Perhaps the single most important safety aspect of a nuclear reactor is the temperature coefficient of reactivity. This value describes how the reactor will react to an increase or a decrease in reactor temperature. If the coefficient is positive, then an increase in core temperature will cause an increase in reactivity, which will lead the reactor to generate more power, which will increase power more, and so forth until the reactor is destroyed. If the reactor has a negative temperature coefficient, on the other hand, an increase in power will lead to a reduction in core reactivity, which will generate less power, and core temperatures will decrease. All reactors licensed in the United States must demonstrate that they have negative temperature coefficients under all operating conditions. The Chernobyl nuclear reactor accident in 1986 was caused by operators allowing the reactor to enter an operational regime where the reactor had a positive temperature coefficient.

Negative Temperature Coefficient

A negative temperature coefficient of reactivity can be thought of with a mechanical analogy. Imagine a mass on the end of a spring attached to a wall. If the mass is subjected to a force, its acceleration, velocity, and ultimate location will be determined by the stiffness (spring constant) of the spring to which it is attached. The stiffness of the spring represents the negative temperature coefficient of reactivity; the force pulling on the spring represents the power demand on the reactor. If there is no power demand on a critical reactor with a negative temperature coefficient, it will produce essentially no power. Upon the addition of a power demand, the reactor responds by increasing its power, until it is producing the power demanded.

If the negative temperature coefficient is infinitely large (corresponding to an infinitely stiff spring) then the reactor will quickly reach its power demand level with no oscillation or overshoot in power. Similarly, if the demand for power is lost, through interruption or accident, then the reactor power will quickly move back to zero with no oscillation.

Real World Factors

In a real reactor, with a finite negative temperature coefficient, the response of the reactor to the addition and removal of power demand is more like the response of the mass and the spring. If load is added, then the reactor power goes up but overshoots the demand and has to come back, with damped oscillations that eventually stop and power equals demand. If load is removed, the reactor “bounces” back to the zero power level at a rate that depends on the temperature coefficient. The more negative the temperature coefficient, the more precisely the reactor assumes the desired power level and the less “hunting” for that location takes place.

In typical terrestrial reactors with moderately negative temperature coefficients, there is enough “overshoot” and “bounce” in the reactor’s response that a reactor operator uses control rods to “ride” the oscillations and prevent the reactor from damaging itself during these transients. A properly-designed liquid-fluoride reactor has a very high negative temperature coefficient, since as the reactor temperature increases, the fluoride salt expands in volume, and there is less fissile material in the core to sustain the reaction. Hence, the liquid-fluoride reactor can respond very quickly and accurately to the addition and removal of power load without concern about damage to the reactor during transients.

Extraterrestrial Considerations

This is a prime consideration during operation of a space nuclear power system since the primary load will probably be the electric thrusters that provide propulsion. As was shown during the Deep Space 1 mission, electric thrusters (especially ion engines) can short out very quickly and the load on the power system can be lost nearly instantaneously. Some of the space reactor systems being investigated have positive temperature coefficients of reactivity and rely on fast acting control systems and control rod motors to keep the reactor within operational limits. While such systems can be made to work, they must be extraordinarily reliable and have extensive redundancy since the integrity of the reactor depends on them. Even a reactor with a moderately negative temperature coefficient must employ control systems to prevent damage during transients.

LFTR  Stability

A LFTR Liquid Fluoride Thorium Reactor, with its large negative temperature coefficient, would be inherently stable and not need to rely on mechanical systems for control. Thus the fast-acting control systems, monitors, redundancy, and extensive testing under all conceivable scenarios will not be necessary for such a reactor. It will reliably and swiftly assume the power level desired and quickly shut down if the power load is lost. Such inherent safety is vastly more desirable than the engineered safety of control systems, and it will lead to lower costs in development, testing, and operations.

This capability is not theoretical–it was actually demonstrated during the operation of both of the liquid-fluoride reactors constructed. Here is an excerpt from a paper describing the operation of the Molten-Salt Reactor Experiment in 1968:

“The dynamic behavior of the MSRE was extensively examined, by theoretical techniques before the reactor was operated and by experiments during the operation. Calculations had indicated that the reactor would be inherently stable at all power levels and that the degree of stability would increase with increasing power, and experimental measurements of the reactor dynamic response agreed very closely with the predictions. In addition, measurements made throughout the operation with U-235 fuel showed that there was no change in dynamic behavior with time.

“Similar theoretical and experimental evaluations were made of the dynamic behavior with U-233 fuel. The calculations indicated that, despite the lower delayed-neutron fraction, the reactor stability would be greater with U-233–due primarily to the larger negative temperature coefficient of reactivity of the fuel salt. Experimental measurements of system transfer functions and transient response are in good agreement with predictions.

“Because of the good self-regulating characteristics of the MSRE, the system is quite simple to control. In more than 15,000 hours of critical operation, not once have the nuclear power, period, or fuel temperature gone out of limits so as to cause a control-rod scram.”