Phase Space Ellipse Research Articles

Quantum-enhanced interferometer using Kerr squeezing

Abstract One of the prime applications of squeezed light is enhancing the sensitivity of an interferometer below the quantum shot-noise limit, but so far, no such experimental demonstration was reported when using the optical Kerr effect. In prior setups involving Kerr-squeezed light, the role of the interferometer was merely to characterize the noise pattern. The lack of such a demonstration was largely due to the cumbersome tilting of the squeezed ellipse in phase space. Here, we present the first experimental observation of phase-sensitivity enhancement in an interferometer using Kerr squeezing.

Studying the effect of the bending magnet parameters on focusing of charged particles in beam transport systems via the matrix representation method

The focusing of charged particles beam passing through the transport system is affected by many parameters and depends on the elements that used in the transport beam systems. In this study, a permanent bending C-shape magnet is used to investigate the effect of the geometrical configuration parameters of bending magnet on the focusing of the passing charged particles beam. This investigation is implemented via the method of the matrix’s representation. The results showed that the edges of the bending magnet have opposite focus in the horizontal and vertical planes of beam motion. The deflecting angle effect appeared as a rotation of the phase space ellipse of the charged particle beam without focusing of this beam. The results also, showed that the focus of the charged particles beam is unlike in both horizontal and vertical planes of beam motion.

Wave Anomaly Detection in Wave Measurements

AbstractQuality control measures for ocean waves observations are necessary to give confidence of their accuracy. It is common practice to detect anomalies or outliers in surface displacement observations by applying a standard deviation threshold. Besides being a purely statistical method, this quality control procedure is likely to flag extreme wave events erroneously, thereby impacting higher-order descriptions of the wave field. In this paper we extend the use of the statistical phase-space threshold, an established outlier detection method in the field of turbulence, to detect anomalies in a wave record. We show that a wave record in phase space (here defined as a diagram of displacement against acceleration) can be enclosed by a predictable ellipse where the major and minor axes are defined by the spectral properties of the wave field. By using the parameterized ellipse in phase space as a threshold to identify wave anomalies, this is a semiphysical filtering method. Wave buoy data obtained from a mooring deployed near King George Island, Antarctica [as part of the Antarctic Modeling Observation System (ATMOS)], and laser altimeter data obtained at the Northwest Shelf of Australia were used to demonstrate the functioning of the filtering methodology in identifying wave anomalies. Synthetic data obtained using a high-order spectral model are used to identify how extreme waves are positioned in phase space.

Utilization of RADFET sensors for x-ray undulators: experiential considerations on magnetic field profile before commissioning

Concerning accelerator-based light sources, electrons are accelerated in conformity with specific time structures (i.e. continuous wave, ‘cw’, or bunched), which arise out of accelerating frequencies of employed radiofrequency cavities. Thus, the concept of transverse emittance of electron bunches comes into prominence, simply defining the area of an ellipse in phase space where the electrons are occupied. In nonideal cases (i.e. in real life), when some fraction of these electrons sneak out of a bunch, the concept of ‘energy spread’ automatically arises. Since the energy spread resulting from off-axis relativistic electrons in an insertion device induces considerable radiation damage on magnetic structures of x-ray undulators, radiation-sensitive field effect transistors (RADFETs) are utilized for quantification of radiation intensity. Hence, it is crucial to bring out their influence on magnetic field profiles before commisioning in tunnels. In this respect, two different types of RADFET sensors were investigated over the magnetic poles of an undulator with 40 mm period length (shortened as an U40 undulator). The effects of the sensors on magnetic field were measured using transverse and longitudinal scans through 6.5 m-long magnetic measurement benches (MMBs). The results of two RADFET standard systems are presented, wherein one contains the magnetic material nickel. Finally, novel magnetic measurement techniques for x-ray undulators via unique MMBs are thoroughly explained as well.

Collection and focusing of laser accelerated proton beam by an electromagnetic quadrupole triplet lens

To make use of laser-accelerated protons in real-world applications, specially-designed beamlines are required to control and improve the quality of the beam. At Peking University, the Compact LAser Plasma Accelerator (CLAPA) has been built, and is now coupled with an image-relaying beamline. The primary collection component of this beamline is an electromagnetic quadrupole triplet lens. As this lens is the first and the most crucial step for successful beam transport, we have systematically studied the focusing effect on the laser-driven protons, in terms of emittance, beam profile, and collection efficiency. We found that the normalized rms emittance of the protons can increase significantly, from the order of a fraction of mm⋅mrad to several mm⋅mrad, due to the dispersion of the phase space ellipse caused by the joint effect of the wide energy spread and the nonlinear field at the edge of the quadrupoles. The focusing profile and efficiency are also sensitive to the position and angular deviations of the injected proton beams. With fine adjustment, we found that the collection efficiency can be improved from lower than 10% up to 29%, for protons at the reference energy for CLAPA.

Two-time correlators for propagating squeezed microwave fields in transients

We analyze two-time correlators as the most natural characteristic of a propagating quadrature-squeezed field in the transient regime. The considered system is a parametrically driven resonator with a time-dependent drive. Using a semiclassical approach derived from the input-output theory, we develop a technique for calculation of the two-time correlators, which are directly related to fluctuations of the measured integrated signal. While in the steady state the correlators are determined by three parameters (as for the phase-space ellipse describing a squeezed state), four parameters are necessary in the transient regime. The formalism can be generalized to weakly nonlinear resonators with additional coherent drive. We focus on squeezed microwave fields relevant to the measurement of superconducting qubits; however, our formalism is also applicable to optical systems. The results can be readily verified experimentally.

A System of Two Identical and Opposite Magnets Focusing Beam Charged Particles Passing Through Them

In this work, we use two magnets placed in front of the path of charged particles to obtain the best focusing of charged particles in both the horizontal and vertical planes. We trace the path of charged particles from the extraction region at the ion source, until reach to the target were traced. The process of tracing the path of charged particles is performed using matrices Transfer Matrix (R-Matrix) and. Beam Matrix)in each region in which passing the charged particles, starting from the extraction region reaching to the target by describing the charged particle beams as phase space ellipse in both the horizontal and vertical planes. The ion beam described as phase space ellipse then study the behavior of beam at the edges of magnet with Identical and Opposite.

METAPLECTIC FORMULATION OF THE WIGNER TRANSFORM AND APPLICATIONS

We show that the cross Wigner function can be written in the form [Formula: see text] where [Formula: see text] is the Fourier transform of ϕ and Ŝ is a metaplectic operator that projects onto a linear symplectomorphism S consisting of a rotation along an ellipse in phase space (or in the time-frequency space). This formulation can be extended to generic Weyl symbols and yields an interesting fractional generalization of the Weyl–Wigner formalism. It also provides a suitable approach to study the Bopp phase space representation of quantum mechanics, familiar from deformation quantization. Using the "metaplectic formulation" of the Wigner transform, we construct a complete set of intertwiners relating the Weyl and the Bopp pseudo-differential operators. This is an important result that allows us to prove the spectral and dynamical equivalence of the Schrödinger and the Bopp representations of quantum mechanics.

Parametrization of the driven betatron oscillation

An AC dipole is a magnet which produces a sinusoidally oscillating dipole field and excites coherent transverse beam oscillations in a synchrotron. By observing this driven coherent oscillation, the linear optical parameters can be directly measured at locations of the beam position monitors. The driven oscillations induced by an AC dipole will generate a phase space ellipse which differs from that of free oscillations. If not properly accounted for, this difference can lead to misinterpretations of the actual optical parameters, for instance, 6% or more in the cases of the Tevatron, RHIC, or LHC. This paper shows that the effect of an AC dipole on the observed linear optics is identical to that of a thin lens quadrupole. By introducing a new amplitude function to describe this new phase space ellipse, the motion produced by an AC dipole becomes easier to interpret. The introduction of this new amplitude function also helps measurements of the normal Courant-Snyder parameters based on beam position data taken under the influence of an AC dipole. This new parametrization of driven oscillations is presented and is used to interpret data taken in the FNAL Tevatron using an AC dipole.

Enhanced planar channeling of MeV protons through thin crystals.

At certain tilt alignments between a MeV proton beam and a planar channeling direction, a single interface lattice rotation within a crystal can result in a lower rate of dechanneling than at planar alignment in a perfect crystal. Such planar channeling enhancement arises when the beam passes through a layer thickness which is a half-multiple of the oscillation wavelength and then encounters a small interface rotation which is matched to the beam tilt angle. The beam is projected into the center of the phase space ellipse below the interface, resulting in certain trajectories undergoing a reduction in their transverse energy, in a manner analogous to stochastic cooling or atom laser cooling.

Transverse phase space mapping of relativistic electron beams using optical transition radiation

Optical transition radiation (OTR) has proven to be a versatile and effective diagnostic for measuring the profile, divergence, and emittance of relativistic electron beams with a wide range of parameters. Diagnosis of the divergence of modern high brightness beams is especially well suited to OTR interference (OTRI) techniques, where multiple dielectric or metal foils are used to generate a spatially coherent interference pattern. Theoretical analysis of measured OTR and OTRI patterns allows precise measurement of electron beam emittance characteristics. Here we describe an extension of this technique to allow mapping of divergence characteristics as a function of transverse coordinates within a measured beam. We present the first experimental analysis of the transverse phase space of an electron beam using all optical techniques. Comparing an optically masked portion of the beam to the entire beam, we measure different angular spread and average direction of the particles. Direct measurement of the phase-space ellipse tilt angle has been demonstrated using this optical masking technique.

Simulation of the ESR injection system

Abstract In order to improve the acceptance of the ESR beam injection system the influence of the fringe field of the main dipole magnet on the ion optics has to be analysed. Therefore, we perform a 3D MAFIA simulation of the dipole magnet and calculate the injection line which enters the radial fringe field in a tangential way. Starting from the given ESR beta function we trace the beam ellipse backwards in order to obtain the phase space requirements near the exit plane of the inflector magnet. Simulated phase space “monitors” defined at the start and the end of the curved reference trajectory give insight in the change of the beam emittance ellipse and indicate if aperture limitations may lead to beam losses. We obtain the second-order mapping of the phase space ellipse by calculating the first- and second-order field coefficients along the curved reference trajectory and solving the differential equations corresponding to each matrix element numerically. After an introduction into the field calculation method and the principles used to get the field index and second-order field coefficients, we will discuss our results and compare them with calculations based on measured field data (Spiller et al., GSI Scientific Report, 1996, p. 165).

Tracking study of the new injection bump system of the HLS ring

In this paper, a summary of the existing three-kicker injection bump system of the HLS ring is presented and a new lattice-independent, four-kicker bump system which has been proposed for the second phase project of NSRL is described. Conditions for generating a bump orbit by four kickers are discussed. A theory of multiturn injection based on single-particle dynamics is introduced to analyse the conditions to achieve multiturn injection. Tracking study of the new system are carried out to verify the correctness of the scheme. Parameters such as dimension of the injected beam phase space ellipse, tolerance of the injected beam energy dispersion, timing jitter allowance of the kickers, etc., are calculated.

Ermakov-Lewis invariant from the Wigner function of a squeezed coherent state.

Using the phase-space picture (Weyl-Wigner-Moyal formalism) of quantum mechanics for time-dependent Hamiltonians, we show that the Ermakov-Lewis invariant of a generalized harmonic oscillator can be derived from the Wigner function of a squeezed coherent state. The geometric meaning of this invariant is clarified and realized via the Wigner ellipse in phase space.

185-MeV Injector Design for the ANL 4-GeV Microtron Project

The injector starts with a 5 MeV preinjector followed by an-18 MeV S-band linac. The 23 MeV electrons are transported and injected into a Racetrack Microtron via a 10° achromatic bend system. Twenty-seven turns are used to boost the energy to 185 MeV. Reverse-field stripes on the 180° end magnets and quadrupole focussing on the return paths maintain a matched-dispersion free beam with transverse ß* = 5.0 m in the center of the 4.6 m long linac. The beam is recirculated outside of the RTM linac to shear the longitudinal phase-space ellipse before extraction. The extracted beam is transported and injected into the six-sided microtron at 185 MeV.

RFQ1: A 600 keV, 75 mA CW Proton Accelerator

The RFQ1 accelerator is being built, as part of the ZEBRA program, to study the physics and engineering challenges of launching a moderate energy (600 keV), high current (75 mA) cw proton beam with good beam quality and reliability. The RFQ1 injector will provide a 50 keV proton beam with current variable from zero to ~ 125 mA at fixed energy and filling a defined ellipse in phase space. This beam will be injected into a 269 MHz radio-frequency quadrupole (RFQ) accelerator where it will be shaped, bunched and accelerated to 600 keV. Design output current is 75 mA, however operation at higher current is anticipated. This paper describes the constraints on the design, the preliminary design and the present status of the project.

Global stability analysis of open two-variable quadratic mass-action systems with elliptical limit cycles

We consider open, isothermal and homogeneous two-variable quadratic mass-action systems which exhibit sustained oscillations on an ellipse in phase space [1]. To each system with an elliptic limit cycle there corresponds a conservative one the trajectories of which are curves without contact for the limit cycle system [2]. These trajectories, i.e., the trajectories of all systems oscillating conservatively on an ellipse, are computed analytically. Thus a global stability analysis of every system with an elliptic limit cycle can be performed.

Calculation of the phase-space parameters for the study of quadrupole devices

The coefficients, A O, B O and T O, of the phase-space ellipse used to describe the operation of quadrupole devices have been calculated using equations derived by Hamilton [9]. The method is compared to known methods and is shown to be simple, fast and accurate. Since these coefficients also appear in the transformation matrix, the method is applicable to the theoretical study of quadrupoles by matrix techniques.

The transition matrix for the Mathieu equation: Development and relation to umax

The transition matrix for the Mathieu equation is developed using the general solution of that equation and the coefficients of the phase space ellipse derived from consideration of u max.

The IUCF Transfer Beaime

The transfer beamline between the injector stage and main stage cyclotrons has been designed, constructed and is under test. The beamline provides a good match between the calculated extracted phase space ellipses in the injector and the inflection requirements of the main stage over a wide range of particle types, emittances and energies. Energy dispersion of 0.07% FwHM for 16 MeV protons is available at a waist. Attempts were made to minimlize time dispersion; as a result the time spread through te transfer system is negligible for light ions. For 12C(14+) the time spread will cause an energy spread in the main stage at 200 N4eV of about 100 KeV, under normal operating conditions.