A. Hofmann

Bunches with Local Elliptic Energy Distributions

This distribution fits well with distributions observed in proton synchrotrons and makes several analytical calculations for bunched beams in longitudinal phase space possible. For any shape of the focusing force the line density becomes proportional to the potential well. Self-forces caused by space-charge and inductive wall impedances are thus proportional to the external force, making calculation of bucket area reduction and bunch lengthening easy. The microwave instability threshold, as given by the Keil-Schnell criterion with local values for current and energy spread, is independent of the azimuthal position along the bunch, and again analytical formulae are possible even for strongly non-linear focusing forces. The relative magnitude of the self-force and the microwave threshold turn out to be closely related, as the self-force is always 40% of the external force when the microwave threshold is reached. The classical longitudinal space-charge limit can therefore only be reached within a factor of 0.4. Other calculations with this natural distribution include analytical formulae for the rigid dipole mode threshold, and creation of flat-topped bunches with reduced peak line density resulting in a higher transverse space-charge limit.

Longitudinal Instabilities of Bunched Beams in the ISR

Microwave instabilities occur in bunched beams in the ISR leading to a dilution of the phase space density and limiting the longitudinal density of the stacked beams. According to D. Boussard this instability can be described as a coasting beam instability inside bunches. Experimental investigations of this microwave instability support this theory and give a high frequency impedance ¿ZL¿/n ¿ 14 ohms. Injecting large currents in bunches of large area increases the threshold of this instability. The larger currents can produce coupled bunch mode instabilities which can be cured by a higher harmonic cavity.

Properties and Possible Use of Beam-Beam Synchrotron Radiation

In large electron-positron colliding beam facilities the fields created by one beam in the crossing point are quite large and cause the particles in the other beam to radiate synchrotron radiation. The total power emitted in the form of this beam-beam synchrotron radiation is calculated for beams with a bi-Gaussian cross-section colliding head-on, and its dependence on beam separation is estimated. The radiation emitted in the forward direction is quite hard and has a complicated spectrum. However the radiation emitted at angles much larger than both 1/¿ and the deflecting angle, is softer and has the properties of short magnet radiation. Its spectrum observed at a fixed angle is directly given by the Fourier transform of the longitudinal dependence of the deflecting field, i. e. of the longitudinal distribution of the particles in the other beam. The polarization has a simple azimuthal dependence. This radiation can be used for beam diagnostics, i. e. centring the two beams suffering a natural separation, optimizing the luminosity, measuring the bunch length.

A Computer Code for the Calculation of Beam Stability in Circular Electron Machines

A computer program is presented which assists the designer of a circular electron accelerator or storage ring in finding out the limits of beam stability. The most prominent longitudinal and transverse instabilities are taken into account with emphasis on coherent bunch oscillations.

Measurement of Beam Stability and Coupling Impedance by RF Excitation

The transverse stability limit and coupling impedance of proton beams in the CERN Intersecting Storage Rings have been measured by external excitation of the beam. The impedance values at low frequencies thus obtained are in good agreement with the sum of the skin-effect and the wall-inductance which has been measured previously. The method can be extended to higher frequencies if the beam can be stabilized against low-frequency oscillations, e.g. by feedback.

The 'all Wiggler' Synchrotron Radiation Source

The concept of wigglers as insertions in storage rings dedicated to synchrotron radiation is now old, but only recently have multipole wigglers for S.R. sources actually been brought into use. This confirmed the flexibility of such sources, though experience of matching experimental rigs to them is still somewhat limited. The flexibility arising from the use of wigglers, plus the fact that the radiation flux no longer depends only on the beam current and energy but can be adjusted, at each source point, by choosing the number of wiggler poles and the wiggler field, means that the efficiency of a synchrotron radiation source can be increased. Whereas a conventional x-ray ring may allow extraction of 10% of its radiated power, an Allwiggler-Machine (AWM) with 40 wigglers may allow 50% of its radiated power to enter the beam lines. This concept has been developed for the European x-ray source now under discussion and an example of an outline design is described in the paper.

The variation of γ t with Δp/p in the CERN ISR

The variation of the transition energy γt m_oc² across the momentum aperture in the ISR has been determined by measuring the non-linear change of the revolution frequency as a function of the radial displacement and the momentum deviation and by measuring the phase oscillation frequency variation across the aperture while operating close to transition energy. The ratio of the relative slopes of γ_t and γ was found to be dγ_ttc ≈ -0.75. This value could be changed to nearly zero by strongly exciting the sextupole magnets. All measurements are in good agreement with each other and with computations carried out with a modified version of the program AGS. The change of γ_t across the aperture causes an area change of the empty buckets while traversing the beam during phase displacement acceleration. This leads to a momentum blow-up.

Longitudinal Bunch Dilution Due to RF Noise

The effect of phase noise on a tightly bunched proton beam is investigated taking into account the frequency spread in the beam, the wall impedance and the phase feedback loop. Under normal conditions the measured dilution rates in the ISR correspond typically to a doubling of the bunch length in one to a few hours, and are consistent with the measured noise spectra. Amplitude noise is not investigated.

Combined-Function Electron Stiorage Rings

A combined-function lattice permits reduction of the rf power required for compensation of synchrotron radiation, compared to a separated-function machine of the same circumference. At the same time, the required beam aperture is slightly smaller, and the damping aperture is much larger. Damping of radial betatron oscillations is achieved by making the defocusing magnets slightly stronger than the focusing ones.

An E-P Facility in the CERN SPS

A 25 GeV electron (or positron) storage ring installed in the SPS tunnel above the proton synchrotron would provide e-p collisions with a luminosity in the range of 10/sup 31/ to 10/sup 32/ cm/sup -2/ s/sup -1/. The collisions would normally take place at an intermediate plateau of the SPS-cycle up to 270 GeV, and could be followed by acceleration and extraction of the proton beam for fixed target experiments. The feasibility of such a facility is demonstrated and the essential features presented.