Gas turbine engine having improved core system

A gas turbine engine (44) having a longitudinal centerline axis (12) therethrough, including: a fan section (16) at a forward end of the gas turbine engine (44) including at least a first fan blade row connected to a drive shaft (40); a booster compressor (20) positioned downstream of the fan section (16) including a plurality of stages, where each stage includes a stationary compressor blade row and a rotating compressor blade row connected to the drive shaft (40) and interdigitated with the stationary compressor blade row; and, a combustion system (46) for producing pulses of gas having increased pressure and temperature of a fluid flow (52) provided to an inlet (54) thereof. A first source (64) of compressed air (52) from the booster compressor (20) is provided to the combustion system inlet (54) and a second source (66) of compressed air (65) from the booster compressor (20) is provided to cool the combustion system (46), where the pressure of the compressed air (65) from the second source (66) has a grea