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Prediction of Optimal Focal Lengths in Magnetically Focused Proton Treatments Using Transfer Matrices

Grant A McAuley1* , Steven J Martinez2 , Jerry D Slater1 , Andrew J Wroe1 , (1) Department of Radiation Medicine, Loma Linda University, Loma Linda, CA, USA (2) School of Medicine, Loma Linda University, Loma Linda, California, CA, USA


(Sunday, 7/29/2018) 3:00 PM - 6:00 PM

Room: Exhibit Hall

Purpose: To investigate methods of focal length optimization using transfer matrices in a triplet magnet focusing system for proton therapy

Methods: Monte Carlo (MC) simulations were performed using 127 MeV protons magnetically focused by a triplet of quadrupole magnets. For a range of magnet separations, phase space data was collected in both transverse planes before the first magnet and at the upstream surface of a water tank. Phase space ellipses in each plane were calculated from the acceptance of the focusing system. The acceptance was determined by transporting a pseudo-random sample of phase space points through the system and only retaining particles that were not “collimated�. The phase space ellipses were propagated to the water tank surface using the transfer matrices of the system and then compared using metrics involving the elements of the 2x2 (sigma) matrices associated with each ellipse. The separation between magnets (and thus the effective system focal length) was considered optimized when the ellipses best matched between the two planes.

Results: Preliminary results predict the optimal magnet separation for a 127 MeV beam of initial diameter 9 mm focused by a triplet of 200 T/m gradient magnets to be 43 mm. MC simulations for the same beam suggested an optimal separation of 42 mm. Results for similar comparisons for several triplet focused beams will be presented.

Conclusion: Harmonic focusing and hyperbolic defocusing of quadrupole magnets as well as finite phase space area complicate the optimization of an optical triplet focusing system. A predictive method based on transfer matrices could eliminate the number iterations required for MC optimization. Using transverse phase space contours is a promising method to estimate effective focal lengths that can then be iteratively refined prior to clinical deployment of such systems.

Funding Support, Disclosures, and Conflict of Interest: Funding for this project was provided by the Del Webb Foundation.


Modeling, Phase Space, Protons


TH- External Beam- Particle therapy: Proton therapy - Development (new technology and techniques)

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