s t h a t a s u f f i c i e n t l y l o w peak s t r e s s can be a c h i e v e d w i t h t h e 1 2 s u p p o r t arrangement b u t p r o b a b l y n o t w i t h t h e 6 s u p p o r t arrangement.
RELATED WORK ON HIGH BETA PLASMAS AT PRINCETON
Although t h e H e l i a c machine i s s t i l l i n t h e proposal stage, r e l a t e d work i s now b e i n g done a t P r i n c e t o n t o produce a bean-shaped plasma i n an e x i s t i n g tokamak. The PDX ( P o l o i d a l D i v e r t o r Experiment) i s b e i n g m o d i f i e d and i s renamed PBX ( P r i n c e t o n Beta Experiment). The m o d i f i c a t i o n c o n s i s t s o f moving and adding c o i l s w i t h i n t h e vacuum vessel, w i t h o u t any major disassembly o f t h e machine. F i r s t Plasma w i t h t h e new c o n f i g u r a t i o n i s expected l a t e t h i s c a l e n d a r y e a r .
Also, t h e o r e t i c a l work i s b e i n g done on a H e l i c a l a x i s s t e l l a r a t o r design w h i c h may e l i m i n a t e t h e need f o r a p o l o i d a l f i e l d c o r e by u s i n g n o n c i r c u l a r b u t p l a n a r c o i l S.
Acknowledgements:
We acknowledge t h e work of t h e e n t i r e H e l i a c Design Study Team. We a r e g r a t e f u l f o r i n f o r m a t i o n f r o m t h e ASDEX Group c o n c e r n i n g t h e demountable j o i n t . T h i s work was supported by t h e U.S. Department o f Energy C o n t r a c t No. DE-AC02-76-CHO-3073.
