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Particle accelerators for high energy physics will generate TeV-scaleparticle beams in large, multi-Km size machines colliding high brightness beamsat the interaction point [1-4]. The high luminosity in such machines isachieved by producing very small asymmetric beam size at the interaction point,with short durations to minimize beam-beam effects. Tuning energy, timing andposition of the beam for optimal performance will require high-precisioncontrols of amplitude and phase of high-frequency electromagnetic fields andreal-time processing of complex algorithms. The stability of the collidingbeams has a large impact on the collider's effective luminosity. Therefore, thetechnology readiness level of diagnostic and control systems will be a majorconsideration in the collider design. The technical requirements of suchsystems depend on the specifics of beam parameters, such as transverse andlongitudinal dimensions, charge/pulse and beam pulse format, which are drivenby the accelerating technology of choice. While feedback systems with singlebunch position monitor resolution below 50 nm and latency <300 ns have beendemonstrated in beam test facilities, many advanced collider concepts make useof higher repetition rates, brighter beams and higher accelerating frequencies,and will require better performance, up to 1-2 order of magnitude, demandingaggressive R&D to be able to deliver and maintain the targeted luminosity.

Feedback and control systems for future linear colliders: White Paper for Snowmass 2021 Topical Group AF07-RF