TRITIUM NUCLEAR BATTERY WITH SOLID DIELECTRIC
6.5. TESTING THE BATTERY MODEL AND MODELING THE CHARGING PROCESS
With the switch “S” closed, the battery model was connected to measurement electronics, the residual pressure in the vacuum chamber was reduced below 10-2 Torr and measurement initiated with the switch being closed. The behaviors of Igrd and Iload with time were the same in general for the various dielectrics used. Experimentally measured
dependencies of Igrd and Iload with time for the models using tritium sources (A=500 mCi) and composite dielectric (polyimide with 20%Nd2Zr2O7) are given in Figure 6.16.
-3 10-10 -2 10-10 -1 10-10 0 1 10-10 2 10-10 3 10-10 4 10-10 5 10-10
0 5000 1 104 1.5 104 2 104 2.5 104
Time, s
Igrd
Iload Rload=1 TOhm R
load=3.2 TOhm R
load=300 GOhm
S close S close S close
S open S open
S open
Figure 6.16. The experimentally measured dependencies Iload and Igrd with time
(points) and approximation data by calculation (curves, see text for details). The results are for the battery model using tritium sources with A=500 mCi and composite dielectric, polyimide with 20%Nd2Zr2O7
As can be seen in Figure 6.16, initially Iload was zero (collector is grounded), and Igrd
decreased with time to a steady state. This steady state can be explained by the equilibrium between the rate of charge accumulation in the dielectric and leakage current caused by electric field of accumulated charge. Igrd usually decreases for 30-40 minutes. After that, a load resistor Rload was connected to the collector and the switch was opened. The Igrd dropped and then increased. Simultaneously Iload increased (in absolute value) until both currents reached steady state levels equal in absolute value but opposite sign. When the collector was grounded again, Iload droped to zero and Igrd increased rapidly to the previous steady state level. This condition was reproducible with switch closing and opening but the time to reach
the steady state and the value of the steady state saturation voltage level depended critically on Rload.
For analysis of these changes, we will use the model and equivalent scheme shown in Figures 6.2 and 6.3 (see paragraph 6.1).
Consider the changes in Igrd and Iload with time when the switch is closed. In this case observe Figure 6.3, Iload=0 and
where η(U) is a function accounting for the electrostatic repulsion of beta particles from the charged region. This function estimates that part of the beta spectrum has energy less than qe·U (see paragraph 3.2.3). At low voltages this factor is not significant. For instance, as U goes from 0 to 1000V, η(U) changes from 1 to 0.91. Ignoring η(U), the solution of
Equation (6.12) for U1 is
A comparison of experimental data and calculations by this equation (dash curve) is shown in Figure 6.16. The comparison between experimental and calculated data is close.
Fitting parameters ICh, R1 and y for the battery model using a 500 mCi tritium source and composite dielectric of polyimide-20%Nd2Zr2O7 are given in Table 6.4. The value of Cint was 670 pF.
Consider the change in Igrd and Iload with time when the switch is open. In this case
The solution of this system of differential equation was found numerically using Mathcad software. Dependencies of Igrd and Iload are plotted in Figure 6.16 with time. The comparison between the dependencies and the experimental data was favorable. The value of Cext =1.3 nF was measured directly. Cint depends on the different load resistors although this was not expected in the model. For the predicted steady state calculations, these capacitances are irrelevant.
Table 6.4. Fitting parameters for model equations for 0.5 Ci tritium source and composite dielectric PI-20%Nd2Zr2O7
Type of dependence Rload, TOhm ICh, pA R1, TOhm y
different load resistors
0.015 460 2.1 0.40 Uload=f(Rload) (at saturation) 0.001-10 460 2.3 0.39
Using these equations, it is possible to determine the I-V and P-V characteristics of the battery with charged dielectric. We let t go to infinity at steady state. In this case, the derivative dU/dt is equal to zero. Then Equations (6.15) and (6.16) can be rewritten as:
)
From Equation (6.19), (6.20) follow
1
load
The absolute value of the load current and useful electrical power Pload from voltage are:
Figure 6.17 shows the I-V and P-V characteristics from experimental measurements (points) and approximation by Equations (6.22)-(6.25) (curves) ignoring η(U). The data represents two tritium battery models with charged dielectric. The first tritium battery model had a tritium source with A=1 Ci and As= 0.06 Ci/cm2 and a composite dielectric with polyimide and 25%Gd2Zr2O7 (solid curve). The second tritium battery model had a tritium source with A=0.5 Ci and As=0.03 Ci/cm2 and a composite dielectric with polyimide and 20%Nd2Zr2O7 (dashed curve). The experimental and calculated results match well. The best fitting parameters for the battery model with A=0.5 Ci and composite dielectric polyimide-20%Nd2Zr2O7 are represented in Table 6.4. The best fit for the battery model with 1 Ci tritium and composite dielectric polyimide-25%Gd2Zr2O7 was Ich=670 pA, R1=6.5 TOhm, and y=0.22.
As can be seen in Table 6.4 from the approximation of the I-V characteristic, the values Ich, R1, and y are very close to those received from the approximation of dependencies of Igrd with time when the switch was closed. In addition, the same was observed with the battery model, with A=0.5 Ci and composite dielectric polyimide-20%Nd2Zr2O7, from the approximation of dependencies of Igrd and Iload with time when the switch was open (Figure 6.3). The same agreement was noted in other battery models and was taken as evidence that the above model was suitable for describing the tritium nuclear battery with charged
dielectric.
As can be seen from represented values R1 and y, R2 is less than R1. It was expected that R2 would be greater than R1 because the distance from the charged domain to the rear electrode was farther than from the charged domain to the source (front electrode). It was observed that the charge density in charged domain decreased from the surface toward the inner volume direction (see Figures 6.9 and 6.10). Beta particles penetrated through the charged surface to the dielectric volume, and thermolized in it. Due to an intensely charged domaim, the thermolized electrons move to the rear electrode and cannot move back through the charged domain due to its much larger negative charge. As a result R2 is less than R1 and y<0.5.
Resistance of load, Ohm Points - experimental data Curves - approximation
Voltage on load, V Points - experimental data Curves - approximation
a) Voltage (square) and load current (circles) versus resistance of load.
Approximation by Eq. (6.22) and (6.23)
b) Current-voltage (square) and power-voltage (circles) characteristics.
Approximation by Eq. (6.24) and (6.25) Figure 6.17. Electrical load characteristics of tritium batteries with charged dielectric with 1 Ci (As= 0.06 Ci/cm2) and polyimide-25%Gd2Zr2O7 (solid) and 0.5 Ci
(As=0.03 Ci/cm2) and polyimide-20%Nd2Zr2O7 (dash)
The measured data of useful electrical power permits calculation of the efficiency of this battery model. In the best case, useful electrical power was 4·10-7 W with efficiency of 1.2% as calculated from Equation (6.26).
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