Elastic Coulomb electron-ion and ion-ion collisiors in electron ~ams and piasra are studied.The use of low charged, light ions for cooling multiply charge ions zn Electron Beam Ion Source (EBIS) [ 1],Electron Ring Ion Source (ERIS) [2] and Sletron Cyclotron Resonance Ion Source (ECRIS) [3,4] is substantiated.i.Introduction.EBIS, EBIT[5] and ECRIS are succes-si~lly used now for ion production. Recently, a new type of ion source (ERIS) was proposed. A lot of articles and reviews were devoted to the problem of ionization and charge exc~ processes last yeas [6].The elastic Coulomb collisions of charge particles in plasma have been studied well in connection with the thermontr_&ear fusion arches.lt is descri~=d in the textbooks now [7,8]. S~t these p~are not yet taken into accost in the calculations of ion appearance and accLmulation in ion sources.The elastic Coulomb colli-~ons can explain some o observed effects and show the way to incre~ the ion sources effectiveness.2.General equatioas. Elastic scattering of an electron beam on stored ions, residual gas or solid target is a cause of tran~,er~ team dime]qsion -and mittance increase [3,9]. The ions receive an additional momentum in the Coulomb collisions. The energy increase of ions with charge state Z and mass ~ is determined from the eqtmtion [3]: dE/dt=reaZ~NemC2A/ae3~ , ( 1 ) where ~--Ve/C; m,re,ve are the mass, the clae~ical radius and the velocity of electrons;c is the velocity of light;a-P~S s~l] halfdimention of electron beam;A=10-20 is so called Coulomb lo~thm.In the electron team ions are p~e d as the ~tlt of electron impact ionization of the neutral at~s or molecules in the ~.3m.The energy of a single charged ion eq;~],~ to the electric field potential in the place of ion appearance and as a ~e is much more than the energy of a neutral. The ions ~ in the potential well of the ~eand ~j i n to oscillate.They t~dergo f t~t~r ionization and inc~ase the c~rge and the energy. The average total energy of the ion transverse oscillations With the c~arge Z>I ~ defined as[3,tO] ~/Z/~ Ne re m c z (2) The energy of the ion is approximately equal to the value which does not depend on the c~m~ge in the electron t~3m with the C~t~asian density in crce~ section[3]: E=2 Ne re m c a (3) The f o r~l a s (2) and (3) were obtained without t a k i~ into account the ion neutralization of the electron beam c~g e and ~ithout probable electron heating or electron-ion instabilities. ~ the ion energy increases, the oscillation amplitudes rise and can ~ larger t~n the electron beam size. It was shown, that in this case the ions were o~tside the team most of the time, they don't de~end much on the electron component and we consider these ions to be the lost particles [ 1I]. Let us a?a~e that the energy ~l=Z Ne re m C 2 (4)is the limit ener~ for ions. The ions with E>EI have oscillation amplitudes in constant density ~eam of more t~ the beam size and in Gaussian der~'ity bean of more than 1.6,.5ae. The ions collide in the electron ~m. The variation rate of the one kind particle energy...