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At least 415 records · Page 23

Real-time catheter tracking for high-dose-rate prostate brachytherapy using an electromagnetic 3D-guidance device: A preliminary performance study

Purpose: In order to increase the accuracy and speed of catheter reconstruction in a high-dose-rate (HDR) prostate implant procedure, an automatic tracking system has been developed using an electromagnetic (EM) device (trakSTAR, Ascension Technology, VT). The performance of the system, including the accuracy and noise level with various tracking parameters and conditions, were investigated. Methods: A direct current (dc) EM transmitter (midrange model) and a sensor with diameter of 1.3 mm (Model 130) were used in the trakSTAR system for tracking catheter position during HDR prostate brachytherapy. Localization accuracy was assessed under both static and dynamic analyses conditions. For the static analysis, a calibration phantom was used to investigate error dependency on operating room (OR) table height (bottom vs midposition vs top), sensor position (distal tip of catheter vs connector end of catheter), direction [left-right (LR) vs anterior-posterior (AP) vs superior-inferior (SI)], sampling frequency (40 vs 80 vs 120 Hz), and interference from OR equipment (present vs absent). The mean and standard deviation of the localization offset in each direction and the corresponding error vectors were calculated. For dynamic analysis, the paths of five straight catheters were tracked to study the effects of directions, sampling frequency, and interference of EM field. Statistical analysis was conducted to compare the results in different configurations. Results: When interference was present in the static analysis, the error vectors were significantly higher at the top table position (3.3 {+-} 1.3 vs 1.8 {+-} 0.9 mm at bottom and 1.7 {+-} 1.0 mm at middle, p < 0.001), at catheter end position (3.1 {+-} 1.1 vs 1.4 {+-} 0.7 mm at the tip position, p < 0.001), and at 40 Hz sampling frequency (2.6 {+-} 1.1 vs 2.4 {+-} 1.5 mm at 80 Hz and 1.8 {+-} 1.1 at 160 Hz, p < 0.001). So did the mean offset errors in the LR direction (-1.7 {+-} 1.4 vs 0.4 {+-} 0.5 mm in AP and 0.8 {+-} 0.8 mm in SI directions, p < 0.001). The error vectors were significantly higher with surrounding interference (2.2 {+-} 1.3 mm) vs without interference (1.0 {+-} 0.7 mm, p < 0.001). An accuracy of 1.6 {+-} 0.2 mm can be reached when using optimum configuration (160 Hz at middle table position). When interference was present in the dynamic tracking, the mean tracking errors in LR direction (1.4 {+-} 0.5 mm) was significantly higher than that in AP direction (0.3 {+-} 0.2 mm, p < 0.001). So did the mean vector errors at 40 Hz (2.1 {+-} 0.2 mm vs 1.3 {+-} 0.2 mm at 80 Hz and 0.9 {+-} 0.2 mm at 160 Hz, p < 0.05). However, when interference was absent, they were comparable in the both directions and at all sampling frequencies. An accuracy of 0.9 {+-} 0.2 mm was obtained for the dynamic tracking when using optimum configuration. Conclusions: The performance of an EM tracking system depends highly on the system configuration and surrounding environment. The accuracy of EM tracking for catheter reconstruction in a prostate HDR brachytherapy procedure can be improved by reducing interference from surrounding equipment, decreasing distance from transmitter to tracking area, and choosing appropriated sampling frequency. A calibration scheme is needed to further reduce the tracking error when the interference is high.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

SU-G-TeP1-03: Beam Quality Correction Factors for Linear Accelerator with and Without Flattening Filter

Purpose: The impact of removing the flattening filter on absolute dosimetry based on IAEA’s TPR-398 and AAPM’s TG-51 was investigated in this study using Monte Carlo simulations. Methods: The EGSnrc software package was used for all Monte Carlo simulations performed in this work. Five different ionization chambers and nine linear accelerator heads have been modeled according to technical drawings. To generate a flattening filter free radiation field the flattening filter was replaced by a 2 mm thick aluminum layer. Dose calculation in a water phantom were performed to calculate the beam quality correction factor k{sub Q} as a function of the beam quality specifiers %dd(10){sub x}, TPR{sub 20,10} and mean photon and electron energies at the point of measurement in photon fields with (WFF) and without flattening filter (FFF). Results: The beam quality correction factor as a function of %dd(10){sub x} differs systematically between FFF and WFF beams for all investigated ionization chambers. The largest difference of 1.8% was observed for the largest investigated Farmer-type ionization chamber with a sensitive volume of 0.69 cm{sup 3}. For ionization chambers with a smaller nominal sensitive volume (0.015 – 0.3 cm{sup 3}) the deviation was less than 0.4% between WFF and FFF beams for %dd(10){sub x} > 62%. The specifier TPR{sub 20,10} revealed only a good correlation between WFF and FFF beams (< 0.3%) for low energies. Conclusion: The results confirm that %dd(10){sub x} is a suitable beam quality specifier for FFF beams with an acceptable bias. The deviation depends on the volume of the ionization chamber. Using %dd(10){sub x} to predict k{sub Q} for a large volume chamber in a FFF photon field may lead to not acceptable errors according to the results of this study. This bias may be caused by the volume effect due to the inhomogeneous photon fields of FFF linear accelerators.

60 APPLIED LIFE SCIENCES↗

High dose per fraction dosimetry of small fields with Gafchromic EBT2 film

Purpose: Small field dosimetry is prone to uncertainties due to the lack of electronic equilibrium and the use of the correct detector size relative to the field size measured. It also exhibits higher sensitivity to setup errors as well as large variation in output with field size and shape. Radiochromic film is an attractive method for reference dosimetry in small fields due to its ability to provide 2D dose measurements while having minimal impact on the dose distribution. Gafchromic EBT2 has a dose range of up to 40 Gy; therefore, it could potentially be useful for high dose reference dosimetry with high spatial resolution. This is a requirement in stereotactic radiosurgery deliveries, which deliver high doses per fraction to small targets. Methods: Targets of 4 mm and 12 mm diameters were treated to a minimum peripheral dose of 21 Gy prescribed to 80% of the maximum dose in one fraction. Target doses were measured with EBT2 film (both targets) and an ion chamber (12 mm target only). Measured doses were compared with planned dose distributions using profiles through the target and minimum peripheral dose coverage. Results: The measured target doses and isodose coverage agreed with the planned dose within {+-}1 standard deviation of three measurements, which were 2.13% and 2.5% for the 4 mm and 12 mm targets, respectively. Conclusions: EBT2 film is a feasible dosimeter for high dose per fraction reference 2D dosimetry.

61 RADIATION PROTECTION AND DOSIMETRY↗

An Efficient High-Order Solver for Diffusion Equations with Strong Anisotropy on Non-Anisotropy-Aligned Meshes

This paper concerns numerical solution of the diffusion equation with strong anisotropy on meshes not aligned with the anisotropic vector field. In order to resolve the numerical pollution for simulations on a non-anisotropy-aligned mesh and reduce the associated high computational cost we propose an effective preconditioner, extending our previous work. Similar to the anisotropy-aligned mesh case, we apply the auxiliary space preconditioning framework to design a preconditioner where a continuous finite element space is used as the auxiliary space for the discontinuous finite element space. The key component is an effective line smoother that can mitigate the high-frequency errors perpendicular to the magnetic field. We design a graph-based approach to find such a line smoother that is approximately perpendicular to the vector fields when the mesh does not align with the anisotropy. Finally, numerical experiments for several benchmark problems are presented, demonstrating the effectiveness and robustness of the proposed preconditioner when applied to Krylov iterative methods.

97 MATHEMATICS AND COMPUTING↗

REEXAMINATION OF INDUCTION HEATING OF PRIMITIVE BODIES IN PROTOPLANETARY DISKS

We reexamine the unipolar induction mechanism for heating asteroids originally proposed in a classic series of papers by Sonett and collaborators. As originally conceived, induction heating is caused by the 'motional electric field' that appears in the frame of an asteroid immersed in a fully ionized, magnetized solar wind and drives currents through its interior. However, we point out that classical induction heating contains a subtle conceptual error, in consequence of which the electric field inside the asteroid was calculated incorrectly. The problem is that the motional electric field used by Sonett et al. is the electric field in the freely streaming plasma far from the asteroid; in fact, the motional field vanishes at the asteroid surface for realistic assumptions about the plasma density. In this paper we revisit and improve the induction heating scenario by (1) correcting the conceptual error by self-consistently calculating the electric field in and around the boundary layer at the asteroid-plasma interface; (2) considering weakly ionized plasmas consistent with current ideas about protoplanetary disks; and (3) considering more realistic scenarios that do not require a fully ionized, powerful T Tauri wind in the disk midplane. We present exemplary solutions for two highly idealized flows that show that the interior electric field can either vanish or be comparable to the fields predicted by classical induction depending on the flow geometry. We term the heating driven by these flows 'electrodynamic heating', calculate its upper limits, and compare them to heating produced by short-lived radionuclides.

79 ASTRONOMY AND ASTROPHYSICS↗

SU-F-T-384: Step and Shoot IMRT, VMAT and Autoplan VMAT Nasopharnyx Plan Robustness to Linear Accelerator Delivery Errors

Purpose: To identify the robustness of different treatment techniques in respect to simulated linac errors on the dose distribution to the target volume and organs at risk for step and shoot IMRT (ssIMRT), VMAT and Autoplan generated VMAT nasopharynx plans. Methods: A nasopharynx patient dataset was retrospectively replanned with three different techniques: 7 beam ssIMRT, one arc manual generated VMAT and one arc automatically generated VMAT. Treatment simulated uncertainties: gantry, collimator, MLC field size and MLC shifts, were introduced into these plans at increments of 5,2,1,−1,−2 and −5 (degrees or mm) and recalculated in Pinnacle. The mean and maximum doses were calculated for the high dose PTV, parotids, brainstem, and spinal cord and then compared to the original baseline plan. Results: Simulated gantry angle errors have <1% effect on the PTV, ssIMRT is most sensitive. The small collimator errors (±1 and ±2 degrees) impacted the mean PTV dose by <2% for all techniques, however for the ±5 degree errors mean target varied by up to 7% for the Autoplan VMAT and 10% for the max dose to the spinal cord and brain stem, seen in all techniques. The simulated MLC shifts introduced the largest errors for the Autoplan VMAT, with the larger MLC modulation presumably being the cause. The most critical error observed, was the MLC field size error, where even small errors of 1 mm, caused significant changes to both the PTV and the OAR. The ssIMRT is the least sensitive and the Autoplan the most sensitive, with target errors of up to 20% over and under dosages observed. Conclusion: For a nasopharynx patient the plan robustness observed is highest for the ssIMRT plan and lowest for the Autoplan generated VMAT plan. This could be caused by the more complex MLC modulation seen for the VMAT plans. This project is supported by a grant from NSW Cancer Council.

60 APPLIED LIFE SCIENCES↗

Calibration of EBT2 film using a red-channel PDD method in combination with a modified three-channel technique

Purpose: Ashland Inc. EBT2 and EBT3 films are widely used in quality assurance for radiation therapy; however, there remains a relatively high degree of uncertainty [B. Hartmann, M. Martisikova, and O. Jakel, “Homogeneity of Gafchromic EBT2 film,” Med. Phys. 37, 1753–1756 (2010)]. Micke et al. (2011) recently improved the spatial homogeneity using all color channels of a flatbed scanner; however, van Hoof et al. (2012) pointed out that the corrected nonuniformity still requires further investigation for larger fields. To reduce the calibration errors and the uncertainty, the authors propose a new red-channel percentage-depth-dose method in combination with a modified three-channel technique. Methods: For the ease of comparison, the EBT2 film image used in the authors’ previous study (2012) was reanalyzed using different approaches. Photon beams of 6-MV were delivered to two different films at two different beam on times, resulting in the absorption doses of ranging from approximately 30 to 300 cGy at the vertical midline of the film, which was set to be coincident with the central axis of the beam. The film was tightly sandwiched in a 30{sup 3}-cm{sup 3} polystyrene phantom, and the pixel values for red, green, and blue channels were extracted from 234 points on the central axis of the beam and compared with the corresponding depth doses. The film was first calibrated using the multichannel method proposed by Micke et al. (2010), accounting for nonuniformities in the scanner. After eliminating the scanner and dose-independent nonuniformities, the film was recalibrated via the dose-dependent optical density of the red channel and fitted to a power function. This calibration was verified via comparisons of the dose profiles extracted from the films, where three were exposed to a 60° physical wedge field and three were exposed to composite fields, and all of which were measured in a water phantom. A correction for optical attenuation was implemented, and treatment plans of intensity modulated radiation therapy and volumetric modulated arc therapy were evaluated. Results: The method described here demonstrated improved accuracy with reduced uncertainty. The relative error compared with the measurements of a water phantom was less than 1%, and the overall calibration uncertainty was less than 2%. Verification tests revealed that the results were close to those of the authors’ previous study, and all differences were within 3%, except those with a high-dose gradient. The gamma pass rates (2%/2 mm) of the treatment plan evaluated using the method described here were greater than 99%, and no obvious stripe patterns were observed in the dose-difference maps. Conclusions: Spatial homogeneity was significantly improved via the calibration method described here. This technique is both convenient and time-efficient because it does not require cutting the film, and only two exposures are necessary.

60 APPLIED LIFE SCIENCES↗

SU-E-T-506: Intercomparison Study On Small Field Output Factor Measurements

Purpose In radiotherapy, uncertainties due to small field measurements (SFM) introduce systematic errors to the treatment process and the development of new dosimeters for quality assurance programs is a challenge. In this work we analyze the behavior of seven detectors measuring output factors of 6MV photon beam. Methods The dosimeters employed are: a single cristal diamond detector (SCCD) developed at the University of Rome Tor Vergata, a silicon diode developed within the project MAESTRO, a IBA Razor silicon diode, A1SL and A26 Exradin ion chambers, an EBT3 Gafchromic film and the Exradin W1 Scintillator.Diamond sensitive volume is a cylinder 2.2mm in diameter and 1μm thick. MAESTRO diode is 2×2mm2 active area. Razor sensitive volume is a cylinder 0.6 mm in diameter and 0.02 mm thick. A16 and A1Sl have a collecting volume of 0,015cc and 0,053cc. The W1 is an optical fiber with an active volume of 0.002cc. All measurements were performed in a water phantom, with detector positioned at the isocenter (SSD=90cm, d=10cm), MAESTRO diode being sandwiched in solid water to obtain an equivalent experimental setup. Results These measurements are challenging due to the absence of charged particle equilibrium conditions, detector size and positioning problems. They are in good agreement among each other, especially GAF, Razor, W1 and SCDD. Maximum deviations reported are related to the field 0.8×0.8cm2 for MAESTRO and chambers data with respect to EBT3: around 15% (A1SLvsEBT3), 16% (MAESTROvsEBT3). Razor and W1 show a deviation around 3% with respect to SCDD. Conclusion In this work measurements made with a variety of detectors are compared. These study show the possibility to choose different detectors for SFM and that smaller ion chambers are still not competitive with solid state detectors. Silicon, diamond and optical fiber dosimeters show a similar behavior with minor discrepancies for the smallest field.

60 APPLIED LIFE SCIENCES↗

Storm Surge Modeling in Puget Sound

In this study, a storm surge model of the Salish Sea was developed to simulate storm surge in Puget Sound using the unstructured-grid, finite-volume community ocean model (FVCOM). The model was based on Pacific Northwest National Laboratory’s existing Puget Sound hydrodynamic model that has been validated extensively in previous studies. To identify representative historical storm events, a systematic approach was developed based on the non-tidal residual (NTR) method. A total of 34 storm surge events between 1980 and 2016 were identified and simulated. To accurately simulate storm surge inside Puget Sound, the model was driven by reanalyzed Climate Forecast System Reanalysis meteorological forcing and observed water levels at the entrance of Strait of Juan de Fuca and southern entrance of Johnstone Strait. Model results for total water level, storm surge, and currents were compared with field measurements. A series of error statistics parameters were also calculated to quantify the model’s skills in simulating storm surge in the Salish Sea. Error statistics of model performance metrics demonstrated that the Salish Sea storm surge model was able to simulate storm surge inside Puget Sound with high accuracy. Storm surge propagation into Puget Sound is a nonlinear process that cannot be simply determined by a static approach for the entire domain. The maximum NTR distribution inside Puget Sound suggests that storm surge tends to be amplified in several sub-basins and inlets of the Puget Sound, such as Bellingham Bay, Hood Canal, south Puget Sound, and the multi-inlet basin behind Agate and Rich Passages. Therefore, future study is necessary to further quantify the storm surge level in these high-risk areas through field measurements and refined model simulations.

16 TIDAL AND WAVE POWER↗

SU-E-T-263: Development of Dose Monitor Unit Calculation Using Clarkson Integration for Proton Beam Therapy Using Beam-Wobbling System

Purpose: The purpose of the present study is to develop a calculation method of dose-calibration-factor using Clarkson integration for proton therapy employing the wobbling system and to evaluate accuracy of the calculation by comparison between calculations and measurements. Methods: CF and CALF stand for a dose-calibration-factor and a dose per monitor unit (MU), respectively. A measured dose-calibration-factor CFmeas is defined as a ratio of the measured dose per monitor unit in a patient-specific condition CALFpat to the measured dose per MU in a reference beam condition CALFref. The CFcalc is a product of three factors: CF1, CF2 and CF3. The CF1 and CF2 are a factor reflecting the effect of common beam delivery devices and that of patient specific devices and parameter (an aperture collimator, a range compensator and an air gap), respectively. The CF1 was obtained by interpolation using measured data. The CF2 was calculated using the Simplified Monte Carlo (SMC) method. The SMC method calculates a dose distribution by tracing individual protons and by using a measured Bragg curve in water. The CF3 representing the correction factor of field size effect was obtained by using the Clarkson integration. We compared the calculated and measured CF values for 20 prostate cases. Results: Field size correction was found to be important. The calculations reproduce the measurement results within an error of ±2.0%, except for a few cases. The error was about –3.1% for the small field area of less than19 square centimeters. Conclusion: We have developed a calculation method of dose-calibration-factor. Calculations agreed with measurements within ±2.0% for 90% of 20 prostate cases. Except for a small field size cases, the calculation method can be applied to determine the dose-calibration–factor for majority cases of prostate cancer.

60 APPLIED LIFE SCIENCES↗

Evolution of the Kondo lattice electronic structure above the transport coherence temperature

Significance The temperature ( T )-dependent evolution of the Kondo lattice electronic structure is a long-standing topic of theoretical and experimental investigation, still lacking a truly microscopic theory that agrees with a full experimental characterization. Here multiple characteristic T scales of the interaction of localized f moments with conduction electrons in the Kondo lattice CeCo I n 5 are identified and investigated using angle-resolved photoemission measurements that substantiate dynamical mean-field theory which newly includes the full realism of crystalline electric-field (CEF) f splittings. Thereby errors in the itinerant versus localized f -state classification from standard density functional theory are corrected, microscopic insight into the broad T -range crossover of f -hybridization effects is gained, and a prediction of CEF degeneracy crossover below the lattice coherence T is made.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Reducing Ground-based Astrometric Errors with Gaia and Gaussian Processes

Stochastic field distortions caused by atmospheric turbulence are a fundamental limitation to the astrometric accuracy of ground-based imaging. This distortion field is measurable at the locations of stars with accurate positions provided by the Gaia DR2 catalog; we develop the use of Gaussian process regression (GPR) to interpolate the distortion field to arbitrary locations in each exposure. We introduce an extension to standard GPR techniques that exploits the knowledge that the 2D distortion field is curl-free. Applied to several hundred 90 s exposures from the Dark Energy Survey as a test bed, we find that the GPR correction reduces the variance of the turbulent astrometric distortions ≈12× , on average, with better performance in denser regions of the Gaia catalog. The rms per-coordinate distortion in the riz bands is typically ≈7 mas before any correction and ≈2 mas after application of the GPR model. The GPR astrometric corrections are validated by the observation that their use reduces, from 10 to 5 mas rms, the residuals to an orbit fit to riz-band observations over 5 yr of the r = 18.5 trans-Neptunian object Eris. We also propose a GPR method, not yet implemented, for simultaneously estimating the turbulence fields and the 5D stellar solutions in a stack of overlapping exposures, which should yield further turbulence reductions in future deep surveys.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Automatic tuning of the Community Atmospheric Model (CAM5) by using short-term hindcasts with an improved downhill simplex optimization method

Traditional trial-and-error tuning of uncertain parameters in global atmospheric general circulation models (GCMs) is time consuming and subjective. This study explores the feasibility of automatic optimization of GCM parameters for fast physics by using short-term hindcasts. An automatic workflow is described and applied to the Community Atmospheric Model (CAM5) to optimize several parameters in its cloud and convective parameterizations. We show that the auto-optimization leads to 10 % reduction of the overall bias in CAM5, which is already a well-calibrated model, based on a predefined metric that includes precipitation, temperature, humidity, and longwave/shortwave cloud forcing. The computational cost of the entire optimization procedure is about equivalent to a single 12-year atmospheric model simulation. The tuning reduces the large underestimation in the CAM5 longwave cloud forcing by decreasing the threshold relative humidity and the sedimentation velocity of ice crystals in the cloud schemes; it reduces the overestimation of precipitation by increasing the adjustment time in the convection scheme. The physical processes behind the tuned model performance for each targeted field are discussed. Limitations of the automatic tuning are described, including the slight deterioration in some targeted fields that reflect the structural errors of the model. It is pointed out that automatic tuning can be a viable supplement to process-oriented model evaluations and improvement.

54 ENVIRONMENTAL SCIENCES↗

Automatic tuning of the Community Atmospheric Model CAM5.3 by using short-term hindcasts with an improved downhill simplex optimization method

Traditional trial-and-error tuning of uncertain parameters in global atmospheric General Circulation Models (GCM) is time consuming and subjective. This study explores the feasibility of automatic optimization of GCM parameters for fast physics by using short-term hindcasts. An automatic workflow is described and applied to the Community Atmospheric Model (CAM5) to optimize several parameters in its cloud and convective parameterizations. We show that the auto-optimization leads to 10 % reduction of the overall bias in CAM5, which is already a well calibrated model, based on a pre-defined metric that includes precipitation, temperature, humidity, and longwave/shortwave cloud forcing. The computational cost of the entire optimization procedure is about equivalent to about a single 12-year atmospheric model simulation. The tuning reduces the large underestimation in the CAM5 longwave cloud forcing by decreasing the threshold relative humidity and the sedimentation velocity of ice crystals in the cloud schemes; it reduces the overestimation of precipitation by increasing the adjustment time in the convection scheme. The physical processes behind the tuned model performance for each targeted field are discussed. Limitations of the automatic tuning are described, including the slight deterioration in some targeted fields that reflect the structural errors of the model. It is pointed out that automatic tuning can be a viable supplement to process-oriented model evaluations and improvement.

54 ENVIRONMENTAL SCIENCES↗

Improved Treatment of 1–4 Interactions in Force Fields for Molecular Dynamics Simulations

Traditional force fields commonly use a combination of bonded torsional terms and empirically scaled nonbonded interactions to capture 1-4 energies and forces of atoms separated by three bonds in a molecule. While this approach can yield accurate torsional energy barriers, it often leads to inaccurate forces and erroneous geometries and creates an interdependence between dihedral terms and nonbonded interactions, complicating parametrization and reducing transferability. Here, in this paper, we demonstrate that 1-4 interactions can be accurately modeled using only bonded coupling terms, eliminating the need for arbitrarily scaled nonbonded interactions altogether. Furthermore, by leveraging the automated parametrization capabilities of the Q-Force toolkit, we efficiently determine the necessary coupling terms without the need for manual adjustment. Our approach is first validated on a range of small molecule systems, encompassing both flexible and rigid structures, and shows a significant improvement in force field accuracy, obtaining subkcal/mol mean absolute error for every molecule tested. We further extend the bonded-only model for 1-4 interactions to Amber ff14sb, CHARMM36, and OPLS-AA force fields to reproduce ab initio gas and implicit solvent ϕ,ψ surfaces of alanine dipeptide.

Abdullah, Aalim S. [University of California, Berk↗

Optimization of Stabilization Modes of Optical Frequency Standards Based on the Saturated Absorption Resonance

A theoretical study is carried out within the framework of density matrix formalism of the error signal slope for frequency standards based on the resonance of saturated absorption excited in the field of two counterwaves. Two schemes of error-signal formation are considered: in the first case, the frequency of only the test field is modulated, and, in the second case, the frequency modulation of both waves is carried out. On the basis of the calculations, the optimal parameters of harmonic modulation are determined, at which the slope has the maximum value.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Algorithm to calculate off-plane magnetic field from an on-plane field map

An algorithm is presented to calculate the field components [B x (x,y,z), B y (x,y,z), B z (x,y,z)] of the magnetic field at a point (x,y,z) in space, from the knowledge of the components [B x (x,y = 0,z), B y (x,y = 0,z), B z (x,y = 0,z)] on a ”reference plane”, which is normal to the y-axis at y=0. The algorithm, which is a general one and is not restricted to fields with mid-plane symmetry is based on the Taylor series expansion of the magnetic field components at any point in space in terms of the distance (y) of the point from the reference plane. The coefficients of the Taylor series expansion are expressed in terms of the on-plane field components and their partial derivatives with respect to spatial coordinates (x,z). The field components are usually generated from magnetic field measurements on a rectangular grid on the plane. The required partial derivatives of the field components on the plane can be computed with two methods; numerically, or by fitting a polynomial function to the experimentally measured values of the field components and subsequently take the required partial derivatives of the polynomial function. Each of these two method which calculates the partial derivatives of the field components on the plane, is applied to calculate the off-plane field components of the magnetic field generated by a modified Halbach magnet [1] of inner radius of 4.4 cm and it is found that each method provides accurate results with a relative error <1% deviation from the ”ideal” fields if the y distance of the point from the reference plane is smaller than 2 cm. This algorithm is part of the RAYTRACE computer code [2] and has been applied [3] on a dipole magnet with median plane symmetry.

43 PARTICLE ACCELERATORS↗

Comparison of Full-Field and Integrated CFD Convergence Based on Richardson Extrapolation

This work investigated the usefulness of Richardson extrapolation--based discretization error estimates across all points in a solution field to produce a spatial convergence field for a computational fluid dynamics (CFD) simulation. The presented work used previously developed methods for Richardson extrapolation to compute the convergence orders of a CFD simulation at all points of the base (coarsest) mesh solution. Three test cases of increasing complexity were considered: Poiseuille flow, incompressible flow around a sharp corner, and transonic flow over an RAE 2822 airfoil. These test cases highlighted the potential of the proposed method to identify error sources and their relation to the model system-response-quantity convergence orders. However, these test cases also revealed the immaturity of the proposed method stemming from the unreliability of computing observed convergence orders at single points. Nonetheless, the test cases highlighted that the observed convergence orders allow for a more accurate diagnosis of constructive and destructive error transport than mesh pair error estimates. In the long run, the proposed method can be a tool for developing efficient and advanced error management strategies like adaptive mesh refinement.

Weinmeister, Justin↗