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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