28 



BEAMS OF HIGH-ENERGY PARTICLES 



Ideally the homogeneous electron beam from the betatron travels 

 straight into the tissue a distance equal to the electron range and then 

 stops. Since the ionization density along an electron track is nearly 



constant above 1 mev, we might 

 expect nearly constant dosage out 

 to the end of the range and then 

 zero dosage beyond, possibly a 

 slight increase just at the end. 



This simple picture must be 

 modified somewhat. In passing 

 through the tissue, the electrons 

 can radiate secondary photons 

 having a large fraction or all of 

 the energy of the electron. This 

 causes a large straggling in the 

 range of the electrons which tends 

 to give a decreasing ionization 

 density at increasing depths. Fur- 

 thermore, the radiated secondary 

 x-raj^s now pass beyond the range 

 of the electrons and, upon absorp- 

 tion, contribute to the dosage 

 there. Fortunately, the second- 

 ary photons are so penetrating 

 that the residual dosage is very 

 small beyond the end of the elec- 

 tron beam. The largest modifi- 

 cation comes about because of 

 multiple scattering caused by 

 many very small deflections suf- 

 fered by the electrons as they 

 pass through the atoms of the 

 tissue. The many scatterings 

 add up to very large angular de- 

 viations, and near the end of the range the electron motion is more or less 

 a random diffusion. There are a disadvantage and an advantage to this 

 diffusion. It adds to the straggling in range caused by radiation and so 

 brings the total average straggling to about 30 per cent of the mean range. 

 This tends to reduce the ionization density deep in the tissue compared to 

 that at the surface. The scattering also causes the beam to spread out 

 laterally by several centimeters. Thus, if one directs a needle-like beam 

 into the tissue, the ionization density will be very low near the end of the 



J L 



1 



2 3 4 5 6 7 

 Depth in phantom, cm 



Fig. 3. Depth-dose measurements with 

 x-ray beam from betatron, at various elec- 

 tron energies. The target-to-surface dis- 

 tance was 45 cm in each case. 



