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Abstract
| A proposed electron cooler for RHIC would use 55 MeV electrons to cool fully-ionized 100 GeV/nucleon gold ions.* At two locations in the collider ring, the electrons and ions will co-propagate for 13 m, with velocities close to c and gamma>100. To lowest-order, one can Lorentz transform all physical quantities into the beam frame and calculate the dynamical friction forces assuming a nonrelativisitc, electrostatic plasma. However, we show that nonlinear space charge forces of the bunched electron beam on the ions must be calculated relativistically, because an electrostatic beam-frame calculation is not valid for such short interaction times. The validity of nonrelativistic friction force calculations must also be considered. Further, the transverse thermal velocities of the high-charge ( 20 nC) electron bunch are large enough that some electrons have marginally relativistic velocities, even in the beam frame. Hence, we consider relativistic binary collisions – treating the model problem of two charged particles on a line, comparing nonrelativistic dynamics, marginally relativistic (in the Darwin approximation) and fully relativistic, with retarded potentials. |