Abstract. We attract attention that interaction of particle in downstream undulator with its own wavelet emitted in upstream undulator could be as strong as with the frictional field in undulator itself. This phenomenon could be used for enhancement of signal from pickup undulators in optical stochastic cooling methods as well as for increase of damping.Particle passed an undulator emits undulator radiation wavelet (URW) which length is 1 M where M is the number of undulator periods, 1 -is the wavelength of first harmonic. In system of N identical undulators located along straight line the particle radiates train of wavelets with separation l; both l and 1 defined by Doppler effect, by angle between instant velocity and direction to observer, by distance between undulators 0 l , by period of undulator u and by relativistic factor 1 . In straight forward direction 0. Energy radiated by particle in system of N undulators is N times bigger than the one radiated in just one undulator. Spectrum of radiation emitted in arbitrary direction also changes: appears line-type spectrum. Integrated spectrum changes not much, see [1].In this publication we suggest to increase the loss rate in system of N undulators by introduction of controlled delays in motion of particles relative to the URW between undulators, Fig.1. Delays chosen so that particle enters the following undulator together with the front edge of URW emitted in anterior undulators in decelerating phase. In this case the particle will experience deceleration in its self field generated by its instant motion in a field of undulator (friction force generated by spontantenous incoherent radiation) as well as in the field of URW from anterior undulators (induced radiation in field of co-propagating electromagnetic wave). Under such condition occurs superposition of wavelets which yield the electric field grows ~N so the energy emitted grows ~N 2 . To be effective and optimal, this system must use appropriate focusing elements such as lenses and/or focusing mirrors, see the scheme of installation on Figs
