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Prediction of Optimal Focal Lengths in Magnetically Focused Proton Treatments

G McAuley

GA McAuley1*, JD Slater1,2 , AJ Wroe1,2 , (1) Loma Linda University, Loma Linda, CA, (2) Loma Linda University Medical Center, Loma Linda, CA


SU-I-GPD-T-194 (Sunday, July 30, 2017) 3:00 PM - 6:00 PM Room: Exhibit Hall

Purpose: To investigate methods of focal length optimization in a triplet magnet focusing system required to produce small low-eccentricity target beam spots

Methods: Monte Carlo (MC) simulations were performed of 127MeV proton beams (90% dose range of 9.88cm in water) magnetically focused by a triplet of quadrupole magnets. Phase space data (ie, beam displacement and divergence) was collected in both transverse planes at 8 locations along the beam axis: 1) upstream of final collimator, 2–7) before and after each magnet, and 8) upstream surface of a water tank. Phase space ellipses immediately upstream of the first magnet (position 2) were modeled based on the phase space ellipse at position 1) and the acceptance of the final collimator. Phase space ellipses at the tank surface were calculated using 3rd order transfer matrices of the focusing system, and optimized focal lengths were determined from the sigma matrix associated with this ellipse. Calculated ellipses were compared with the simulated phase space contours at the water tank surface (position 8) as well as MC simulations that produce low eccentricity target beam spots.

Results: Preliminary results suggest phase space contours upstream of the first focusing magnet can be adequately modeled, and optimum focal lengths can be determined by an appropriate choice of the maximum divergence at zero displacement included in the phase contour at position 1. However, the magnitude of this initial divergence is dependent on magnetic field gradient and initial beam diameter. Latest results will be presented.

Conclusion: Harmonic focusing and hyperbolic defocusing of quadrupole magnets as well as finite phase space area complicate the optimization of a 3rd order optical triplet focusing system. 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.

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