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Al-Khateeb, A.M.

Paper Title Page
THPCH034 Transverse Coupling Impedances From Field Matching in a Smooth Resistive Cylindrical Pipe for Arbitrary Beam Energies 2853
 
  • A.M. Al-Khateeb, A.M. Al-Khateeb, W.M. Daqa
    Yarmouk, Irbid
  • O. Boine-Frankenheim, R.W. Hasse, I. Hofmann
    GSI, Darmstadt
  
  The transverse coupling impedance is investigated analytically. For an off-axis motion of the beam, the perturbed charge distribution of the beam becomes a function of the azimuthal angle, resulting to first order in the beam displacement in a dipole term which is the source of the transverse impedance. All six components of the electromagnetic field are different from zero and, therefore, both TM and TE modes will be excited in the beam-pipe and coupled to the beam at the inner surface of the resistive wall. Using the dipole source term, a linear combination of TM and TE modes is used to get closed form expressions for the transverse electromagnetic field components excited in the beam-pipe, and a generalized analytic expression for the corresponding transverse coupling impedance. It has been found that the contributions of the TM and the TE modes to the real part of the transverse resistive-wall impedance have similar dependence on the relativistic parameter but with opposite signs, the sum of both always being positive. Some approximate simple formulas for three important regions corresponding to small, intermediate and large frequencies in the ultrarelativistic limit were also obtained analytically.  
THPCH034 Transverse Coupling Impedances From Field Matching in a Smooth Resistive Cylindrical Pipe for Arbitrary Beam Energies 2853
 
  • A.M. Al-Khateeb, A.M. Al-Khateeb, W.M. Daqa
    Yarmouk, Irbid
  • O. Boine-Frankenheim, R.W. Hasse, I. Hofmann
    GSI, Darmstadt
  
  The transverse coupling impedance is investigated analytically. For an off-axis motion of the beam, the perturbed charge distribution of the beam becomes a function of the azimuthal angle, resulting to first order in the beam displacement in a dipole term which is the source of the transverse impedance. All six components of the electromagnetic field are different from zero and, therefore, both TM and TE modes will be excited in the beam-pipe and coupled to the beam at the inner surface of the resistive wall. Using the dipole source term, a linear combination of TM and TE modes is used to get closed form expressions for the transverse electromagnetic field components excited in the beam-pipe, and a generalized analytic expression for the corresponding transverse coupling impedance. It has been found that the contributions of the TM and the TE modes to the real part of the transverse resistive-wall impedance have similar dependence on the relativistic parameter but with opposite signs, the sum of both always being positive. Some approximate simple formulas for three important regions corresponding to small, intermediate and large frequencies in the ultrarelativistic limit were also obtained analytically.