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A simple quasi-analytic model is developed for the dynamics of electron cloud generated by synchrotron radiation of the beam in the LHC beam pipe. The model allows to obtain a multipacting condition for the LHC parameters, takes into account the space charge efiect and predicts an equilibrium density of the electrons. Based on this model, we flnd the electron lifetime and estimate the energy deposition of the electron cloud to the wall. We also estimate the emittance growth of the beam due to random ∞uctuations of the electric fleld of the cloud and flnd the growth rate of the beam instability caused by the electrons.

In a recent paper [1] Kaplan and Shkolnikov propose to generate intense ultrashort pulses of electromagnetic radiation in the range {approx} 10{sup -21}s (zeptosecond) and large magnetic fields by using a petawatt electron laser irradiating a small solid particle or a piece of wire of a submicron size. In this comment we would like to point out that the method proposed in Ref. [1] will not achieve the desired results.

We extend analysis of Ref. [1] of the closed orbit instability driven by the resistive wall impedance for the case of strong focusing lattice. A numerical estimate for the Low Energy Ring of PEP-II shows that the threshold current is three times higher than the nominal one.

The coherent synchrotron radiation of a bunch in a bunch compressor may lead to the microwave instability producing longitudinal modulation of the bunch with wavelengths small compared to the bunch length. It can also be a source of an undesirable emittance growth in the compressor. We derive and analyze the equation that describes linear evolution of the microwave modulation taking into account incoherent energy spread and finite emittance of the beam. Numerical solution of this equation for the LCLS bunch compressor gives the amplification factor for different wavelengths of the beam microbunching.

If a beam is injected into the ring with an offset a, it undergoes betatron oscillation. After the oscillation decoheres, the beam transverse emittance increases by Δe. To avoid this emittance increase one typically uses a feedback (damper) that takes out the oscillation before it damps down. We show that using echo one can recover a fraction of Δe long after the beam oscillation decoheres.

A systematic exposition of the basic concepts of wakes and impedances is given for relativistic beams in accelerators., Comment: Lecture presented at JAS'2000 Accelerator School On Frontiers Of Accelerator Technology: High Quality Beams, St. Petersburg - Moscow, Russia, 1-7 July 2000

The concept of the surface impedance is applicable to the case, when obstacles on the surface of a vacuum chamber are small compared to characteristic dimensions of the problem. We apply this concept to the calculation of a synchronous mode that can propagate in a tube with slightly corrugated walls. We also show that such a mode can propagate in a pipe with a rough surface, or a perforated pipe with a large number of holes.