Difference in Results Between Repeated /run/beamOn 1 and Single /run/beamOn 10000 in Modified ExampleB1

Particles, Track, Event, Run and Biasing
1

_Geant4 Version:_10.5
_Operating System:_CentOS 7
Compiler/Version:
CMake Version:

Dear Geant4 experts,

I am running a modified version of the exampleB1 simulation in Geant4 and noticed a difference in results when executing the following commands:

  1. Running /run/beamOn 1 10,000 times
  2. Running /run/beamOn 10000 once

The results from the first approach appear to be more ideal for my use case, while the second approach shows discrepancies.

I have G4Random::setTheEngine(new CLHEP::RanecuEngine); in my exampleB1.cc file. When I commented out this line, the discrepancy was somewhat reduced, but there was still a noticeable difference.

Could someone explain why this difference occurs and how I can ensure consistent results? Is there a recommended way to manage the random seed or simulation execution to achieve results similar to the repeated /run/beamOn 1 case?

Thank you!

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( In the graph above, the green is the average of the results after executing /run/beamOn 1 several times, and the orange is the average of /run/beamOn 10000 divided by 10000 after executing it once.)