Lateral Fluence

My model is based on the Hadrontherapy advanced example.

I was able to replicate the ProBeam Proton Therapy System depth-dose curves for different energies using different energy sigmas for each energy. Now I am trying to model the lateral fluence in air at isocenter. My set up is a GPS (proton) in a vacuum chamber with a Kapton window, two ionization chambers, and a phantom filed with air with the detector at 15mm depth and centered. The detector voxels are /changeDetector/size .02 3 3 cm ; /changeDetector/voxelSize .2 .1 30 mm. I am using the /gps/ang/sigma_r , /gps/pos/sigma_r , and /changePhantom/position to try and match the fluence of the ProBeam for energies 100 and 170 MeV. I have not been able to figure out a way to match the beam spot sigmas of both energies without having to change the sigma_r or phantom position when I change the energy. The beams are supposed to have a sigma of 5.03mm at 100MeV and 3.79mm 170MeV.

Will I have to change the /gps/pos/sigma_r for each energy in order to get the correct lateral fluence? Is there a way you know to find the correct sigma_r and phantom position so that I will not need to change these parameters each time I change the energy?

I have attached the beam spot sigmas I am trying to recreate in Hadrontherapy for all energies, just in case that would help.

your help is appreciated