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Submitted on 1 Jan 1979
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ABLATION OF SOLID HYDROGEN IN CONTACT WITH MAGNETIZED PLASMAS : CAN THE EXTERNAL MAGNETIC FIELD BE THE UPPER
LIMIT OF THE SELF CONSISTENT ELECTRIC FIELD AT THE SOLID SURFACE ?
S. Mercurio
To cite this version:
S. Mercurio. ABLATION OF SOLID HYDROGEN IN CONTACT WITH MAGNETIZED PLAS-
MAS : CAN THE EXTERNAL MAGNETIC FIELD BE THE UPPER LIMIT OF THE SELF CON-
SISTENT ELECTRIC FIELD AT THE SOLID SURFACE ?. Journal de Physique Colloques, 1979,
40 (C7), pp.C7-447-C7-448. �10.1051/jphyscol:19797217�. �jpa-00219198�
JOURLVAL DE PHYSIQUE
ABLATION OF S[XID HYDROGEN
IN
CONTACT WITH MAGNETIZED PLASMAS : CAN THE EXTERNAL MAGNETIC FIELD BE THE UPPER LIMIT OF THE SELF CONSISTENT ELECTRIC FIELD AT THE SOLID SUWACE ?S. Mercurio.
Department o f Physios, University o f Wisconsin, Madison, W I , 53706 U.S.A.
Charge c o l l e c t o r s o r "probesf1 were f i r s t cor- r e c t l y used by ~angmuir'in h i s s t u d i e s of s t e a d y a r c discharges. Later Bohm 2 extended t h e i r use t o
a r c s i n t h e presence of high magnetic f i e l d s . Probe t h e o r i e s even today, a r e q u a s i - s t e a d y - s t a t e theor- i e s . Behavior o f charge c o l l e c t o r s f a r from equi- l i b r i u m a r e o f extreme i n t e r e s t i n r e s e a r c h f i e l d s i n which s h o r t p u l s e s o f c u r r e n t a r e c o l l e c t e d .
I n t h i s n o t e t h e a b l a t i o n mechanism o f s o l i d hydrogen i n c o n t a c t w i t h magnetized plasmas i s d i s - cussed i n terms o f a t r a n s i e n t process proper t o charge c o l l e c t o r s approaching an equilibrium.
The semiempirical approach proposed s u g g e s t s a
"novel" plasma-solid boundary condition, whose con- sequences a r e a l s o found t o be i n e x c e l l e n t agree- ment with a l l experiments a v a i l a b l e t o d a t e f o r a v a r i e t y of plasma conditions.
Since s o l i d hydrogen has a very low binding energy, s a y W=0.01 eV, u s u a l l y much l e s s t h a n t h e e l e c t r o n temperature, KTe, we can s a f e l y assume t h a t t h e a b l a t i o n mechanism i s d r i v e n by t h e charge and h e a t c a r r i e d only by t h e e l e c t r o n s . The abla- t i o n f r o n t speed U, r e l a t i v e t o t h e s o l i d , j u s t ex- p r e s s e s t h e " c l o s e link" between momentum and
of r e f e r e n c e which c a r r i e s along t h e o s c i l l a t i n g Maxwell's Displacement f i e l d a s s o c i a t e d with a b l a - t i n g d i e l e c t r i c .
Taking 6 t o be equal t o one mean f r e e p a t h of t h e plasma e l e c t r o n s of average energy i n a super- dense gas o f number d e n s i t y n;, we have
6 = R = (n a o i n t ) - I (1) where aint is t h e i n t e r c e p t i o n c r o s s s e c t i o n . 3
The r e l a x a t i o n time t * i s h e r e assumed t o be t h e time t h e displacement D t a k e s t o b u i l d up and c o l l a p s e . I f t h e e l e c t r o n - s e l f - c o l l i s i o n time tee, such t h a t tee << t * << t r e c ( t h e e l e c t r o n - i o n r e - combination t i m e ) , t h e n t * w i l l i n f a c t be e x a c t l y t h e p e r i o d f o r t h e heat-cycle of t h e e l e c t r o n s which have enough energy t o reach t h e s o l i d . Since a c o l l a p s i n g time i s expected t o be much s m a l l e r than t h e charging time T , we j u s t have t * = 7 . We can e a s i l y o b t a i n T by i n t e g r a t i n g t h e following s e t o f standard equations a t any p o i n t x , with r e s p e c t t o time t . I n one dimension t h e equations r e a d
a J
ap
- + - =
a
Da x - 4 ~ p ; D =
5
Jax
a t
O;-
- awhich g i v e
D(t) = D,[1-exp(-t/~)]; Dm
-
T T-
~ / 4 ~ r aa t 1 t = o
where J i s t h e c u r r e n t d e n s i t y , p t h e charge d e n s i t y , energy t r a n s f e r s . The l a t t e r determines t h e range 0 t h e e l e c t r i c c o n d u c t i v i t y , E t h e d i e l e c t r i c con-
?
of t h e plasma e l e c t r o n s i n t h e s o l i d ; t h e former, s t a n t . By i d e n t i f y i n g t h e i n i t i a l v a l u e of t h e t h e r e l a x a t i o n time t * f o r t h e t r a n s i t i o n between displacement c u r r e n t J (0) w i t h plasma-electron-d
t h e i n i t i a l ( s o l i d ) and f i n a l ( f l u i d - l i k e ) s t a t e s random c u r r e n t Jr = - 1 enc ( a t t = O t h e r e i s no
-
4 e
of t h e hydrogen. The a b l a t i o n f r o n t motion w i l l s h e a t h ) , t h e n we have
be regarded h e r e a s a wave-type motion. I t w i l l T = D,/4rJd(0) = ~ , / ~ e n c
e ( 2 )
be described p r e c i s e l y a s t h e motion o f t h a t frame While Jd(0) does n o t change when B+O, t h e 30
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797217
ultimate value of D does change, because a solid tively, upon leaving the solid. If we now use the can never be in equilibrium with a plasma. For a
steady sheath to exist, the ion flow requires a
"tailf' in the electron velocity distribution and therefore a continuous flow exists across the sheath.
The self-consistent displacement field can be ob- tained from an equation for dynamic equilibrium, in which the Hall's electric field has to be taken into account, that is
-Dm/& + Eth + vB/c = u/p 'L = 0
.
(3) Where Eth= kTe/ehD,AD
being the Debye length arid u and v two mutually perpendicular drifts across B. + We might content ourselves with assuming that the displacement will collapse whenDm= &(B+E th ) = EB (if Eth<< B) (4) and see whether the above assumption is able to pass some (indirect) ,experimental test. Deviding
(1) by (2) we obtain an expression for the ablation speed U, suitable for comparison with experi- m e n t ~ , ~ ~ ~ ~ ~ ~ ~ . a s shown in Fig. 1, that is
noU m/Uint
- -
=EB
We now try to test (4) more directly. For instance, solid hydrogen pellets have been observed to devi- ate from the straight path, when injected into Risg$'s Puffatron. The latter produces a rotating plasma because it has strong external field. The measured average deviation is 0.2 cm. By simply 7 using (4) to estimate the net charge on the pellet and the equation of motion for projectiles we get 0.23 cm.
We can verify that the dense ablation cloud is not so dense as to have a negligible Hall's current in the sheath, by estimating its density.
By invoking mass conservation across the disassem- bling surface layer of thickness 8, that is:
n U= V; where
I-+,
and V are the number density and0
I-+,
the average speed of hydrogen molecules respec-
experimental values for U and V we get %$,1017ci3 to which correspond 6.1 T
toll?
1. We note, incident- ally, that by introducing (4) into the energy bal- ance we obtain V in excellent agreement with experi-~nent.~'~ In order to convince ourselves that (4) is independent of a chosen symmetry, we notice (3) can be recovered from (D,/E+E )sin +vB/c=u/p; v/c =
th + +
uBsin8/c, for any 8, the angle between B and J r' (Gaussian units have been used throughout.)
REFERENCES
1. Langmuir, I, Science
58,
290 (1923)2. Guthrie and Wakerling, The characteristic of electrical discharge in magnetic fields (1949) 3. Erode, R.B., Review of Modern Physics
5,
263(1953)
4. Jorgensen, L.W. et al., Plasma Physics
g,
453 (1975)5. Foster, C.A. et al., Nuclear Fusion
2,
1067(1977)
6. Amenda, W. et al., Fusion Fueling Workshop, Princeton, N. J. (USA)
7. Sillesen, A. (Risa, Denmark)private communica;
tion
8. Milora, S.L. et al., ORNL TM-6496, October
Fig. 1 o Ormak; + Puffatrorif
