Search Results (5 total)

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.

The longitudinal coupling impedance of a cylindrical beam pipe for arbitrary relativistic γ₀ 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 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 r=a 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, 1998), Chap. 6]. A fitting formula for the space-charge impedance at the beam surface (r=a), 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 (EPAC96), edited by S. Myers, A. Pacheco, R. Pascual, Ch. Petit-Jean-Genaz, and J. Poole (Institute of Physics, Bristol, 1996), Vol. 1, p. 328], 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.

A hybrid model has been developed for investigating the excitation of electron plasma waves in unmagnetized plasmas in the presence of a time-varying laser radiation field and a static Coulomb field. Energy spectral density of the excited plasma modes has been calculated analytically in wave number time space. The model also provides analytical expressions in a closed form for both the time-resolved and the time-averaged spectral density of the rate of energy absorption at resonance (ω_k→ω₀).

Using a ballistic dynamic equation (oscillator model) in the presence of an intense laser field (υ_osc≫υ_th) the time-resolved and time-averaged electron stopping force and electron-ion collision frequency are determined at the critical density (ω₀=ω_p) in the presence of laser field harmonics. An expression for the time-averaged energy absorption rate is given. Results show the contributions of single-particle effects and the generated laser harmonics to the electron-ion collision frequency and energy absorption rate. This work also discusses the time-resolved electron-ion collision frequency.