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 (27.00±0.15) 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=27.00±0.16 cm, and using
Q2, Leff=27.24±0.22 cm. Since fits using series 1 measurements
gave Leff=25.5±2.0 cm, the 3 results were combined to give the
following value, which is used in all subsequent calculations:
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.
| Energy | Waist Size | Divergence | Location | RMS error | Emittance |
| 60 keV | 1±1 mm | 4.7±0.2 mrad | 47±5 cm | 0.6 mm | 5±4 pmm-mrad |
| 30 keV | 1.5±0.8 mm | 3.8±0.4 mrad | 55±9 cm | 0.4 mm | 6±3 pmm-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.
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Figure 1: Typical operational GPS tune, calculated with quadrupole
effective length 30.0 cm, emittance = 26 pmm-mrad.
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Figure 2: Typical operational GPS tune, calculated with quadrupole
effective length 27.0 cm, emittance = 26 pmm-mrad.
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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.
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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.
| Quad | Op. tune | New tune |
| GPS.QS030 | -1700 | -1576 |
| QP040 | 3370 | 2975 |
| QP050 | -1740 | -1576 |
| QP170 | -93 | -797 |
| QP180 | 457 | 961 |
| QP520 | 2271 | 1677 |
| QP530 | -2737 | -1241 |
| QP540 | -2654 | -1241 |
| QS550 | 2660 | 1677 |
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.
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Figure 4: Typical operational HRS tune, calculated with quadrupole
effective length 30.0 cm, emittance =
26 pmm-mrad. Multipoles are off.
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Figure 5: Typical operational HRS tune, calculated with quadrupole
effective length 27.0 cm, emittance =
26 pmm-mrad. Multipoles are off.
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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.
| Quad | Op. | A | B |
| HRS.QS030 | -1554 | -1506 | -1393 |
| QP040 | 2662 | 2691 | 2701 |
| QP050 | -1590 | -1506 | -1393 |
| QP170 | -1658 | -1640 | -1732 |
| QP180 | 2382 | 2463 | 2671 |
| QP330 | -998 | -1165 | -1648 |
| QP540 | -0 | -0 | -0 |
| QP550 | 20 | 0 | 0 |
| QP640 | -212 | -198 | -136 |
| QP720 | 1905 | 1905 | 1905 |
| QS730 | -1725 | -1725 | -1725 |
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
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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.
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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.
