A STATIONARY

MAGNETOPLASMADYNAMIC

SOURCE

V . S. E r m a c h e n k o , F. B. Yurevich, M. N . R o l i n , A. Ya. Venger, a n d V. N . B o r i s y u k

UDC 533.95:538.4:621.384,6

A m a g n e t o p l a s m a d y n a m i c s o u r c e of output up to 400 kW is d e s c r i b e d , and m e a s u r e m e n t s on the m a j o r e l e c t r i c a l and t h e r m a l c h a r a c t e r i s t i c s a r e r e p o r t e d . It is p o s s i b l e to produce high enthalpy in the flowing gas with c o m p a r a t i v e l y s m a l l loss in the cooled components of the d i s c h a r g e c h a m b e r in a s y s t e m employing a ring a r c in a m a g n e t i c field; this has r a i s e d considerable i n t e r e s t in such d e v i c e s . It is usual to employ devices of c o m p a r a t i v e l y low p o w e r (10-100 kW) with working flow r a t e s not m o r e than 0.5 g/sec [1-5]. The working gas is f r e e f r o m oxygen. D e v i c e s of this type have r e c e n t l y been used in examining heat and m a s s t r a n s f e r for hot gas flows [6-8]; this r e q u i r e s the u s e of higher power inputs and higher gas flow r a t e s (G in e x c e s s of 2 g/sec), together with r e a s o n a b l y high enthalpy and stagnation p r e s s u r e . The m a g n e t i c field in the d i s c h a r g e zone in such a device has a m a r k e d effect on the e n e r g y input to the gas and also on the attainable values f o r the enthalpy and stagnation p r e s s u r e , and it is t h e r e f o r e n e c e s s a r y to build solenoids that can produce strong fields in the steady state. This is a m a j o r difficulty in the design of a p l a s m a a c c e l e r a t o r of this type. F i g u r e 1 shows our design of s o u r c e , which consists of the anode nozzle 1 and cathode 2, which a r e coaxial, together with the solenoid 3, which is placed with axial s y m m e t r y on the body of anode 4. The anode is made of copper and has an i n t e r n a l d i a m e t e r of 24 m m and wall thickness 5 m m . This anode also acts as a s u p e r s o n i c nozzle, whose l a r g e angle (90 ~ f a c i l i t a t e s the attainment of high t h e r m a l efficiency and a l s o allows one to use highly d i v e r g e n t m a g n e t i c fields, which avoids leakage of the field into the s p a c e between the cathode and anode, while f o r c i n g the c u r r e n t to flow to the anode a c r o s s the field l i n e s , as is e s s e n t i a l f o r this type of device [2]. A cooling section of a p p r o p r i a t e shape is f o r m e d between the anode nozzle 1 and the body 4, and this c a r r i e s cooling w a t e r at 25 arm. The cathode 2 is m a d e of l a n t h a n u m - i m p r e g n a t e d tungsten and has a length of 50 m m and a d i a m e t e r of 8 m m . The tungsten cathode is mounted in the copper tube 5, which cools the cathode. This tube is insulated f r o m the anode by the sleeve 6 made of polymethyl m e t h a c r y l a t e . The working gas

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Design of the m a g n e t o p l a s m a d y n a m i c source.

A. V. Lykov Institute of H e a t and Mass T r a n s f e r , A c a d e m y of Sciences of the B e l o r u s s i a n SSR, Minsk. T r a n s lated f r o m I n z h e n e r n o - F i z i c h e s k i i Zhurnal, Vol. 35, No. 3, pp. 459-465, S e p t e m b e r , 1978. Original a r t i c l e s u b mitted March 24, 1977. 1060

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F i g , 2. V o l t - a m p e r e c h a r a c t e r i s t i c s f o r the m a g n e t o p l a s m a d y n a m i c source. e n t e r s the d i s c h a r g e c h a m b e r via the gap between the s l e e v e 6 and the anode. The tungsten cathode is i n s u l a t e d by the f u s e d - q u a r t z j a c k e t 7. T h e r e is an a n n u l a r s l o t between the j a c k e t 7 and the cathode that p r o v i d e s a m e a n s of p r o t e c t i n g the tungsten f r o m oxidation by i m p u r i t i e s in the i n e r t gas. The d e s i g n of the cathode allows the l a t t e r to be moved along the a x i s of the a c c e l e r a t o r . The s o l e n o i d is wound with a s q u a r e - s e c t i o n c o p p e r tube having a side of 5 m m and a w a l l t h i c k n e s s of 1 m m . The solenoid c o n s i s t s of 34 s e p a r a t e s e c t i o n s which a r e connected in s e r i e s as r e g a r d s c u r r e n t but in p a r a l l e l as r e g a r d s w a t e r cooling. The individual turns and s e c t i o n s a r e i n s u l a t e d with s t r i p s of g l a s s cloth i m p r e g n a t e d with h e a t - r e s i s t a n t l a c q u e r . The lengths of the s e c t i o n s , the d i m e n s i o n s of the winding, and the t h i c k n e s s of the i n s u l a t i o n w e r e chosen to p r o v i d e the m a x i m u m induction at the a x i s of the s o l e n o i d [9]. The d i m e n s i o n s w e r e as follows: length 130 m m ; i n s i d e and outside d i a m e t e r s of the windings 60 and 230 ram. The s o l e n o i d p r o v i d e s an induction of 3.5 T on the axis at the c e n t e r for an input of 500 kW; the m a x i m u m p e r m i s s i b l e c u r r e n t f o r a c o o l i n g - w a t e r p r e s s u r e of 20 a t m is 1700 A. The p o w e r supply to the a c c e l e r a t o r w a s f r o m two m e r c u r y r e c t i f i e r s of total output 2.5 MW; the m a x i m u m c u r r e n t w a s 3000 A at 825 V. Two w a t e r - c o o l e d r h e o s t a t s w e r e u s e d to a d j u s t the a r c and s o l e n o i d c u r rents. T h e s e c u r r e n t s w e r e m e a s u r e d with a 2000-A shunt; the c u r r e n t and v o l t a g e w e r e m o n i t o r e d continuously with N-340 c h a r t r e c o r d e r s . The h e a t l o s s e s in the anode and cathode w e r e m e a s u r e d with d i f f e r e n t i a l t h e r m o c o u p l e s , which w o r k e d into an I~PP-09 pen r e c o r d e r . The j e t flowed into an e v a c u a t e d c h a m b e r of v o l u m e about 3.5 m3; this c h a m b e r w a s e v a c u a t e d by four VN-6G p u m p s . The w o r k i n g gas w a s a i r , while n i t r o g e n was u s e d to p r o t e c t the cathode f r o m oxidation. The flow r a t e s of the two g a s e s w e r e c o n t r o l l e d and m o n i t o r e d with r e d u c t i o n v a l v e s and t h r o t t l e s giving c r i t i c a l p r e s s u r e d i f ferences. The p r e s s u r e in the e v a c u a t e d c h a m b e r w a s in the r a n g e 2-11 m m Hg and w a s a p p r o x i m a t e l y p r o p o r t i o n a l to the m a s s flow r a t e for G~ = 0.8-6.5 g / s e c . The m a x i m u m d i s c h a r g e input w a s 400 kW, which was r e s t r i c t e d by the e r o s i o n r e s i s t a n c e of the tungsten cathode. The r e s u l t s r e s e m b l e d those of [4] in i n d i c a t i n g that the w o r k i n g voltage w a s s u b s t a n t i a l l y dependent on the d i s p o s i t i o n of the cathode; if the cathode was d i s p l a c e d d o w n s t r e a m f r o m the z e r o p o s i t i o n (x c = 0), t h e r e w a s a fall in the v o l t a g e , but the a c c e l e r a t o r worked unstably f o r x c--- + 10 m m . The d i s c h a r g e was then no l o n g e r a x i a l l y s y m m e t r i c a l . The voltage i n c r e a s e d as the cathode w a s moved i n s i d e the anode nozzle. The a c c e l e r a t o r w o r k e d s t a b l y up to a p o s i t i o n w h e r e the tip of the cathode was at x c - - 2 0 r a m ; any f u r t h e r d i s p l a c e m e n t of the cathode within the anode r e s u l t e d in u n s t a b l e o p e r a t i o n . 1061

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Fig. 3. M a s s - m e a n enthalpy (MJ/kg) as a function of d i s c h a r g e input kW: 1) B = 2.2 T; 2) 0.95. Fig. 4. T h e r m a l efficiency (~) as a function of d i s c h a r g e p o w e r (kW): 1) B = 2.2 T; G~ = 6.5 g/sec; 2) 0.95 and 6.5; 3) 2.2 and 4; 4) 0.95 and 4; 5) 2.2 and 0.8; 6) 0.95 and 0 , 8 . We found that the o p t i m u m position of the cathode f o r the v a r i o u s working conditions w a s Xc = - 2 0 m m ; this evaluation is based not only on the v o l t a g e , but also on the stability and reproducibility of the t h e r m a l characteristics. All c h a r a c t e r i s t i c s a r e subsequently given for this position of the cathode. F i g u r e 2 shows the v o l t - a m p e r e c h a r a c t e r i s t i c s for three gas flow r a t e s and three values f o r the m a g netic field at the tip of the cathode; the flow r a t e s for the a i r and nitrogen w e r e as follows: 1) G~ = G a + Gn = 5 + 1.5 = 6.5 g/sec; 2) GE = 2.5 + 1.5 = 4 g/sec; 3) GE = 0.5 + 0.3 = 0.8 g/sec. The shape of the v o l t - a m p e r e c h a r a c t e r i s t i c s is r e l a t e d to the following f e a t u r e s of the c u r r e n t in the d i s c h a r g e in a s t r o n g m a g n e t i c field; the c u r r e n t flow in the p l a s m a can be d e s c r i b e d a p p r o x i m a t e l y via a generalization of O h m ' s law [10]:

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(i)

The s t r o n g axially s y m m e t r i c a l m a g n e t i c field is such that ~eTe > 1, and the r a d i a l conductivity of the p l a s m a was m u c h l e s s than ~0, so the field i n c r e a s e d the r e s i s t a n c e . The conductivity along the field r e mained ~0. The nonuniformity in the field caused s o m e t r a n s f e r of the c u r r e n t to the region of l o w e r B. The a c c e l e r a t i n g f o r c e acting on unit volume of p l a s m a is due to i n t e r s e c t i o n between the c u r r e n t and the field lines and is [jB]. An induction effect a r i s e s when the field lines i n t e r s e c t the p l a s m a , which c o r r e s p o n d s to the [~B] in (1). The p l a s m a conductivity is of t e n s o r c h a r a c t e r , so there a r e c u r r e n t s in the r a d i a l , a z i m u t h a l , and axial directions; the i n t e r a c t i o n between the m a g n e t i c field and these c u r r e n t s s e t s up f o r c e s in the c o r r e s p o n d i n g d i r e c t i o n s . The r a d i a l component of the f o r c e is d i r e c t e d along the axis. The v o l t - a m p e r e c h a r a c t e r i s t i c s a r e of falling type at low c u r r e n t s on account of the rapid i n c r e a s e in the conductivity as the p l a s m a t e m p e r a t u r e r i s e s , which r e s u l t s f r o m a rapid i n c r e a s e in the f r e e - e l e c t r o n concentration. The e l e c t r o n mobility tends to fall at high t e m p e r a t u r e s or when the ion concentration r e a c h e s

1062

a certain level on account of the i n c r e a s e in the frequency of collisions between the ions and e l e c t r o n s , which r e t a r d s the i n c r e a s e in the conductivity, in spite of the i n c r e a s e in the e l e c t r o n concentration. Consequently, the v o l t a g e - a m p e r e c h a r a c t e r i s t i c b e c o m e s of r i s i n g type. The values for the Hall f a c t o r C0eTe may be e x t r e m e l y large at low d e g r e e s of ionization; this results in v e r y considerable d i s p l a c e m e n t of the current. However, this quantity falls rapidly as the t e m p e r a t u r e r i s e s on account of the i n c r e a s e in the collisional frequency, and this reduces the c u r r e n t displacement. When the region of complete ionization is approached, the fall in We~e tends to become r a t h e r l e s s , and ultimately r begins to r i s e , which is due to the reduction in the collisional c r o s s sections at high t e m p e r a t u r e s . The shape of the v o l t - a m p e r e c h a r a c t e r i s t i c s is only slightly affected by the inherent field set up by the a r c c u r r e n t in the range of a r c c u r r e n t s and gas flow r a t e s used. The COe~e p a r a m e t e r i n c r e a s e s with the field strength, which causes the voltage to r i s e . The radial conductivity v a r i e s roughly in inverse proportion to the square of COeTe; however, the i n c r e a s e in the c u r r e n t displacement a c c o m p a n i e s i n c r e a s e s in the p r e s s u r e and t e m p e r a t u r e in the discharge zone to cause the voltage to i n c r e a s e linearly. A s i m i l a r r e s u l t has been r e p o r t e d previously [2, 4, 7]. The slopes of the two branches in the v o l t - a m p e r e c h a r a c t e r i s t i c i n c r e a s e with the field strength for a given flow rate because the enthalpy is m o r e dependent on the c u r r e n t at high fields (high voltages). The m i n i mum on the v o l t - a m p e r e c h a r a c t e r i s t i c shifts to the left as the field strength i n c r e a s e s . The voltage minima c o r r e s p o n d to enthalpies of about 100 and 50 MJ/kg for working flow r a t e s of 0.8 and 6.5 g/sec, respectively. The voltage i n c r e a s e s and the slope of the v o l t - a m p e r e c h a r a c t e r i s t i c d e c r e a s e s as the w o r k i n g - g a s flow rate is raised. Figure 3 shows the enthalpy as a function of d i s c h a r g e power for various field strengths and flow r a t e s ; the enthalpy i n c r e a s e s considerably as the flow rate is reduced or the power input is increased. Fields in the range 0.95-2.2 T have virtually no effect on the enthalpy at high flow r a t e s (GE = 4 and 6.5 g/sec), which is due to the v e r y slight dependence of the efficiency on the induction in that range for a given input power. There is a slight i n c r e a s e in the enthalpy with the field for Gy = 0.8 g/sec, which is due to an appreciable increase in the efficiency as the field i n c r e a s e f r o m 0.95 to 2.2 T. Figure 4 shows the t h e r m a l efficiency as a function of input power for two field strengths and three flow r a t e s ; there is an appreciable i n c r e a s e in the efficiency with flow rate. The loss in the anode was approximately proportional to the a r c c u r r e n t and was a l m o s t independent of the flow rate and magnetic field; this indicates that the loss is l a r g e l y due to the potential drop in the region near the anode [2]. The behavior of the t h e r m a l efficiency is in a c c o r d a n c e with ~l =

1

hva

,

U (6 z, B, I) where &va is a coefficient of proportionality, which itself is related to the t h e r m a l loss a s s o c i a t e d with the a r c current. The r e s u l t f r o m p r o c e s s i n g the experimental data was/Xv a = 40 V. Major p a r a m e t e r s related to the a e r o d y n a m i c heating are the heat flux and the stagnation p r e s s u r e ; these w e r e estimated for v a r i o u s working conditions and various distances from the end of the anode nozzle. The heat flux was m e a s u r e d with t r a n s d u c e r s of c a l o r i m e t r i c type; we used stationary devices (water cooled) and nonstationary ones (regular mode). The d i a m e t e r of the flat end of a detector was 20 mm. The stagnation p r e s s u r e was m e a s u r e d with a t o t a l - p r e s s u r e device; stagnation p r e s s u r e s up to 0.05 atm were obtained with our working conditions, which c o r r e s p o n d e d to plasma jets r e p r e s e n t i n g heat fluxes at the cold wall of the c a l o r i m e t e r in the range 0.05-4 kW/cm 2. We found that an e r o s i o n - r e s i s t a n t cathode capable of working at c u r r e n t s above 2000 A allowed us to inc r e a s e the input power at the m a x i m u m attainable magnetic field strength in the discharge zone. This made it possible to produce a i r - p l a s m a jets having a m a s s - m e a n enthalpy H > 300 MJ/kg.

1063

NOTATION is Is Is is is is is is is is is ~s is

I

U N B H Xc

J E V e m e Te

the the the the the the the the the the the the the

current; voltage; d i s c h a r g e power; induction; enthalpy; t h e r m a l efficiency; distance between the cathode and end of anode cone; c u r r e n t density; e l e c t r i c field; p l a s m a speed; e l e c t r o n charge; electron mass; m e a n t i m e between e l e c t r o n collisions;

We = eB

/me uleTe

is the cyclotron frequency; is the Hall p a r a m e t e r ; is the p l a s m a conductivity in absence of magnetic field. LITERATURE

CITED

1. 2. 3. 4. 5. 6. 7. 8.

W. G r o s s m a n , R. V. Hess, and H. A. H a s s a n , AIAA J . , No. 6 (1966). R, M. P a t r i c k and A. M. Schneiderman, AIAA J . , No. 2 (1966). P. B r o c k m a n , R. H e s s , F. Bowen, and O. J a r r e t , AIAA J . , No. 7 (1966). A . M . Schneiderman and R. M. P a t r i c k , AIAA J . , No. 10 (1966). G . A . Luk'yanov a n d V . V. Sakhin, Zh. P r i M . Mekh. Tekh. F i z . , No. 6 (1975). G . W . G a r r i s o n and R. T. Smith, AIAA J . , No. 9 (1970). E . R . Pugh, R. M. P a t r i c k , a n d A . M. Schneiderman, AIAA J . , No. 2 (1971). A c a d e m i c i a n L. A. A r t s i m o v i c h (editor), P l a s m a A c c e l e r a t o r s , [in R u s s i a n ] , M a s h i n o s t r o e n i e , Moscow

9.

(1972). D.B. Montgomery,SolenoidMagnet Design, Wiley (1969).

10.

1064

D.A.

F r a n k - K a m e n e t s k i i , L e c t u r e s on P l a s m a P h y s i c s [in R u s s i a n ] , A t o m i z d a t , Moscow (1968).