Abstract: A particle beam bending system having a geometry that applies active bending only beyond the chord of the orbit for any momentum component. Using this bending configuration, all momentum components emerge dispersed in position only; all trajectories are parallel by construction. Combining a pair of such bends with reflective symmetry produces a bend cell that is, by construction, achromatic to all orders. By the particular choice of 45° individual bends, a pair of such achromats can be used as the basis of a 180° recirculation arc. Other rational fractions of a full 180° bend serve equally well (e.g., 2 bends/cell×90°/bend×1 cell /arc; 2 bends/cell×30°/bend×3 cells/arc, etc), as do combinations of multiple bending numerologies (e.g., 2 bends/cell×22.5°/bend×2 cells+2 bends/cell×45°/bend×1 cell).