Search Results (14 total)

Modern colliders bring into collision a large number of bunches to achieve a high luminosity. The long-range beam-beam effects arising from parasitic encounters at such colliders are mitigated by introducing a crossing angle. Under these conditions, crab cavities (CC) can be used to restore effective head-on collisions and thereby to increase the geometric luminosity. Such crab cavities have been proposed for both linear and circular colliders. The crab cavities are rf cavities operated in a transverse dipole mode, which imparts on the beam particles a transverse kick that varies with the longitudinal position along the bunch. The use of crab cavities in the Large Hadron Collider (LHC) may not only raise the luminosity, but it could also complicate the beam dynamics, e.g., crab cavities might not only cancel synchrobetatron resonances excited by the crossing angle but they could also excite new ones, they could reduce the dynamic aperture for off-momentum particles, they could influence the aperture and orbit, also degrade the collimation cleaning efficiency, and so on. In this paper, we explore the principal feasibility of LHC crab cavities from a beam dynamics point of view. The implications of the crab cavities for the LHC optics, analytical and numerical luminosity studies, dynamic aperture, aperture and beta beating, emittance growth, beam-beam tune shift, long-range collisions, and synchrobetatron resonances, crab dispersion, and collimation efficiency will be discussed.

We have measured and corrected chromatic X-Y coupling at an interaction point to improve the luminosity of KEKB. We have measured the beam position of betatron oscillations induced by the kicker using turn-by-turn beam position monitors. A phase space structure reconstructed by the beam position provides us not only the Twiss parameters but also information regarding X-Y coupling. We have also determined chromatic X-Y coupling using the measured X-Y coupling at each momentum deviation from the designed beam energy. Skew sextupole magnets are used to correct the chromatic X-Y coupling.

Proton beams were successfully steered through the entire ring of the CERN Large Hadron Collider (LHC) on September the 10th of 2008. A reasonable lifetime was achieved for the counterclockwise beam, namely beam 2, after the radiofrequency capture of the particle bunch was established. This provided the unique opportunity of acquiring turn-by-turn betatron oscillations for a maximum of 90 turns right at injection. Transverse coupling was not corrected and chromaticity was estimated to be large. Despite this largely constrained scenario, reliable optics measurements have been accomplished. These measurements together with the application of new algorithms for the reconstruction of optics errors have led to the identification of a dominant error source.

Optics correction is an important issue in the KEKB B-factory. Especially, the correction of beta functions is performed so as to reach near half-integer resonance of the horizontal betatron tune as closely as possible. Consequently, the luminosity can be improved during experiments of the B-meson in e⁺e^- collisions. Therefore, we have developed a correction method of the beta function not only at the designed beam energy, but also at an energy deviated from the nominal value. We present the procedures used to measure the behavior of the beta function, which depends on the momentum deviation, and the results compared with the model optics in the KEKB rings.

With detailed experimental studies and hydrodynamics and particle-in-cell simulations we investigate the role of the prepulse in laser proton acceleration. The prepulse or pedestal (amplified spontaneous emission) can completely evaporate the irradiated region of a sufficiently thin foil; therefore, the main part of the laser pulse interacts with an underdense plasma. The multiparametric particle-in-cell simulations demonstrate that the main pulse generates the quasistatic magnetic field, which in its turn produces the long-lived charge separation electrostatic field, accelerating the ions.

A helical quadrupole focusing channel has continuous field symmetry and a stronger focusing power compared with a conventional FODO focusing channel. The good field symmetry allowed us to construct an explicit transfer matrix under the paraxial approximation. In the present paper, we report the paraxial analysis of the helical quadrupole focusing channel and compare its characteristics with those of a conventional FODO focusing channel.

A compact proton synchrotron using combined function magnets is proposed to help realize the wider availability of charged particle cancer therapy facilities. This combined function magnet was designed with the help of three-dimensional magnetic field calculations to take account of a realistic fringe and the interference among the magnetic poles. An evaluation scheme for tune values based on particle tracking was developed to improve the magnet design. To verify the magnet design, a model magnet was fabricated and measured. In order to achieve a tune value evaluation from the measured magnetic field, schemes for accurate field mapping and field interpolation were developed. From the tune value evaluation of the measured magnetic field, it was thought that the performance of the model magnet was good enough to construct a synchrotron. In this paper, we report details of the design and the evaluation scheme for the combined function magnet and the results of the field measurements of the model magnet.

The Smoluchowski equation for the Brownian motion of two interacting particles through a square-well potential whose heights are infinitely large at the origin and finite at the other positions of u (>0) is solved exactly for the Laplace transform of the conditional density with respect to time t. The analytical expression for the distinct part of the dynamic structure factor at the initial time with the δ function has also been obtained exactly. Moreover, we have calculated the asymptotic behavior of the mean-square displacement expressed as an explicit function of t and found that it is a function of the height of the potential at u, which directly indicates a deviation from the Einstein relation.

Dynamic behavior of free Brownian motion of a particle driven by dichotomous (random telegraphic) colored noise has been treated based on the ordinary Langevin equation. The treatment makes direct use of the characteristic function without using the Fokker-Planck equation. The conditional probability density in the case where inertial effects are neglected has been obtained exactly as a function of the position of the particle, and it is shown that starting from the Dirac δ function at t=0, the probability density exhibits δ functions at both extremes at early times, and the amplitudes of the δ functions gradually vanish as time goes on. It is shown that this presence of δ functions at the early stage is associated with dichotomous noise. The characteristic function for the Langevin equation with complete consideration of inertial effects has also been obtained exactly.

Transient responses and stationary processes with alternating fields are treated in the nonlinear regime in order to clarify their relations in the time and frequency domains. It is shown that a frequency-domain experiment in which a weak ac field is superimposed on a strong biasing dc field corresponds to the transient process of a strong constant biasing field with the sudden application of weak constant field. Furthermore, it is found that the Fourier-Laplace transform of the second-order nonlinear transient rise process corresponds to the amplitude for the ω component of the stationary experiment with coupled dc and ac fields with the angular frequency ω. For a simple ac input, we demonstrated how the stationary nonlinear response may conveniently be calculated with the help of the theory of random walk. Also, interrelations among the rise, decay, and rapidly re- versing transients are clarified.

A simple convergent and analytical solution valid for the whole time range for the stochastic Verhulst equation is obtained by treating the strength of the external Gaussian white noise as a perturbation without using the existing approach where the moments are expressed by means of an integral representation. In the case when the deterministic behavior is coupled weakly with the stochastic one induced by the perturbation, it is found that the analytical result is in good agreement with the numerical one. This perturbation technique is also used for treating a class of multiplicative nonlinear stochastic differential equations, and the moments valid for the whole time range are calculated analytically. The result shows explicitly the behavior of the long-time decay of t^-1/2, and it also compares satisfactorily with the numerical one in the limit of weak noise strength.

The problem of nonlinear response is considered by employing a general time-evolution equation, and a Green’s function which is the transition or conditional probability density for an unperturbed system. Expansion of the Green’s function in terms of orthonormal functions enables us to express the distribution function describing the nonlinear behavior by means of matrix products whose elements are composed of correlation functions in the absence of the perturbation. In other words, it is shown how the distribution function induced by a strong perturbation may be calculated by knowing the Green’s function without the perturbation. As the special case of the linear response, we have obtained Kubo’s relation. The Laplace-transform technique with respect to time is found quite useful in developing the present theory in which the transient effect is also taken into account. As an application of the theory, a new relation valid in the region of the second-order perturbation connecting the transient rise and decay with the stationary alternating perturbations has been obtained.

Soft-x-ray emission (Kβ emission) and absorption (K absorption) spectra of a black P single crystal polarized along each crystalline axis are presented for the first time. The experimental results indicate (1) the upper part of the valence band near the Fermi level is largely contributed by the 3p_z states, (2) the 3p_y orbital forms the middle to lower part of the 3p-derived (or the first) valence band, (3) the 3p_x states spread over a whole range in the band, and (4) the conduction band has a clear but less drastic dependence on the nature of the constituent atomic orbitals. The emission and absorption curves were numerically calculated with the results of the band calculation of black P based on the self-consistent pseudopotential method and were compared with the experimental results. Excellent agreement has been found in the features of each spectrum, although a relative displacement of the emission and absorption spectra was observed between the experiment and the calculation. This discrepancy may be attributed to the overestimation of the 3p-band width in the band calculation, although a many-body effect in the emission or absorption process cannot be entirely excluded.

The electron-capture cross section of the deep trap due to a lattice vacancy in Si is calculated by taking into account the distortion of the lattice vibrations by the lattice vacancy. It is assumed that the trap is a neutral center for electron capture. The results show that although the distortion effect enlarges the calculated cross section by three orders of magnitude at 300°K, it is not enough to explain the magnitudes of observed cross sections.