Thermionic Energy Conversion

Definition
“ A thermionic converter is a static device that converts
heat into electricity by boiling electrons from a hot emitter
surface (≈1800 °K) across a small inter electrode gap (< 0.5
mm) to a cooler collector surface (≈ 1000 °K)”

Note: Since this is a form of a heat engine, it is limited by

the Carnot efficiency, at best.

History
Edison-1883.....discovered release of electrons from a hot
body

Fleming-1904.....Invented themionic diode rectifier

Schlicter-1915.....First proposed thermionic conversion

Serious work on thermionic devices began in the early

1950’s

Components of Thermionic Converter- Figure

• Anode must be kept cool to avoid back
emission of electrons
• Note Potential for Topping cycle
• If the gap contains only a vacuum it is called a
vacuum diode,..if it contains a vapor, it is called a
plasma diode.

Factors that limit the efficiency of energy transfer in a

thermionic device
 1.) Radiation heat transfer between the
cathode and the diode,

2.) Space charge effect that limits the

flow of electrons,

3.) Thermal energy losses to the environment.

Principles of Operation

Electron distribution follows Fermi-Dirac Law;

 3  
 4 π ( 2m e ) 2   E 
n ( E )dE =  dE
 h 3   E − E F 
  1 + exp 
 kT  
Probability that any energy state is occupied:
1
P (E ) =
 E − EF 
1 + exp
 kT 

2
 h  2
 3n  3
Where E F =  •
 2m e 8π 

n= # of free electrons/unit volume

=========================
Figures (2) + Graph
In order for an electron to escape the surface it must have
sufficient energy to move it from the Fermi surface to a
point outside the metal.

That energy, per unit charge, is called the work

function,Φ. We designate the work function of the emitter
(cathode) as Φ E and that for the collector (anode) as Φ c .

Note V = Φ E - Φ c

For the time being , assume that no space charge or other

phenomena limit the current flow. For an ideal diode one
gets the Richardson-Dushman equation.

 ΦE 
J
amps  2
 cm 2 
= AT E exp − 
 kT E 
where
• A depends on material and ranges from
amps
3-100
cm 2 ° K 2
Note; as long as V+Φ c <Φ E , the barrier to electron flow is
Φ E and the current is independent of the thermionic device
voltage and is called the saturation current.

 amps   11, 600Φ E 

J = ATE exp −
2

 cm 2   TE 
where T =°K, ΦE=volts

However, when the Φ c +V> Φ E , then the barrier is Φ c +V,

and any increase in V will reduce J.
 Work Function Values for Metallic Elements

W +Cs 1.5
Cs 1.89
K 2.25
Na 2.28
Ca 3.2
Th 3.35
Mn 3.95
Ag 4.08
V 4.11
4.16
Element

Ga
Ta 4.2
Mo 4.2
Zn 4.27
Cr 4.45
Cu 4.48
W 4.53
Ge 4.62
Fe 4.63
Se 4.87
Re 5
Ni 5
Pt 5.36
Os 5.5
0 1 2 3 4 5 6

Work Function-eV
 Problem is that work functions are too high (to get 1
amp/cm2 from W need to run at 2600 °K)

Solution: Use Cs to Lower work function.

(See 2 Graphs)
---------------------------------------------------
Space Charge Effects

Once the electron cloud builds up between the electrodes,

the flow of electrons from the emitter is retarded by an
additional potential, ∆VEB ( Barrier Index). Adding in the
voltage loss across the leads ∆V l and the voltage loss across
the load, ∆V L ,

See Figure

 ( Φ E + ∆V EB ) 
J= AT E2 exp  − 
 kT E 
or
 ( Φ + ∆V cB + ∆V l + ∆V L ) 
J = AT E2 exp  − c 
 kT E 

Major difficulty with Thermionics;

• Large current requires small work function,

• Large voltage (V=ΦE-Φc) requires large work
function.

Efficiency of Vacuum Diodes

Determined by power losses
a.) Radiation Heat Losses
b.) Heat Conduction and I2R Losses.
---------------------------------------------------
Radiation Heat Losses
 

Pr = 
[
σ T E4 − T c4 ] 

  1   1  
+
  ε   ε  − 1 
  E   c  

Heat loss can be reduced by using materials with low

emissivities
--------------------------------------------------
Heat Conduction and I2R Losses
Conduction
k A  TE − TL 
Pk =  l l  •
 AE   ℵ 

= heat /unit area of emitter(conduction

from anode neglected)

where A E = area of emitter (cathode)

k l = thermal conductivity of lead
A l = Cross-sectional area of lead
ℵ = length of electrical lead
T L = temperature of load

I2R
  1 
Pj =  (
 n E Rl
I A ) 2

 AE  (heat load per unit area of emitter)

R l = electrical resistance of lead

• Assume that 1/2 of loss flows toward cathode

Combined losses from the cathode

 1   k l A l (T E − T L )   ( I n A E )2 R l  
Pk, j =  ∑   −  
 A E    ℵ   2  
===========================
Efficiency of diode, η, is,
PL
η=
P e + Pr + Pk, j

where P L = I n ∆V L (useful heat load/unit area of emitter)

P e = Potential energy imparted to the

electrons + K.E. at emitter temperature

 2kT E 
P e = I n ∆V E +
 e 
  2kT E 
= I n  ∆V L + ∆V l + ∆V c +  
  e 
(e is the charge on the electron)
and ∆V l = I n A E R l
 Rl A l
using; ρl =
ℵ
and Wideman-Franz law

 π2  k2
ρ lk l =   • • Tl
 3   e 

where T l =
(T E + TL )
2

I n ∆V L
η =
 2

 π
2 k
 e ( 2 2
TE − TL ) 2 
 I n  ∆V L 
2kT E I n A E Rl
+ I n A E R l + ∆V c + + Pr + − 
  e  6 A E Rl 2 
 

 1
d 
 η
Maximizing =0
dR l
See El Wakil, Nucl. Energy Conversion, Ch. 13
1
η max =
1+Γ

 eP r   1 
and current at ηmax, I n* =   • 
 kT E Γ

and
  e∆V c  2(1 + 2Γ )
  + 2 + π
 kT E  3
Γ=
 AkT E3   e∆V c 
ln   + ln Γ −   −1
 eP r   kT E 

Problem-Calculate the efficiency of the thermionic diode

with the following characteristics;

In = 100 amp Emitter area =10 cm2

eE = 0.25 TE = 1800 °K

ec =0.50 Tc = 800 °K

P r = 5. 67x10 −12
[(1800 4
− 800 4 )]
 1  +  1  −1
 0.25   0.5 

Pr = 11.34 Watts/cm2
and In =100/10 = 10 amps/cm2

 ePr   11.34 • 11, 600 

Γ= *
= = 7.31
 kTE In   10 • 1800 

1 1
and efficiency = = = 12. 03%
1 + Γ 8. 31
=========================================
Miscellaneous
 • In vacuum diode, the gap is reduced to a few micons
to reduce space charge. The gaps can be a problem for
thermionic units near to nuclear fuel which can swell much
more than that.

• One solution is to ‘cesiate’ the surfaces to lower the

work function and neutralize the plasma in the gap
( now the spacing can be as much as 50 microns).

• Present devices achieve less than half of Carnot (≈ 10 -

15 %) but other attractive features keep thermionics ‘in the
hunt’.
• Absence of rotating machinery
• Compactness
* Work well at high temperatures
• Higher efficiency than thermoelectrics

Arrangement for Power Sources

A.) In pile;

Figure 13-15

• Cathode directly heated by fissioning fuel.

Figure 13-18

• Anode cooled by liquid metals

B.) Surface Concept;

Thermionic cells placed in contact with the outside

of the compact core
C.) Out-of - pile;

Cells placed in the exterior of the reactor.

Figure 13-16
Advantage is very little radiation damage to elements.

Figure

==========================================
In - Pile Convertors

Common fuel materials;

UC, UC-ZrC, UO and UO -W
2 2

Example UC, can be used as an unclad emitter.

Major problem is the swelling of the fuel and closing of the

gap.

Solution; encase the fuel with a refractory metal,

Penalty; loss in work function

Tantalum used originally but ran into embrittlement, also

not corrosion resistant........ moved to Re then later to Mo
==========================================
Isomite (Figure 13-21)
• small power ( few Watts)
• low efficiency ( 0.3 -3.4 %)
• Pacemakers
===============================================================

Figure-Comparisons of Operating Temperatures

 Comparison of Critical Material Temperatures for Static Conversion Systems

Thermionic

..

Thermoelectric

0 500 1000 1500 2000

Temperature ° K