Speaker
Thomas Planche
(TRIUMF)
Description
We present a formula to calculate the Jacobian matrix of a numerical root-finding problem that is often encountered when designing fixed-field accelerators: the iterative search, with a 3-dimensional finite element code such as OPERA, for the optimal gap profile of a dipole magnet. We start by deriving exact closed-form formulae for this Jacobian in two limit cases: the non-saturated magnet (using conformal mapping) and the fully-saturated magnet (using current sheets). We thereafter present a method to combine these two formulae and cover all intermediate cases. We apply this method to design isochronous cyclotron magnets and numerically evaluate the rate of convergence of the algorithm.
| Region represented | America |
|---|---|
| Paper preparation format | LaTeX |
Author
Thomas Planche
(TRIUMF)
