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Considered is the diffraction radiation of a flat modulated beam of electrons flowing between two identical circular nanotubes made of silver. The electromagnetic field of such a beam is a two-dimensional H-polarized surface wave, which propagates in the same direction as the beam, with the phase velocity equal to the beam velocity. This field excites the currents on the nanotubes that radiate even if the beam does not touch the scatterers. For numerical solution, we use the method of partial separation of variables and the addition theorems for cylindrical functions that reduces the diffraction radiation problem to a matrix equation. On casting this equation to the Fredholm second-kind form, we compute far-field scattering cross-sections and field patterns with controlled accuracy. The obtained results show that a shift of the beam trajectory from the central-symmetric position triggers the excitation of certain resonances, which are absent otherwise. This may serve as a basis for the design of novel optical-range beam position monitors of nanoscale dimensions.

Accurate measurements of optics functions, β, α, D, are essential for proper operation of a synchrotron both for machine protection and for performance. β functions can be obtained from different observables: phase and amplitude of the transverse betatron oscillations and change of the tune by modulating the current of quadrupoles (K-modulation). Reconstruction of β function using the betatron phase, in combination with K-modulation, has been the main measurement approach in the LHC IRs. Nonetheless, challenges have appeared in the β calculation using these two techniques when aiming for smaller β^{*}, i.e., β-values at the interaction point (IP) in the LHC and the HL-LHC. The third β measurement technique, based on the beam position monitor (BPM) signal amplitude, has not been used as widely in the LHC as the other methods since it requires accurate BPM gain calibration. This paper presents the development of a technique based on optics measurements to calibrate accurately LHC IR BPMs, allowing to use of the amplitude information in the measurement of IR β functions.

A beam position monitor (BPM) has been developed to monitor the position of an electron beam in the laser heater of the X-ray free electron laser at the Pohang Accelerator Laboratory (PALXFEL). The BPM for the laser heater (LH-BPM) is based on a strip-line type. The LH-BPM consists of a pair of upper and lower blocks. Two strip-lines are in each block. In this paper, we report on the physical motivation, design considerations, cold tests, and typical results for the LH-BPM currently in use at the PAL-XFEL.

Graphical abstract, A compact beam-position monitor was constructed using a linear contact image sensor attached to a plastic scintillator and tested using a 230 MeV proton beam. The results indicate that the beam position can be obtained in real-time, and the beam position with a precision of up to 0.03 mm. The compactness and high precision of the device hold considerable potential for it to be used as a beam-position monitor and offline, daily quality assurance monitor in hadron therapy. • The method can provide a high precision and high resolution beam position for flash irradiation in particle therapy in real-time. • The method using contact image sensor with scintillator does not require a long focal length for camera and it is free of image distortion. • The method can be integrated into medical particle accelerator for feedback control and daily quality assurance.

Graphical abstract, We introduce a novel technique to implement gate functionality for the beam position monitors (BPM) at the National Synchrotron Light Source II (NSLS-II). The functionality, now implemented in FPGA, allows us to acquire two separated bunch-trains’ synchronized turn-by-turn (TBT) data simultaneously with the NSLS-II in-house developed BPM system. The gated position resolution is improved about 3 times by narrowing the sampling width. Experimentally we demonstrated that the machine lattice could be transparently characterized with the gated TBT data of a short diagnostic bunch-train Cheng et al., 2017; Li et al., 2017. Other applications, for example, precisely characterizing storage ring impedance/wake-field through recording the beam positions of two separated bunch trains has been experimentally demonstrated. • Gated BPM signal processing improves the position resolution. • Transparent lattice measurement using the gate function with diagnostic bunches. • Collective effect study with simultaneous position measurement from two gates.

As an X-ray Free Electron Laser, PAL-XFEL is about to start beam commissioning. X-band cavity beam position monitor (BPM) is used in the PAL-XFEL undulator beam line. Prototypes of cavity BPM pick-up were designed and fabricated to test the RF characteristics. Also, the beam test of a cavity BPM pick-up was done in the Injector Test Facility (ITF). In the beam test, the raw signal properties of the cavity BPM pick-up were measured at a 200 pC bunch charge. According to the RF test and beam test results, the prototype cavity BPM pick-up design was confirmed to meet the requirements of the PAL-XFEL cavity BPM system.

We propose a method to simultaneously correct linear optics errors and linear coupling for storage rings using turn-by-turn (TbT) beam position monitor (BPM) data. The independent component analysis (ICA) method is used to isolate the betatron normal modes from the measured TbT BPM data. The betatron amplitudes and phase advances of the projections of the normal modes on the horizontal and vertical planes are then extracted, which, combined with dispersion measurement, are used to fit the lattice model. The fitting results are used for lattice correction. The method has been successfully demonstrated on the NSLS-II storage ring.

The noninterceptive four-dimensional transverse emittance measurements are essential for commissioning the high power continue-wave (CW) proton linacs as well as their operations. The conventional emittance measuring devices such as slits and wire scanners are not well suited under these conditions due to sure beam damages. Therefore, the method of using noninterceptive Beam Position Monitor (BPM) is developed and demonstrated on Injector Scheme II at the Chinese Accelerator Driven Sub-critical System (China-ADS) proofing facility inside Institute of Modern Physics (IMP) [1] . The results of measurements are in good agreements with wire scanners and slits at low duty-factor pulsed (LDFP) beam. In this paper, the detailed experiment designs, data analysis and result benchmarking are presented.

In order to pursue high-precision beam position measurements for free-electron laser facilities, a cavity beam position monitor (CBPM) is employed to measure the transverse position that can meet the requirement of position resolution at a sub-micrometer or even nanometer scale. However, for the pill-box cavity BPM, crosstalk between the cavities will have an effect on the accurate measurement of beam position. To reduce the effect of crosstalk on CBPM performance and ease the measurement of the isolation between the cavities, the cavities with a slight difference in resonant frequency were designed and applied in the Dalian coherent light source and Shanghai soft X-ray free-electron laser facilities. Furthermore, two methods, the principal component analysis method and the method of harmonic analysis, are proposed in this paper to evaluate the crosstalk. The results demonstrate that the two methods are feasible in evaluating the crosstalk between the cavities.

A system has been developed to measure the vertical position and angle of the electron beam at a single location from a synchrotron source. The system uses a monochromator tuned to the absorption edge of a contrast material and has a sensitivity comparable with other beam position monitors., The stability of the photon beam position on synchrotron beamlines is critical for most if not all synchrotron radiation experiments. The position of the beam at the experiment or optical element location is set by the position and angle of the electron beam source as it traverses the magnetic field of the bend-magnet or insertion device. Thus an ideal photon beam monitor would be able to simultaneously measure the photon beam’s position and angle, and thus infer the electron beam’s position in phase space. X-ray diffraction is commonly used to prepare monochromatic beams on X-ray beamlines usually in the form of a double-crystal monochromator. Diffraction couples the photon wavelength or energy to the incident angle on the lattice planes within the crystal. The beam from such a monochromator will contain a spread of energies due to the vertical divergence of the photon beam from the source. This range of energies can easily cover the absorption edge of a filter element such as iodine at 33.17 keV. A vertical profile measurement of the photon beam footprint with and without the filter can be used to determine the vertical centroid position and angle of the photon beam. In the measurements described here an imaging detector is used to measure these vertical profiles with an iodine filter that horizontally covers part of the monochromatic beam. The goal was to investigate the use of a combined monochromator, filter and detector as a phase-space beam position monitor. The system was tested for sensitivity to position and angle under a number of synchrotron operating conditions, such as normal operations and special operating modes where the photon beam is intentionally altered in position and angle at the source point. The results are comparable with other methods of beam position measurement and indicate that such a system is feasible in situations where part of the synchrotron beam can be used for the phase-space measurement.

Simultaneous photon beam position and intensity monitoring is becoming of increasing importance for new generation synchrotron radiation sources and free electron lasers (FEL). Thus, novel concepts of beam diagnostics are required in order to keep such beams under control. From this perspective diamond is a promising material for the production of semitransparent in situ photon beam monitors, which can withstand the high dose rates occurring in such radiation facilities. Here, we report on the development of freestanding, single-crystal chemical-vapor-deposited diamond detectors with segmented electrodes. Due to their direct, low-energy band gap, InGaAs quantum well devices operated at room temperature may also be used as fast detectors for photons ranging from visible to X-ray. These features are valuable in low-energy and time-resolved FEL applications. In particular, a novel segmented InGaAs/InAlAs device has been developed and will be discussed. Dedicated measurements carried out on both these devices at the Elettra Synchrotron show their capability to monitor the position and the intensity of the photon beam with bunch-by-bunch temporal performances. Furthermore, preliminary tests have been performed on diamond detectors at the Fermi EEL, extracting quantitative intensity and position information for 100-fs-wide FEL pulses with a photon energy of 28.8 eV. (C) 2013 Elsevier B.V. All rights reserved

This paper summarizes the results of the study of a bunch length monitor based on the button BPM (Beam Position Monitor). The monitor consists of a BPM installed on the beam pipe and a spectrum analyzer. We use the button-BPM's button pickups as the electrodes to pick up the signal. The bunch length can be derived from the spectrum of the beam-induced signal got by the spectrum analyzer. We show the theoretical results and the simulations performed by CST

The $N$ beam position monitor method ($N$-BPM) which was recently developed for the LHC has significantly improved the precision of optics measurements that are based on BPM turn-by-turn data. The main improvement is due to the consideration of correlations for statistical and systematic error sources, as well as increasing the amount of BPM combinations which are used to derive the $\ensuremath{\beta}$-function at one location. We present how this technique can be applied at light sources like ALBA, and compare the results with other methods.

A button-type beam position monitor (BPM) has been designed and fabricated for the upgraded Pohang Light Source. The BPM consists of four buttons located symmetrically at top and bottom of the vacuum chamber. In the process of simulation, the Wakefield Simulator of CST Particle Studio is mainly used as the tool to calculate the wakefields and the electromagnetic fields. The BPM is tested by using a test stand to check its performance before installation. The calibration of BPM is also performed to check its position offsets and its sensitivities.

A non-destructive large-aperture beam position monitor has been developed to measure the beam position of the 150 MeV Fixed Field Alternating Gradient (FFAG) accelerator at Center for Accelerator and Beam Applied Science of Kyushu University. The results of the performance test of a prototype of the new beam position monitor with multi-electrodes are described.��

The external Q (Qext) of the dipole mode is a key parameter of the Cavity Beam Position Monitor (CBPM). It determines the amplitude and length of the dipole mode signal. In this paper, Qext of a CBPM whose waveguides were open to the air was simulated and measured, and the results agreed with each other. Then four waveguide-to-coaxial cable adpaters were adjusted and assembled to the CBPM, and Qext remained unchanged. This progress provides a reliable method to evaluate Qext in the physics design without simulating the structurally complex adapters.

A prototype of resistive beam position monitor was designed and built for Mini-LIA. The design parameters and bench test results are presented. A beam displacement nearly 1 mm off-axis can be observed. The relationship between the signal amplitude and decay time constant to current rising time was studied.

A detector to monitor online the protontherapy beam at the Istituto Nazionale di Fisica Nucleare (INFN), Laboratori Nazionali del Sud (LNS) has been built and characterized. The detector is made of two ionization chambers: each chamber has the anode splitted into 256 0.5 mm strips with vertical and horizontal orientation. The chambers are part of the beam line: signals can be processed online at a speed up to 100 Hz and results are promptly available. Thus the beam geometry can be controlled continuously during patient treatment, and in case of deviation from the required conditions, the treatment can be directly concluded.

The coordinate sensitive ionization chamber for measurement of parameters of a synchrotron radiation beam in the X-ray range was designed. The parameters of the chamber are as follows: (1) coordinate resolution better than 1 μm; (2) range of measurements in the cross-section of SR beam is 10 mm; (3) dynamic ranges ∼10 5 ; (4) the apertures of the entrance window are 12×24 mm; (5) the material of the window is Be; (6) Ar gas; (7) frequency of measurements is 6–50 Hz; (8) interface is Ethernet.

Estimation and correction of the optics errors in an operational storage ring is always vital to achieve the design performance. To achieve this task, the most suitable and widely used technique, called linear optics from closed orbit (LOCO) is used in almost all storage ring based synchrotron radiation sources. In this technique, based on the response matrix fit, errors in the quadrupole strengths, beam position monitor (BPM) gains, orbit corrector calibration factors etc. can be obtained. For correction of the optics, suitable changes in the quadrupole strengths can be applied through the driving currents of the quadrupole power supplies to achieve the desired optics. The LOCO code has been used at the Indus-2 storage ring for the first time. The estimation of linear beam optics errors and their correction to minimize the distortion of linear beam dynamical parameters by using the installed number of quadrupole power supplies is discussed. After the optics correction, the performance of the storage ring is improved in terms of better beam injection/accumulation, reduced beam loss during energy ramping, and improvement in beam lifetime. It is also useful in controlling the leakage in the orbit bump required for machine studies or for commissioning of new beamlines.

At present, the beam-based alignment of the LHC collimators is performed by touching the beam halo with both jaws of each collimator. This method requires dedicated fills at low intensities that are done infrequently and makes this procedure time consuming. This limits the operational flexibility, in particular in the case of changes of optics and orbit configuration in the experimental regions. The performance of the LHC collimation system relies on the machine reproducibility and regular loss maps to validate the settings of the collimator jaws. To overcome these limitations and to allow a continuous monitoring of the beam position at the collimators, a design with jaw-integrated Beam Position Monitors (BPMs) was proposed and successfully tested with a prototype (mock-up) collimator in the CERN SPS. Extensive beam experiments allowed to determine the achievable accuracy of the jaw alignment for single and multi-turn operation. In this paper, the results of these experiments are discussed. The non-linear response of the BPMs is compared to the predictions from electromagnetic simulations. Finally, the measured alignment accuracy is compared to the one achieved with the present collimators in the LHC., peer-reviewed

At BSRF we have designed and constructed a four-blade slit for 4W1B XAFS beamline to improve its performance. The slit also functions as a beam position monitor by detecting the signal of photoemission from the blades. The key features of this design are: (1) adopting a new mechanism for blade adjustment; (2) combining the functions of two types of BPM (the single wire monitor and the double blade monitor) with the slit. Those features enable us firstly to accurately align the slit with the center of the beam, secondly to monitor the stability of the beam position during operation, and thirdly to diagnose the beam characteristics with this single device. The principle, the features and the testing results are presented in the following sections. (C) 2001 Elsevier Science B.V. All rights reserved.

A new type of beam-position monitor (BPM) has been developed in the KEKB accelerator. The BPM employs an I/Q (In-phase and Quadrature phase) demodulator operating at an acceleration frequency of 509 MHz without down converting. The peak value of a demodulated beam pulse is sampled every revolution period. Not only horizontal and vertical positions, but also the longitudinal position can be detected turn by turn. The performance of this four-dimensional BPM is described in detail. A monitor is indispensable for tuning a beam injected into the KEKB.

A beam position monitor using higher order mode (HOM) couplers is proposed. This has the possibility to detect beam positions through superconducting accelerators in long cryostats where normal beam position monitors cannot be installed. The primary measurement was done to show the correlation between the beam position and the HOM power.

International audience; Diamond is a promising material for the production of semitransparent in situ photon beam monitors which can withstand the high dose rates occurring in new generation synchrotron radiation storage rings and in free electron lasers. We report on the development of a 500 mu m thick freestanding, single crystal chemical vapor deposited diamond detector with segmented electrodes. Performances in both low and radio frequency beam monitoring are presented as well. By using charge integration techniques at a frame rate of 6.5 kHz in combination with a needle synchrotron radiation beam and mesh scans, the inhomogeneity of the sensor was found to be of the order of 2%; with a measured electronics noise of 2 pA / root Hz a 0.05% relative precision in the intensity measurements (at 1 mu A) and a 0.1 mu m resolution in the position encoding have been estimated. Moreover, the high electron-hole mobility of diamond compared with other active materials enables very fast charge collection characterized by rise-times below 1 ns; this allowed us to utilize single pulse integration to simultaneously detect the intensity and the position of each synchrotron radiation photon bunch generated by a bending magnet

The construction and performance of a nondestructive beam position monitor using high-permeability chips (high-permeability chips: HPCs) are presented. This monitoring system consists of the HPCs, pickup coils, a monitor housing, an automatic precision XY -stage and a four-channel fast-response digitizing oscilloscope. The beam aperture of the beam position monitor has a diameter of 45 mm. The beam position was detected by a pickup coil which is wound around the HPC. Four of these sensors were positioned 90° apart in azimuth about the beam axis. The development of a nondestructive beam position monitor for experiments requiring linear accelerator operations has been long awaited. This monitoring system measures beam positions in the horizontal and vertical directions independently of each other. The magnetic field induced by an electron beam is measured by the four sensors. It is possible to measure the beam position with an accuracy of 0.5 mm for a calibration area of 30 mm × 20 mm. Agreement between results from the experiment using a linear accelerator and test bench is obtained.

Performance characteristics of beamline X8C at the National Synchrotron Light Source are described. Beamline optics consist of a rhodium coated collimating mirror, a two (optional four) crystal monochromator and a rhodium coated focussing mirror. X-ray source diagnostic information is provided by a dual wire beam position monitor that precedes all beamline components. Measurements are presented for three different optical configurations using the non-dispersive two crystal geometry. Advantages and disadvantages of this beamline design are discussed, with particular emphasis placed on details of the collimating mirror performance. A brief description of experimental apparatus is also given including computing resources, which have been optimized to handle biological macromolecular diffraction data from a CCD area detector.

New generation Synchrotron Radiation (SR) sources and Free Electron Lasers (FEL) require novel concepts of beam diagnostics to keep photon beams under surveillance, asking for simultaneous position and intensity monitoring. To deal with high power load and short time pulses provided by these sources, novel materials and methods are needed for the next generation BPMs. Diamond is a promising material for the production of semitransparent in situ X-ray BPMs withstanding the high dose rates of SR rings and high energy FELs. We report on the development of freestanding, single crystal CVD diamond detectors. Performances in both low and radio frequency SR beam monitoring are presented. For the former, sensitivity deviation was found to be approximately 2%; a 0.05% relative precision in the intensity measurements and a 0.1-μm precision in the position encoding have been estimated. For the latter, single-shot characterizations revealed sub-nanosecond rise-times and spatial precisions below 6 μm, which allowed bunch-by-bunch monitoring in multi-bunch operation. Preliminary measurements at the Fermi FEL have been performed with this detector, extracting quantitative intensity and position information for FEL pulses (~ 100 fs, energy 12 ÷ 60 eV), with a long-term spatial precision of about 85 μm; results on FEL radiation damages are also reported. Due to their direct, low-energy band gap, InGaAs quantum well devices too may be used as fast detectors for photons ranging from visible to X-ray. Results are reported which show the capability of a novel InGaAs/InAlAs device to detect intensity and position of 100-fs-wide laser pulses.

This paper describes the development of a digital-based Beam Position System which was designed, developed, and adapted for the Tevatron during Collider Run II., Comment: 20 pp

Design and performance of a UHV compatible dual wire beam position monitor are presented with specific applications to beamline X8C at the NSLS. This device can determine the relative vertical position of the X-ray beam to within ±5 μm . At X8C, the wire monitor is used to observe the reproducibility of the X-ray beam position after each new electron fill and to watch for instabilities that may arise during stored beam conditions. Data from the NSLS X-ray ring pick-up electrodes are presented to independently assess wire monitor accuracy.

Recent progress in the development of a beam position monitor system (BPM), based on the log‐ratio technique, is described in this paper. A complete electronic analysis is presented, showing linearity, dynamic range, noise, RF burst response, and temperature dependence. A calibration technique has been developed, which corrects the errors due to mismatched channels and electronics drift. This technique is particularly effective because of the log‐ratio property for beam position monitoring. This circuit is the most likely candidate for beam position monitor electronics at the SSC.

This note describes the design, fabrication and calibration of the NDCX-II capacitive beam position monitor.

The beam position monitor (BPM) for the final focus test beam (FFTB) is newly designed to have 1 μm precision and repeatability within 500 μm from center. The system design and the performance test of the prototype electronics are described.

Techniques to characterize attosecond harmonic pulses based on thecross-correlation between harmonic and IR laser pulses are presented. The selfcompressionof an attosecond harmonic pulse in the harmonic generation itself has been demonstrated, obtaining near transform-limited attosecond harmonic pulses.

The European XFEL will be a free electron laser based on self amplified spontaneous emission in the X-ray regime. The FEL is driven by a superconducting 17.5 GeV linear accelerator, followed by 5 separate undulators both for SASE FEL radiation and incoherent radiation. Start of operation is foreseen for 2013. This paper presents the layout of the European XFEL, with an emphasis on beam dynamics issues.

The beam commissioning of J-PARC LINAC has been started in November 2006. Beam position monitors (BPMs) which had been calibrated on the bench setup with a scanning wire, take beam-based-calibration method in order to enable the beam to pass at the centre of a quadrupole magnet (Q-magnet). In this presentation, the installed BPMs and their calibration methods are described.

The offset beam from the axis induces the HOMs in the cavities. These HOMs in superconducting cavities are usually damped by HOM couplers to suppress the beam instability. The induced HOM field of dipole mode is proportional to the beam offset and can be used to measure the beam position inside the cavity. Measuring the HOM power by scanning the beam permits to estimate the beam position using a known function of the HOM power. The steering magnet was installed to the JAEA superconducting ERL-FEL to vary the beam position. The beam position in the cavity was estimated with the measured HOM power from the HOM coupler.

Changes in the longitudinal impedance budget occur due to the changes in the machine structure. Following the installation in ELETTRA storage ring of the new vacuum chambers in the last three years, estimation of the longitudinal loss factor are carried out. The measurements are performed by mapping the horizontal closed orbit deviation, taking full advantage of the newly installed high resolution BPM electron system. The current results are compared with those of the previous measurements and presented in this paper.

During the last PEP-II run a major goal was to bring the Low-Energy Ring optics as close as possible to the design. A large number of BPMs exhibited sudden artificial jumps that interfered with this effort. The source of the majority of these jumps had been traced to the filter-isolator boxes (FIBs) near the BPM buttons. A systematic approach to find and repair the failing units had been developed and implemented. Despite this effort, the instrumental orbit jumps never completely disappeared. To trace the source of this behavior a test setup, using a spare Bergoz MX-BPM processor (kindly provided by SPEAR III at SSRL), was connected in parallel to various PEP-II BPM processors. In the course of these measurements a slow instrumental orbit drift was found which was clearly not induced by a moving positron beam. Based on the size of the system and the limited time before PEP-II closes in Oct. 2008, an accelerator improvement project was initiated to install BERGOZ BPM-MX processors close to all sextupoles.

We present the electrical and mechanical design of a button beam position monitor (BPM) recently developed and installed in the UVX electron storage ring at the Brazilian Synchrotron Light Laboratory (LNLS). The first characterization results will also be presented. This development started when we observed strong correlation between false stripline BPM readings and the external temperature of this BPM. Simulations indicate that the temperature gradient in the BPM body can cause deformations that could explain the false readings in some BPMs. The small dimension of the button compared to the stripline and the better thermal isolation between the button and the BPM body should contribute to minimize this problem.

The proposed HAPPEX experiment at CEBAF employs a three cavity monitor system for high precision (1um), high bandwidth (100 kHz) position measurements. This is performed using a cavity triplet consisting of two TM110-mode cavities (one each for X and Y planes) combined with a conventional TM010-mode cavity for a phase and magnitude reference. Traditional systems have used the TM010 cavity output to directly down convert the BPM cavity signals to base band. The multi-channel HAPPEX digital receiver simultaneously I/Q samples each cavity and extracts position using a CORDIC algorithm. The hardware design consists of a RF receiver daughter board and a digital processor motherboard that resides in a VXI crate. The daughter board down converts 1.497 GHz signals from the TM010 cavity and X and Y signals from the TM110 cavities to 3 MHz and extracts the quadrature digital signals. The motherboard processes this data and computes beam intensity and X-Y positions with resolution of 1um, 100 kHz output bandwidth, and overall latency of 1us. The results are available in both the analog and digital format.

Electron Linac at the Pohnag Accelerator Laboratory (PAL) has been operated continuously as full energy for storage ring, 2.0-GeV since 1994 Dec. and 2.5-GeV since 2002 Oct. At the BTL, BCM (Beam Current Monitor), BLM (Beam Loss Monitor), BPRM (Beam Profile Monitor) and BPM (Beam Position Monitor) are used for beam operation. Thirteen BPMs has been installed from Linac end to BTL end at Aug. 2004. In order to measure of the beam position, 500 MHz Log-Ration (LR) BPM boards are used. Data acquisition system consists of NI S-series data acquisition board and NI Lab-View Version 7.1. For monitoring of BPM data at EPICS control system, BPM data acquisition system is developed as EPICS IOC. BTL BPMs are going to use optic correction and beam energy feedback at PLS normal beam operation.

We present an improved system for orbit and betatron phase measurement utilizing nonlinear models of beam position monitor (BPM) pickup response. We first describe the calculation of the BPM pickup signals as nonlinear functions of beam position using Greens reciprocity theorem with a two-dimensional formalism. We then describe the incorporation of these calculations into our beam position measurements by inverting the nonlinear functions, giving us beam position as a function of the pickup signals, and how this is also used to improve our calculation of the betatron phase advance. Measurements are presented comparing this system with the linearized pickup response used historically at CESR.