A Novel Large Energy Acceptance Beamline
for Hadron Therapy
Adam Steinberg for IPAC’23
Motivation
At the University of Melbourne, we are working towards a closed-dispersion arc, such that we are able to transport a beam with a large energy spread around a nontrivial bend without introducing any position offset as a function of energy.
A beamline with an extremely large energy acceptance would have potential applications for charged particle therapy, where a current limiting factor is the time taken to change the beam energy: treatments could be made more efficient and effective with a rapid beam delivery system.
For our beamline, we propose Fixed Field Accelerator (FFA) optics to transport beams with a momentum acceptance of ±42%. As part of the TURBO project, this beamline will eventually be constructed at the University of Melbourne, using low energy proton beams from a DC Pelletron accelerator.
Design
In a standard dispersion suppressor, the phase advance to the midpoint is set to an odd-integer multiple of π.
In an FFA, for the phase advance to be independent of energy, the magnetic fields must be nonlinear, following a ‘scaling law’.
However, the closed orbit trajectories in a scaling FFA are fixed, as seen in this plot: although the phase advance is right to suppress dispersion, the closed orbits are not.
Rather than allowing particles to follow their closed orbits, we instead launch them all from a reference trajectory.
By the end of the arc, the particles do not return to the same transverse position: dispersion has been introduced.
In our optimisation, we will seek to reduce the dispersion at the end, and at the midpoint (otherwise the magnet bore would be infeasibly large).
In the optimised arc, the dispersion at the end is reduced by several orders of magnitude by varying multipolar fields up to the decapole term.
Even at the midpoint of the arc, the dispersion is sufficiently reduced to ensure that magnet design will be feasible.
In this case, the dipole field of each magnet is not included in the optimiser: a later study will investigate that option, as this may reduce the dispersion and required B-field magnitude.
Key Results
The dispersion function is symmetrical, as would be expected.
(Note that this is the linear dispersion, the actual variation with momentum is less.)
The maximum magnetic field is kept below 0.8T, which is a limit we have imposed to ensure permanent magnet Halbach arrays are suitable.
This study has used a hard-edge approximation for the magnetic fields, which will be superseded when initial magnet designs are completed (see below).
We recall that the phase advance in the base arc is approximately 2π.
To bring in the dispersion at the midpoint, the horizontal focusing strength has been significantly increased during optimisation. This has raised the horizontal phase advance to the level seen here.
The phase advance is a function of energy, as the lattice does not follow the scaling law. Further optimisation may be able to reduce the working point variation, if required.
(An interactive version of this graph can be found here)
Particle Transport
Here we see beams of five different energies travelling through the beamline, with the lowest energy on the far left.
The apparent ‘bumps’ in the particle motion come from the rotation of the reference axis in every third drift – the beamline is made of several straight sections in a polygon, rather than a smooth curve.
Magnets
This is a dipole.
Which part of the image is the magnetic field, and which one is magnetisation? It’s not possible to tell, as there the two are related by a reciprocal theorem. We can use this reciprocity to give us our first-order magnet design.
We can test this idea against magnets that have been designed separately: here we use the BDT2 magnets from the CBETA arc, which are combined function with strong dipole and quadrupole fields.
Below, on the left we have the magnetisation from the analytical solution, and on the right is a possible segmentation using trapezoidal wedges (as was the case for CBETA).
Even though this segmentation has not been optimised, we see that it does a good job reproducing the desired fields. Even though this design has been completed without reference to the actual CBETA magnets, comparison with their results suggests that this initial solution is not far from the optimal one.
Here, we look at the first magnet in the TURBO beamline shown previously.
The analytical solution for the required field is looks feasible at a glance.
Note how much further out the magnet extends on the right side than the left: this is due to some of the multipole terms cancelling, and some combining.
Whereas CBETA used custom-built trapezoidal permanent magnet wedges, we are planning to use commercially available blocks to lower costs. This will slightly reduce the maximum achievable field and increase the field errors, but we expect this should be fine as our beamline is just a short demonstrator.
A possible segmentation, if we use only one type of permanent magnet block (these ones specifically), is shown here. The magnet placement is not optimised, so the field quality could be improved – but this is not a bad initial solution.
Next Steps
The work presented here is the initial optics design for our large energy acceptance beamline. The most pressing question is probably the magnets: once we have an optimised design for those, we can begin to iterate the magnets and beamline together, aiming towards future construction of our beamline at the University of Melbourne.