Radial Betatron Oscillations Research Articles

Coupling resonance correction and avoidance for the TRIUMF 500 MeV cyclotron

The linear coupling resonance νr - νz = 1 in a cyclotron is driven by the first harmonic in the radial gradient of the radial magnetic field. In the TRIUMF 500 MeV cyclotron, this resonance is encountered multiple times. When the circulating beam is off-centred radially passing through the resonance, the radial betatron oscillation can be converted into vertical oscillation, which can cause beam losses and radio-activation. We investigated this resonance with goal to correct it by using the available harmonic correction coils. Moreover, we improved the cyclotron vertical tune measurement by using trim coils to create a flat-top radial field, and thus confirmed an extra νr - νz = 1 coupling resonance passage as this is unexpected from the historical tune diagram. To avoid this passage, the local vertical tune is adjusted to stay farther away from the resonance line by using the trim coils axial field, but at the cost of a local excursion in isochronism. After the correction and the avoidance of this resonance, both the coherent and incoherent vertical oscillations are decreased, thus helping to reduce the machine tank spills under high intensity operation. In this paper, we present the results of calculations and simulations as well as measurements that we undertook.

Analytical description of stripping foil extraction from isochronous cyclotrons.

Analytical expressions are derived describing beam parameters on a stripping foil (SF) as a function of radial amplitude of betatron oscillations and of energy gain. The results computed from these expressions are in good agreement with those from numerical calculations. These results indicate the existence of a parametric relationship between radial emittance and energy spread, via the amplitude of radial betatron oscillations. This relationship enables one to generate the working diagram of expected beam parameters on a SF. Such a diagram can be particularly useful for designers of extraction systems, since it gives the relationship between quantities used as extraction system input parameters. The derived analytical expressions can make the design of cyclotrons easier and significantly reduce the need of numerical simulations.

Investigation of 3D effects on FEL operation

An investigation is made of 3D effects on FEL operation by comparing the 3D simulation code TDA with a 1 1 2 D model. In the latter model, the full spatial dependence of the radiation field is taken into account, whereas the electrons are treated as moving in a 1D, density-averaged ponderomotive potential. Three dimensional effects like a radial beam profile, emittance and betatron oscillations are investigated. For FELIX parameters, the 1 1 2 D model is in good agreement with TDA.

Formation of the synchrotron radiation continuum

The process of formation of the SR spectrum in a weak-focusing magnetic field is investigated in detail and expressions for the combined spectral structure are given. It is shown that the radial betatron oscillations determine the wavelength region where it is possible to select spectral harmonics.

Non-linear coupling from the beam-beam force in electron-positron storage rings

The non-linear beam-beam forces in storage rings can excite the coupling resonance 2 Q v – 2 Q h = m between vertical and radial betatron oscillations, giving rise to an increase in the smaller emittance. It is shown that the magnitude and the sign of the tune difference between vertical and horizontal motion are of particular importance for electron-positron storage rings. Criteria for avoiding this effect are established and the predictions of the theory are compared with some recent experimental results.

Development and investigation of relativistic electron beams with finite energy spread and improved emittance

This paper presents experimental results in the development of low-emittance relativistic electron beams with finite energy spread, which—among other applications—is suitable for suppressing collective instabilities in an electron-ring accelerator. The measurements were performed with a divided cathode in an electron-beam gun, one half of which is connected via a resistor with the high-voltage terminal. The energy difference can be varied up to 100 keV in proportion to the resistance, with equal subcurrents. The beam parts are well separated, and their radial distance is about equal to the radial difference of the corresponding electron closed orbits, such that electron-ring formation with minimum radial betatron oscillations should be possible. The beam emittance is as small as about 100 mrad cm and the current is 800 A.

Measurements and Corrections to the Beam Properties in the TRIUMF Cyclotron

The recent commissioning of two centring probes and four pairs of internal slits has for the first time made possible systematic measurements and improvements to the central orbits, and internal selection of beam emittance and phase acceptance. The beam signals are digitized and computer-processed to allow rapid analysis and correction of the centring by means of steering electrodes and harmonic trimming coils. Radial-longitudinal coupling effects agree with theory and are used to optimize the injection conditions for the wide phase acceptance. With the internal slits it has been possible to improve the incoherent radial betatron oscillation amplitude and to observe isolated turns to 220 MeV and turn structure out to 500 MeV. Fluctuations in the dee voltage (~ ±0.1%) and the magnetic field (± 2 x 10r-6) give rise to fluctuations in the energy and intensity of highly selected beams. Improved stability has been achieved by regulation of both RF voltage and frequency with beam-derived signals.

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.

Synchrotron radiation spectrum for an intense relativistic E layer

The synchrotron radiation spectrum is calculated for an intense relativistic nonneutral E layer including self-field effects. The analysis is carried out for the class of thin E-layer equilibria described self-consistently by equilibrium distribution functions of the form fe0 (x, p) = R0F(H)δ(Pθ − P0), where H is the energy, is the canonical angular momentum, and R0 and p0 are constants. Since individual electrons execute radial betatron oscillations about a helix with mean radius R0, the single-particle emission spectrum is modified from the conventional Schott-Trubnikov result. To determine the spectrum of radiation emitted by all electrons in the E layer, the single-particle emission spectrum is averaged over the distribution function fe0 (x, p) that self-consistently generates the E layer equilibrium.

Shadow measurements in a cyclotron

In this paper the connection between shadow measurements on a cyclotron beam and the concepts of coherent and incoherent radial betatron oscillation is studied. Conditions for the determination of the amplitude of the coherent oscillation from shadow measurements are discussed, and the influence of a coherent oscillation on the shadowwidth is investigated. Finally the maximal and minimal shadowwidths are calculated for a beam with an elliptical emittance, in the case of zero amplitude of the coherent oscillation.

Polarization and angular distribution of the radiation of electrons moving in a focusing magnetic field

The angular distribution of the linear-polarization components is found for the radiation of an electron moving in a nonuniform weak-focusing magnetic field. The distribution shape is studied as a function of the amplitudes of the axial and radial betatron oscillations. It is shown that the minimum intensity of the π component of the radiation does not vanish, in contrast with the case of a uniform field.

Method of attenuating radial betatron oscillations in cyclic accelerators

Method of attenuating radial betatron oscillations in cyclic accelerators

Excitation of radial betatron oscillations by a longitudinal accelerating field

Excitation of radial betatron oscillations by a longitudinal accelerating field

Radial and axial betatron oscillation amplitude spectra in the Dubna synchrocyclotron

A method for the determination of the radial and axial betatron oscillation amplitudes of the synchrocyclotron beam particles is described. This method has made it possible to find the distribution of particles as a function of the amplitude (an oscillation spectrum). For the Dubna synchrocyclotron the values of radial and axial betatron oscillations at the full radius are 15 cm and 2 cm, respectively.

Stimulation and Measurement of Radial Betatron Oscillations in the Bevatron Using the RF Accelerating System

Recent activity in resonant extraction of the circulating proton beam at the Bevatron spurred interest in accurately measuring the radial betatron oscillation frequency. Calculations indicated that it would be practical to use the existing RF system tuned to the betatron-oscillation frequency for excitation of the desired oscillations. Measurement of the proton rotational frequency and the betatron oscillation frequency has been carried out with the aid of a small digital data processor. The system we have used allows dynamic on-line presentation of beam radius, betatron frequency, and rotational frequency to precision of approximately one part in 10 000.

Amplitude nonuniformity of the magnetic field in a betatron

The effects of the amplitude nonuniformity of the magnetic field in a betatron on the forced and betatron radial oscillations of electrons during extraction (or discharge toward the target) at the end of the acceleration cycle are examined. The amplitude and phase dynamics of radial betatron oscillations are studied by means of an analog computer.

One-Third Resonance Extraction from INS AG Electron Synchrotron

Slow beam extraction from the INS-AG electron synchrotron was done by using a one-third resonance of the betatron oscillation. A current strip was used to change the number of the radial betatron oscillation per revolution from 2.25 to 7/3 and to enlarge the amplitude of the oscillation. The extracting beam orbit was analysed using an approximate Hamiltonian which has a separatrix represented by three straight lines and the result was in good agreement with that pursued by a computer. The properties of the extracted beam were as follows; The efficiency was 50% for electrons of 300 MeV up to 1 GeV. The maximum beam intensity was 4×1011 electrons per second. The maximum duty cycle was 3%. Phase volumes for the horizontal and the vertical motions were 10-3 rad cm and 0.75×10-3 rad cm, respectively. The beam transport system and the radiation shielding system are also described.

A method for measuring the frequency of radial betatron oscillations in a synchrotron

A method for measuring the frequency of radial betatron oscillations in a synchrotron

Control of Btatron Oscillations in a Cyclotron by Use of an On-Line Computer

A system is described which is used to control radial betatron oscillations in the Karlsruhe AVF Cyclotron. The output of a radial current density target is digitized and fed into the memory of a CDC 3100 on-line computer. As different orbits are separated up to extraction radius in the Karlsruhe cyclotron they can be indentified by a computer program. Their radii can either be displayed on an oscilloscope screen or used for further calculations in order to obtain information on necessary corrections of the magnetic field.

The electron accelerator Desy

Before giving a short report of the present status of the electron accelerator at Hamburg, let me describe very briefly the principal features of the design. The electron accelerator is a strong focusing synchrotron for accelerating electrons up to about 6 GeV. Such a machine differs in two essential features from a proton synchrotron: (i) At an injection energy of 40 MeV, the velocity of the electrons is practically equal to that of light, so no frequency modulation of the R. F. accelerating units is necessary. (ii) A very intense synchrotron radiation is emitted when an electron moves in a transverse magnetic field. Since the radiated power is inversely proportional to the fourth power of the rest mass of the accelerated particles, the radiation from electrons is about 10 13 times more intense than that from protons with the same energy. The radiation loss at 6 GeV amounts to 3.6 MeV per turn; so the radio-frequency power requirements are greatly increased. In addition, the motion of the particles is strongly influenced by radiation forces, and while the vertical betatron oscillations are damped, the radial betatron oscillations are rather strongly antidamped. Figure 102 demonstrates this effect. Further, particles can be lost from the stable region of the synchrotron oscillations by too small a radio-frequency amplitude of the accelerator units. Since the radiation loss per turn is inversely proportional to the radius, it was necessary to choose a rather large radius of curvature for the accelerator; namely 31.7 m. One accelerates 50 times per second to keep small the excursions of the particles from the mean orbit. The acceleration time is therefore about 10 ms. Figure 103 shows the dependence with energy of the oscillation amplitudes. One sees that the amplitudes reach a minimum in the region of 2 to 3 GeV, due to the adiabatic damping of the synchro­tron and betatron oscillations, and afterwards they increase due to the radiation effects.