Photoionization of cesium atoms by solar radiation Application to a low-temperature cesium thermionic diode

Photoionization of Cesium Atoms by Solar Radiation Application to a Low-Temperature Cesium Thermionic Diode Keung

P. Luke

Unified Science A s s o c i a t e s , Inc., P a s a d e n a , C a l i f o r n i a

T IS well known that in the cesium thermionic energy converter, most of the ions needed for neutralization of electron space charge are produced by surface ioniza-

where N+ = number of cesium ions/cma N_ = number of electrons/cm3

tion of cesium atoms impinged on the hot emitter surface2.2.3, 4 The condition usually assumed for complete neutralization of electron space charge is

J_ = e l e c t r o n c u r r e n t / c m ~ - s e c M~ = electron mass M+ = cesium ion mass

I

N+ > N_ or J+ > ( M ~ ' =

1 4-92

J--_ = \ M + /

l

(1)

/ NOT ENOUGH /

ENOUGH

IONIZATION/IONIZATION

64o

= ion current/cm~-sec

For cesium diodes using a tungsten emitter, the condition specified by Eq. (1) has been worked out by Nottingham 4 as a function of cesium reservoir temperature Tc~ and emitter temperature T E. His result is reproduced in Fig. 1. At each of the constant emitter current density curves (dashed lines), there is a minimum emitter temperature (TE)~I, below which not enough ions are produced by surface ionization to neutralize the electron space charge. Thus, this lack of sufficient

ionization

determines

a low-temperature

limit of operation of the cesium thermionic energy

620~.

-- -- -- --/--

600.

4 0 Amp/

/ ~ ~ _/---

. 580 "O

/

,J

I.U

~

~

~

~

~

/

16X1016

"~""" ~" ~" ~

/

o~

14

2

~10 Amp/cm -.. "~-

12

/,

560

>

/

~

I0

540

\

x

F-

///J

>~2o

//

~.

-"

/

/

/

/ ~

....

/

2

48o

1200

(TE)rain .

.

.

.

,400 EMITTER

~

8

6

" =,

IAmp/cm

//

"- \

Amp/cm2

i0 Amp/cm~

I

/

~.1

(T~) rain

/

//

"~ 500.

I

1600'

2 I J

I

2

40 Amp/cm (TE) rain

' 1

18'00'

TEMPERATURE,

2000' TE ,

4

2'200 ' ~ o

M a n u s c r i p t r e c e i v e d F e b r u a r y 17, 1965.

2

K

FIG. 1 - - L i n e s of c o n s t a n t c u r r e n t d e n s i t y as d e t e r m i n e d b y c e s i u m r e s e r v o i r t e m p e r a t u r e Tc~ a n d e m i t t e r t e m p e r a t u r e TE (Ref. 4).

110

J+

o

,

, 2

, 3

4

PHOTON

ENERGY

5 hy,

7,

, 6

eV

FIG. 2 - - S o l a r r a d i a t i o n in quanta/cm~--sec-eV, S(hv) (Ref. 5).

Solar Energy

24

XlO -2O

I i

i

2o

/

w,.0ow -,

¢q~

"~ 12

8

/

I//

SOLAR

=

[]

RADIATION - - ~

h

F]

U

.-~"I'~"

-_ . . . .

I~,X~\\, ~

4

,

0

xx, COLLECTOR-~

3.3

3.5

3.?

3.9

PHOTON

4.1

4.3

4.5

i

,1.7

ENERGY by, *V

F i e . 3--Photoionization cross section of cesium a(hv) (Refs. 6-7). l 20 XlO

EMITTER

\\

"- INTERELECTRODE SPACE

FIG. 5--A possible configuration for a cesium thermionie diode using solar radiation for producing cesium ions.

I t is clear then that the number of cesium ions /3+ produced per second per cesium atom is ~+ = k

-"

~-- HOLE FOR RADIATION PASSAGE

f

S(bv)tr(hv) d(h~,)

(2)

where k is the solar radiation intensity-multiplication factor. The ion production rate per cm s is N + = ~+NI,

,5

(3)

where No is the number of cesium atoms per cm 3. If we assume that the ion loss rate (N+)l is given solely by the recombination rate of ions and electrons, then the loss rate is written as (N+)z = R N + N _ = R N _ 2

where R is the recombination coefficient. Equating ion production rate to the ion loss rate and solving for N_ yields

"b I0

N_ = \ ~ /

5

(4)

~

= x~

Equation (5) can be rewritten in a more explicit way by making use of the following information. 1--The random electron current density J_ corresponding to the electron density N_ is

J

J_ = 2.48 X lO-14N-T-½amp/em 2

.....

3.4'

i.s

~.8' PHOTON

~.o~ L2 ENERGY

L4'

Ls'

hv, eV

Fro. 4 Product curve S(hv)~,(b~,) ion (sec-eV-atom) 1. c o n v e r t e r . O n e p o s s i b l e w a y to c o m p e n s a t e for t h i s l a c k of sufficient i o n i z a t i o n a t e n f i l t e r t e m p e r a t u r e less t h a n ( T s ) m i . is I0 p r o d u c e a d d i t i o n a l c e s i u m ions b y t h e p h o t o i o n i z a t J o n of c e s i u m a t o m s w i t h s o l a r r a d i a t i o n . I n Fig. 2 l h e s o l a r r a d i a t i o n S ( h v ) in q u a n t a / e n ~ 2sec-eV is p l o t t e d a g a i n s t p h o t o n e n e r g y hv (Ref. 5 w i t h a c h a n g e of so'des). I n F i g . 3, t h e p h o t o i o l f i z a t i o n cross s e c t i o n of c e s i u m z ( h , ) is p r e s e n t e d as a f u n c t i o n of photon energyfi, 7 The product S(hu)o-(hv) plotted versus hr is shown in Fig. 4. Vol. 9, No. 3, 1965

(5)

(6)

where T_ is the electron temperature. 2--The value of ¢~+ as determined by graphical integration of the curve in Fig. 4 is

~h~=4-s0~v (3+ = /~ I S(hv)(~(hr) d(b~) a bu = 3.41eV = 6.1 X 10-4k

(7)

ion see - "~tom

3 Mohler s reported a value of 3.4 X 10-~° em3/sec for the recombination eoeffieient of cesium ion and electron. 4 The number of cesium atoms per cm s is related to the cesium reservoir temperature by the following relation 9. /_8910 \ X,, = 2.37 X 1027Tc2 exp ( ~ atonls/cm 3 (8) " \ Tc~ ] 5--Assunm that, the eleetron temperature T_ is equal to the emitter temperature TE. Thus, substituting the respective equations and values for N_ , ~_ , N, and R into Eq. (g) yields 111

TABLE 1--VALUES OF J_ FOR TE = 1500°K J amp/cm ~

rc,, °K 400 450 5oo 550 600

k= 1

k = 1000

0.0103 0.0324 0.0807 o. 167 0.314

0.325 1.023 2.55 5.29 9.9

J_ = 1.63 X lO~kiT~½Tc~ exp {/--4455\ ~ J amp/cm~ (9) \ cs / Some typical values for J_ at TE = 1500°K are given in Table 1. It is seen that current density of 1-10 amp/cm 2 can be obtained if the intensity of solar radiation is increased by a factor of 10~. A possible configuration for a cesium thermionic energy converter using solar radiation for producing ions is shown in Fig. 5. Ions needed for space-charge neutralization are produced in the interelectrode space by solar radiation entered through holes in the collector. By proper design it should be possible to minimize undesirable heating of the collector by the radiation. Of course, additional heating of the emitter by absorbed radiation is desirable as are photoelectric emission of positive ions '0 and electrons from the emitter. In the preceding analysis the transmission coefficient through the window and collector was assumed to be unity but in fact will be less than unity. Furthermore, recombination with electrons was taken to be the sole loss mechanism for ions. These are optimistic assumptions. On the other hand, ions produced b y surface ionization and by photoelectric emission from the adsorbed cesium layer on the emitter were not considered. Thus, the ion production rate m a y actually be larger than t h a t computed here on the basis t h a t only the photoionization process was responsible for producing ions. I t is probable t h a t these over-optimistic

and under-optimistic assumptions will compensate for each other to a certain extent in a practical device. The result just obtained indicates that solar radiation is capable of producing a significant number of cesium ions in the cesium thermionic energy converter. I n light of this information, it is interesting to return to Fig. 1, which shows that each constant emitter current density line extends over a wide range of emitter temperatures (for example, see the 1 a m p / c m 2 line). I n contrast to the conventional cesium thermionie energy converter, which must be operated in the region marked "enough ionization" (the region to the right of the solid line in Fig. 1), a cesium converter using solar radiation to produce ions can be operated at considerably lower emitter temperature because its emitter surface is no longer required to produce the ions needed for the neutralization of space charge. Therefore, for a given emitter current density the required heat input to the emitter of such a cesium diode is less than the corresponding heat input to the emitter of a conventional cesium diode. REFERENCES 1. P. M. Marchuk, Trudy Inst. Fiz. Akad. Nauk., SSSR, 7, 3 (1956). 2. K. G. Hernquist, iV[. Kanefsky, and F. H. Norma, RCA Review, 19, 244 (1958). 3. J. M. Houston and M. D. Gibbons, Report on 21st Conference on Physical Electronics, M.I.T., (1961), p. 106. 4. W. B. Nottingham, An Application of Langmuir-Taylor Data to the Thermionic Converter (TEE-7002-8), Thermo Electron Engineering Corporation, Waltham, Mass. 1960. 5. F. S. Johnson, J. of Meteorology, 11,431 (1954). 6. Braddick, H. J. J., and Ditchburn, R. W. Proc. Royl. Soc. A., 143, 472 (1935). 7. Mohler, F. L., Foote, R. D., and Chenault, R. L., Phys. Rev., 27, 37 (1926). 8. Mohler, F. L., Bureau of Standards J. Research, I9, 447, 559 (1937). 9. W. B. Nottingham, Report on 20th Annual Conference on Physical Electronics, M.I.T., (1960), p. 95. 10. H. Moesta, Z. Naturforch, 17a, 578 (1962).

Abstracts of Phoenix Conference Papers Available The authors' abstracts of the papers given at the annual meeting of the Solar Energy Society held in Phoenix, March 15-17 have been collected and are available from Society headquarters. To

112

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