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A M A G N E T O G A S D Y N A M I C

POWER GENERATION STUDY

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F r e d r i c k H. S h a i r

prepared for

N A T I O N A L AERONAUTICS A N D SPACE A D M I N I S T R A T I O N

C/on.tr.act N A S 3 - 6 2 6 0 Q u a r t e r l y R e p o r t N o . 1

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N65-21774 (ACCESS IO U M BE R i

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(NASA CR OR TMX OR AD NUMBER) (CATEQORYI

SPACE SCIENCES LABORATORY

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https://ntrs.nasa.gov/search.jsp?R=19650012173 2020-05-29T02:46:58+00:00Z

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First Quarterly P r o g r e s s Report

A MAGNETOGASDYNAMIC POWER GENERATION STUDY

Fredr ick H. Shair

prepared for

NATIONAL AERONAUTICS AND SPACE ADMINISTRATION

November 20, 1964

CONTRACT NAS 3-6260

,. .

Technical Management NASA Lewis Resea rch Center

Cleveland, Ohio 44135 N. J. Stevens

GENERAL ELECTRIC COMPANY Missile and Space Division Space Sciences Laboratory

Box 8555, Philadelphia, Pa. 19101

t

t t ' .

INTRODUCTION

L

i' I

~~

During the f i r s t quarter , a 48 channel oscil lograph sys t em has been

This will enable ordered and is currently being hooked-up and checked out.

al l the data (p re s su res , temperatures , magnetic field, induced voltages,

induced cur ren ts , pre-ionization power, etc. ) to be recorded quickly and

continuously. During this t ime experiments have been conducted in order

to I ' calibrate" the microwave system with an equilibrium plasma.

resu l t s a r e shown in F igures 1 and 2,

Typical

Calibration is satisfactory.

Also during this period the following calculations were performed to

determine:

1.

2.

3.

The optimum seed concentration in a non-equilibrium plasma and the

effect of a variable seed injection rate.

Maximum temperature depression due to seeding, taking into account

vaporization, heat of seed gas, ionization, and resonance radiation

loss.

Elec tron-beam efficiencies.

The discussions of these calculations follow.

1

P c t

t

-

. I

THEORETICAL OPTIMUM SEED CONCENTRATIONS

I N SLIGHTLY IONIZED NON-EQUILIBRIUM PLASMAS

The electr ical conductivity of a gas can be greatly increased by the

addition of a smal l amount of an easily ionized l 1 seed," and also by the

creation of a non-equilibrium condition of the electrons. The creation of

such non-equilibrium conditions (where the average electron temperature

i s higher than the average neutral par t ic le temperature) is being widely

studied in near atmospheric p re s su re plasmas.

MHD power generation," the creation of such a non-equilibrium plasma is

essential .

much grea te r for the seed (typically an alkali metal) than for the parent gas

(typically a noble gas) , the increase in electron density can be offset by the

increase in electron collision frequency when too much seed is added.

(see Reference 2) has briefly discussed the optimum seed concentration in

an equilibrium plasma.

have greatly extended the analysis of the optimum composition of a gas

mixture , also a t equilibrium. Presented below is the derivation of an

expression for the seed concentration which gives r i s e to the maximum

electr ical conductivity in a slightly ionized non-equilibrium plasma. Al-

though the analysis is s t r ic t ly valid only when a very smal l amount of the

seed is ionized, the values of optimum seed concentration and corresponding

conductivity a r e in e r r o r by at most 5% when even 10% of the seed i s ionized.

In the field of "closed cycle

Since the electron elastic collision cross-sect ion is usually

Rosa

Russians Zimin and Popov ( s e e References 6 and 7)

\

\

2

8 f

,

+a ?

The various species a r e assumed to possess Maxwellian velocity distributions.

Radiation losses a r e neglected.

Equations

The total plasma electrical resist ivity is taken to be the sum of con-

tributions due to electron-atom collisions and electron-ion collisions ( see

Reference 1) .

qp = Va + V i

where q is the total plasma resistivity P

qa is the electron-atom contribution to the plasma resis t ivi ty

vi is the electron-ion contribution to the plasma resist ivity

The resist ivity due to electron-atom collisions is given by the hard

sphere Maxwellian model ( see References 3 and 4).

1 -

f

where me is the electron m a s s

k is the Boltzman constant

Te is the average electron temperature

ns i s the seed particle density

Qes is the electron-seed atom elast ic collision cross-sect ion

nn is the parent particle density

Qen is the electron-parent atom elast ic collision c ros s -section

e i s the electron charge

3

!

t r

F o r convenience of calculations purposes, Equation (2) becomes:

I

I i

1 2

1 - -1 = 2.21 x l o 9 P 'Tn n (nsQe, t nnQen), ohm-cm ?a e (3 )

where p is the temperature ra t io Te/Tn

Te is the electron tempera ture , OK

Tn is the neutral particle tempera ture , OK

ne is the electron density, e lectrons / c m 3

ns is the seed atom density, a t o m s / c m 3

nn is the parent atom density, a t o m s / c m 3

Qes is the elast ic electron collision cross-sect ion for the

2 cross-sect ion for the seed, c m

Qen is the elast ic e lectron collision cross-sect ion for the

2 parent gas, cm

These calculations a r e performed with constant e las t ic electron collision

cross-sect ions for the temperature range 1 000-3000°K, thus neglecting

any Ramsauer effect.

The resis t ivi ty due to electron-ion collisions is given by the modified

Lorentz gas expression ( see References 4 and 5).

3 3 - - - 3 - - qi = 6.62 x 10 p Tn In h , ohm-cm

where I\ is the rat io of the Debye shielding 1

impact parameter

ngth t th aver

(4)

4

.

The electron density is given by the Saha equation:

3 3 - 1 1 , 6 0 6 E 0 - electrons

cm3 c T n 9

15 2 - = 2.4146 X 10 < Tn2 e ne

ns - ne

where Eo is the ionization potential of the seed, e . v.

Note that only the alkali metal seed is taken to ionize at temperatures l e s s

than 3000°K, and thus the rat io of the s ta t is t ical weights is taken to be unity.

The ideal gas law is used to determine the number density of parent

gas atoms:

22 3 P / T n , a toms /cm nn = 0. 734 x 10 (7)

where P is the p re s su re ; atomspheres.

The mole fraction of seed, X, is defined:

3 n = Xn,, a toms /cm (8) S

F o r the case of a slightly ionized plasma, ne << ns, the above equation may

be combined to yield an explicit expression of the mole fraction of seed which

produces the maximum electrical conductivity in a seeded gas plasma.

Under the conditions ne << ns, Equations ( 7 ) and (8) may be substituted

into Equation (6 ) to yield: 5803 Eo

TTn 3 ' 1 i -

e le c t r ons - -

"e 4.210 x 10l8 p Tn 4 ~ 2 P 2 e 9 3 ( 9 ) c m

Substituting Equations (7) , (8) and (9 ) into Equations ( l ) , (3) and 4 yields:

5

3 1 5803 Eo 1 - - 1 -- -- 4 4 2 c T n 2

= 3.853 x T, P e X (XQes t Qen) P

9 1 1 1 1 3 3 2 - 5 8 8 4 4

- -- - - t 6 . 6 2 x l o 3 Tn 21n 6.037 x 10 c Tn P X - - - - [

2902 E o I

e , ohm-cm

F o r m o r e convenience Equation (10) is rearranged:

- 1

= a x ' (XQ + Q I t s - y l n X , ohm-cm P e s en

1 3 1 5803 Eo -z P T n --

1 2 4 whereU f 3.853 x 10 < T P e n

9 11 _ _ 1 2 -5 8 8 4

- 3

8 . 6 . 6 2 x l o 3 < x l 0 p Tn P

I 2902 Eo

--mT e

In orde r to obtain the minimum plasma resis t ivi ty with respect to

var iable seed concentration, Equation (1 1) is differentiated with respec t to

X and the result ing expression se t equal to zero. Thus,

6

+ I

1

-1 3 1 2 a 2

- 2 QesXo 2 en o

- - -- - y X o = o - - Q X U

where Xo is the optimum mole fraction of seed,

Solving for Xo:

2

(16)

- 5803 Eo 3 1 -' T (17) - - - 5

w h e r e p - = 8. 61 x 10 - l o c 'T 4~ z ~ e s e

i- (q2 i- Qes 2

2 Y Tn a Qes

This Xo is the required mole fraction to give the optimum non-equilibrium

conductivity.

ponential t e r m in U , for low Te the t e r m CP in Equation (16) becomes negligible;

in this l imit Equation (1 6) reduces to the well known equilibrium expression

for low temperatures ( see Reference 2);

Because of the strong temperature dependence i n the ex-

Xo = QenIQes

Equation (1 5) does indeed represent a minimum value of 7 since P

(3) ' 0 .

XO

Calculations show the negative root omitted i n Equation (16) to be extraneous,

s ee F igure 3 .

F o r convenience of computation, the logarithmic form of Equation (1 7)

is presented:

7

5 3 1 = 9.0659 - 4 loglo - loglo Tn - l o g l o p

In order for the analysis to be valid and to thus yield values of (5 P

and Xo which a r e better than 9570 accurate , the following cr i te r ion should

be followed:

< 0. 1 ne nS

-

A typical cr i ter ion graph is shown in F igure 4. Calculations involvilg the

values of c , X, Tn, the combinations which l ie in the lower left corner of

the Cri ter ion Graph, are the most accurate. The analysis becomes l e s s

valid the fur ther up and to the right the values l ie on the cr i ter ion graph;

however, i t should be noted that the analysis is at l eas t 9570 accurate for

most prac t ica l seeded plasma applications such as in MHD power generation

and in high p r e s s u r e diodes.

Discussion

Various equilibrium gas systems a t the optimum seed mole fraction,

are compared with pure alkali metal vapors in F igure 5.

seeded gas sys tems can yield much higher e lectr ical conductivities than

other seeded gas sys tems o r pure alkali meta l vapors a t the same p r e s s u r e

In general , ces ium

8

and temperature .

given in Table I. F o r non-equilibrium electron temperatures , the con-

ductivities a r e of course much higher.

concentrations vs. temperature is shown in F igure 6 for an argon-cesium

plasma.

presented in Reference 6.

optimum mole fraction of seed can be an o r d e r of magnitude higher than

the low temperature equilibrium value. During an actual experiment, the

The physical constants used during the calculations a r e

A typical plot of optimum seed

The equilibrium limit-curve is in agreement with the resu l t s

F o r some cases of pract ical interest , the

seeding mole fract ion will actually va ry (probably about some mean value

such as the optimum value); the influence of such variations upon the con-

ductivity can be determined f rom a plot of 0 F o r a

cesium seeded argon plasma, with 1000°K < Tn < 2600°K and with 1 . 0 < c < 1.3,

as much a s a 5070 variation in seed mole fraction about the optimum value

will give r i s e to no more than a 1570 reduction in the electr ical conductivity.

This is shown for one case in Figure 7. F o r the above mentioned range, in

seeded gas non-equilibrium and equilibrium plasmas, the conductivity r i s e s

sharply with increasing seed concentration until the optimum point is reached;

then the conductivity decreases l inearly with increasing seed concentration.

F o r increasing values of X > X o , the l inear decrease in U

by an approximately l inearly increase in ne ( see Figure 8).

i n 0 P

sect ion.)

seed than to under-seed; that is, a variation of U

vs X ( s e e F igure 7). P

is accompanied

(The decrease

P

is due to the overpowering influence of the increasing coulomb c r o s s -

I t should also be noted f rom Figure 8 that i t i s sa fer to over-

due fluctuations in X P

9

when X < Xo will be much la rger than when X 1. Xo.

MAXIMUM TEMPERATURE DEPRESSION DUE TO SEED INJECTION

Herein developed is a simple model which allows a quick calculation

to the maximum temperature depression possible due to vaporization of

cold seed, heating of cool seed g a s , par t ia l ionization of the seed, and

line radiation lost f rom the seed resonance levels. Experimental depressions

i n temperature have been observed as shown in F igure 9.

Temperature Depression Due t o Loss of Line Radiation

Let \k be the total ra te of energy loss, due to line radiation, f rom

an optically thin plasma. Let

where (pi r epresents the contribution f r o m the ith to the j th level. Only , j

spontaneous (downward) transitions will be considered. Thus,

Q = C c co j i > j i j

Since the plasma is near thermal equilibrium and a t temperatures l e s s than

2000°K, only the f i r s t two levels (resonance a t 8521 A and 8943 A) will be 0 0

considered. Population of the upper s ta tes i s negligible a s shown in F igure

10. The population density ratio of the f i r s t two levels a s a function of

temperature , i s shown in Figure 11.

unit volume of plasma which is optically thin, in which transit ions take

place f rom the excited s ta tes 1 and 2 to the ground state 0 , is given by

The ra te of energy emitted f rom a

10

the following expression:

* = nl A10 E10 + n2 A20 E20

where n l is the population density of the 1s t excited level

A10 is the reciprocal mean life of the 1st excited level

E10 is the energy of the 1st excited level with respect

to the ground level

n2 is the population density of the 2nd excited level

A20 i s the reciprocal mean life of the 2nd excited level

E20 is the energy of the 2nd excited level with respect to

the ground level

number of Unit check: (atom;: level transitions 11 energy )= energy

atom in level-sec. transit ion cm3- s e c

Note that induced transit ions have been neglected ( see Reference 8).

This is indicated on the energy diagram shown i n F igure 12. The t e r m s

A10 and A

oscil lator strength by the following expression ( see Reference 8):

sometimes called Einstein coefficients, a r e related to the 20’

. 6669 x l o 8 transit ions

X 1 2 * lo =

t rans i t ions A20 = f 0 2 , atom in 2nd level-sec

where X1 is the wave length associated with the f i r s t

A2 is the wave length associated with the second excited

level , in microns

11

8

I '

I -

!

' . I

i :

go is the s ta t is t ical weight of the ground level (25 t 1 )

gl is the s ta t is t ical weight of the f i r s t level (25 t1)

g2 is the s ta t is t ical weight of the second level (25 t 1 )

J is the quantum number represent ing the total angular

momentum of the electrons ( s e e Reference 9)

fO1 is the oscil lator s t rength associated with the first

level

f O 2 is the oscil lator s t rength associated with the second

level

The osci l la tor strengths associated with the energy levels of the cesium

a tom have been recently reported in Reference 10.

i n Equation (24) are determined f r o m the Boltzmann expression and the

The terms nl and n2

ideal gas law: - 11,606 'lo/' a toms in 1 s t level

3 c m , = 0. 734 x P T - l X (5) 80 e nl

- 11, 606 E2o/T a toms in 2nd level 0. 734 x P T - l X (2) e , 3 cm n2 = go

where P is the total p r e s s u r e , in a tmospheres

T is the static temperature , in OK

Xs is the mole fraction of seed

E10 is the energy associated with the 1st level , i n e . v.

E20 is the energy associated with the 2nd leve l , in e . v.

g r e f e r s to the s ta t is t ical weight

12

Thus Equation (24) becomes:

- 11,606 E l o / T 734 x 1022PT-1Xs (2) e

(21 f o l ] E10 t [.0734 x 1022PT-1Xs [- 666:1: lo*

In the above equation 9 has the units of e . v. /cm3-sec.

1. 602 X joules /e .v . and since there a r e 4. 186 joules /ca l . , Equation

( 30) be comes

Since there a r e

L

- 11, 606 E2o/T f02E2oe

x,2 ’ cm3-sec t

In order to give an upper l imit on the temperature depression observed in

a volume of plasma with velocity u, and heat capacity c

downstream of a reference point, the calculation was made with the

at a distance 1 P’

13

population density of the initial temperature. Thus,

where 1 is length in cm

3 m i s the total mole density, mo les / cm

u is velocity in c m l s e c

c

T1 is the initial temperature, OK

is the heat capacity - 5 cal. /mole - OK for a perfect gas P

T 3 is the final temperature a t point 1 downstream of reference,

OK

Since m = 1. 219 X 10'2PT-1 rnoles/cm3 f rom the ideal gas law, Equation (32)

be comes : - 11, 606 E l o / T

1 xs T i - T3 = 1.54 X 10

- 11, 606 E2o/T fo 2E2 oe

x2L t

where 1 is distance from reference point, i n c m

X, is the mole fraction of seed

u is the p lasma velocity

c is the heat capacity

fO1 is the oscillator s t rength of 1s t level

f O 2 i s the oscillator s t rength of 2nd level

P

( 3 3 )

14

E10 is the energy of 1 s t level, e. v.

E20 is the energy of 2nd level, e .v .

T is the s ta t ic temperature , OK

A, is the wave length associated with the 1s t level, in microns

x 2 is the wave length associated with ' the 2nd level, in microns

Temperature Depression Due to Vaporization

The temperature depression due to vaporization of the liquid seed is

obtained f r o m the following expression:

m c (T1 - T3) = m2AH2 1 P

Thus,

(34)

where ml is the mole density of Argon

c

m2 is the mole density of cesium

AH2 is the heat of vaporization p e r mole of seed

T1 is the initial temperature , OK

T 3 is the final temperature , OK

is the heat capacity (taken a s ideal gas) P

Since m2 << m l , m2/ml t m2 m m2/ml m Xs, the mole fraction of seed.

In o r d e r to obtain an upper limit, the heat of vaporization is assumed constant

a t the lowest temperature encountered, s e e Figure 13.

Temperature Depression Due to Heating of Seed

The temperature depression associated with heating the seed is

15

obtained f rom the following expression:

m l ( T l - T 3 ) = mZ(T3-Tz)

where ml is the mole density of argon

m2 is the mole density of seed

T1 is the initial argon temperature

T

T 2 is the initial seed temperature

i s the final mixture temperature 3

Note that in Equation (36), the heat capacity of argon is assumed to be equal

to that of the seed. Since m2 << m l , Equation (36) becomes:

(T1-T3) = X , (T3-T2)

Temperature Depression Due to Pa r t i a l Ionization of Seed

If c represents the mole fraction of seed ionized, then since c << 1

for atmospheric p r e s s u r e plasmas near 1 500°K,

the Saha equation and the ideal gas law a s follows:

can be approximated from

(37)

where T3 is the plasma temperature , OK

Xs i s the seed mole fraction

P is the static pressure , in atmospheres

E i is the ionization potential of the seed

Thus

m c (T1-T3) = 2.31 x lo4 Cm2Ei 1 P (39)

16

i

3 where ml is the mole density of argon, m o l e s / c m

c

T I is the initial temperature, OK

T3 is the final plasma temperature , OK

m2 is the mole density of seed, m o l e s / c m

i s the heat capacity, cal. /mole OK P

3

Ei is the ionization potential

Note:

4 = 2. 31 x 10 cal.

Thus, the temperature depression is:

5 1 1

r J

of the seed , e .v .

1. 602 x e . v. 4. 186 joules

- 5803 Ei

Eie *3

where T1 i s initial temperature , OK

T3 is final temperature , OK

X s is mole fraction of seed

P is the s ta t ic p re s su re , a tmospheres

E is the ionization potential, e. v.

c

i

P is the heat capacity, cal. /mole - OK

Calculations are performed for the experimental case

where T1 = 1500 K (initial temperature) 0

l = 5 c m

17

4 u = 10 c m / s e c

X, = 5 X

T1 = 1500°K

E1O = 1. 39 e. v. ( F i r s t excited level)

EZ0 = 1 .46 e. v. (Second excited level

E i = 3. 87 e. v. (Ionization potential)

T 2 = 300°K (Minimum possible)

cp = 5 ca l /mole -

(Cesium seed in argon)

0 K (Ideal Gas)

h H2 = 20, 000 cal. /mole (Maximum possible)

= .394 (See Reference 10)

fO2 = . 814 (See Reference 10)

X = .8521 p (See Reference 10)

A, = .8943 p (See Reference 10)

fO1

1

The maximum temperature depressions due to the above mentioned

mechanisms a r e l isted in Table 11. Since this maximum temperature

depression model does not account for the observed temperature drops,

i t i s postulated that the seed is entering as a par t ia l liquid spray which

impinges upon the thermocouple. At higher temperatures ( see Figure 15)

m o r e of the spray is vaporized within the injection tube before it en te rs the

duct. Downstream of the point, where the tempera ture depression is

observed, a r e molybdenum screens through which the flow is forced to pass .

Beyond these screens no temperature depression has ever been observed

thus indicating that if a depression does exis t , i t is l e s s than 5K0.

18

THEORETICAL ELECTRON BEAM EFFICIENCY

/ . ! ! ' - I .

I' -

Presen ted below a r e prel iminary calculations which indicate the

maximum possible power increase as a function of energy imparted to

the working fluid f rom the electron beam. Recombination f rom the point

of injection to the magnetic field region and radiation effects a r e neglected.

F o r the case where radiative recombination is the p r i m a r y mechanism

for de-ionization, the power input p e r unit volume, Pi, f rom the electron

beam is:

2 P. = a n e I 1

where a is the recombination coefficient

n is the e lec t rondens i ty e

I is the ion-pair production energy.

The power generated p e r unit volume in a segmented electrode generator

is

where K is the loading factor which is the rat io of the load voltage

to the open circuit voltage

0

u is the average plasma velocity

B is the magnetic field s t rength

is the p lasma electr ical conductivity P

8, s u 7

we i s the electron cyclotron frequency

e e

19

Te is the average time between electron and non-electron

collisions

wi is the ion cyclotron frequency

T i is the average time between ion and non-ion collisions.

The electron beam efficiency, 77, i s defined as follows:

Pi r ) = 1 -- P O

F o r the case K = 1 / 2 and B,Bi << 1, the above expression becomes

(4 3)

in o rde r for the electron beam to be a practical pre-ionization technique,

77 1. F o r convenience of computation, the following expression is

presented:

2 6.41 1 0 - 3 ~ ~ ~ I

q = l - (J u2B2 P

3 w h e r e a is in c m / s e c

n is in e lectrons/cm 3 e

I is in e .v .

0 is m h o s / c m P

u is in c m / s e c

B is in gauss

(4 5)

20

t

In order for there to be a significant fraction of the plasma enthalpy

to be converted into electr ical energy, the magnetic interaction pa rame te r ,

Q, will be close to unity. F o r convenience, the following fo rm of the

magnetic interaction parameter i s presented:

Pu

where (5 is in mhos /cm P

B is in gauss

L is in cm

p is in g r / c m 3

u is in c m / s e c

Substitution of Equation (46) ( f o r a magnetic interaction parameter of unity)

into Equation (45) yields:

ane21L

Pu 3 -12 v = 1 - 6.41 x 10

2 -4 3 F o r a typical case of I - 40 e . v . , L = 10 c m , P = 10 g r / c m

5 and u = 10 c m / s e c , Equation (48) becomes:

(47)

77 = 1 - 2.56 x 6Cne2 (48)

The efficiency vs . number density of electrons is presented i n

Figure 14 for various radiative recombination ra tes .

21

TABLE I

Element 2 Q,, cm Eo, e . v .

~

Lithium

Sodium

Pot as s ium

Rub idi urn

Ce s ium

Argon

Helium

2 .0 x 1 0 - l ~

3. o x 1 0 - l ~

4. o x 10-l4

4 . 7 x 1 0 - l ~

5 .3 x 1 0 - l ~

2 x 10-17

-16 5 x 10

5.363

5.12

4. 318

4. 159

3. 87

---- - - - e

22

TABLE I1

AT - Mechanism

Res onanc e Radiation < 4 2 KO

Vaporization <20 KO

Heating of Seed < 9 KO

Partial Ionization of Seed < l K o

Total AT <72 KO

Equation Used

# 33

# 34

# 36

# 39

23

1.

2.

3.

4.

5.

6.

7.

8.

9.

REFERENCES

Lin, S. C . , Res le r , E. L. , and Kantrowitz, A. R . , J. Applied

Phys ics , - 26, 96 (1955).

Rosa, Richard J . , Phys ics of Fluids , Vol. 4 , No. 2 . , p. 182 (1961).

Cowling, T. C. , Magnetohydrodynamics, Interscience Pub l i she r s ,

Inc. , New York, (1957).

Spi tzer , J r . , L . , Phys ics of Ful ly Ionized Gases , Interscience

Publ i shers , Inc. , New York (1956).

Spi tzer , L . , and Harm, R . , Phys ica l Review, 89, 977 (1953).

Zimin, E. P . , and Popov, V. A . , P a p e r #24 of Session IV f r o m

-

the Proceedings of the Symposium of Magnetoplasmadynamic

Elec t r ica l Power Generation, I. E. E. King's College, Newcastle

Upon Tyne, September 1962.

Zimin, E. P . , and Popov, V. A. , P a p e r #14 of Session 2a presented

at the International Symposium on Magnetohydrodynamic Elec t r ica l

Power Generation, 0. E. C. D. European Nuclear Energy Agency,

Paris, July 1964.

Allen, C. W. , Astrophysical Quantities, Essent ia l Books P r e s s ,

Fair Lawn, New J e r s e y , 1955 p. 51.

Moore, C. E . , Atomic Energy Levels , Ci rcu lar of the N. B. S. 467,

Superintendent of Documents, U. S. Government Pr int ing Office,

Washington, 1958.

24

Stone, P. M . , and Agnew, L . , Phys ica l Review, 127, No. 4 , 1962,

p. 1151.

- 10.

11. Weatherford, J r . , W. D . , Tyler , J. c. , Ku, p. M. WADD

Technical Report 61 -96 A. S, D. U. S. A. F. Wright-Patterson A i r

F o r c e Base, Ohio, Southwest Research Institute, Contract No.

A. F. 33(616)-7206, 1961.

25

.

Id E v1

d Id

pc E 5 k P

.rl

4 .rl

% w k 0 w Q) k 3 Id k al

c,

E" a,

3 b

++

m

VI Q) m Id A pc

rl

a, k

.rl %. c.l

I O'O

10' 1000 1100 1200 1300 1400 1500 1600 1700

Tn ,O K F i g u r e 2 . Equilibrium E lec t ron Density vs T e m p e r a t u r e f o r

x=5*2x10-3, P = 2 atm. C e s i u m Seeded Argon

40

' I I

I I I

20

0

- 20

-40

-60

-80

ohm-cm -140

OF SEED -I 60 MOLE FRACTION

-180

-200

-220

-240

-260

-280

-300

AROON-CESIUM PLASMA

5 9 1.3 P = I ATMOSPHERE

Tn 2000' K

/ i

I I I I I I I ' I

I I I I I I I I I I

I I I

I I

X = 5.382 x lo4 I I ;/ X=2.664xlO (EXTRANEW!)/ I

I I

-41

I I I I I I - 4 - 4 - 4 -3

IO- 2 x 1 0 ~ ~ 4x10 6x10 8 x 10 IO

X e MOLE FRACTION OF SEED F i g u r e 3.

I8

17

16

15

14

13

12

II

IO

9 -LOG,, 5 x

0

7

6

5

4

3

2

I

0

Cp & X o < 95% ACCURATE

- CRITERION BOUNDARY CURVE

-

-

- - -

Cp & Xo > 95% ACCURATE - - - -

I I I I I I I I I I 1000 1400 1800 2200 2600 3000

1200 1600 2000 2400 2800

Figure 4.

.

cm

1000 I100 1200 1300 1400 1500 1600 1700

T " , O K Figure 5.

c

.- .

I- o O K X L

W J 0 I

- a

b

6.5

6.4

=P * m hos/c m.

6.3

6.2

6. I

6.0

I

ARGON - CESIUM PLASMA

P = I ATMOSPHERE T, = 2600° K

I I I I J

X , MOLE FRACTION OF CESIUM

Figure 7.

- 15 4 % IO

"e , ELECTRONS/Cm3

- 15 3 x IO

I x lOlg

0

ARGON - GESl UM PLASMA P = I ATMOSPHERE

5 = 1.3

I .o

.8

FRACTION OF CESIUM IONIZED .6

ne/%

.4

.2

>" I = 2 0 0 0 O K I

1 -0

0 ~ X I O - ~ 4 x ~ ~ - 3 6 x ~ ~ - 3 B ~ I O - ~ IO-*

X, MOLE FRACTION OF CESIUM

F i g u r e 8.

c,

.r( El 0

0 0 Ln

0 0 m

0 0 cu

al 5 Id k e,

c,

? Q)

E-c

0

.x

: 4

.rl Id

d 5 2 {

8

e, cn 0 c, e,

El 0 .A

m m e, k a d : Q)

c, Id k e,

F Q)

I3

rn 0) k

2 J .rl

Gc

O Y 'IV

, .

r I o - ~

1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 34 36 vk , e.v.

Figure 10. Boltzmann's Fac tor as a Function of Energy Level for Cesium at T=1500 K

0

I o - ~

I o - ~

I o-6

I o - ~

/

I 1000 1100 1200 1300 1400 1500 1600 1700

T, O K

F i g u r e 11. Population v s T e m p e r a t u r e For Resonance Levels of C e s i u m

i

e

i

” .

30

25

20

15

IO

5

0 2S 2F O 2Po 2D

ENERGY DIAGRAM OF C,I 2G 2Ho

Figure 12.

c

alou e 16

0 0 a -

0 0 d- -

0 0 N -

0 0 0 -

x 0 - ol - Q)

0

0 0 (D

0 0 d-

0 0 cv

0

,

I

.

c Y

€ 0

E

0 0

N

0 d-

C

/

/ I

0 0 -

F