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This study presents two methods for uniformly generating random directions within an elliptical cone, crucial for particle transport simulations. These algorithms enhance modeling of asymmetric beam divergence and scattering interactions.

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Area of Science:

  • Computational Physics
  • Applied Mathematics

Background:

  • Accurate simulation of particle transport is vital for fields like nuclear engineering and medical physics.
  • Existing algorithms for generating random directions often struggle with non-spherical distributions, such as elliptical cones.

Purpose of the Study:

  • To extend spherical surface sampling for uniform random direction generation within elliptical cones.
  • To develop and compare two distinct methods for this purpose, addressing limitations in current simulation techniques.

Main Methods:

  • The study extends the spherical surface sampling algorithm.
  • Two methods are proposed: one strictly adhering to the elliptical cone boundary, and a second that relaxes this constraint.
  • The performance and applicability of both methods are analyzed.

Main Results:

  • Both presented methods successfully generate uniform random directions within an elliptical cone.
  • The second method expands the range of generated directions by up to 10% for highly eccentric cones.
  • The second method can generate directions beyond the cone's equator, offering increased flexibility.

Conclusions:

  • The developed algorithms provide efficient and accurate tools for generating random directions in elliptical cones.
  • These methods improve the fidelity of Monte Carlo particle transport simulations, particularly for asymmetric scenarios.
  • The relaxed boundary method offers a valuable extension for simulations requiring a broader directional sampling range.