Effective source size, yield and beam profile from multi-layered bremsstrahlung targets

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Abstract
Modern conformal radiotherapy benefits from heterogeneous dose delivery using scanned narrow bremsstrahlung beams of high energy in combination with dynamic double focused multi-leaf collimation and purging magnets. When using a purging magnet to remove electrons and positrons the target space is limited and unorthodox thin multi-layered targets are needed. A computational technique has therefore been developed to determine the forward yield and the angular distributions of the bremsstrahlung beam as well as the size and location of the effective and the virtual photon point source for arbitrary multi-layer bremsstrahlung targets. The Gaussian approximation of the diffusion equation for the electrons has been used and convolved with the bremsstrahlung production process. For electrons with arbitrary emittance impinging on targets of any multi-layer and atomic number combination, the model is well applicable, at least for energies in the range 1 - 100 MeV. The intrinsic bremsstrahlung photon profile has been determined accurately by deconvolving the electron multiple scattering process from thin experimental beryllium target profiles. For electron pencil beams incident on a target of high density and atomic number such as tungsten, the size of the effective photon source stays at around a tenth of a millimetre. The effective photon source for low-Z materials such as Be, C and Al is located at depths from 3 - 7 mm in the target, decreasing with increasing atomic number. The effective photon source at off-axis positions then moves out considerably from the central axis, which should be considered when aligning collimators. For high-Z materials such as tungsten, the location of the effective photon source is at a few tenths of a millimetre deep. The virtual photon point source is located only a few tenths of a millimetre upstream of the effective photon source both for high- and low-Z materials. For 50 MeV electrons incident on multi-layered full range targets the radial energy fluence distributions will have a full width at half maximum (FWHM) of 80 to 100 mm at 1 m from the target. The best target composition made of two layers when the space is limited to 15 mm was found to be 9 mm Be followed by 6 mm W. A thin beryllium target () results in a high-intensity bremsstrahlung lobe with a FWHM of about 35 mm at the isocentre. Interestingly, the forward dose rate in such a beam is as high as 62% of the maximum achievable with an optimal target design, even if on average only 1 MeV is lost by the electrons.