Protons, like all charged particles, deposit their energy in proportion to the inverse square of their velocity (as they slow down they deposit more energy, but a halving of velocity results in a quadrupling of energy deposition. This pattern leads to a Bragg Peak. The entry dose is low and the peak is high and deep (at maximal depth).
The beam is modulated for clinical use
- by altering the energy of the beam, or
- by degrading the beam with a material that reduces the energy of the beam (like bolus for other beams).
Both produce lower energy beams with shallower Bragg peaks that can be overlapped to give a plateau of dose. However the entry dose is increased by each overlaying beam.
I have provided two images here. The first is an animated GIF file that shows what happens as you add 170MeV protons beams together. The proton beams all have the same intensity but are modulated to produce their peak at 0.5cm increments. You can see that the resultant proton distribution has none of the purported advantages of a clinical beam, and frankly isn't very useful.
[This was developed using a spreadsheet of individual beams that add together to produce a composite. The beam does not exceed 100% because the maximum dose intensity at any depth is converted to 100%.]
The second image uses the same spreadsheet, but the strengths of each beam are modified. My attempt was trial and error, but you can see that already the beam looks like what the books tell you is possible and is 'useful'. I have overlaid a 6MV X beam for comparison.
The spreadsheet that calculates this can be found here.