A turbine engine comprising a multistage radial compressor system, wherein the multistage radial compressor system comprises: a first stage radial compressor comprising a first stage impeller that rotates about a longitudinal axis of the compressor system and a first stage diffuser positioned radially-outward, with respect to the longitudinal axis, from the first stage impeller and downstream therefrom with respect to an air flow path through the compressor system; a second stage radial compressor comprising a second stage impeller that rotates about the longitudinal axis of the compressor system and positioned downstream from the first stage radial compressor with respect to the air flow path; an interstage region positioned between the first stage radial compressor and the second stage radial compressor, wherein the interstage region comprises a first, radially-outward oriented section positioned immediately downstream from the first stage diffuser, a second, longitudinally-oriented section positioned immediately downstream from the first radially-outward oriented section, and a third, radially-inward oriented section positioned immediately downstream from the second longitudinally-oriented section, wherein the first radially-outward oriented section transitions to the second longitudinally-oriented section at a first approximately 90-degree bend, and the second longitudinally-oriented section transitions to the third radially-inward oriented section at a second approximately 90-degree bend; and a particle separation system comprising an extraction slot and an aspiration slot located downstream from the extraction slot, wherein either: the particle separation system is positioned at an outer wall of the second approximately 90-degree bend and the extraction slot is located at or immediately upstream from an upstream end of the second approximately 90-degree bend and the aspiration slot is located at or immediately upstream from a downstream end of the second approximately 90-degree bend; or the particle separation system is positioned at an outer wall of the third radially-inward oriented section immediately downstream from the second approximately 90-degree bend and the extraction slot is located along the second approximately 90-degree bend and the aspiration slot is located at or immediately downstream of a downstream end of the second approximately 90-degree bend, and, wherein the extraction slot fluidly connects with a scavenge plenum of the particle separation system positioned outside of the air flow path, and wherein the aspiration slot allows air from the scavenge plenum to recirculate back into the air flow path. a first stage radial compressor comprising a first stage impeller that rotates about a longitudinal axis of the compressor system and a first stage diffuser positioned radially-outward, with respect to the longitudinal axis, from the first stage impeller and downstream therefrom with respect to an air flow path through the compressor system; a second stage radial compressor comprising a second stage impeller that rotates about the longitudinal axis of the compressor system and positioned downstream from the first stage radial compressor with respect to the air flow path; an interstage region positioned between the first stage radial compressor and the second stage radial compressor, wherein the interstage region comprises a first, radially-outward oriented section positioned immediately downstream from the first stage diffuser, a second, longitudinally-oriented section positioned immediately downstream from the first radially-outward oriented section, and a third, radially-inward oriented section positioned immediately downstream from the second longitudinally-oriented section, wherein the first radially-outward oriented section transitions to the second longitudinally-oriented section at a first approximately 90-degree bend, and the second longitudinally-oriented section transitions to the third radially-inward oriented section at a second approximately 90-degree bend; and a particle separation system comprising an extraction slot and an aspiration slot located downstream from the extraction slot, wherein either: the particle separation system is positioned at an outer wall of the second approximately 90-degree bend and the extraction slot is located at or immediately upstream from an upstream end of the second approximately 90-degree bend and the aspiration slot is located at or immediately upstream from a downstream end of the second approximately 90-degree bend; or the particle separation system is positioned at an outer wall of the third radially-inward oriented section immediately downstream from the second approximately 90-degree bend and the extraction slot is located along the second approximately 90-degree bend and the aspiration slot is located at or immediately downstream of a downstream end of the second approximately 90-degree bend, and, wherein the extraction slot fluidly connects with a scavenge plenum of the particle separation system positioned outside of the air flow path, and wherein the aspiration slot allows air from the scavenge plenum to recirculate back into the air flow path.