2D Transport Calculations for Carbon Ions in the Plasma Edge

Abstract

i t e r ') I. I n t r o d u c t i o nFor p r e s e n t day tokamaks t h e i m p u r i t y t r a n s p o r t t h e o r y is m a r g i n a l l y a p p l i c a b l e in the low c o n c e n t r a t i o n l i m i t , s i n c e t h e i n e q u a l i t y h o l d s ( -, + , z denote r e s p e c t i v e l y e l e c t r o n s , hydrogen ions and z-fold i o n i z e d i m p u r i t i e s ) .The t r a c e i m p u r i t y t r a n s p o r t problem is u s u a l l y t r e a t e d f o r given hydrogen plasma par a m e t e r s (from experimental o b s e r v a t i o n s o r simple t h e o r e t i c a l c o n s i d e r a t i o n s ) , a lthough t h e u l t i m a t e g o a l is t o combine t h e impurity.transport c a l c u l a t i o n s with t h o s e f o r t h e hydrogen background i n t r o d u c i n g s coupling v i a t h e r a d i a t i o n l o s s e s and t h e e l e c t r o n temperature dependence of both Langmuir s h e a t h p o t e n t i a l and p h y s i c a l s p u tt e r i n g y i e l d of t h e l i m i t e r ( o r d i v e r t o r t a r g e t ).There a r e b a s i c a l l y t h r e e methods t o t r e a t t h e t r a c e impurity t r a n s p o r t problem: a s t a t i s t i c a l Monte-Carlo method / l / , a d i r e c t k i n e t i c method a t t e m p t i n g t o o b t a i n an exact a n a l y t i c a l s o l u t i o n / 2 / or a numerical e v a l u a t i o n of t h e k i n e t i c e q u a t i o n satisf y i n g microscopic boundary c o n d i t i o n s , and t h e moment method. The l a t t e r s o l v e s t h e k i n e t i c e q u a t i o n and t h e corresponding boundary c o n d i t i o n s only approximately by int r o d u c i n g a t r u n c a t i o n when expanding t h e d i s t r i b u t i o n f u n c t i o n i n t o b a s i s f u n c t i o n s with expansion c o e f f i c i e n t s s u b j e c t t o moment ( t r a n s p o r t ) e q u a t i o n s . Whereas a l l t h r e e methods can i n p r i n c i p l e handle t h e whole c o l l i s i o n a l i t y regime of t h e p a r t i c l e spec i e s under c o n s i d e r a t i o n (concerning t h e s e r i e s expansion s e e , f o r i n s t a n c e , / 3 / ) , t h e moment method h a s i t s s p e c i a l merits in d e a l i n g w i t h c o l l i s i o n dominated t r a n s p o r t phenomena ( f l u i d model, see / 4 / ) , s i n c e t h e convergence of t h e s e r i e s expansion im-proves with i n c r e a s i n g c o l l i s i o n a l i t y when u s i n g a p p r o p r i a t e b a s i s f u n c t i o n s . * In t h e following ue use t h e moment method t o d e s c r i b e t h e c l a s s i c a l ( " 8 ) andanomalous (xB) i m p u r i t y i o n t r a n s p o r t in a high density-low temperature edge plasma in c o n t a c t w i t h a l i m i t e r (assumed t o have a plane s u r f a c e IS). In t h i s c a s e t h e b a s i s f u n c t i o n s f o r t h e moment E t h o d should i n z e r o o r d e r approximation reduce t o a s h i f t e dMaxwellian accounting f o r t h e p o s s i b i l i t y of l a r g e p a r a l l e l ("B) i o n flow v e l o c i t i e s i n f r...