12 Gev Dipole Magnet Measurement Analysis Using Curved Beam Trajectories
June 28, 2007 JLAB-TN 07-050
12GeV Dipole Magnet Measurement Analysis using Curved Beam Trajectories
K. Baggett, L Harwood, T. Hiatt
Thomas Jefferson National Accelerator Facility, Newport News, Virginia 23606
An analysis routine has been developed to evaluate the field quality and integrated field strength for 12GeV dipole magnets. This analysis differs from previous analysis methods in that it calculates results based on the curved trajectories the beam will follow as it moves through the bending dipoles.
Analysis Theory
Data for the analysis is collected using the Magnet Measurement Facility (MMF) Stepper Stand DAQ. A Hall probe is used to collect field () measurements at multiple Z and X locations in a grid format along the vertical center plain. Once the data collection is completed, the data points are imported into Excel and arranged into a grid format. The data grids can then be copied to text files and read by an analysis program.
Of interest in the 12GeV dipole magnet measurements are field integral and field quality. First, the field integral, BL, is computed along the curved beam trajectory to define the field strength. Second, the field quality is evaluated by comparing the ratio to the specification where =.
It was noted that the z-derivative of the field () increases at the ends of the dipole and should be accounted for in the field quality calculations. A radial derivative method was developed and used to pick up the z-derivative contribution. In this method a grid of z-derivatives and a grid of x-derivatives are created from the base data grid using:
A defined number of points are then computed along the beam trajectory. For each point on the trajectory, a z-derivative point and an x-derivative point is established by a linear interpolation of the points in the z and x derivative grids. These interpolated points, and, are then rotated into the coordinate frame using
where is the angle between the x and axes as shown in Figure 1. The radial derivatives, , are then integrated along the beam path to establish.
Figure 1. Rotation to establish the radial derivative
To evaluate field strength, coordinate points are again calculated along the beam trajectory. A field values for each point is then calculated from the original data grid using linear interpolation. These values are then integrated along the beam path length to establish the field integral,.
Analysis Software
Because this type of analysis is complicated in Excel, a program was created to compute the field quality and field integral strength calculations. “GridFit” was developed to read the data grid, compute trajectories based on DIMAD information, interpolate points to “fit” field values to coordinates along the beam trajectory, and to compute the values needed to evaluate magnetic field quality.
Original field quality calculations were done by evaluating the transverse derivative,, at different radial locations. GridFit differs in that it computes radial derivatives of each coordinate point on the trajectory by rotating the z and x derivatives, into the R, coordinate frame, as described earlier. The integral of these values then becomes the value for a specific X and R location. is then computed over a range of radial locations at one trajectory and compared to the specification as shown in Figure 2. The GridFit software, shown in Figure 3, calculates at definable intervals in both R (radial) and X (transverse).
Figure 2. Field quality graph example.
Figure 3. GridFit software.
Summary
An analysis routine has been developed and implemented to assess field quality and field integral strength for 12GeV dipole magnet measurements. Values for at multiple R and X locations will be computed using the GridFit software program. Excel is used to graph the field quality curves and compare data to the specification.
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