How could this small nuclear reactor power two jet engines?
The answer is, it couldn't and was never even utilised in that way.
This nuclear powered bomber concept, first thought of in the 1950's, had two major problems to contend with, neither of which were solved. The first was how to harness the nuclear power, either directly as a propulsion unit or indirectly using a heat exchanger and the second was how to protect the crew, either by directly shielding the reactor, which made the aircraft unstable to fly, due to concentration of weight, or by distributed shielding, which was not as efficient but spread the weight around the aircraft in a more balanced fashion.
The B36 shielding test aircraft, accompanied by an aircraft with a cleanup crew in case the B36 crashed.
On September 5, 1951, Convair was formally granted a contract to construct, or rather convert, one of their B-36 aircraft to enable it to carry out the testing of the reactor and the shielding associated with it.
To illustrate how stupidly ridiculous this idea was, every test flight of the B 36 had to have a troop carrying aircraft flying behind it, in case the B 36 crashed. The soldiers could then attempt to clean up the nuclear waste.
Two methods of nuclear propulsion were proposed. The first was the indirect cycle, which was designed to heat up incoming cold air by the use of hot air from the reactor, and the second was the direct cycle engine, which simply used atmospheric air as a working fluid and ignored the environmental effects of exhausting nuclear waste straight out of the engine tailpipe.
One early design of indirect nuclear propulsion power plant.
A illustration of a direct nuclear propulsion power plant .
Image Sources and excerpts from Nuclear Powered Aircraft
This was the only known airborne reactor experiment by the U.S. with an operational nuclear reactor on board. The NTA flew a total of 47 times testing the reactor over West Texas and Southern New Mexico. The reactor, named the Aircraft Shield Test Reactor (ASTR), was operational but did not power the plane, rather the primary purpose of the flight program was shield testing. Based on the results of the NTA, the X-6 and the entire nuclear aircraft program was abandoned in 1961.
In reality, because this was part of the cold war, I would tend to disbelieve claims such as any power outputs quoted.
The Soviet program of nuclear aircraft development resulted in the experimental Tupolev Tu-119, or the Tu-95LAL (Flying Nuclear Laboratory) which derived from the Tupolev Tu-95 bomber. It had 4 conventional turboprop engines and an onboard nuclear reactor.
It actually turns out that the Soviets were prepared to risk pilots who volunteered to endure the inevitable radiation hazards. The Soviets used little or no shielding to save weight during 40 test flights, and used direct cycle nuclear reactors. Most of the aircrew died through radiation induced illness.
The obvious potential of the ICBM made the expensive program superfluous, allied with the fact that these slow bombers were easy targets for surface to air missiles and around the mid-1960s, both countries cancelled their projects.
You can watch an hour long video of the story at Nuclear Powered Bombers