Acceleration Cycle Research Articles

Damping Bunch Shape Oscillations in the Brookhaven AGS

Bunch shape oscillations are present in the AGS both before and after the transition energy (?8 BeV) is reached. At transition, they can be excited by timing, phase and radial misadjustments, and beyond by rapid large radial position changes used for targeting or by rapid large (> 20%) targeting losses. They can also be excited before transition by misadjusting the low level RF control system. In addition, excitation before transition can occur when 2fs = 720 Hz, the magnet ripple frequency, or when 2fs = 360 Hz, the ripple frequency on the RF cavity tuning servo systems. An analysis of the RF phase control systems including second order effectsl indicates that it should damp these oscillations but at a rate~fs/s? except in the vicinity of transition. At 200 ms, E ? 6.5 BeV, ? ? 6.9, fs 200 Hz, and the damping rate is ? 0.46 s-1. Thus adequate inherent damping is present only early in the acceleration cycle. This, plus the fact that the sensitivity of the phase control electronics to bunch shape variations can at times produce antidamping, has led to the design and testing of various feedback damping systems to control these oscillations. An analysis of RF phase and amplitude feedback, using a peak detected signal, as applied to the RF control system, will be given. Operational results using both types of feedback will be described.

Extraction Studies for the Modified Nevis Synchrocyclotron

Computer studies of a regenerative beam extraction system using magnetic peeler-regenerator have been performed. We have also investigated the use of a time varying first harmonic magnetic bump as a beam stretcher. The results indicate, that we can expect a turn separation of the order of 0.8 in. at the mouth of the magnetic channel. The time varying bump makes it possible to stretch the external beam over most of the RF-off time of the acceleration cycle. For the, magnetic channel, a current configuration has been found which does not perturb the main cyclotron field outside itself and reduces the field by 4 kG inside the channel. The step from no field to full field is only 0.2 in. This 4 kG field extending over a distance of 20-in. is sufficient to lead the beam out of the machine.

Improvement in the RF Capture by Using Nonsinusoidal Accelerating Voltages

In order to improve the RF capture in PPA, calculations and experiments have been perfarmed with higher harmonic terms added to the accelerating voltage. Computer calculations of the synchrotron phase space acceptance, using the phase potential, have shown that by adding the second harmonic it should be possible to increase the acceptance of PPA at capture by a factor of 2. Since in PPA the acceptance increases with energy, second harmonic needs to be added only during the first part of the acceleration and a suitable voltage program for the RF has been calculated. Initial experiments with the second harmonic added during the first 300 microseconds of the acceleration cycle showed an intensity gain in excess of 50%. Although only described for PPA, the method can easily be adapted to other machines.

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.

Studies of Beam Behavior in the Energy Region of 50-400 MeV with the Brookhaven Alternating Gradient Synchrotron

The "fast kicker" of the Brookhaven National Laboratory's AGS, normally used for orbit perturbation at high energy as part of the fast ejected beam system is used to eject the circulating proton beam in the energy region of 50-400 MeV. Beam behavior in the early part of the acceleration cycle is studied by measuring the ejected beam vertical phase space emittance and density distribution. Effective phase space dilution and beam intensity dependent effects have been observed. The observed distributions are consistent with a four or six dimensional gaussian distribution.

Earthquake-Induced Displacements in Sand Embankments

If an embankment of dense granular material is accelerated so that all points of the slope experience approximately the same acceleration at the same time the result of overstressing is a surface slide involving a thin layer of soil. The yield acceleration at which this slide will begin to move on any cycle of acceleration can be expressed in terms of the angle of friction and a shear strength intercept both of which are functions of the cumulative downslope displacement. Procedures for computing the magnitude of slope displacements resulting from a sequence of acceleration pulses are presented. Surface displacements determined using these procedures have been shown to be in reasonable agreement with those measured in banks of sand subjected to base acceleration, provided allowance is made for the variation in soil strength and yield acceleration with increasing displacements./ASCE/

Resonant Extraction from the 1 GeV Frascati Electron Synchrotron

The 1000MeV electron beam has been extracted from the Frascati Constant Gradient Synchrotron (t) on February 11, 1965 by exciting the 2 radial betatron oscillations/3 revolutions resonance (2). The first successful extraction ~rials were made at 400MeV on November 23, 1964. In this method, pulsed currents are fed at the end of the acceleration cycle into few wires of the pole face windings, connected in a noninduetive loop (see Fig. 1), in order to obtain the eight regenerative (~ • regions~> of ref. (2). This perturbation is strongly nonlinear: the corresponding ABz(x) variat ion is represented in Fig. 2.

Feasibility of Accelerating Polarized Protons with the Argonne ZGS

A computing program was developed for simultaneously tracing trajectories and classical, relativistic spin precessions around the zero gradient synchrotron (ZGS). Depolarizing resonances, previously predicted, were found and their properties were computed; there were 36 significant resonances, 12 of which were serious. A method is proposed for avoiding these 12 resonances by using two or four pulsed quadrupole magnets around the ZGS ring. These would rapidly shift νz, the vertical betatron oscillation frequency, at appropriate energies during the acceleration cycle. With this method, a proton beam, injected into the ZGS with P=1, would have P>0.7 at the end of the acceleration cycle.

High-frequency storage of a beam in cyclical accelerators

In the theory of high-frequency storage of a beam in accelerators with a constant magnetic field, it is important to take into account the disturbances of the already stored beam by successive cycles of acceleration. Such a disturbance leads, on the whole, to an increase in the energy spread of the stored particles and to a change of their mean energy. The general formulation of the problem and its solution for some special cases are presented in this article.

High frequency beam stacking in a cyclic accelerator

When working out the theory of high frequency beam stacking in accelerators operating with a constant magnetic field it is important to take into account the perturbations of the beam which has already been stacked caused by later acceleration cycles. The main effect of these perturbations is to increase the energy spread of the beam and to alter its mean energy. This paper presents a general formulation of this problem and a solution is given for certain particular cases.

Depolarisation d'un faisceau de protons polarises dans un synchrotron

An initially polarized proton beam, when injected in a synchrocyclotron, may suffer substantial depolarization effects, in view of magnetic field inhomogeneities “seen” by individual particles within the beam. A semiquantitative study is made for the 3 GeV Saclay synchrocyclotron. There, the combined effect of vertical betatron oscillations and passage through the straight sections fringing fields is critical. One finds indeed that a certain resonance condition is fulfilled for two values of the energy within the acceleration cycle, which entails a large depolarization in the present case. On the other hand, perturbations due to magnetic inhomogeneities inside the quadrants and the accelerating cavity as well as effects due to synchrotron oscillations prove to be small. It is felt that the analysis presented here could be extended to other machines and other types of accelerated particles. In particular, it is easy to see whether the resonance condition implies the existence of “dangerous” energy regions or not.

Problems of Generating High Circulating Currents of Relativistic Electrons

The basic problems can be summarized in terms of (a) the internal kinematics, including the factors tending to dissipate the system or degrade its energy; (b) the stability of the system as a whole; (c) the initial formation, which in the view adopted here, is to be done by injection in an external magnetic field, or by some repetitive cycle of injection, acceleration and storage. Item (a) involves Coulomb scattering, especially multiple, and radiation arising from motion in the total field. The losses are described in terms of equivalent injection currents necessary to maintain a fictitious system with arbitrarily prescribed characteristics. Item (b) is discussed, mainly with reference to the ``kink'' instability in terms of a dynamical analogue, the breakdown of which leads to a formulation of the usually accepted necessary condition for stability. A stronger condition is also suggested, which, however, is probably much more than sufficient. The experimental difficulties of item (c) are discussed in only a general way, with no definite conclusions being drawn.

Nonlinear effects in alternating-gradient synchrotrons

Nonlinear effects in alternating-gradient synchrotrons are responsible for resonances in the betatron-oscillation mechanism over and above those which arise in linear theory. These effects are here investigated by means of a perturbation procedure which leads directly to practical formulas. The larger part of the paper is given to “static” theory which ignores the acceleration process and concomitant synchrotron oscillation. Results are represented diagrammatically in three ways: by invariant contours in the phase plane; by “configuration diagrams” which are convenient transformations of the preceding diagrams; and by curves which relate the amplitudes of closed orbits to the characteristic phase. The resonances are associated with the following critical relations between the characteristic phases Θ x , Θ y , which denote the phase-change of radial and vertical oscillations, respectively, over one revolution: r x Θ x + r y Θ y = 2 kπ, where r x , r y , k are integers. In an ideal machine, composed of N identical sections, the above resonances are restricted to values of k which are integral multiples of N; the remaining resonances must therefore be attributed to departures of the machine from its ideal form due to constructional inaccuracies. For this reason, an analysis of nonlinear effects is necessary for the evaluation of tolerances. The resonance with “coordinates” r x , r y , is due principally to fluctuations in the nth radial derivative of the magnetic field strength, ∂ n H y/∂x n, where n = | r x | + | r y | − 1. The following general observations may be made: (i) The relation | r x | + | r y | ≤ 3 determines values of the characteristic phases in some neighborhood of which betatron oscillations of indefinitely small amplitude will grow to finite, possible large, amplitude. If | r x | + | r y ≥ 5, there is no such neighborhood. Resonances associated with | r x | + | r y | = 4 may have the characteristics of either of the preceding categories, depending upon the “quartic phase-independent term” Q, which is due principally to ∂ n H y/∂x 3, but there is reason to expect that in practice its properties will be those of the second category. Static theory therefore suggests that resonances for which | r x | + | r y | ≥ 4 may be ignored. (ii) Among the coupling resonances, for which r x , r y are both nonzero, those for which r x , r y have opposite signs lead only to an exchange of betatron-oscillating energy, which in alternating-gradient synchrotrons is harmless. (iii) Since deviations of the magnetic field which violate the (mirror) symmetry of the accelerator will be slight compared with those which are compatible with this symmetry, a resonance associated with an even value of r y and odd value of r x is more serious than that for which these values are interchanged. Calculation of the effect of fluctuations in the nonlinear contribution to the magnetic field may be based upon first-order perturbation theory. However, the consideration of a specific example shows that the combined influence of linear fluctuations with the average nonlinear contribution may be of comparable importance. Calculation of such effects involves second-order perturbation theory, formulas for which are derived in an appendix. Some attempt is made to consider the “dynamic” problem which takes account of the influence upon the betatron-oscillation mechanism of synchrotron oscillation and progressive saturation of the magnets. The two extremes of slow and rapid traversal of a resonance are discussed: the former should be appropriate to the possible crossing of low-order resonances near ejection due to magnet saturation; the latter should be appropriate to the inevitable crossing of high-order resonances during the complete acceleration cycle, and to the possible crossing of low-order resonances due to the large amplitude of synchroton oscillation near injection. Slow traversal of a resonance will give drastic expansion of at least part of the beam for at least one of the two directions, but the effect may be reduced by increasing Q. The effect of repeated rapid traversal may, under certain conditions, be approximated to a diffusion process which leads to progressive expansion of the entire beam; this effect is independent of Q and receives contributions from resonances of all orders. According to the simple theory of this paper, this effect is sufficiently serious to warrant more thorough investigation.

An apparatus for the accurate control of the peak X-ray energy of a 20 MeV betatron

Two methods on the accurate control of the electron energy of a 20 MeV betatron are described in detail. In one method a current transformer supplies a reference voltage in phase with the current in the betatron magnet coils to a trigger and potentiometer control unit. The second method uses a peaking transformer which is connected in series with the betatron magnet coils and supplies a pulse to a differentiating amplifier. The time of firing of the peaking transformer during the acceleration cycle is controlled by means of a high-current, low-voltage stabilizer. The same trigger circuit and expander modulator are used in both methods. A detailed comparison of the performance of the two methods is made and their advantages and limitations are discussed.

Space-Charge Forces in Strong-Focusing Synchrotrons

A new principle, strong focusing, has recently been put forward as the basis for the design of synchrotrons, particularly proton synchrotrons in the energy range above about 10 Bev. In this new proposal the field gradient index, $n$, is alternatively positive and negative and has a numerical value of some thousands as opposed to conventional, weak-focusing synchrotrons and betatrons, where $0lnl1$. The object of this note is to examine the effect of space-charge forces in strong-focusing synchrotrons on the stability of the radial and axial motion of the particles being accelerated.It is shown that, by virtue of the decrease of these forces as the particle velocity approaches that of light, the average field index is gradually altered throughout the cycle of acceleration. Such modulation, if sufficiently large, can make it impossible to provide radial and axial stability for the whole of this cycle. If the number of sectors, $N$, is much greater than 10, however, much smaller amounts of modulation may create conditions favorable for forced radial or axial resonances in the presence of inevitable magnet alignment errors, and it is this effect which places stringent limits on the strength of space charge forces permitted in a strong-focusing accelerator. The limitations discussed are far more serious in the case of proton beams than in the case of electron beams.

On Resonance Damping at Injection in Betatrons and Synchrotrons

It is shown that under special conditions of injection, damping of electron oscillations can occur in `imperfect' cyclic accelerators, i e those with an azimuthally inhomogeneous electromagnetic field, in the presence of resonance between their different periodic motions. This mechanism is invoked to explain the successful injection of electrons in most betatrons and synchrotrons. The necessary coupling inhomogeneity to induce resonance damping at injection can be created by the large currents circulating during this period in the acceleration cycle.

Synchrotron-Oscillation Resonance

The frequency of phase oscillation in a synchrotron is so low as to make possible resonances with harmonics of the power-supply frequency. The interaction may take place through ripple in the magnetic field or in the frequency or amplitude of the accelerating voltage, the first two interacting very strongly and the third moderately. Thus, a small ripple in the magnet power supply output, though it produces only an extremely small ripple in the magnetic field because of the magnet's inductance, may tend to cause large phase oscillations. The detuning effect of the fall in phase oscillation on frequency with increasing amplitude limits the resulting amplitude, however, and may even reduce the amplitudes of initially large phase oscillations. The ripple in the accelerating field is unlikely to be sufficient at a resonant frequency to cause trouble. In addition to ripple, there will be noise which, particularly through modulation of the frequency of the accelerating field, may result in time in considerable phase oscillations because the noise contains a wide range of frequencies, one of which is always in resonance throughout the acceleration cycle.

On the Classical Radiation of Accelerated Electrons

This paper is concerned with the properties of the radiation from a high energy accelerated electron, as recently observed in the General Electric synchrotron. An elementary derivation of the total rate of radiation is first presented, based on Larmor's formula for a slowly moving electron, and arguments of relativistic invariance. We then construct an expression for the instantaneous power radiated by an electron moving along an arbitrary, prescribed path. By casting this result into various forms, one obtains the angular distribution, the spectral distribution, or the combined angular and spectral distributions of the radiation. The method is based on an examination of the rate at which the electron irreversibly transfers energy to the electromagnetic field, as determined by half the difference of retarded and advanced electric field intensities. Formulas are obtained for an arbitrary charge-current distribution and then specialized to a point charge. The total radiated power and its angular distribution are obtained for an arbitrary trajectory. It is found that the direction of motion is a strongly preferred direction of emission at high energies. The spectral distribution of the radiation depends upon the detailed motion over a time interval large compared to the period of the radiation. However, the narrow cone of radiation generated by an energetic electron indicates that only a small part of the trajectory is effective in producing radiation observed in a given direction, which also implies that very high frequencies are emitted. Accordingly, we evaluate the spectral and angular distributions of the high frequency radiation by an energetic electron, in their dependence upon the parameters characterizing the instantaneous orbit. The average spectral distribution, as observed in the synchrotron measurements, is obtained by averaging the electron energy over an acceleration cycle. The entire spectrum emitted by an electron moving with constant speed in a circular path is also discussed. Finally, it is observed that quantum effects will modify the classical results here obtained only at extraordinarily large energies.

PHYSICAL GROWTH DURING ADOLESCENCE

THERE ARE three major phases in the progress of growth from conception to full maturity. The first and the last of these phases are characterized by cycles of acceleration followed by deceleration in growth rates, both are accompanied with striking developmental changes. The middle phase, in contrast, is one of relatively steady, moderate progress in both growth and maturation. The term adolescence refers rather loosely to the last of these three major phases, to the time during which the child becomes a man or woman. The earliest and latest changes of this transformation take place insidiously and are not easily recognized or defined. They reach back well into what is usually thought of as childhood, or the stable middle period of growth, and they extend forward into what is, in most respects, adulthood. The major changes of adolescence, however, take place within a much shorter period and are recognized more