Engineering topics
Welch, J
Publications and source records attributed to Welch, J.
On the Kinematics of Undulator Girder Motion
The theory of rigid body kinematics is used to derive equations that govern the control and measurement of the position and orientation of undulator girders. The equations form the basis of the girder matlab software on the LCLS control system. The equations are linear for small motion and easily inverted as desired. For reference, some relevant girder geometrical data is also given. Equations 6-8 relate the linear potentiometer readings to the motion of the girder. Equations 9-11 relate the cam shaft angles to the motion of the girder. Both sets are easily inverted to either obtain the girder motion from the angles or readings, or, to find the angles and readings that would give a desired motion. The motion of any point on the girder can be calculated by applying either sets of equations to the two cam-planes and extrapolating in the z coordinate using equation 19. The formulation of the equations is quite general and easily coded via matrix and vector methods. They form the basis of the girder matlab software on the LCLS control system.
Absolute beam flux measurement at NDCX-I using gold-melting calorimetry technique
We report on an alternative way to measure the absolute beam flux at the NDCX-I, LBNL linear accelerator. Up to date, the beam flux is determined from the analysis of the beam-induced optical emission from a ceramic scintilator (Al-Si). The new approach is based on calorimetric technique, where energy flux is deduced from the melting dynamics of a gold foil. We estimate an average 260 kW/cm2 beam flux over 5 {micro}s, which is consistent with values provided by the other methods. Described technique can be applied to various ion species and energies.
Estimate of Undulator Magnet Damage Due to Beam Finder Wire Measurements
Beam Finder Wire (BFW) devices will be installed at each break in the Undulator magnet line. These devices will scan small wires across the beam causing some electrons to lose energy through bremsstrahlung. The degraded electrons are subsequently detected downstream of a set of vertical dipole magnets after they pass through the vacuum chamber. This signal can then be used to accurately determine the beam position with respect to the BFW wire. The choice of the wire diameter, scan speed, and operating parameters, depends on the trade-off between the signal size and the radiation damage to the undulator magnets. In this note I estimate the rate of undulator magnet damage that results from scanning as a function of, wire size, scan speed, and average beam current. A separate analysis of the signal size was carried out by Wu. The damage estimate is primarily based on two sources: the first, Fasso, is used to estimate the amount of radiation generated and then absorbed by the magnets; the second, Alderman et. al., is used to estimate the amount of damage the magnet undergoes as a result of the absorbed radiation. Fasso performed a detailed calculation of the radiation, including neutron fluence, that results from a the electron beam passing through a 100 micron diamond foil inserted just in front of the undulator line. Fasso discussed the signficance of various types of radiation and stated that photoneutrons probably play a major role. The estimate in this paper assumes the neutron fluence is the only significant cause of radiation-induced demagnetization. The specific results I use from Fasso's paper are reproduced here in Figure 1, which shows the radial distribution of the integrated neutron fluence per day in the undulator magnets, and Figure 2, which shows the absorbed radiation dose all along the undulator line. In the longitudinal dimension, Fasso's calculation, (see Figure 2), shows that the radiation dose is widely distributed all along the undulator line, but is highest around 70 m from the front of the undulator line where the foil is. At the 70 m point, for the purpose of calculating the demagnetization, I chose a conservative estimate for the effective neutron flux of 1.0 x 10{sup 13} n/cm{sup 2}/day. As can be seen in Figure 1, this choice is representative of the flux nearest the beam where it is the highest. A less conservative estimate, but perhaps more accurate, estimate of the effective flux, would be the average flux in the magnet block, which is roughly one half as much.
QM02 Strength Measurement
In late April, Paul Emma reported that his orbit fitting program could find a reasonably good fit only if the strength of QM02 was changed from design value of -5.83 kG to -6.25 kG - a strength change of 7.3%. In late May, we made a focal length measurement of QM02 by turning off all focusing optics between YC07 and BPMS1 (in the spectrometer line) except for QM02 and adjusted the strength of QM02 so that vertical kicks by YC07 did not produce any displacements at BPMS1 (see Figure 1). The result was quoted in the LCLS elog was that QM02 appeared to 6% too weak, and approximately agreed with Paul's observation. The analysis used for the entry in the log book was based on the thin lens approximation and used the following numbers: Distance YC07 to QM02 - 5.128 m; Distance QM02 to BPMS1 - 1.778 m; and Energy - 135 MeV. These distances were computed from the X,Z coordinates given the on the large plot of the Injector on the wall of the control room. On review of the MAD output file coordinates, it seems that the distance used for QM02 to BPMS1 is not 1.778 m. The correct value is Distance, center of QM02 to BPMS1 - 1.845 m. There may be a typo on the wall chart values for the coordinates of BPMS1, or perhaps there was a misinterpretation of edge versus center of QM02. In any case, the effect of this change is that the thin lens estimate changes from 6% too weak to 9% too weak. At John Galayda's suggestion, we looked into the thin lens versus thick lens approximation. A Mathematica program was written to solve for the K value of the QM02, in the thick lens approximation, that provides point to point focusing from YC07 to BPMS1, and to compare this number with the value obtained using the thin lens approximation. The length of QM02 used in the thick lens calculation is the effective length determined by magnetic measurements of 0.108 m. The result of the Mathematica calculation is that the thin lens approximation predicts less magnet strength is required to produce the same focusing by about 1.3%. When both the distance correction and the thick lens approximation are taken into account, the result is: K{sub thick} - K{sub mm}/K{sub thick} = -7.6% where K{sub mm} is the value obtained from magnetic measurements and K{sub thick} is the value of K obtained from the focal length measurement in the thick lens approximation. That is, QM02 acts weaker than it was measured by magnetic measurements by 7.6%. This is remarkably close to Paul's original estimate. The unexpected weakness could in principle be due to several things: shorted turns, a current calibration error, magnetic measurement error; it could even be due to the presence of an gradient from QM01, which is of opposite sign and right next to QM02, despite it being set to zero current (although it was not DAC-zeroed). Plans have been implemented to remove and replace QM02 at the earliest ROD.
BXS Re-calibration
Early in the commissioning it was noticed by Cecile Limborg that the calibration of the BXS spectrometer magnet seemed to be different from the strength of the BX01/BX02 magnets. First the BX01/BX02 currents were adjusted to 135 MeV and the beam energy was adjusted to make the horizontal orbit flat. Then BX01/BX02 magnets were switched off and BXS was adjusted to make the horizontal orbit in the spectrometer line flat, without changing the energy of the beam. The result was that about 140-141 MeV were required on the BXS magnet. This measurement was repeated several times by others with the same results. It was not clear what was causing the error: magnet strength or layout. A position error of about 19 mm of the BXS magnet could explain the difference. Because there was a significant misalignment of the vacuum chamber in the BXS line, the alignment of the whole spectrometer line was checked. The vacuum chamber was corrected, but the magnets were found to be in the proper alignment. So we were left with one (or conceivably two) magnet calibration errors. Because BXS is a wedged shaped magnet, the bend angle depends on the horizontal position of the incoming beam. As mentioned, an offset of the beam position of 19 mm would increase or decrease the bend angle roughly by the ratio of 135/141. The figure of 19 mm is special and caused a considerable confusion during the design and measurement of the BXS magnet. This is best illustrated in Figure 1 which was taken out of the BXS Traveler document. The distance between the horizontal midplanes of the poles and the apex of the beam path was chosen to be 19 mm so the beam is close to the good field region throughout its entire path. Thus it seemed possible that there was an error that resulted in the beam not being on this trajectory, or conversely, that the magnetic measurements were done on the wrong trajectory and the magnet was then mis-calibrated. Mechanical measurements of the vacuum chamber made in the tunnel indicated that the vacuum chamber was in fact in the proper position with respect to the magnet - not 19 mm off to one side - so the former possibility was discounted. Review of the Fiducial Report and an interview with Keith Caban convinced me that there was no error in the coordinate system used for magnet measurements. I went and interviewed Andrew Fischer who did the magnetic measurements of BXS. He had extensive records, including photographs of the setups and could quickly answer quite detailed questions about how the measurement was done. Before the interview, I had a suspicion there might have been a sign flip in the x coordinate which because of the wedge would result in the wrong path length and a miscalibration. Andrew was able to pin-point how this could have happened and later confirmed it by looking an measurement data from the BXG magnet done just after BXS and comparing photographs. It turned out that the sign of the horizontal stage travel that drives the measurement wire was opposite that of the x coordinate in the Traveler, and the sign difference wasn't applied to the data. The origin x = 0 was set up correctly, but the wire moved in the opposite direction to what was expected, just as if the arc had been flipped over about the origin. To quantitatively confirm that this was the cause of the observed difference in calibration I used the 'grid data', which was taken with a Hall probe on the BXS magnet originally to measure the FINT (focusing effect) term, and combined it with the Hall probe data taken on the flipped trajectory, and performed the field integral on a path that should give the same result as the design path. This is best illustrated in Figure 2. The integration path is coincident with the desired path from the pivot points (x = 0) outward. Between the pivot points the integration path is a mirror image of the design path, but because the magnet is fairly uniform, for this portion it gives the same result. Most of the calibration error resulted simply from the different path length between the design path and the measured path. The results of the integration on the equivalent path are given in Table 1. The corrected calibration has been used to generate a new polynomial for BXS which was implemented in the control system.