Accelerator Physics

A general theory of the beam interaction with small discontinuities of the vacuum chamber is developed taking into account the reaction of radiated waves back on the discontinuity. The reactive impedance calculated earlier is reproduced as the first order, and the resistive one as the second order of a perturbation theory based on this general approach. The theory also gives, in a very natural way, the results for the trapped modes due to small discontinuities obtained earlier by a different method.

A proposal for a 10-120 mA proton linac employing superconducting beta-graded, CERN type, four cell cavities at 352 MHz is presented. The high energy part (100 MeV-1 GeV) of the machine is split in three beta-graded sections, and transverse focusing is provided via a periodic doublet array. All the parameters, like power in the couplers and accelerating fields in the cavities, are within the state of the art, achieved in operating machines. A first stage of operation at 30 mA beam current is proposed, while the upgrade of the machine to 120 mA operation can be obtained increasing the number of klystrons and couplers per cavity. The additional coupler ports, up to four, will be integrated in the cavity design. Preliminary calculations indicate that beam transport is feasible, given the wide aperture of the 352 MHz structures. A capital cost of less than 100 M at10mA,reachingupto280M for the 120 mA extension, has been estimated for the superconducting high energy section (100 MeV-1 GeV). The high efficiency of the proposed machine, reaching 50% at 15 mA, makes it a good candidate for proposed nuclear waste incineration facilities and Energy Amplifier studies.

The performance of a scintillating fiber (2mm diameter) position sensitive detector ( 4.8×4.8 cm 2 active area) for the single bremstrahlung luminosity monitor at the VEPP-2M electron-positron collider in Novosibirsk, Russia is described. Custom electronics is triggered by coincident hits in the X and Y planes of 24 fibers each, and reduces 64 PMT signals to a 10 bit (X,Y) address. Hits are accumulated (10 kHz) in memory and display (few Hz) the VEPP-2M collision vertex. Fitting the strongly peaked distribution ( ∼ 3-4 mm at 1.6m from the collision vertex of VEPP-2M ) to the expected QED angular distribution yields a background in agreement with an independent determination of the VEPP-2M luminosity.

A single electron circulating in a storage ring is a very peculiar object. Synchrotron radiation quantum fluctuation causes stohastic process in the synchrotron oscillation of an electron. The radiation from a undulator permits one to obtain discret moments of longitudional electron motion. Experiments with a single electron on on the VEPP-3 optical klystrons are described.

Polarized protons have never been accelerated to more than about 25 GeV. To achieve polarized proton beams in RHIC (250GeV), HERA (820GeV), and the TEVATRON (900GeV), ideas and techniques new to accelerator physics are needed. In this publication we will stress an important aspect of very high energy polarized proton beams, namely the fact that the equilibrium polarization direction can vary substantially across the beam in the interaction region of a high energy experiment when no countermeasure is taken. Such a divergence of the polarization direction would not only diminish the average polarization available to the particle physics experiment, but it would also make the polarization involved in each collision analyzed in a detector strongly dependent on the phase space position of the interacting particle. In order to analyze and compensate this effect, methods for computing the equilibrium polarization direction are needed. In this paper we introduce the method of stroboscopic averaging, which computes this direction in a very efficient way. Since only tracking data is needed, our method can be implemented easily in existing spin tracking programs. Several examples demonstrate the importance of the spin divergence and the applicability of stroboscopic averaging.

This report provides a description of unbunched beam stochastic cooling in the framework of control theory. The main interest in the investigation is concentrated on the beam stability in an active cooling system. A stochastic cooling system must be considered as a closed-loop, similar to the feedback systems used to damp collective instabilities. These systems, which are able to act upon themselves, are potentially unstable. The self-consistent solution for the beam motion is derived by means of a mode analysis of the collective beam motion. This solution yields a criterion for the stability of each collective mode. The expressions also allow for overlapping frequency bands in the beam spectrum and thus are valid over the entire frequency range. Having established the boundaries of stability in this way, the Fokker-Planck equation is used to describe the cooling process. This description does not include collective effects and thus a stable beam must be assumed. Hence the predictions about the cooling process following from the Fokker-Planck equation only make physical sense within the boundaries of beam stability. Finally it is verified that the parameters of the cooling system which give the best cooling results are compatible with the stability of the beam.

Analytical solution of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases. For their derivation we have used the method of solution of an infinite set of linear algebraic equations, based on its transformation into dual integral equations.

The perturbative approach for describing the underdense plasma--ultrarelativistic electron bunch system is developed, using the ratio n 0 n b as a small parameter ( n b --bunch, n 0 --plasma electron densities). Focusing of the electron bunch emerged in the first approximation of the perturbative procedure as a result of the plasma electrons redistribution. Focusing gradient and strength for ultrarelativistic, flat, uniform and short bunch are obtained and compared with the previous results.

The beam coupling impedances of small obstacles protruding inside the vacuum chamber of an accelerator are calculated analytically at frequencies for which the wavelength is large compared to a typical size of the obstacle. Simple formulas for a few important particular cases, including both essentially three-dimensional objects like a post or a mask and axisymmetric irises, are presented. The analytical results are compared and agree with three-dimensional computer simulations. These results allow simple practical estimates of the broad-band impedance contributions from such discontinuities.

We discuss the various beam dynamics problems in muon collider systems, starting from the proton accelerator needed to generate the muon beams and proceeding through the muon storage ring.