Optimizing a Quadrupole Magnet

In this example the Optimizer is used with Opera-3d to optimize the performance of a quadrupole magnet used in charged particle beam lines.

Auto-optimisation tools are not new, but they usually require manual intervention if a globally-optimal solution is to be found. And simulation times often make such a process impractical. A new tool – Optimizer – automatically selects and manages multiple goal-seeking algorithms to eliminate the need for manual intervention, making optimisation feasible in virtually all design cases.

It starts by creating a parameterised model of a quadrupole magnet (used to control particle beams). The initial model creation and simulation process took approximately 4 hours – with the simulation itself taking approximately 15 minutes [on an inexpensive dual-core 3GHz PC].

In this case the optimum solution requires finding just one objective: the best field shape, which depends on two parameters: the length of the magnet pole tip, and the blend radius.

At this point, the designer could vary model parameters manually and re-simulate each time. However, even though this is a relatively simple design case with only one design objective, there are contraints (higher order harmonics) that need to be minimised, and it is unlikely that manual searching could find the optimum solution easily.

The Optimizer tool starts the auto optimisation process by running a series of simulations across the chosen design space, which provides a basis for understanding where the likely globally optimum solution lies. It then homes in on the best fit. As can be seen, there are possible design solutions right across the space, so it is quite likely that manual efforts might only find a local minima.

Setting up the auto optimisation process took only a few minutes using the tool’s templates. The PC was left on overnight to optimise, with a total run time of around 10 hours. To find the best solution, Optimizer analyses the stochastic properties of the input space and utilises a Kriging-assisted surrogate method to predict the shape of its solution surface and thus determine where to position the next model. There is an algorithmic balance between examining exploratory and minimization locations in the input space to guard against falling into a local minima, and wasting time on seeking tiny improvements. Where multiple objective functions are specifed, solutions are ranked according to their location between Pareto surfaces in the objective space.