Electron Cooling of Positrons and Possibilities of Positron Beam Crystallization

The possibility of an electron or positron beam crystallisation is connected with a decrease of the temperature of the beam longitudinal degree of freedom during acceleration. At fast acceleration the temperature increases after acceleration due to relaxation of initial density fluctuations. To avoid this process the beam acceleration has to be slow and can be performed using induction acceleration of the beam in cyclic accelerator. Other process limiting the minimum beam temperature is the transverse-longitudinal relaxation. This process excludes a possibility of a crystalline beam formation in classical betatron accelerator. The relaxation can be substantially suppressed using longitudinal magnetic field. The betatron with additional longitudinal magnetic field, so called "modified betatron", was proposed as a candidate for electron cooling system with circulating electron beam in the GeV ion energy range [1,2]. An installation of such a type - LEPTA (Low Energy Particle Toroidal Accumulator) is presently under construction in JINR. Its general aim is an electron cooling of positrons and positronium generation, however the ring will be equipped with an inductor to provide electron or positron beam acceleration. Experimental investigations of the particle motion stability during induction acceleration are very important for design of the electron cooling system with circulating electron beam. After acceleration one can expect formation of the crystalline state of the electron or positron beam and life time of this state can give an information about the intra beam scattering rate which is necessary to determine optimum period of the electron beam circulation during ion cooling. A crystalline state of the beam is of an interest as an object for investigation also. Possibilities and advantages of experiments with crystalline electron and positron beam are discussed in this paper. An optimum experiment scenario and LEPTA parameters are described.