Obtaining range from bethe-bloch formula

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SUMMARY

The discussion focuses on obtaining the range from the Bethe-Bloch formula in particle physics, specifically addressing the integration of dE/(dE/dx) without a direct variable E. Participants suggest utilizing programming languages and numerical methods, particularly the trapezoidal rule, for this integration. The integration process involves iterating through energy loss calculations using the Bethe-Bloch equation, where the independent variable is β. Key steps include updating energy and position iteratively based on the derived equations.

PREREQUISITES
  • Understanding of the Bethe-Bloch formula for energy loss in particle physics
  • Familiarity with numerical integration techniques, specifically the trapezoidal rule
  • Basic knowledge of programming for implementing numerical methods
  • Concept of beta (β) as a velocity parameter in particle physics
NEXT STEPS
  • Research the implementation of the trapezoidal rule in programming languages like Python or MATLAB
  • Study the Bethe-Bloch equation in detail, focusing on its application to protons
  • Explore numerical methods for integration in physics simulations
  • Learn about energy loss mechanisms in particle interactions
USEFUL FOR

Particle physicists, computational physicists, and students studying energy loss in particle interactions will benefit from this discussion.

Cemil
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While studying particle physics, i saw that the range formula is the integration dE/(dE/dx) but as you know that there are no variable E in the formula. how could that integration be done?

well i think we can do it by ourselves and we must use a programming language and i think the trapezoidal rule would be useful to solve that.

But i could not find out how could that integration be done please help me. thank you
 
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Cemil said:
but as you know that there are no variable E in the formula.

But there is a velocity. From velocity you can get energy.
 
Look at Equation (1) and Figure 1 in
http://beamdocs.fnal.gov/DocDB/0010/001068/001/A%20tutorial%20on%20beam%20loss%20monitoring.pdf
Eq (1) is the Bethe Bloch energy loss equation for protons. The independent variable is β. The integrated range is obtained by iteration of

dx = dE/[dE/dx]
E=E-dE
x=x+dx
etc.

Bob S
 
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