Parallel Magnet Trimming
C H Gough
Introduction
This Note is one of a series, documenting the development of the five Storage Ring Kicker systems for the SLS. The pulser current was found to depend upon which magnet was used. The magnet reactances were carefully measured [1], and to a good approximation, the inductances were identical, but the resistances varied in inverse proportion to the DC resistances of the metallised ceramic chamber.
This Note explores this situation using Pspice simulations. The goal is to keep identical pulsers, with the different magnets trimmed to be reasonably identical.
Basic Circuit
The magnet can be modelled as the primary of a transformer, with the metallised ceramic chamber as the secondary, as shown in Fig.1. The coupling and secondary inductance is scaled by a factor (62mm/104mm) which comes from the mechanical drawing in the Appendix.
Fig.1 Basic circuit.
The circuit of Fig.1 matches the inductance and resistance measurements up to 100kHz.
The non-linear CORE model of Pspice gives access to the magnetic field information, if used in the time domain. The CORE model is set with the area and gap of the magnet. A feature of this model is that coupling from the coil to the core scales the inductance also. Since the gap is large, the linearity is assumed perfect.
Fig.2 Basic circuit with CORE model.
Parallel Trimming
Comparisons are made between two different magnets, with parallel resistive and series resistive trimming of the magnet, using the circuit of Fig.3. The pulser circuit is indicative of a real circuit.
Fig.3 Comparison between two circuits that are identical, except for a 10% difference in the secondary resistance.
The matching of the currents and magnetic fields to tens of parts per million was possible. To evaluate the effect of component tolerances, various values of resistance were tried and the results are shown in Table 1.
R52
Reference Circuit
R53
Trial Circuit
B Matching for 1% change in R53
Current Matching for 1%
change in R53
10 8.225 <630ppm <1210ppm
50 24.05 <230ppm <430ppm
250 39.15 <160ppm <310ppm
Table 1. Sensitivities for parallel trimming resistors.
Series Trimming
In contrast to parallel trimming, series trimming is relatively poor performance, giving field matching to within a few parts per thousand only. Fig.4a-b show typical results. The results were similar for series resistances around 10m as well (the results are not shown).
Fig.4a Effect on magnetic field matching of varying series resistance 100, 200, 300, 400 and 500m against 100m in the reference circuit (4m represents 0.4%).
Fig.4b As for Fig.4a, but for proportional current difference (10mA represents 1%).
Conclusions
Contrary to all expectations, it is possible with simple resistive trimming to match the magnetic fields to an arbitrarily low value, with +/-10% variation of the resisitivity of the metallised ceramic chamber. This matched condition corresponds also to the minimum for the pulser current matching.
References
"SR Kicker Inductance Measurements", C H Gough, 1 October 2000 Appendix 1
Cross-Section of Magnet
Appendix 2
Non-Symmetric Coupling
With a standard transformer, the primary and secondary current each give magnetic flux, and there is coupled flux between the two circuits. The present situation is unusual because one circuit is "immersed" in the field of the other in a large volume with r=1.
In the extreme case that the secondary is small with respect to the vertical gap, the primary flux couples to it in proportion the secondary area, but the secondary flux is highly localised and may not couple to the primary; in other words, the coupling matrix Mij is asymmetric.
Appendix 3 - to be finished later
In the frequency domain, the impedance of a transformer is given by:
where : Z11 is the total loop impedance on the primary Z22 is the total loop impedance on the secondary M is the mutual inductance
The admittance is given by:
where : Y11 is the total loop admittance on the primary Y22 is the total loop admittance on the secondary M is the mutual inductance