Effect of transverse electron velocities on the longitudinal cooling force in the Fermilab electron cooler

In Fermilab's electron cooler, a 0.1A, 4.3MeV DC electron beam propagates through the 20 m cooling section, which is immersed in a weak longitudinal magnetic field. A proper adjustment of 200 dipole coils, installed in the cooling section for correction of the magnetic field imperfections, can create a helix-like trajectory with the wavelength of 1-10 m. The longitudinal cooling force is measured in the presence of such helixes at different wavelengths and amplitudes. The results are compared with a model calculating the cooling force as a sum of collisions with small impact parameters, where the helical nature of the coherent angle is ignored, and far collisions, where the effect of the coherent motion is neglected. A qualitative agreement is found.