Improving the Understanding of CERN ISOLDE Optics

Rick Baartman

October, 2001

This note is released jointly as TRIUMF internal note TRI-DN-02-8 and CERN PS/OP/Note 2002_085.

1  Abstract

For some time, it has been difficult to reconcile ISOLDE operational tunes with GIOS calculations. The author visited CERN during October, 2001 to try to discover why and to hopefully resolve the situation. Experiments were performed to characterize the quadrupoles and the initial beam. The main result is that the measured effective length is (27.000.15) cm: 10% less than the length used in calculations until now.

2  Differences from ISAC design

As with ISAC, the ISOLDE low energy optics is electrostatic, except for the magnetic dipoles needed for mass separation. There are two separators: GPS = general purpose separator, and HRS = high resolution separator. All quadrupoles are identical and very large compared with ISAC's: electrodes are 30 cm long, aperture diameter = 14 cm (cf. ISAC's 5 cm long by 5 cm dia.). Quad doublets are typically 3 to 5 m apart (cf. 2 m at ISAC). This implies the optics scale is roughly 4 times ISAC's, and beam sizes for a given emittance are roughly 2 times larger. In principle, one length scale works as well as any other, but the complication at ISOLDE is that the electrostatic bender apertures are much smaller than the quadrupoles' (3 cm aperture by 10 cm height; in ISAC, 3.8 cm by 15 cm height). Additionally, ground planes are inserted into the gap at the top and bottom. My guess is that the good field region is only about 3 cm vertically, but this should be verified. This design forces tight foci (H&V) and good beam alignment at each bender. In consequence, though the acceptance is still sufficient, tuning is dominated by the requirement of getting good transmission through the benders.

It is TRIUMF experience that roll angle errors in electrostatic benders are the major source of beam misalignment. (My guess at the reason is that though magnetic dipoles can be accurately aligned for roll by placing an accurate level on the pole, electrostatic dipoles, having curved surfaces, cannot.) In anticipation, non-bend-plane correctors were placed near all ISAC benders. ISOLDE may benefit from more such strategically-placed correctors as well.

3  Measurements

In a first series of measurements, the HRS frontend triplet was used to characterize the beam at the profile grid immediately downstream. 12 x and y profiles were taken for 60 keV beam energy, and 12×2 more for 30 keV. The profiles were used to calculate the 2s beam sizes, and these were fitted by TRANSOPTR to find the source parameters (radius, divergence, waist location) plus the effective length of the quadrupole. Still, a fairly wide range of these 4 parameters gave acceptable fits, so a different series of measurements was undertaken.

In this second series, the first quadrupole of the triplet was used as a steerer while either the second or the third quadrupole was used to focus the beam from the steerer to the profile grid: such condition being detected by the fact that the steerer could no longer move the profile at the grid. The advantage of this technique is that it is only necessary to know the distances between steerer and quad and between quad and grid; the steerer effective length needs not be known, and the source parameters need not be known. The quadrupole voltages were corrected by measuring them directly with a DVM. The corrections were less than 1%. TRANSOPTR was used to fit the effective length of the quadrupole. The results are as follows. Using the third quad, we find Leff=27.000.16 cm, and using Q2, Leff=27.240.22 cm. Since fits using series 1 measurements gave Leff=25.52.0 cm, the 3 results were combined to give the following value, which is used in all subsequent calculations:

Leff=27.0 cm.
This is substantially different from the length 30.0 cm which has been used in calculations until now.

Series 1 data were re-analyzed. Best fits give the following parameters.

Table 1: Source parameters fitted from profile measurements. `Location' is distance of waist from the edge of the first quadrupole. Emittance is product of `Size' and `Divergence'. `RMS error' is rms of difference between measured and calculated profile sizes.
EnergyWaist SizeDivergenceLocationRMS errorEmittance
60 keV11 mm4.70.2 mrad475 cm0.6 mm5pmm-mrad
30 keV1.50.8 mm3.80.4 mrad559 cm0.4 mm6pmm-mrad

Large uncertainties in the waist size, and therefore also in emittance, are due to the fact that smallest beam sizes are too small compared with the wire spacing of 2.5 mm. Typical measured beam sizes were 5 mm, so the rms measurement errors indicate good fits. In order to use this technique to measure emittance accurately, it should be repeated with smallest beam sizes measured by sweeping the beam across the wires with the steerer, thus effectively creating a wire scanner with resolution equal to wire thickness instead of spacing.

At the present stage, it is uncertain whether the above results can be used in general, since the location of the extractor with respect to the ion source is essentially a free parameter. One could think of first adjusting the extractor for maximum yield, then performing a standard experiment such as the above to determine the resulting source parameters, and using these in a transport code to fit optimum values for the quads in the frontend. Such a procedure could even be automated.

4  GPS Tunes

An example of a GIOS calculation using an operational tune in the GPS (see table 2 for values, click here for GIOS input file) and old effective lengths is shown in the figure 1. This is to be compared with the same calculation using the measured effective length of 27 cm, figure 2 (GIOS input file). The beam envelopes predicted by the calculation with the new effective length are clearly more realistic.

Figure 1: Typical operational GPS tune, calculated with quadrupole effective length 30.0 cm, emittance = 26 pmm-mrad.

Figure 2: Typical operational GPS tune, calculated with quadrupole effective length 27.0 cm, emittance = 26 pmm-mrad.

Figure 3: Suggested GPS tune, with reduced horizontal beam size in doublet before dipole, emittance = 26 pmm-mrad. This is for comparison with the previous figures. Real emittances are probably much smaller.

One of the features of this tune is large horizontal beam size in quadrupoles GPS.QP170 and 180. This makes these quads extremely sensitive. A new tune with reduced beam sizes is shown in figure 3 (GIOS input file). This gives a lower resolution than the operational tune of 200 for an emittance of 20 pmm-mrad. If the emittance is closer to that found above, resolution is 400.

Table 2: GPS tunes in volts.
QuadOp. tuneNew tune

The new tune has two other features worthy of note. The operational tune appears to have an unnecessary crossover between QP530 and 540. The new tune gets rid of it and is thereby able to use much lower voltages for QP520 through 550.

The new tune sets QS030=QP050, QP520=QP550, QP530=QP540. This should be possible for any desired tune. One should evaluate whether at least 520&550 and 530&540 can simply be jumpered together. (30&50 is a more complicated case, since 30 is steerable, but there may be a way.) This would not only save power supplies, but more importantly would making tuning easier, reducing the number of `knobs' in this section from 9 to 6.

5  HRS Tunes

Typical operational tune is shown in figure 4 (GIOS input file) with old effective length, and in figure 5 (GIOS input file) with newly measured effective length. Values used are shown in table 2. The calculation with the new effective length looks more realistic than that with the old, though the difference is not as dramatic as it is for the GPS. This can be thought of as due to the fact that the HRS optics is relatively more dependent on the (correctly-described) magnetic dipoles than the quadrupoles.

Figure 4: Typical operational HRS tune, calculated with quadrupole effective length 30.0 cm, emittance = 26 pmm-mrad. Multipoles are off.

Figure 5: Typical operational HRS tune, calculated with quadrupole effective length 27.0 cm, emittance = 26 pmm-mrad. Multipoles are off.

Table 3: HRS tunes in volts. A and B are theoretical: for an emittance of 5 pmm-mrad, tune A has resolution 2500 and tune B 4500. Higher resolution is of course possible by closing down the object slit.

Theoretical tunes are also shown in table 3. Tune A (GIOS input file) is simply the operational tune with QP550 set to zero. Tune B (GIOS input file) is a tune for roughly twice the resolution. Beam envelopes for this tune are shown in figure 6

Figure 6: HRS high resolution tune, emittance = 5 pmm-mrad. Multipole MP 650 is set to a sextupole component of -700 volts. Resolution with an emittance of 5 pmm is 4500. Higher resolution is of course possible by closing down the object slit.

I've set up a TRANSOPTR file in such a way that one can specify desired resolution, and the 3 source parameters, and it will calculate quadrupole settings for a tune with the minimal amount of higher order effects. (TRANSOPTR input data file.) I've calculated tunes for many different conditions, and have not needed QP540 or QP550 for any. These two quads could in principle be shorted to ground. Additionally, QS030 and QP050 can in principal be wired together, as for the GPS.

The character of the beam at the mass slit (small size, large divergence) is ideally suited to the small ( 10cm by 10cm) emittance scanner we use at TRIUMF. Using such a scanner is by far the easiest way to tune higher order optics.

6  For Further Work

GIOS input files which generated the plots shown in this note are given below. One notices from these that quadrupole fringe fields are specified as `F F 0 0. 0. 0. 0.'. This effectively sets fringe fields to the hard-edge limit, without actually shutting them off. Such an approximation is good enough and avoids worries about whether fringe field integrals have been specified to sufficient accuracy. The same is not true of benders, electrostatic or magnetic, because it would neglect a significant correction to the linear focusing. (See TRANSPORT manual under codes 2. and 16.)

All TRANSOPTR work was performed in one directory. This also contains Linux executables both for finding new tunes and for fitting profile data, and the profile datasets. The current report, in both PS and HTML formats is in the report/ subdirectory.

7  Conclusion

The measured quadrupole effective length of 27.0 cm is 10% less than the length used in calculations until now. This may be the main reason for the difficulty in reconciling theoretical tunes with operational ones.

8  Acknowledgment

The present study was undertaken under the ISAC-ISOLDE agreement. I would like to thank Mats Lindroos and Uwe Georg for facilitating my visit and Uwe also for helping with beam setup and data-taking.

File translated from TEX by TTH, version 2.87.
On 24 May 2002, 16:06.