Numerical Simulation of Alpha Particle Scattering Based on the Symplectic Euler and Heun Methods
DOI:
https://doi.org/10.54097/4t2nwa44Keywords:
Symplectic Euler Method, Heun Method, Coulomb Force ModelAbstract
This paper constructs a two-dimensional numerical model of α-particle scattering based on Coulomb forces and compares simulations using the Rutherford concentrated-charge model and the Thomson uniform-charge model. The Symplectic Euler method and the Heun prediction-correction algorithm were employed to calculate particle trajectories, scattering angles, and energy changes, which were then validated against theoretical scattering angles. The results show that in the Rutherford model, the scattering angle exhibits an approximately linear relationship with 1/b, with a maximum deflection angle of approximately 160°; in the Thomson model, the overall deflection is weaker, and the scattering angle is generally less than 3.5°. The Symplectic Euler method exhibits smaller energy fluctuations and superior long-term stability, while the Heun algorithm provides better trajectory fitting accuracy. This study establishes a general simulation framework applicable to charged particle scattering processes, which can serve as a reference for classical scattering modeling and numerical calculations of conservative systems.
Downloads
References
[1] Gao, Q., Peng, H. J., Zhang, H. W., et al. (2013). A second chiral algorithm based on the new variational principle of Hamiltonian dynamical systems: Proof of the algorithm’s chiral properties. Journal of Computational Mechanics, 30(4), 468 472.
[2] Quan, J. (2018). Simulation study on the gravitational drift motion of charged particles in a magnetic mirror. University Physics, 37(2), 34 37. https://doi.org/10.16854/j.cnki.1000 0712.170174
[3] Zhao, L. Q. (2019). Damped oscillations of charged particles in the electric field of four fixed point charges. University Physics, 38(9), 15 18. https://doi.org/10.16854/j.cnki.1000 0712.180694
[4] Sun, L., Liu, F. Y., Wang, Y., et al. (2021). Classification and development of symplex methods. Advances in Astronomy, 39(2), 211 233.
[5] Li, Y. D. (2023). Solving initial value problems of nonlinear fractional order ordinary differential equations using a prediction correction method based on non uniform grids. Advances in Applied Mathematics, 12(12), 4907 4913. https://doi.org/10.12677/AAM.2023.1212483
[6] Jiang, J. Q. (2015). Numerical simulation of electron motion in the magnetic field of a pair of current carrying circular coils. University Physics, 34(6), 19 23. https://doi.org/10.16854/j.cnki.1000 0712.2015.06.005
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Academic Journal of Applied Sciences
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
