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amplitude angle anode antiproton atomic beam particles beam-beam interaction betatron bremsstrahlung bunch calculations cathode cavity CERN charge circuit circulating beam coil colliders Conf cross section cyclotron density device diagnostics dipole distribution effects electric field electron beam emittance equation extraction Fermilab flux focusing foil frequency function harmonic HERA high energy horizontal IEEE Trans increase inflector injection instability Instr intensity ion sources ionization kicker laser laser cooling linac linear longitudinal loss machine magnetic field measurement methods mode molecules momentum motion negative ions neutralisation Nucl obtained orbit oscillation parameters Particle Accelerator phase space plane plasma pole positron positron source potential Proc produced proton pulse quadrupole radius residual gas resonance septum sextupole shown in Fig steel stochastic cooling storage rings superconducting surface synchrotron radiation target temperature transverse trapped tube tumor vacuum chamber velocity vertical voltage yoke zero