An in-vacuum measurement system for CPMUs at Diamond Light Source

An in-vacuum Hall probe measurement system was designed, built, and used to measure four Cryogenic Permanent Magnet Undulators (CPMUs) at Diamond Light Source. The devices were tuned to correct the phase error at cold temperatures based on the measurements from the in-vacuum system. The in-vacuum system consists of a stretched wire system supplied by Danfysik and an in-house built Hall probe system. The Hall probe system has gone through two iterations: the first beam was prone to deforming with temperature changes; the second was made thicker following design changes to the magnet holders and girders of the CPMUs which allowed more space for the beam inside the vacuum vessel. The design and commissioning of the measurement system will be presented, along with some measurements of the CPMUs at room temperature and at 77 K. Details such as triggering of the Hall probe measurements, height compensation, and temperature compensation will be covered.


Introduction
Diamond has been undergoing an upgrade of the crystallography beamlines over the last few years.As a large part of this, the Pure Permanent Magnet (PPM) undulator sources have been replaced by in-house designed and built 17.6 mm period Cryogenic Permanent Magnet Undulators (CPMUs), providing 2 to 4 times more flux and a 2 to 3 increase in brilliance.A large challenge in delivering the CPMUs, as seen at other synchrotrons [1,2,3,4], is the ability to measure and shim them while cold.An in-vacuum measurement system comprised of a Hall probe carriage moving on rails mounted to an aluminium beam and a stretched wire was developed in ordered to measure the CPMUs while cold.This measurement system has since been used to measure and aid shimming of CPMUs 1-4 [5].

The Hall probe system
The Hall probe is mounted on a carriage that runs along two guide rails fixed upon an aluminium beam and driven by a pulley system coupled to a stepper motor.Hall step scans must be used rather than on-the-fly measurements due to positioning errors arising from the pulley system (slippage and stretch in the cable).The longitudinal position of the probe is measured using a Renishaw laser interferometer with 316 nm resolution [6].The probe is driven to a set motor position at which point Keithley 2700 multimeters for Hall voltage and PT100 measurements are triggered.The position from the interferometer is recorded via a Geo Brick motor controller and used in the processing of the Hall voltage data into field.

The Hall probe beam
The first version of the Hall probe supporting beam distorted on first use at cold temperatures when the first CPMU was cooled down.Measurements taken once the CPMU and Hall probe beam were warmed to room temperature showed clear differences to the measurements taken before cooling.The changes in the phase error plot of CPMU-1 coincided with the positions of the beam support mounts.There were no changes to the measurements before and during vacuum pumping, therefore the differences in the measurement system were due to the temperature change.At the same time there were issues with the CPMU magnet holders, leading to a holder re-design.More space inside the vessel was made available to the in-vacuum Hall probe beam upon the re-design.Therefore, version two was able to be made twice as thick as the first version.The design was also changed from the three supports on one side of the beam shown in Fig. 1 to supports at the top and bottom of the beam at each end, as shown in Fig. 2.This method of supporting the beam is designed to keep the forces on the beam balanced as it travels up and down, and to reduce the bending moments placed on the beam.The revised mount fully compensates for vacuum loads through bellows.A further change was to have the cable for the pulley running on both sides of the beam rather than one to allow an increase in spring tension applied to the pulley cable.

Hall probes
Arepoc Hall sensors with a sensitivity of 1 V/T and two PT100s were mounted on a ceramic holder to make the original Hall probe, shown in Fig. 3.This probe was used to measure CPMUs 1 to 3, down to an ID gap of 5 mm.A smaller gap could not be measured due to a vertical offset of the Bz sensor in the holder.Arepoc sensors are no longer available and so a swap to a SENIS S-type probe (5 V/T) [7] mounted inside a 3 mm thick epoxy glass holder was made for measuring CPMU-4, with the hope of measuring a smaller ID gap.However, due to a curvature across the width of the CuNi foil when cold caused by the differing thermal expansion rates of the bimetal components it was not possible.The SENIS probe is now mounted on a 1 mm thick epoxy glass holder so that the next CPMUs may be measured at a 4 mm gap.A disadvantage to using such a thin holder is the introduction of a pitch error on the probe due to a slight curvature of the holder material.However, from characterisation measurements of the SENIS probes, a maximum of 0.1 mT error is expected.

Beam sag adjustment
The Hall probe beam in the second version of the measurement system is motorised in the vertical direction, in order to compensate for the sag of the beam as the Hall probe travels along the length of the device.The sag is measured once the beam is installed in the vacuum chamber using a Leica absolute laser tracker (AT960-M), as shown in Fig. 4. The motion is transferred through eccentric drives at each end.Due to the eccentric drives, the motion is limited to 1 mm total range, over which one can consider 0.5 mm to be linear in order to use the Geo Brick motion controller, already in use for the other axes.Each end of the beam is mechanically levelled and the motors are used only to compensate for the sag.A compensation table in the Geo Brick is used to apply the vertical correction based on the longitudinal position of the Hall probe.

Temperature compensation
While the Arepoc sensors were calibrated by the supplier to 4.2 K, the SENIS probe is only calibrated at 23 • C. The temperature of the SENIS probe when outside the 77 K CPMU girders is ∼288 K (15 • C), and while travelling through the CPMU at a 5 mm gap, can reach around 253 K (-20 • C) in the time taken to do a Hall scan.Therefore, the probe needed to be calibrated to -20 • C. The sensitivity of the SENIS probe was measured down to -25 • C using a Peltier cooler mounted to an aluminium block.The block was mounted to a 1.44 T magnet, keeping a  suitable distance such that the magnet did not experience any temperature change.However, this distance meant that the maximum field that could be measured was 0.19 T. This field was measured using the known sensitivity of the SENIS probe at 23 • .The sensitivity of the probe versus temperature to be used in the calibration was averaged from a set of eight measurements, shown in Fig. 5.

Reproducibility
The reproducibility is key to any measurement system used to measure and inform shimming of undulators.Magnetic field measurements were performed four times with the same conditions on the same CPMU at 77 K to investigate the reproducibility.A good agreement in the phase error plots of CPMU-4 can be seen in Fig. 6 where the maximum RMS phase error variation is 0.3 • ; the same as observed on the out-of-vacuum measurement system.The reproducibility is checked for each CPMU and has been found to be the same each time the in-vacuum measurement system is used.The in-vacuum measurement system was compared to the out-of-vacuum measurement system by setting it up in air and measuring CPMU-1 before the magnet girders were dismounted for vacuum assembly.A good agreement can be seen in the phase error plot (Fig. 7), with a RMS phase error difference of 0.4 • ; only slightly larger than the inherent reproducibility of each system.

The stretched wire
The stretched wire part of the in-vacuum measurement system has been adapted from a system supplied by Danfysik.The wire is a 0.1 mm diameter titanium alloy, chosen for minimal sag.It is vertically positioned between the ID girders using capacitance measurements, shown in Fig. 8.The transverse and vertical motion of the wire is translated through bellows to the wire at 20 mm/s and 1 mm/s respectively.A Hilbert transform of Iz to Ix is necessary due to the slow speed of the vertical motor causing a low Signal-to-Noise Ratio (SNR).The voltage measurement taken on a Keithley 2182A nanovolt meter is triggered on position by the Geo Brick.As standard practise an average of two measurements is made: one taken in the forwards direction of the wire and one taken in the reverse direction to reduce the effect of integrator drift on the measurement [8].This is followed by averaging ten sets of data, rejecting any greater than the running average by 0.5 Gm.A large tolerance was allowed due to vibrations on the wire that could not be reduced further.

Hall vertical drives upgrade
The Hall probe beam vertical drives are currently being upgraded to linear leadscrews.These have several advantages over the eccentric cams: the main advantage being the ease of setting up the beam and aligning it to the magnetic centre of the CPMUs.With the eccentric drives' limited motion the CPMU girders must be mechanically aligned around the Hall probe, which is a time-consuming task of changing the limit switches, software limits and hard-stops that form the safety system of the CPMU structure.

Conclusions
The in-vacuum measurement system has successfully been used to measure and aid in shimming at cold temperatures of four CPMUs at Diamond.Future work includes completing the Hall vertical drives upgrade and improving the calibration of the SENIS Hall probe at cold temperatures before the measurements of the next CPMUs.

Figure 1 .
Figure 1.Model of version 1 of the in-vacuum measurement system.There are three Hall probe beam supports on the outboard side.

Figure 2 .
Figure 2. Version 2 of the in-vacuum measurement system.The Hall probe beam supports are at each end and above and below the beam.The Hall probe is mounted on a carriage that runs along the beam via a pulley system.

Figure 3 .
Figure 3. Left: Arepoc sensors mounted on ceramic.Middle and right: SENIS probe mounted in a 3 mm thick and 1 mm thick epoxy glass holder respectively.

Figure 4 .
Figure 4.The sag of the Hall probe beam measured using a laser tracker.

Figure 5 .
Figure 5.The sensitivity of the SENIS Hall probe with respect to temperature.

Figure 6 .
Figure 6.Phase error reproducibility from the in-vacuum measurement system.A good agreement between measurements can be seen.

Figure 7 .
Figure 7. Phase error comparison between the out-of-vacuum and in-vacuum measurement systems.

Figure 8 .
Figure 8. Capacitance measurements at different vertical wire positions.The fit to the data is a cosh function.