**3.1 Impact of the neutron spectrum**

The advantage of thermal spectrum reactors is that criticality can be achieved with less fissile material in the core. In turn, the advantages of fast reactors are that no moderator is necessary, thereby allowing more space for fuel, and that the fuel matrix can be constructed from refractory metals without suffering from parasitic absorption at small neutron energies. Fast reactor designs are simpler and more robust because there is no need for a moderator that is either sensitive to elevated temperature, hot hydrogen, or both. In addition, the technological challenges of startup are smaller for fast reactors because of the smaller temperature defect and H2 worth [37]. Finally, flooding with water leads to negative feedback effect in fast reactors [22].

Fast spectrum NTPs during the ANL-200/2000 and GE-710 projects were designed using HEU CERMET in hexagonal assemblies. It is impossible to achieve criticality in a fast reactor with LEU CERMETs [33]. However, it is possible to design a core with sufficient excess reactivity using UN fuel plates with refractory metal cladding [33]. This is enabled by the much smaller ratio of refractory metal to fuel volume than in the LEU CERMETs.

#### **3.2 Neutronics parameters of interest**

The moderator-to-fuel density ratio (MTFR) [38] is an important characteristic for the reactivity of a reactor. There exists an MTFR at which the core multiplication factor assumes a maximum and the core is optimally moderated, while for smaller or larger MTFRs, the core is undermoderated or overmoderated, respectively. From a control perspective, it would be desirable to have an undermoderated core to avoid positive feedback from increasing power. For overmoderated reactors, reduction in hydrogen density caused by an increase in power can lead to a positive reactivity feedback loop. NERVA and derived designs are all undermoderated, as the addition of hydrogen leads to an increase in core reactivity [39]. For LEU reactors, multiplication factor, size, weight, and thermodynamic performance depend heavily on the moderator-to-fuel ratio [40].

Power peaking measures how uniformly the power is produced in the core, and can be computed by taking the maximum power density observed in the reactor and dividing it by the average power density [41]. In practice, it is more common to consider fuel element or fuel assembly peaking, and considering both axial and radial components. These are computed by taking the maximum fuel element power and dividing it by the average fuel element power. The importance of the power peaking is that limiting core conditions, such as peak temperatures, are usually experienced in peak fuel elements.

The temperature peaking factor is related to the power peaking factor, but is influenced by both the power peaking and thermal-fluid conditions in the core. It is defined as the peak fuel element temperature divided by the average temperature of the fuel compacts. Larger power peaking factors can be addressed by directing more flow to the high-power regions, which leads to reduced temperature peaking factors.

Reactivity feedback is the effect that non-neutronic parameters have on the reactivity of the core. When reactivity is positive, reactor power increases, while the opposite is true for negative reactivity. The most important feedback mechanism and the parameters to which they are sensitive are:

• *Doppler Broadening:* Doppler broadening increases the absorption by increasing resonance width with increasing material temperature [38]. While any
