## Suhas Kumar December 5, 2011

### Submitted as coursework for PH240, Stanford University, Fall 2011

 Fig. 1: Ragone plot for various batteries including Atomic batteries. [2,3].

Waste from nuclear fission reactors produce radiations. There are other radioactive materials that produce radiations too. This radiation has energy and this document looks at this energy.

Let us do a calculation to estimate the energy in 1000 kg of U-235. Its half life is 4.5 × 109years. The energy released in each alpha particle is 4.27 MeV. [1] The decay constant is k = ln(2)/(half life) ~ 4.9 × 10-18 sec-1. The number of nuclei is N = 1000 kg / (235 × mass of proton) ~ 2.6 × 1027. The activity is thus k × N ~ 1.3 × 1010sec-1. Now, power is activity × energy per particle, which is about 0.0085 W. If we convert all this energy to electricity, we might barely have enough to power an LED! If we replace U-235 with Cs-137 with a half life of about 30 years, it would yield 1 MW of power, which is sizable, yet not even close enough to run a power plant. The conversion could be lossy too. This hints at the domains of operation: long lasting power supply, low power, high energy. Electrical technology being mature, we consider harnessing and/or storage in terms of electricity.

## Atomic Batteries - Energy and Power

The family of devices that convert these radiations to electrical power is known as Atomic Batteries. Conversion is classified into two main types: Thermal and non-thermal. Thermal conversion uses the energy in the radiation to heat a target, which is then converted to electricity, for instance using a thermocouple. Non thermal converters do not depend on the thermal energy of radiation; for instance radiation can be used to induce charge which is then converted to electricity. The efficiency of these can be about 20% at best. To compare their performances, we consider the power and energy density of storage devices. Such a plot is known as a Ragone plot. [2,3] Fig. 1 presents a Ragone plot of atomic batteries made of some commonly used radioactive materials and compares them to commonly used batteries. The sloped lines are constant-time lines. The numbers for atomic batteries were calculated as shown in the previous section, assuming an efficiency of 0.1. This shows that atomic batteries are high energy density and relatively low power density devices.

 Fig. 2: Cost per unit energy (\$/kJ) plotted against power density (W/kg) of various batteries. [9-14]

## Applications

The applications follow from the position of these in the Ragone plot. These batteries have been employed to enable compact and high energy capacity power generators for applications ranging from implantable cardiac pacemakers to space stations. [4,5] Currently, radioisotope power generators are being developed for realizing safe, compact, high energy capacity, and long lifetime batteries for remote wireless sensor microsystems in applications ranging from environmental health monitoring to structural health monitoring. [6,7] These are also employed in a variety of industrial applications including electron capture devices for gas chromatography. [8]

## Costs

The costs that matter are the cost per unit energy (\$/kJ) and the cost per unit power (\$/kW). The costs for various commonly used batteries were obtained from a market survey - by obtaining the cost per kilogram of the packaged product and using Fig. 1 to get to \$/kJ of the storage system. The costs of atomic batteries were approximated to the cost of the radioactive material required to build it, since the \$/kg of these materials are many orders of magnitude higher than the cost of processing or packaging. The cost of most of these substances were found to be about 105\$/kg. Fig. 2 shows the data obtained from this analysis. We observe that some of the atomic batteries, especially those of Sr-90 and Cs-137 are comparable in power density to chemical batteries and lower in cost.

## Conclusions

Atomic batteries can be used for high energy applications typically with low power and 20% efficiency at best. The cost analysis shows Sr-90 and Cs-137 batteries to be very promising. The approximations made in the cost analysis must be borne in mind while reading Fig. 2; and also the regulations on the markets and products of these materials.

© Suhas Kumar. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

## References

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[9] L. J. Wittenberg, "The Cost of Tritium Production in a Nuclear Reactor," Fusion Technology Institute, Univ. of Wisconsin, UWFDM-871, November 1991.

[10] R. van Ginderdeuren, E. van Limbergen, and W. Spileers, "18 Years' Experience With High Dose Rate Strontium-90 Brachytherapy of Small to Medium Sized Posterior Uveal Melanoma," Br. J. Ophthalmol. 89, 1306 (2005).

[11] R. D. Rogers et al., "Encapsulation Method for Maintaining Biodecontamination Activity," U.S. Patent 7026146, 11 Apr 06.

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[13] J. E. Hoisington, "Radioisotopes for Heat-Source Applications," DPST-82-842, Savannah River Laboratory, October 1982.

[14] A. C. Baisden, "ADVISOR-Based Model of a Battery and an Ultra-Capacitor Energy Source for Hybrid Electric Vehicles," IEEE Trans. Vehicular Technol. 53, 199 (2004).