Transverse beam jitter damping along the Future Circular Collider <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></

Transverse stabilization of the beam is crucial for optimizing the performance of a particle accelerator, regardless of its application. The most common method for minimizing transverse beam jitter is the Balakin-Novokhatsky-Smirnov (BNS) damping technique. Although this method has been successfully implemented worldwide, it has limitations since a significant fraction of the accelerating structures are operated off crest. In this work, we propose an alternative approach to induce the required energy spread, utilizing the natural curvature of the accelerating rf field in combination with a relatively long bunch and a longitudinal wakefield. This approach achieves strong damping of the transverse beam oscillations, similar to BNS damping, while simultaneously optimizing beam quality and maximizing acceleration efficiency. We have applied this method to the design of the Future Circular Collider injector linacs, designed to reach a beam energy of up to 20 GeV. However, this method is general and can be applied in principle to any accelerator.