Beam loading of RF cavities is a subject of great concern for the design and operation of high current circular accelerators and storage rings. The steady state and transient perturbations of the accelerating voltage by the beam current lead to undesirable beam behaviour, like for instance the onset of instabilities or particle loss by lack of longitudinal acceptance. To some extent, it is possible to alleviate or even completely suppress these effects by a proper control of the RF power amplifier - cavity combination, using feedback or feedforward techniques. Several new developments in this field have taken place during the past years. For instance, the implementation of fast feedback technology, the use of cavity compensation schemes or digital filtering of signals in long delay feedback systems have resulted in considerably improved machine performance. Such techniiques will be reviewed in this paper and their performance and limitations will be presented.

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Control of Cavities with High Beam Loading

A numerical mesh calculation which computes the fields and frequency for a resonant cavity has been developed. Fields for any cavity which has cylindrical symmetry, and for which the magnetic field has only a θ component, can be computed. The program has been used on the IBM 7094 to study 805 MHz proton linac cavities. These design studies have shown that cavities having curved walls and triangular drift tubes give improved performance. Calculated values of ``shunt impedance'' per unit length ZT2 for such cavities range from 32.4 MΩ/m at β=v/c=0.45 to 53.0 MΩ/m at β=1. Experimental measurements have verified the calculations.

Computer Designed 805 MHz Proton Linac Cavities

The excess resistivity of niobium foil samples due to doped hydrogen increases with concentration up to 8–12 at.% H, which is almost independent of temperature. The Nb‐H structure at room temperature or above is quenched to 77 K or 9.5 K by relatively rapid cooling. The abrupt decrease of resistivity is observed, which corresponds to the precipitation of the ordered orthorhombic hydride phase. The superconducting transition temperature Tc is rather insensitive to hydrogen concentration in α solid solution. Hydride phase, however, shows no sign of superconductivity down to 1.3 K. Hydrogen is found to be reabsorbed in niobium after UHV outgassing by storage in air or by immersion in etchants. This is confirmed by weighing the samples and cross‐checked by the proton NMR measurements.

Hydrogen absorption and its effect on low-temperature electric properties of niobium

For linear acceleration of high energy protons an alternating periodic structure operated in a ½π standing wave mode has the advantage of relative immunity from beam loading and detuning effects while sacrificing little in shunt impedance when compared to π mode operation in a uniform periodic structure. The dispersion curve of the alternating periodic structure is derived from an analysis of a chain of coupled cavities, in each of which the fields are expanded in normal modes. By introducing the effect of coupling between alternate cells in addition to adjacent cell coupling, the passband of any one cavity mode is then found to split into two unequal passbands separated by a stop band, the width of which depends on the structure's geometrical parameters. The relative distribution of energy between cells is also found as a function of frequency. Measured dispersion curves were used to check the theory and the dependence of theoretical parameters on structure geometry. It is shown that the stop band may be reduced or eliminated simply by introducing a fixed detuning of one of the two different alternating periodic cells. It is also shown that the advantages of reduced beam loading and detuning effects resulting from operation in the ½π mode is obtained even when the group velocity vanishes, as occurs in a split passband.

Dispersion Relation and Frequency Characteristics of Alternating Periodic Structure for Linear Accelerators

We describe in this letter a cw single‐mode dye laser whose mode frequency can be tuned continuously over a relatively wide range of typically 10 GHz.

Single‐mode cw dye laser with large frequency range tunability

A 8.665‐GHz deflecting cavity, machined from solid niobium, electron beam welded, chemically polished, anodized and heat treated, yielded a peak magnetic field of 740 G corresponding to a peak electric field of 25 MV/m and a deflecting field of 6.9 MV/m. The maximum Q value was 4.5 × 109. Based on these results, design parameters and suggestions for the fabrication of an X‐band rf beam separator are given.

Investigation of a superconducting niobium X‐band deflecting cavity

In circular accelerators and particularly in storage rings it is essential that the total impedance, as seen by the beam, be kept below some critical value A model of the accelerating system was built using a single ended cathode follower amplifier driving a ferrite loaded cavity The system operated at 2345 KHz with a peak output voltage of ± 10 kV on the gap The dynamic output impedance, as measured on the gap, was < 15 ohms

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A Cathode Follower Power Amplifier

https://epaper.kek.jp/p65/pdf/pac1965_0213.pdf

Some New Radio Frequency Accelerating Structures

Studies of Multi-Drive Excitation for Alvarez Structures

The study of S-Band superconducting niobium cavities is being carried out for application to long-pulse rf beam separators in the momentum range of the AGS, whereas, X-Band frequencies are being considered for the NAL accelerator. Results for a 5-cell S-band prototype are: a peak field of 410 G, corresponding to an equivalent deflecting field of over 2 MV/m, and a loss improvement factor of 2 × 105. The fabrication and post-fabrication treatments are described. Perturbation measurements to determine deflector parameters are summarized. A new type of mode stabilizer is suggested. A 7-cell X-Band deflector is under construction.

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S. Giordano

Papers

Investigation of a superconducting niobium X‐band deflecting cavity

A Cathode Follower Power Amplifier

Some New Radio Frequency Accelerating Structures

Studies of Multi-Drive Excitation for Alvarez Structures

Superconducting Niobium Deflectors