Search Results (33 total)

Gravitational instability of the distribution of stars in a galaxy is a well-known phenomenon in astrophysics. This report is an attempt to analyze this phenomenon by applying standard tools developed in accelerator physics. It is found that a nonrotating galaxy would become unstable if its size exceeds a certain limit that depends on its mass density and its temperature.

We used an rf solenoid to study the widths of rf spin resonances with both bunched and unbunched beams of 1.85  GeV/c polarized deuterons stored in the COSY synchrotron. With the unbunched beam at different fixed rf-solenoid frequencies, we observed only partial depolarization near the resonance. However, the bunched beam’s polarization was almost fully flipped; moreover, its resonance was much narrower. We then used Chao’s recent equations to explain this behavior and to calculate the polarization’s dependence on various rf-solenoid and beam parameters. Our data and calculations indicate that a bunched deuteron beam’s polarization can behave as if the beam has zero momentum spread.

A paper proving a result now commonly known as “Robinson sum rule” was published by Orlov and Tarasov {J. Exp. Theor. Phys. 34, 651 (1958) [Sov. Phys. JETP 34, 339 (1958)]} at about the same time that Robinson himself published the result [Phys. Rev. 111, 373 (1958)]. We assigned ourselves the task of reviewing this work, as narrowly as possible, in hopes of understanding how it should be considered in view of the existing attribution. The chronology of the work is reviewed and the degree to which the two works were independent and have qualitatively different content is considered.

We recently tested a new spin resonance crossing technique, Kondratenko Crossing (KC), by sweeping an rf-solenoid’s frequency through an rf-induced spin resonance with both the KC and traditional fast crossing (FC) patterns. Using both rf bunched and unbunched 1.85  GeV/c polarized deuterons stored in COSY, we varied the parameters of both crossing patterns. Compared to FC with the same crossing speed, KC reduced the depolarization by measured factors of 4.7±0.3 and 19_-5⁺¹² for unbunched and bunched beams, respectively. This clearly showed the large potential benefit of Kondratenko Crossing over fast crossing.

The Chao matrix formalism allows analytic calculations of a beam’s polarization behavior inside a spin resonance. We recently tested its prediction of polarization oscillations occurring in a stored beam of polarized particles near a spin resonance. Using a 1.85  GeV/c polarized deuteron beam stored in the COoler SYnchrotron, we swept a new rf solenoid’s frequency rather rapidly through 400 Hz during 100 ms, while varying the distance between the sweep’s end frequency and the central frequency of an rf-induced spin resonance. Our measurements of the deuteron’s polarization near and inside the resonance agree with the Chao formalism’s predicted oscillations.

We recently started testing Chao’s proposed new matrix formalism for describing the spin dynamics due to a single spin resonance. The Chao formalism is probably the first fundamental improvement of the Froissart-Stora equation in that it allows analytic calculations of the beam polarization’s behavior inside a resonance. We tested the Chao formalism using a 1.85  GeV/c polarized deuteron beam stored in COSY, by sweeping an rf dipole’s frequency through 200 Hz, while varying the distance from the sweep’s end frequency to an rf-induced spin resonance’s central frequency. Since the Froissart-Stora equation itself can make no prediction inside a resonance, we compared our experimental data with the predictions of the Chao formalism and those of an empirical two-fluid model based on the Froissart-Stora equation. The data strongly favor the Chao formalism.

A general formalism for treating simultaneously the transverse coupled-bunch and transverse coupled-mode instabilities is presented. In this approach, the equations of motion of a coupled multibunch beam are expanded to yield a system of equations involving correlation moments of the transverse and longitudinal motions. After a proper truncation, the system of equations is closed and can be solved. This approach allows us to formulate within one framework several known instability mechanisms including the single-bunch mode-coupling instability, the coupled-bunch instability, the mode-coupling instability, and the coupled-mode coupled-bunch instability as particular cases.

As a polarized beam is accelerated through a depolarization resonance, its polarization is reduced by a well-defined calculable reduction factor. When the beam subsequently crosses a second resonance, the final beam polarization is considered to be reduced by the product of the two reduction factors corresponding to the two crossings, each calculated independently of the other. This is a good approximation when the spread of spin precession frequency Δν_spin of the beam (particularly due to its energy spread) is sufficiently large that the spin precession phases of individual particles smear out completely during the time τ between the two crossings. This approximate picture, however, ignores two spin dynamics effects: an interference-overlap effect and a spin echo effect. This paper is to address these two effects. The interference-overlap effect occurs when Δν_spin is too small, or when τ is too short, to complete the smearing process. In this case, the two resonance crossings overlap each other, and the final polarization exhibits constructive or destructive interference patterns depending on the exact value of τ. Typically, the beam’s energy spread is large and this interference-overlap effect does not occur. To study this effect, therefore, it is necessary to reduce the beam energy spread and to consider two resonance crossings very close to each other. The other mechanism, also due to the interplay between two resonance crossings, is spin echo. It turns out that even when the precession phases appear to be completely smeared between the two crossings, there will still be a sudden and short-lived echo signal of beam polarization at a time τ after the second crossing; the magnitude of which can be as large as 57%. This echo signal exists even when the beam has a sizable energy spread and when τ is very large, and could be a sensitive (albeit challenging) way to experimentally test the intricate spin dynamics in a synchrotron. After giving an analysis of the interference-overlap and the echo effects, two possible experiments to explore them are suggested.

Linear dynamics in a storage ring can be described by the one-turn map matrix. In the case of a resonance where two of the eigenvalues of this matrix are degenerate, a coupling perturbation causes a mixing of the uncoupled eigenvectors. A perturbation formalism is developed to find eigenvalues and eigenvectors of the one-turn map near such a linear resonance. Damping and diffusion due to synchrotron radiation can be obtained by integrating their effects over one turn, and the coupled eigenvectors can be used to find the coupled damping and diffusion coefficients. Expressions for the coupled equilibrium emittances and beam distribution moments are then derived. In addition to the conventional instabilities at the sum, integer, and half-integer resonances, it is found that the coupling can cause an instability through antidamping near a sum resonance even when the symplectic dynamics are stable. As one application of this formalism, the case of linear synchrobetatron coupling is analyzed where the coupling is caused by dispersion in the rf cavity, or by a crab cavity. Explicit closed-form expressions for the sum/difference resonances are given along with the integer/half-integer resonances. The integer and half-integer resonances caused by coupling require particular care. We find an example of this with the case of a crab cavity for the integer resonance of the synchrotron tune. Whether or not there is an instability is determined by the value of the horizontal betatron tune, a unique feature of these coupling-caused integer or half-integer resonances. Finally, the coupled damping and diffusion coefficients along with the equilibrium invariants and projected emittances are plotted as a function of the betatron and synchrotron tunes for an example storage ring based on PEP-II.

A matrix formalism is developed to describe the spin dynamics in a synchrotron near a single depolarization resonance as the particle energy (and therefore its spin precession frequency) is varied in a prescribed pattern as a function of time such as during acceleration. This formalism is first applied to the case of crossing the resonance with a constant crossing speed and a finite total step size, and then applied also to other more involved cases when the single resonance is crossed repeatedly in a prescribed manner consisting of linear ramping segments or sudden jumps. How repeated crossings produce an interference behavior is discussed using the results obtained. For a polarized beam with finite energy spread, a spin echo experiment is suggested to explore this interference effect.

We analyze the stop band due to crab cavities for horizontal tunes that are either close to integers or close to half integers. The latter case is relevant for today’s electron/positron colliders. We compare this stop band to that created by dispersion in an accelerating cavity and show that a single typical crab cavity creates larger stop bands than a typical dispersion at an accelerating cavity. We furthermore analyze whether it is beneficial to place the crab cavity at a position where the dispersion and its slope vanish. We find that this choice is worth while if the horizontal tune is close to a half integer, but not if it is close to an integer. Furthermore we find that stop bands can be avoided when the horizontal tune is located at a favorable side of the integer or the half integer. While we are here concerned with the installation of a single crab cavity in a storage ring, we show that the stop bands can be weakened, although not eliminated, significantly when two crab cavities per ring are chosen suitably.

In the proximity of a nonlinear resonance ν≈m / n, the beam distribution in a storage ring is distorted depending on how close is the resonance and how strong is the resonance strength. In the 1-dimensional case, it is well known that the particle motion near the resonance can be described in a smooth approximation by a Hamiltonian of the form (ν-m / n)J+D_ν(J)+f₁(φ,J), where (φ,J) are the phase space angle and action variables, D_ν is the detuning function, and f₁ is an oscillating resonance term. In a proton storage ring, the equilibrium beam distribution is readily solved to be any function exclusively of the Hamiltonian. For an electron beam, this is not true and the equilibrium distribution is more complicated. This paper solves the Fokker-Planck equation near a single resonance for an electron beam in a storage ring. The result is then applied to obtain the quantum lifetime of an electron beam in the presence of this resonance. Resonances due to multipole fields and due to the beam-beam force are considered as examples.

The longitudinal dynamics and its coupling with the transverse dynamics of bunched beams with strong space charge are analyzed. We introduce a self-consistent Vlasov description for the longitudinal phase space similar to the familiar description for the transverse phase space using a Kapchinskij-Vladimirskij distribution. A longitudinal beam envelope equation is derived. An exact solution is then obtained when coupling to the transverse dynamics is ignored. This longitudinal envelope equation is coupled to the transverse envelope equation to form a set of coupled dynamical equations, which is then solved numerically. This analysis is prompted by the surprising results of recent experiments which showed that by driving an intense laser pulse into matter, which in turn creates a plasma, short bright relativistic electron bunches are produced, surprisingly narrowly focused. We find that because the space charge forces weaken with increasing transverse and longitudinal phase space, both the transverse and longitudinal emittance blowouts anticipated of bright compact bunches are mitigated by this coupling. It should be possible to capture these bunches into an rf cavity to accelerate to higher energies.

An electron cloud causes various effects in high intensity positron storage rings. The positron beam and the electron cloud can be considered a typical two-stream system with a certain plasma frequency. Beam-beam interaction is another important effect for high luminosity circular colliders. Colliding two beams can be considered as a two-stream system with another plasma frequency. We study the combined phenomena of the beam-electron cloud and beam-beam interactions from a viewpoint of two complex two-stream effects with two plasma frequencies.

Beginning with the Green function for a rod beam in a round beam pipe we derive the space charge induced average energy change and rms spread for relativistic beams that are slowly converging or diverging in round beam pipes, a result that tends to be much larger than the 1/γ² dependence for parallel beams. Our results allow for beams with longitudinal-transverse correlation, and for slow variations in beam pipe radius. We calculate, in addition, the space charge component of energy change and spread in a chicane compressor. This component indicates source regions of coherent synchrotron radiation (CSR) energy change in systems with compression. We find that this component, at the end of example compressors, approximates the total induced voltage obtained by more detailed CSR calculations. Our results depend on beam pipe radius (although only weakly) whereas CSR calculations do not normally include this parameter, suggesting that results of such calculations, for systems with beam pipes, are not complete.

A highly accurate self-consistent particle code to simulate the beam-beam collision in e⁺e^- storage rings has been developed. It adopts a method of solving the Poisson equation with an open boundary. The method consists of two steps: assigning the potential on a finite boundary using Green's function and then solving the potential inside the boundary with a fast Poisson solver. Since the solution of Poisson's equation is unique, our solution is exactly the same as the one obtained by simply using Green's function. The method allows us to select a much smaller region of mesh and therefore increase the resolution of the solver. The better resolution makes more accurate the calculation of the dynamics in the core of the beams. The luminosity simulated with this method agrees quantitatively with the measurement for the PEP-II B Factory ring in the linear and nonlinear beam current regimes, demonstrating its predictive capability in detail.

The betatron difference resonance, Q_x-2Q_z=-6, where the Q_x,z are the number of betatron oscillations per revolution, was studied at the Indiana University Cyclotron Facility cooler ring. Measurements of both vertical and horizontal coherent betatron oscillations were made, at a nonlinear resonance, after a pulsed dipole kick. We found that the Poincaré surface of section for the nonlinear resonance could be described by a simple Hamiltonian. The resonance strength and phase, as well as the tune shift, as a function of betatron amplitude, were deduced from the experimental data. Attempts to deduce the amplitude and phase of the time dependent fluctuations around the time averaged Poincaré surface of section will also be discussed.

The response of particles trapped in one-dimensional resonance islands to betatron tune modulation resembles, yet is not equivalent to, that of a parametric resonant system. Experimental data obtained at Indiana University Cyclotron Facility for the fourth-order resonance islands have confirmed this characteristic feature. The beam, driven by betatron tune modulation, was observed to travel from near the center of resonance islands toward the separatrix. The experimental data are characterized by the onset of a large response at a critical modulation amplitude and frequency, which are compared with theoretical models. Possible future experiments are suggested.

The synchro-betatron coupling induced by modulating a transverse dipole field at a frequency close to the synchrotron frequency was studied experimentally. The combination of the electron cooling and transverse-field modulation on the synchrotron oscillation is equivalent to a dissipative parametric resonant system. Six-dimensional Poincaré maps were measured at ten-turn intervals. The proton bunch was observed to split longitudinally into two pieces, or beamlets, converging toward attractors of the dissipative system within a rf bucket. Based on our experimental results, the effects of ground vibration on the superconducting supercollider beam and the effects of power-supply ripple on the relativistic heavy-ion collider beam are examined.

Synchrotron motion with rf phase modulation was studied experimentally. Poincaré maps in the resonant precessing frame were obtained from the experimental data and compared with the tori of the resonant Hamiltonian. Our experimental data revealed island structure in longitudinal phase space. Experimental results for synchrotron motion excited by phase modulation at the third harmonic of the synchrotron frequency are also reported.

Synchrotron motion with an external rf voltage modulation was studied experimentally. Beam particles, in the presence of electron cooling, were observed to damp to the basins of resonance islands, which were produced by the parametric resonance due to rf voltage modulation. The measured phase amplitudes of the centers of these resonance islands were found to agree well with theory.

Synchro-betatron coupling in a proton storage ring with electron cooling was studied experimentally by modulating a transverse dipole field close to the synchrotron frequency. The combination of the electron cooling and transverse field modulation on the synchrotron oscillation is equivalent to a dissipative parametric resonant system. The proton bunch was observed to split longitudinally into two pieces, or beamlets, converging toward attractors of the dissipative system. These phenomena might be important in understanding the effect of ground vibration on the Superconducting Super Collider beam, and the effect of power supply ripple on the Relativistic Heavy-Ion Collider beam.

The synchroton motion of a beam was tracked for the first time by digitizing the phase of the beam signal from a high bandwidth wall gap monitor relative to the rf phase and the momentum deviation with a transverse beam position measurement in a high dispersion region. The measured synchrotron tune as a function of the synchrotron amplitude agrees well with theory. When the rf stable phase angle was modulated harmonically, the response of the synchrotron motion showed characteristics of chaos and bifurcations of a parametric resonant system. Manipulating the rf system to create islands in the synchrotron phase space may offer applications in future hadron colliders.