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Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra.
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Electrons revolving around a nucleus are analogous to a circular current carrying loop. This current produces a magnetic dipole moment proportional to the electron's orbital angular momentum. Since the orbital angular momentum is quantized in terms of the reduced Planck's constant, the dipole moment is quantized in the Bohr Magneton. The value of the Bohr magneton is 9.27 x 10-24 Am2. Electrons also have an intrinsic spin angular momentum, and the associated spin magnetic moment is...
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Updated: Oct 4, 2025

Finite Element Modelling of a Cellular Electric Microenvironment
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Empirical formulation for small circular electron fields.

Imran Khan1,2, Sunil Kumar2, Sushil Kumar3

  • 1Department of Physics, Cornell University, Ithaca NY, United States of America.

Biomedical Physics & Engineering Express
|February 7, 2022
PubMed
Summary
This summary is machine-generated.

A new empirical model accurately predicts therapeutic depth for small electron fields, aiding treatment planning. This model offers a simple, time-saving method for predicting electron beam characteristics.

Keywords:
EGSnrc/BEAMnrcMonte Carlo methodelectron beam therapyleast square fittingprescription depthsmall circular fieldstherapeutic depth

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Area of Science:

  • Medical Physics
  • Radiation Oncology
  • Dosimetry

Background:

  • Accurate dosimetry is crucial for effective radiation therapy.
  • Small electron fields present unique challenges in treatment planning.
  • Existing models may not fully capture the dosimetric properties of small electron fields.

Purpose of the Study:

  • To develop an empirical model for predicting therapeutic depth in small circular electron fields.
  • To analyze dosimetric properties including depth dose, inverse-square fall-off, and beam profiles.
  • To provide a method for creating predictive models for various linear accelerator systems.

Main Methods:

  • Developed an empirical exponential model for therapeutic depth (90% of Dmax).
  • Conducted a dosimetric analysis using a 3D water phantom and pin-point ion chamber.
  • Utilized EGSnrc/BEAMnrc Monte Carlo simulations for Varian Clinac 2100 C accelerator.

Main Results:

  • The exponential model accurately predicts therapeutic depth (better than 2 mm accuracy).
  • Penumbra widths were studied and fitted to a quadratic model.
  • Monte Carlo simulations provided detailed dosimetric profiles for small circular electron fields.

Conclusions:

  • A simple two-parameter model effectively predicts therapeutic depth for small electron fields.
  • The developed model and methodology can be adapted for other linear accelerators.
  • This approach can significantly aid treatment planning for small and irregularly shaped electron fields.