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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2026-06-11 23:58 |
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Conference: Bucharest University Faculty of Physics 2026 Meeting
Section: Theoretical and Computational Physics, Applied Mathematics
Title:
Numerical Evidence of Kapitza-Dirac Momentum Transfer in Weakly Relativistic Crossed Lasers
Authors:
Richard A. RADU
Affiliation:
University of Bucharest, Faculty of Physics, Str. Atomiștilor 405, Magurele, Romania
E-mail
richard-andrei.radu@s.unibuc.ro
Keywords:
Kapitza-Dirac effect, Klein-Gordon formalism, WENO-Z scheme
Abstract:
We present a numerical investigation of the Kapitza-Dirac effect for a free electron in counter-propagating laser pulses. Utilizing the Klein-Gordon formalism, we simulate this dynamic within a weakly relativistic regime. Preliminary attempts revealed that extreme localized compression of the probability density renders direct integration computationally intractable over expansive domains. To overcome this, we apply a semiclassical approximation, neglecting the dispersive quantum potential to reduce the system to a pressure-less Hamilton-Jacobi model. This cleanly isolates the interference-driven phase gradient governing the observable kinematic momentum, albeit introducing inherent restrictions. The resulting hyperbolic conservation law is integrated using a 5th-order WENO-Z spatial reconstruction scheme [2, 3] on a statically mapped non-uniform grid and stabilized by Local Lax-Friedrichs numerical flux. Our integrations demonstrate a massive, sustained bulk momentum transfer consistent with the deep Raman-Nath diffraction regime. The macroscopic momentum bounds saturate at approximately 44 000 photon recoils, slightly exceeding the non-relativistic ponderomotive limit. Furthermore, non-zero initial electron momenta break the laser-electron coupling symmetry, inducing state-dependent baseline shifts in momentum saturation. Ultimately, this work establishes that partially retaining second-order kinematics is sufficient to expose a significant macroscopic momentum spread, providing a physical departure from the unchanged momentum distributions implied by purely analytical reduced-equation treatments [1].
References:
[1] M. Gavrila, Phys. Rev. A 99, 012120 (2019).
[2] G.-S. Jiang and C.-W. Shu, J. Comput. Phys. 126, 202 (1996).
[3] M. Castro, B. Costa, and W. S. Don, J. Comput. Phys. 230, 1766 (2011).
Acknowledgement:
I would like to express my sincere gratitude to my coordinator, Conf. Dr. Mădălina Boca, for her theoretical guidance, insightful feedback, and continuous support throughout the development of this research.
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