Open Access IJMPCERO
‐10 ‐50 510
Figure 18. Calculations and measurements for the case with
a field size diameter of 12 cm.
Figure 19. Calculations and measurements for the case with
a field size diameter of 30 cm.
4. Discussion and Conclusion
It could be shown that in conventional linear accelerators
used in medicine a multi-target consisting of a Tungsten
wall (thickness of the wall at least 2 mm) and 31 very
thin plates (thickness of a plate: ca. 0.01 mm) is superior
to the standard accelerator. The BS beam (inclusive di-
vergence) can be formed according to the desired proper-
ties. The energy spectrum is significantly increasing even
in the absence of a focusing magnetic field and is even
better than a conventional beam, which has passed a flat-
tening filter. Thus the omission of such a filter provides a
further yield of the factor 3 - 4. The optional amplifica-
tion of the focusing effect by suitable external magnetic
fields (with regard to the required properties, see e.g.
Figure 6) can be taken into account, in particular, if the
outcoming γ-beam should be very efficient by restricting
rather small fields. These properties are important for
scanning methods, stereotaxy, IMRT or tomography. It is
possible to reach some essential progress in the domain
of linear accelerators in radiotherapy, since the modern
irradiation techniques such as IMRT, stereotaxy, etc. do
not require large field sizes, e.g. a 40 × 40 cm2 at a dis-
tance of 100 cm from the focus. This progress can be
achieved by exploiting small angle reflectance of fast
electrons at a Tungsten wall. The wall has to map the
desired divergent properties of the beam. A further aspect
of this study is that we are able to save heavy high
Z-material for the shielding of the accelerator head. The
attached appendix deals with stopping power and heat
production of high energy electrons. By that, we have
been able to estimate the heat production in each thin
plate, which turned out to be lower 20˚C per 600 MUs.
Thus the systems even works without further cooling of
plates, if the rate of MUs will be increased to 1000 or more.
 R. Svensson and A. Brahme, “Effective Source Size,
Yield and Beam Profile from Multi-Layered Bremss-
trahlung Targets,” Physics in Medicine and Biology, Vol.
41, No. 8, 1996, pp. 1353-1379.
 W. Ulmer, “On the Creation of High Energy Bremss-
trahlung and Intensity by a Multi-Target and Repeated
Focusing of the Scattered Electrons by Small-Angle Back-
scatter at the Wall of a Cone and Magnetic Fields—A
Possible Way to Improve Linear Accelerators in Radio-
therapy and to Verify Heisenberg-Euler Scatter,” Radia-
tion Physics and Chemistry, Vol. 81, No. 4, 2012, pp.
 “GEANT4 Documents,” 2005.
 L. Eyges, “Energy Loss and Scatter of Neutrons and
Charged Particles,” Physical Review, Vol. 74, 1948, pp.
 G. Molière, “Multiple Scatter of Charged Particles Pass-
ing through Matter,” Zeitschrift für Naturforschung, Vol.
10a, 1955, pp. 177-187.
 R. P. Feynman and A. R. Hibbs, “Quantum Mechanics
and Path Integrals,” Mac Graw Hill, New York, 1965.
 W. Ulmer, J. Pyyry and W. Kaissl, “A 3D Photon Super-
position/Convolution Algorithm and Its Foundation on
Results of Monte-Carlo Calculations,” Physics in Medi-
cine and Biology, Vol. 50, No. 8, 2005, pp. 1767-1781.
 W. Ulmer, “Inverse Problem of Linear Combinations of
Gaussian Convolution Kernels (Deconvolution) and Some
Applications to Proton/Photon Dosimetry and Image
Processing,” Inverse Problems, Vol. 26, No. 8, 2010, Ar-
ticle ID: 085002.
 W. Ulmer, “Deconvolution of a Linear Combination of
Gaussian Kernels by Liouville-Neumann Series Applied
to an Integral Equation of Second Kind with Applications
to Radiation Physics/Image Processing,” In: A. Mishra,
Ed., An Introductory Guide to Digital Image Processing,
iConcept Press, 2013.
 W. Ulmer and E. Matsinos, “Theoretical Methods for the
Calculation of Bragg Curves and 3D Distributions of Pro-
ton beams,” European Physics Journal (ST), Vol. 190,
2011, pp. 1-81.
 M. J. Berger, J. S. Coursey and M. A. Zucker, “ESTAR,
PSTAR and ASTAR: Computer Programs for Calculating