Computer Simulation Permits Tightest Spec Ever from Pulse-forming Network
By Jerry Fireman
Computer simulation allowed research scientists at TRIUMF to achieve the tightest specification to date for a magnetic field generated by a pulse-forming network. The 66 kV pulse-forming network (PFN), designed for use by CERN, has a measured ripple in the flat-top of only ±0.3%. This is a much flatter pulse than the ±1% ripple that previously represented the state of the art for these devices. The TRIUMF researchers attribute their ability to achieve this level of performance to using precise computer simulation rather than traditional calculations and mechanical tuning by trial and error in the design of the PFN. Electromagnetic simulation made it possible to determine a single frequency that could then be used to determine the ideal circuit parameters needed to achieve the desired flat-top of the pulse. Once the researchers had that information, they were able to optimize the design of the PFN to produce the desired pulse shape. Next, the researchers used electromagnetic simulation to evaluate the geometry of the pulse-forming network’s coil to specify precise manufacturing tolerances.
The main reason such a tight specification had not been achieved previously was because earlier pulse-forming networks were designed to be tuned by hand. A pulse-forming network consists of one or more coils (inductors), resistors and capacitors. The inductance and resistance properties of the coil, which determine the shape of the pulse, are frequency-dependent. Previously there was no accurate way to simulate the effect of different frequencies on the inductance and resistance characteristics, so pulse-forming networks were designed to be tuned after they were built.
“After a pulse-forming network was built, researchers measured the output pulse and then spent considerable time tuning the network,” says Michael Barnes, PhD, a research scientist at TRIUMF. “Our goal on this project was to create a pulse-forming network that required no adjustments. To do that, we had to specify the capacitors, resistors and the coil very precisely, which meant that we had to understand the properties of all of these components and how they varied according to frequency.”
TRIUMF (the TRI- University Meson Facility) is Canada’s national laboratory for particle and nuclear physics. It is operated as a joint venture by the University of Alberta (Edmonton, AB), the University of British Columbia (UBC) (Vancouver, BC), Carleton University (Ottawa, ON), Simon Fraser University (Burnaby, BC), and the University of Victoria (Victoria, BC), with the University of Manitoba (Winnipeg, MB), the University of Montreal (Montreal, QC), Queen’s University (Kingston, ON), the University of Regina (Regina, SK) and the University of Toronto (Toronto, ON) participating as associate members.
TRIUMF is located on the UBC campus, and provides world-leading facilities for experiments in subatomic research with beams of pions, muons, protons, neutrons and radioactive ions. In 1995, TRIUMF was made responsible for co-ordinating Canada’s $30-million contribution to the construction of the Large Hadron Collider (LHC) at CERN, the European Organization for Nuclear Research, located near Geneva, Switzerland. The LHC will consist of two superconducting magnetic channels installed in the existing 27-km LEP (large electron-positron collider) tunnel. Protons delivered by the injector synchrotrons will be accelerated in two counter-rotating LHC rings, to 7 TeV each, and brought to collide at four experiment locations. First collisions are scheduled for 2005.
Tight Specifications
One aspect of TRIUMF’s contribution to this effort involves designing the resonant power supplies and a series of pulse-forming networks for the LHC’s injection kicker systems. The kickers are magnetic devices that play a key role in the LHC: switching the beams from ring to ring.
“The particle beams must switch cleanly from one ring to another or they will crash into the sides of the channel and cause not only radioactivity but also severe damage due to the very high beam power,” Barnes says. “That requires that the kicker magnets go from the off position to full power very quickly.” Each kicker system must produce a field of 1.3 mT with a flat-top duration adjustable between 4.25 s and 7.8 s, and rise and fall times of less than 900 ns and 3 s, respectively. Ripple in the field flat-top must be less than ±0.5%. “That’s a very tight specification for a pulsed field. To our knowledge, no one has ever achieved better than a ±1% ripple,” Barnes says.
In order to gain an understanding of which component values were critical to the performance of the PFN, a sensitivity analysis of the field to the value of both individual and groups of circuit components was carried out.
The 5 PFN consists of two lumped element delay lines, each of 10 ohms impedance, connected in parallel (Fig. 1). There are two thyratron switches connected to the PFN, referred to as a main switch (MS) and a dump switch (DS). Each 10 PFN consists of 26 seven-turn cells, a five-turn cell at the DS end, and a nine-turn cell at the MS end. A cell consists of a series inductor, a damping resistor connected in parallel and a grounded capacitor. Each capacitor is mounted in a coaxial housing to minimize parasitic inductance. The PFN capacitors are selected in pairs from a batch of capacitors with 5% tolerance to provide an effective tolerance of 0.5% for each pair. Each capacitor per pair is mounted in the same corresponding cell of the parallel lumped element delay lines. Two 4.3-m long, 196-turn coils are mounted on rigid fibreglass coil formers.
Barnes and his colleagues used the 2-D finite element-based electromagnetic analysis software Opera from Vector Fields Ltd. (Aurora, IL) to gain a detailed understanding of the coil behaviour. The first step was modelling the coil configuration in Opera. This was done using the software’s CAD facilities. Each coil is surrounded by a 3-mm thick, Omega-shaped aluminum screen with an inner radius of 140 mm. Both lines were mounted in a rectangular tank with mild steel walls. The Omega shield and steel tank were both modelled as circular. After creating the 2-D model, the researchers specified the material properties of the system components using the library of material data contained in the software. The program then automatically divided the model into finite elements.
The researchers then ran the electromagnetic analysis to determine self-inductance, mutual inductance and resistive losses at each frequency. They repeated the analysis 60 times to evaluate coil behaviour at 60 different frequencies, ranging from 0 Hz to 10 MHz. The results showed a reduction in inductance as frequency increased from DC to a few hundred hertz. This was mainly due to screen shielding. The reaction field from the eddy currents induced in the Omega shield reduced the flux density along the axis of the coil from 0.343 T near DC to 0.315 T, for a current of 6 kA. As the frequency increased beyond a few hundred hertz, the inductance decreased mainly due to skin and proximity effects. Conduction losses along the coil would result in droop of the pulse of approximately 0.5%. The capacitance values are therefore graded linearly from the MS to the DS with a gradient of +0.09% per cell to compensate for the conduction losses.
The next step was to use this information to design a circuit that would deliver the desired coil performance. “With Opera, we were able to look at the geometry of the coil and predict the inductance and resistance at different frequencies,” Barnes says. “Once we had that data, we could design a circuit that produced the pulse shape we wanted.”
Designing for Production Issues
Once they had the coil configuration they wanted and a circuit that would deliver the correct pulse shape, the researchers performed additional electromagnetic simulations. These were carried out to understand the effect on coil performance of subtle changes in geometry resulting from the production process.
“Opera had allowed us to determine the important characteristics of coil geometry that would give us the kind of performance we wanted. Now we were ready to go into the manufacturing phase and we wanted to make sure we would get those characteristics. For example, the coil would be wound very precisely within grooves on a fibreglass epoxy former. We wanted to be able to specify to the manufacturer the precise tolerances for those grooves,” Barnes explains. This was done by making slight changes to the Opera model, running a series of electromagnetic analyses, and observing the effect on inductance.
Other production-related issues were investigated as well. One related to the fact that when a coil is wound into a groove, its shape is slightly distorted. Rather than a perfect circle, it has more of a “keystone” appearance. Researchers used Opera to assess the effect of a coil cross-section that is no longer completely circular after winding.
“The ‘keystoned’ conductor had an outside diameter of 8.15 mm to 8.3 mm, measured longitudinally relative to the coil axis, and 7.7 mm to 7.8 mm measured radially,” Barnes says. “In Opera, we modified the model of the coil to be two semicircular tubes joined by two straight sections, with the straight sections being parallel to the axis of the coil.”
They then ran a simulation at 40 kHz, to determine both self and mutual inductances. The results showed that reducing the outside diameter of the tube by 0.2 mm, with negligible change in length (0.04 mm) of the straight section, increased the predicted inductance from 1,869 nH to 1,882 nH (+0.7%). However, introducing straight sections of 0.4 mm in length reduced the inductance to nearly the original value. Opera was also used to assess the effect of an error in the inside radius of the Omega shield. An increase in the average inside radius by 1 mm (0.71%) increased the predicted inductance, at 40 kHz, by 0.12%.
Using the information gained from these analyses, TRIUMF and CERN produced a prototype pulse-forming network that exceeded the original requirement for a ±0.5% ripple in the field flat-top. Their network, which has now been tested by CERN for more than one million pulses, delivers a ripple in the flat-top of ±0.3%. CERN has asked TRIUMF to contribute nine more pulse-forming networks to the LHC project: the first one of this series is shown on page seven and on the cover.
“We believe this is the first time anyone has used computer simulation the way we did in the design of a pulse-forming network,” Barnes says. “When you have to work within a certain window of inductance and resistance, using simulation enables you to try out enough iterations to achieve your design goals.”
For further information, contact Vector Fields, 1700 N. Farnsworth Ave., Aurora, Ill. 60505. Phone: 630-851-1734 Fax: 630-851-2106 Web: www.vectorfields.com
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