A permanent magnet excited synchronous machine comprising: - a stator , said stator having a plurality of circumferential stator teeth ; - a rotor configured to rotate in said stator ; - a rotary shaft supporting said rotor for rotation on its axis; - a salient pole on said rotor , said salient pole including a shank , said salient pole including a shoe on said shank ; - a rectangular cross-section cavity in said salient pole , said rectangular cavity having a cross-section major axis coincident with a chord of a circle delimited by the rotor diameter, said rectangular cavity having a radially-outer top wall parallel to said chord and said major axis; - an exciter permanent magnet in said rectangular cavity ; - a plurality of selective flux barrier slots in said salient pole , said plurality of slots disposed radially outwardly of said permanent magnet and between said radially-outer top wall of said rectangular cavity and an external surface of said shoe ; characterised in that : - said plurality of slots are disposed in a fan arrangement relative to said chord so that slots of said plurality that are located circumferentially nearer to a main axis (D) of said pole are inclined at a lesser absolute value of inclination angle relative to the main pole axis (D) than are others of said slots relatively located circumferentially farther from the main pole axis (D); and, - said plurality of slots is a number selected to correspond to the number of said stator teeth radially opposite to said shoe . - a stator , said stator having a plurality of circumferential stator teeth ; - a rotor configured to rotate in said stator ; - a rotary shaft supporting said rotor for rotation on its axis; - a salient pole on said rotor , said salient pole including a shank , said salient pole including a shoe on said shank ; - a rectangular cross-section cavity in said salient pole , said rectangular cavity having a cross-section major axis coincident with a chord of a circle delimited by the rotor diameter, said rectangular cavity having a radially-outer top wall parallel to said chord and said major axis; - an exciter permanent magnet in said rectangular cavity ; - a plurality of selective flux barrier slots in said salient pole , said plurality of slots disposed radially outwardly of said permanent magnet and between said radially-outer top wall of said rectangular cavity and an external surface of said shoe ; characterised in that : - said plurality of slots are disposed in a fan arrangement relative to said chord so that slots of said plurality that are located circumferentially nearer to a main axis (D) of said pole are inclined at a lesser absolute value of inclination angle relative to the main pole axis (D) than are others of said slots relatively located circumferentially farther from the main pole axis (D); and, - said plurality of slots is a number selected to correspond to the number of said stator teeth radially opposite to said shoe . - said plurality of slots are disposed in a fan arrangement relative to said chord so that slots of said plurality that are located circumferentially nearer to a main axis (D) of said pole are inclined at a lesser absolute value of inclination angle relative to the main pole axis (D) than are others of said slots relatively located circumferentially farther from the main pole axis (D); and, - said plurality of slots is a number selected to correspond to the number of said stator teeth radially opposite to said shoe . <EOS>