Calculation of the variable-profile electron beam for electron coolers

Interaction of an electron beam with a cooled ion beam makes it possible to reduce its phase volume, perform accumulation of particles, and suppress various “heating” effects. The electron beam can also be used as a target for an electron-ion recombination reaction, which offers a chance to carry out atomic physics experiments and ensure slow uniform extraction of the ion beam from the storage ring. A high-perveance electron beam with a variable profile is required for effective cooling, while a high current density and a low energy of transverse motion of electrons in the beam is needed for extraction by means of recombination. It is shown that a convex cathode placed in a magnetic field can be used to form such a beam. A high current density can be attained with this shape of the cathode, but additional efforts must be focused on optimizing the gun’s optics in order to obtain a low energy of transverse motion of particles. Since ions repeatedly pass through the cooling section during their lifetime at different values of the betatron oscillation phase, the rates of recombination and cooling are dependent on the rms electron velocity averaged over the volume in which the beam interaction occurs. The proposed design of the gun with a convex cathode 10.2 mm in diameter ensures formation of a variable-profile electron beam with a nominal current of 1 A and a current density of 1.2 A/cm². The rms energy of Larmor gyration of electrons at the exit from the gun, averaged over the beam cross section (the “transverse” temperature) is 1 eV. A focusing electrode that forms the Pierce optics near the edge of the cathode, an electrode controlling the beam profile, and an anode are included in the optics of the electron gun.