The longitudinal space charge and resistive wall impedances have been investigated in a smooth cylindrical beam pipe. At any point from the beam axis, we obtained an expression for the total impedance, which at the beam surface rϭa for infinite pipe wall conductivity gives the expression for the total impedance that was derived by Zotter and Kheifets in studying the impedance of uniform beams in concentric cylindrical wall chambers, when a single cylindrical chamber is considered ͓B. W. Zotter and S. A. Kheifets, Impedances and Wakes in High-Energy Particle Accelerators ͑World Scientific, Singapore, 1998͒, Chap. 6͔. A fitting formula for the space-charge impedance at the beam surface (rϭa), which is valid for arbitrary wavelengths, is given. Rather than calculating the impedance with the field on the axis ͓Joseph J. Bisognano, Fifth European Particle Accelerator Conference ͑EPAC96͒, edited by S. Myers, A. Pacheco, R. Pascual, Ch. Petit-Jean-Genaz, and J. Poole ͑Institute of Physics, Bristol, 1996͒, Vol. 1, p. 328͔, the fitting formula is obtained by averaging over the transverse beam distribution. We also give another approach for the calculation of the resistive wall impedance using the flux of the Poynting vector at the pipe wall and then compare it with the expression obtained from the volume integral over the beam distribution.

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The longitudinal coupling impedance of a cylindrical beam pipe for arbitrary relativistic gamma(0) and mode frequency is obtained analytically for finite wall conductivity and finite wall thickness. Closed form expressions for the electromagnetic fields excited by a beam perturbation are derived analytically. General expressions for the resistive-wall impedance in the presence of a metallic shield and for the rf shielding effectiveness of the beam pipe have been obtained and then compared with approximate expressions. The results are applied to the GSI synchrotron SIS, where the thickness of the vacuum chamber in the dipole magnets is much smaller than the skin depth at injection energy.

The effects of the presence of a uniform magnetic field on the growth rate and the threshold intensity of the two-plasmon decay in a homogeneous plasma have been investigated. Analytical expressions for the growth rate and threshold intensity have been obtained. It has been shown that the presence of a magnetic field affects significantly the growth rate and the threshold intensity for the two-plasmon decay.

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Using field matching techniques, closed form analytic expressions for the transverse impedance and for the shielding effectiveness of a smooth cylindrical beam pipe of arbitrary thickness are presented. In the limit of thick and thin beam pipes the well-known expressions are reproduced. The transverse transmission coefficient is compared with the longitudinal one that has been obtained in our previous work [A. M. Al-Khateeb, O. Boine-Frankenheim, R. W. Hasse, and I. Hofmann, Phys. Rev. E 71, 026501 (2005).]. The results are applied to the heavy ion synchrotron SIS 18 and to the planned SIS 100 at GSI. In both machines the stainless steel beam pipe in the dipole sections is much thinner than the skin depths at the revolution frequency and, therefore, the impedance value and the transmission are of concern.

In this paper, we present the derivation of the magnetoionic dispersion equation and the corresponding index of refraction and propagation constant for characterizing wave propagation in warm plasma immersed in a uniform magnetic field. To demonstrate the effects of plasma temperature on wave propagation and attenuation, a numerical example of the developed theory has been given. It is well known that there are two forward propagating modes of cold plasma: one is weakly attenuated and the other is weakly amplified. By comparing the cold plasma complex propagation constant of the classical Appleton-Hartree theory with the propagation constant obtained for the warm plasma case, we observed that the attenuated mode is thermally enhanced while the amplification of the other mode decreases by increasing the temperature where it becomes damped beyond a certain electron thermal speed.Index Terms-Appleton-Hartree theory, electromagnetic waves, index of refraction, magnetized plasma, magnetoionic theory, microwave propagation, warm plasma. Muhammad S. Bawa'aneh (SM'10) received the B.Sc. and M.Sc. degrees in physics from Yarmouk University, Irbid, Jordan, in 1989 and 1992, respectively, and the Ph.D. degree in theoretical and computational plasma physics from the University of Essex, Colchester, U.K., in 1999. . His current research interests include electromagnetic wave interaction with plasma and microstrip patch antenna printed on ferrite substrate in free space.

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