The HMS quadrupoles
in the HMS-100 tune

Abstract: The tuning of the HMS quadrupoles in the HMS-100 (small angle) tune has been revisited after it became clear that the optical properties of the tune are very sensitive to even small aberrations of the quadrupole fields from their setpoints. The three parts of this document are a compilation of the study of the optics sensitivity to these aberrations, a revision of saturation effects in the quadrupoles and an outline of the new field setting and cycling procedure.

Part 1: Quadrupole missetting and optics changes
Part 2: Saturation effects in the Quadrupoles
Part 3: Revised field setting and cycling procedure
Part 4: The HMS-100 Golden Tune
Conclusion

Part 1: Quadrupole missetting and optics changes

A TRANSPORT simulation was done to determine the effect of missettings of the quadrupole fields on the optical properties of the tune, that is the z-positions of the delta- and the Y-focus at X_fp=0 cm.

In he first step, the ideal settings for HMS-100 (and parallel for HMS-1) were calculated out of Chen Yan's initial TRANSPORT deck, letting all three quadrupole fields vary, with the constraints on <x|x'>=0, <y|y'>=0 and another variable being fixed at X_fp=0 cm.

Then the focal plane was shifted to Z_fp=+10 cm and the outcome of the first TRANSPORT run inserted into the input deck.

• To study the motion of the delta-focus, only the constraint <x|x'>=0 at X_fp=0 cm and Z_fp=+10 cm was kept, and subsequently the fields of Q1, Q2 and Q3 were let vary.
• To study the motion of the Y-focus, only the constraint <y|y'>=0 at X_fp=0 cm and Z_fp=+10 cm was kept, and subsequently the fields of Q1, Q2 and Q3 were let vary.

The backdraw of this kind of study is that there is no control over the other properties of the new tune, because they are no longer constrained. However, by making only a small change, those changes stay small, too. It still is advisable to include small changes in the quadrupole currents to observe the effects of the changes on the motion of the foci.

The result is shown in the following table:

Older data from D. Mack suggest that the Y focus motion in X_fp is about 7cm/% for Q2.

Part 2: Saturation effects in the Quadrupoles

The B.dl(I) of the quadrupoles is determined as the product of the effective length L_eff of the magnet and the L_eff independent magnetic field B_o on the face of a pole tip in or near the center of the quadrupole. Two sorts of effects cause the B_o and the L_eff to be nonlinear:

• Saturation effects influence both B_o and L_eff,
• B_o(I) is offset by a residual field characteristic to each quadrupole.

My study concentrates on currents up to 500 Amps.

1. Effective Length L_eff
   For L_eff I took the data S. Lassiter and S. Wood took in 1995:
   Picture 1: L_eff
   The data shown in the graphs are taken as a medium out of several data points for each current that have been taken at several cycles. The dips at low current are an artefact of the way Lassiter and Wood derived L_eff. The range that interests us here is up to 500 Amps. Because of poor quality of the data I approximated L_eff only linearly. For Q1 and Q3 I set it to a constant, since saturation effects did not (unambiguously) start below 500 Amps.
   
   The error made in this approximation is of the order 2-4^.10^{-4
   .}
2. Magnetic Field B_o
   The study of B_o has been done by means of attaching a Hall probe (type Group3 LPT-141 with digital Hall effect Teslameter type DTM-141DG) on one of the pole tips in each quadrupole, at a position near the center of of the magnet.
   Picture 2: Residual fields shows the residual fields of Q1, Q2 and Q3 vs the central HMS momentum the current translates to in the HMS-100 tune. The residual fields are simply
   B_o(I) - current*constant.
   Notice the change in the field at polarity reversal, especially with Q2.
   The relative contribution of the residual field, and thus the error made by setting the quadrupoles with an assumed constant gain is shown in
   Picture 3: Relative residual fields
   For the fitting of the B_o response, only the returning curve after cycling were taken:
   Picture 4: Rel. res. fields and effect on Y focus motion
   The lower right plot in picture 4 shows the effect of a Q2 offset on Y focus motion in X_fp, where a 7cm/% dependence has been assumed. This agrees with earlier observations by Rolf Ent (see also picture 4a).
   
   Picture 5: B_o/I with offsets shows the magnetic response B_o/I offset by indivdual residual fields of the three quadrupoles (that is (B_o-offset)/I). The x-axis is the central HMS momentum the current translates into for HMS-100. The red lines indicate the linear fit at low currents, the blue lines show the adaptation to saturation effects and come into play only above the interception of the blue and the red curve. The nonlinearities at low momenta/currents are entirely due to the inaccuracy of the Hall probe meter in the least significant bit. The error made by these fits is always smaller than 4^.10^-4, for momenta above 0.8 GeV/c even smaller than 1^.10^-4.

Part 3: Revised field setting and cycling procedure

• Magnet Cycling and Setting Procedure
  To obtain a high reproducibility, I devised the following cycling procedure for the HMS quadrupoles:

1. following every polarity reversal, drive the quadrupole current from 0 Amps to 500 Amps, then back to 0 Amps. Go to 500 Amps and to the first setpoint from there.
2. Stepping down from one setpoint to the next is ok.
3. For stepping up to the next setpoint, go to the next setpoint+100 Amps and go down to the setpoint from there. This will ensure a reproducibility of the field of 1^.10^-4.
   
• Calculating the Current for a given Field
  The new field setting code takes advantage of both the earlier experience manifest in Rolf Ent's field settings program, and the saturation and residual field effects discussed above. Note that the
  two programs serve different needs. While Rolf Ent's program serves the entire range of the quadrupoles up to 1250 Amps, the new one is only designed to hold up to 500 Amps. However, the old code does not take the residual field into account at all.
  
  The field setting program works as follows:
• calculate the Q_i specific B.dl for a given HMS central momentum
• calculate the current as f_i(B.dl)^.B.dl (where i=1,2,3).
• Normalizing the new fits
  The measurements of the B_o(I) have taken place at, albeit carefully chosen, rather arbitrary places inside the quadrupoles. Therefore there is a need to normalize the setcurrent calculations to match the older ones in the flat region arount 300 Amps, in which region the old parametrization has been known to be sufficient.

Picture 6: I/B.dl shows a comparison between the old (Rolf's fit, red) and the new (Q_i, black) code, with the normalization worked in.

A factor of 0.985 in Rolf Ent's script has been taken into account in the I/B.dl.

back

Part 4: The HMS-100 Golden Tune

The ratios of the quadrupole fields (B.dl)_Q1/(B.dl)_Q2/(B.dl)_Q3 determine the optical properties of the tune. Model cases have been calculated with the TRANSPORT code and taken as start values for the fine tuning, the Search for the Golden Tune of HMS-1, during the first commissioning of HMS in 1994/95.
Since the calculation of start values have been done with basically the same TRANSPORT input deck, modified only by the changed drift distances between target and Q1 entrance and Q3 exit and Dipole entrance, it can be viewed as an educated guess to fudge them with the same factors as in the HMS-1 tune for a start.
The new factors are calculated as

new (B.dl)_Qi(real)=old (B.dl)_Qi(real) * new (B.dl)_Qi(TRANSPORT) / old (B.dl)_Qi(TRANSPORT)

Conclusion

The goal of the investigation of the HMS quadrupole field nonlinearities was to arrive at a new field setting procedure and program that would ensure enhanced reproducability and accuracy. The new field setting and cycling procedure has been explained in Part 3, the study of the B_o/I response function and the change in effective length L_eff are condensed into the new field setting program field100.f.

• The estimated reproducibility with the new cycling and setting procedure is about 1^.10^-4. Without regard of the direction of the approach of a new setpoint, the reproducibility was not better than 5^.10^-3 for currents arount 100 Amps, and were in the % range for very small currents.
• The estimated accuracy of the magnet setting is 1-5^.10^-4 as compared to earlier 10^-4 -5^.10^-3. The gain in accuracy and reproducibility is considerable.

This site is maintained by Jochen Volmer
it was last updated October 20th, 1997