A cyclotron for accelerating a particle beam over a given path comprised within a gap, said cyclotron comprising: (a) A chamber defined within a yoke, wherein said yoke is formed by a first and second base plates normal to a central axis, Z, and separated from one another by a flux return yoke defining a lateral outer wall of the cyclotron, (b) first and second magnet poles located in the chamber and symmetrically positioned opposite to one another with respect to a median plane normal to the central axis, Z, and separated from one another by said gap, and wherein each of the first and second magnet poles comprises, (c) at least N = 3 hill sectors having an upper surface and a same number of valley sectors comprising a bottom surface, said hill sectors and valley sectors being alternatively distributed around the central axis, Z, such that the gap separating the first and second magnet poles comprises hill gap portions defined between the upper surfaces of two opposite hill sectors and having an average gap height, Gh, measured along the central axis, Z, and valley gap portions defined between the bottom surfaces of two opposite valley sectors and having an average valley gap height, Gv, measured along the central axis, Z, with Gv > Gh; (d) the bottom surfaces of each valley sector are defined by a valley peripheral edge, said valley peripheral edge being bounded by a first and a second lower distal ends, and is defined as the edge of the bottom surface located furthest from the central axis, Z; (e) the bottom surfaces of each valley sector further comprise an abyssal opening extending through a thickness of the yoke base plates and defining an abyss gap portion of height, Ga, at least five times as large as Gh, said abyssal opening having a cross-section normal to the central axis defined by an abyss perimeter, which is separated from the valley peripheral edge by a shortest distance, Lap, measured along an abyss radial axis, Lar, intersecting perpendicularly the central axis, Z, and wherein the valley peripheral edge is separated from the central axis, Z, by a distance, Lv, measured along the abyss radial axis, Lar; (f) the flux return yoke has a wall thickness varying with the angular position about the central axis, with a lowest wall thickness value, Tv, measured along the abyss radial axis, Lar, of each valley sector; characterized in that, the ratio, (Lap x Tv) / Lv 2, of the product of the distance, Lap, of the abyss perimeter to the valley peripheral edge of each valley sector times the flux return yoke thickness, Tv, to the square of the distance, Lv, of the peripheral edge to the central axis, Z, is less than 5%. (a) A chamber defined within a yoke, wherein said yoke is formed by a first and second base plates normal to a central axis, Z, and separated from one another by a flux return yoke defining a lateral outer wall of the cyclotron, (b) first and second magnet poles located in the chamber and symmetrically positioned opposite to one another with respect to a median plane normal to the central axis, Z, and separated from one another by said gap, and wherein each of the first and second magnet poles comprises, (c) at least N = 3 hill sectors having an upper surface and a same number of valley sectors comprising a bottom surface, said hill sectors and valley sectors being alternatively distributed around the central axis, Z, such that the gap separating the first and second magnet poles comprises hill gap portions defined between the upper surfaces of two opposite hill sectors and having an average gap height, Gh, measured along the central axis, Z, and valley gap portions defined between the bottom surfaces of two opposite valley sectors and having an average valley gap height, Gv, measured along the central axis, Z, with Gv > Gh; (d) the bottom surfaces of each valley sector are defined by a valley peripheral edge, said valley peripheral edge being bounded by a first and a second lower distal ends, and is defined as the edge of the bottom surface located furthest from the central axis, Z; (e) the bottom surfaces of each valley sector further comprise an abyssal opening extending through a thickness of the yoke base plates and defining an abyss gap portion of height, Ga, at least five times as large as Gh, said abyssal opening having a cross-section normal to the central axis defined by an abyss perimeter, which is separated from the valley peripheral edge by a shortest distance, Lap, measured along an abyss radial axis, Lar, intersecting perpendicularly the central axis, Z, and wherein the valley peripheral edge is separated from the central axis, Z, by a distance, Lv, measured along the abyss radial axis, Lar; (f) the flux return yoke has a wall thickness varying with the angular position about the central axis, with a lowest wall thickness value, Tv, measured along the abyss radial axis, Lar, of each valley sector;