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

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.

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 L_{eff}=27.00±0.16 cm, and using
Q_{2}, L_{eff}=27.24±0.22 cm. Since fits using series 1 measurements
gave L_{eff}=25.5±2.0 cm, the 3 results were combined to give the
following value, which is used in all subsequent calculations:

| (1) |

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

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.

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

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

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.

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.

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

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

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

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.

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.

File translated from T

On 24 May 2002, 16:06.