Pebble bed modular reactors (PBMR) are small, helium-cooled reactors that use small tennis ball size fuel balls consisting of only 9 grams of modified uranium per pebble to form a porous bed through which helium coolant flows. The pebbles are placed at the top of the core and fall with gravity then, depending on scheme in use, the pebbles are either recycled back to the top to be used again or are discharged after one cycle.  This form of fuel extraction is a popular focus for research and development amongst scientists because of it is a safe way to extract fuel from uranium.
The safety features of the PBMR are attributed to a number of its design features. The pebbles are comprised of 7 to 9 gram uranium oxide and/or uranium carbide kernels that are subsequently coated in many layers of material to form a pressure boundary and retention zone for fission products. The uranium is typically enriched to 8% but there has been progress towards increasing this enrichment level to over 18%.  The specific layers include pyrolytic carbon, silicon carbide, and buffer graphite.  It is this confinement of radioactive fission products that make the PBMR much safer than any other light water reactor (LWR). Gougar, et al. describe this layering in detail:  "The pyrolytic carbon layers are applied in a chemical vapor deposition process to form a fuel particle of just under 1 mm diameter. Many thousands of these so-called TRISO particles are then mixed with graphite and a binder. The mixture is formed into a sphere of about 5 cm in diameter (or a cylindrical compact for use in a prismatic core). A 0.5 cm layer of pure graphite surrounds the fuel zone to form the 6 cm pebble." Further research is being conducted to increase the thermal conductivity of these layers in order to increase the reactors maximum temperature.
The PBMR is a safer alternative to LWR as it can attain a much higher temperature before failure. Although it is producing the same amount of power, the core of the PBMR is much smaller and thus has a lower power density of 3.0 W/cm as compared with 104 W/cm of the LWR. This is a significant difference that can be attributed to the use of graphite; graphite is a thermal conductor and can transfer heat away from the fuel and out of the core quickly. 
The coupling of high temperature reactor systems and gas turbines has removed the need for engineering systems. As Ion, et al. explains, "The fuel retains its integrity under high temperature accident conditions and has good resistance to chemical attack, e.g. from water or air ingress. Further, the introduction of an annular core allows fuel decay heat to be conducted through the reactor structures to the vessel cavity and then to atmosphere without the need for AC electrical power or early operator intervention."
The PBMR was derived from the High Temperature Reactor (HTR) designed by the Germans in the 1970s.  Since then years of research and development have been invested by governments to make the PBMR more economic, safer, less wasteful, and resistant to proliferation. Additionally, researchers have experimented with the way that pebbles are inputted into the reactor in an effort to increase the power density and recyclability of the pebbles and thus increase efficiency and decrease wastage. [1-3]
Eskom, a South African company, lead research into improving the PBMR in 1993. Since then the South African government and various international investors have backed the program in order to accelerate the development of the reactor. Most recently, clearance from the South African government has allowed a full-sized Demonstration reactor to be built in Koeberg. This design has high quality fuel with extremely low particle failure rates. They have proven that as long as the temperature remains below about 1600°C, fission products will be contained within the fuel and its TRISO coatings. 
Boer et al. conducted an experiment that used heuristic methods to find the reloading pattern that would best improve the power density of PBMR.  They found one approach to testing fuel-loading patterns was altering the number of radial fueling zones. They discovered that the less radial zones there are in the core reactor the higher the power density. The process is explained for a two zone core, "by recycling the pebbles eight times in the outer zone and two times in the inner zone consecutively, the peak in the radial power profile reduce from 10 MW/m3 to 8 MW/m3." Another method investigated was the recycling of the pebbles through the system they found that after the pebble passes through the core six times there is no longer a benefit to the maximum fuel temperature in normal operating conditions.  This information can inform further research and allow scientists to improve the maximum fuel temperature and thus safety of the PBMR.
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 S. Ion, et al., "Pebble Bed Modular Reactor - the First Generation IV Reactor to Be Constructed," Nucl. Energy. 43, 55 (2004).
 H. D. Gougar, A. M. Ougouag, and W. K. Terry, "Advanced Core Design and Fuel-Management for Pebble-Bed Reactors," Idaho National Laboratory, INEEL/EXT-04-02245, October 2004.
 B. Boer et al., "In-Core Fuel Management Optimization of Pebble-Bed Reactors," Ann. Nucl. Energy 36, 1049 (2009).