Neutrons, besides being one of the building blocks of matter, are also an essential tool in many scientific experiments. And the most cost-effective source of neutrons is a nuclear reactor.
In a research reactor, neutrons are produced by uranium fission; some are used to sustain the chain reaction while the rest are leaked onto an experimental target. Various tricks can be used to maximize the neutron production of a reactor but, beyond that, if you need more neutrons than a given reactor can provide, you build a bigger reactor. But some experiments depend instead on the neutron flux - the neutron density in volume times time. Increasing a reactor's power increases the total number of neutrons produced, but if the size of the reactor also increases then the flux remains the same, since the neutrons are spread out over a larger volume. A higher neutron flux requires not just more power, but a higher power density in the reactor core.
Power density is limited by cooling. Fission produces heat as well as neutrons, and if the reactor produces more heat than the cooling system can remove, the fuel rods melt. This is generally considered a design flaw. A higher flux can be produced by "pulsing" the reactor - running it at very high power, then shutting down to allow the cooling system to catch up - but this can only produce a high flux for a brief period at a time.
Los Alamos scientists in the late 60s wanted to go beyond the limits of conventional research reactors. Neutron flux is limited because heat cannot be removed quickly enough from the fuel. But what if, instead, they removed the fuel from the heat?
In the Liquid-Jet Super-Flux Reactor (LJSFR), a fluid fuel would be pumped into the reactor, then, after fissioning, be pumped rapidly back out. By cooling the fuel outside of the reactor vessel, a power density - and therefore neutron flux - far beyond conventional reactors could be achieved.