My answer was based on the jet engine being used in an aviation environment. A jet engine running in a relatively static ground position, within moderate temperature ranges (above freezing; 32°F or 0°C) would run on Diesel... however, the internal components lifespan may be affected, and you would possibly no longer have an engine certified for flight, after running for a period, on a fuel that was outside the manufacturers specified fuels list.
Diesel is a heavier fuel, and has a higher energy content, pound for pound, than JetA/Jet A-1, and burns for longer during combustion, and at a higher temperature.
The major restriction on Diesel energy output is the amount of air fed in with the fuel.
Jet fuel has an S.G. of .62 -.88... Diesel has an S.G. of .82-1.08.