Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Projectile Motion: Equations01:26

Projectile Motion: Equations

13.8K
Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping into the pool, all undergo projectile motion.
Any projectile motion problem can be solved by using the following strategy:
13.8K
Velocity and Position by Graphical Method01:34

Velocity and Position by Graphical Method

9.3K
Velocity and position can be calculated from the known function of acceleration as a function of time. The total area under the acceleration-time graph and the velocity-time graph gives the change in velocity and position, respectively. In the case of an airplane, its acceleration is tracked using the inertial navigation system. The pilot provides the input of the airplane's initial position and velocity before takeoff. The inertial navigation system then uses the acceleration data to...
9.3K
The Uncertainty Principle04:08

The Uncertainty Principle

30.8K
Werner Heisenberg considered the limits of how accurately one can measure properties of an electron or other microscopic particles. He determined that there is a fundamental limit to how accurately one can measure both a particle’s position and its momentum simultaneously. The more accurate the measurement of the momentum of a particle is known, the less accurate the position at that time is known and vice versa. This is what is now called the Heisenberg uncertainty principle. He...
30.8K
Castigliano's Theorem01:18

Castigliano's Theorem

833
Castigliano's theorem analyzes displacements and rotations in elastic structures. It relates the derivative of elastic strain energy to the applied forces or moments, allowing for the calculation of deformations. The theorem states that the partial derivative of the total strain energy of a system with respect to a specific load results in the displacement at the point where the load is applied. This principle applies to both forces and moments.
833
Position and Displacement Vectors01:00

Position and Displacement Vectors

12.3K
To describe the motion of an object, one should first be able to describe its position (where it is at any particular time). More precisely, the position needs to be specified relative to a convenient frame of reference. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference to describe the position of an object in relation to stationary objects on Earth.
Further, several important kinds of...
12.3K
Position and Displacement01:31

Position and Displacement

23.9K
The position of an object defines its location relative to a convenient frame of reference at any particular time. A frame of reference is an arbitrary set of axes from which the position and motion of an object are described. Earth is often used as a frame of reference, and we often describe the position of an object as it relates to stationary objects on Earth. For example, a rocket launch could be described in terms of the position of the rocket with respect to Earth as a whole. On the other...
23.9K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Trajectory displacement in a multi beam scanning electron microscope.

Ultramicroscopy·2021
Same author

Robustness of Light-Transport Processes to Bending Deformations in Graded-Index Multimode Waveguides.

Physical review letters·2018
See all related articles

Related Experiment Video

Updated: Dec 15, 2025

Picometer-Precision Atomic Position Tracking through Electron Microscopy
15:04

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

8.1K

Analytical formulae for trajectory displacement in electron beam and generalized slice method.

Jan Stopka1

  • 1Institute of Scientific Instruments, Czech Academy of Science, Královopolská 147, Brno 612 64, Czech Republic.

Ultramicroscopy
|July 10, 2020
PubMed
Summary

Accurate estimation of charged particle beam trajectory displacement is crucial. This study unifies analytical models and enhances the slice method for improved accuracy in non-ideal systems.

Keywords:
Coulomb interactionElectron opticsHoltzmark regimePencil-beam regimeSlice methodTrajectory displacement

More Related Videos

Sample Preparation and Experimental Design for In Situ Multi-Beam Transmission Electron Microscopy Irradiation Experiments
08:31

Sample Preparation and Experimental Design for In Situ Multi-Beam Transmission Electron Microscopy Irradiation Experiments

Published on: June 27, 2022

2.1K
Use of Sacrificial Nanoparticles to Remove the Effects of Shot-noise in Contact Holes Fabricated by E-beam Lithography
07:47

Use of Sacrificial Nanoparticles to Remove the Effects of Shot-noise in Contact Holes Fabricated by E-beam Lithography

Published on: February 12, 2017

7.5K

Related Experiment Videos

Last Updated: Dec 15, 2025

Picometer-Precision Atomic Position Tracking through Electron Microscopy
15:04

Picometer-Precision Atomic Position Tracking through Electron Microscopy

Published on: July 3, 2021

8.1K
Sample Preparation and Experimental Design for In Situ Multi-Beam Transmission Electron Microscopy Irradiation Experiments
08:31

Sample Preparation and Experimental Design for In Situ Multi-Beam Transmission Electron Microscopy Irradiation Experiments

Published on: June 27, 2022

2.1K
Use of Sacrificial Nanoparticles to Remove the Effects of Shot-noise in Contact Holes Fabricated by E-beam Lithography
07:47

Use of Sacrificial Nanoparticles to Remove the Effects of Shot-noise in Contact Holes Fabricated by E-beam Lithography

Published on: February 12, 2017

7.5K

Area of Science:

  • Physics
  • Accelerator Physics
  • Beam Optics

Background:

  • Statistical Coulomb interactions significantly impact charged particle beam performance.
  • Accurate trajectory displacement estimation is vital for designing charged particle beam systems.
  • Existing methods include Monte Carlo simulations, the slice method, and analytical formulas.

Purpose of the Study:

  • To revise and improve existing methods for calculating trajectory displacement in charged particle beams.
  • To address the limitations of current analytical formulas, particularly during transitions between different interaction regimes.
  • To develop a more accurate and versatile slice method for non-ideal beam trajectories.

Main Methods:

  • Revision of Jansen's slice method and integral formulae derivations.
  • Analysis of Holtzmark and pencil-beam regimes and their transition.
  • Derivation of a new unified analytical expression.
  • Generalization of the slice method for arbitrary beam trajectories.

Main Results:

  • The existing integral formula was found to be inaccurate during regime transitions.
  • A new analytical expression was derived, unifying the Holtzmark and pencil-beam regimes.
  • The generalized slice method demonstrated significantly increased accuracy for non-ideal systems.

Conclusions:

  • A unified analytical formula provides a more accurate description of trajectory displacement across different regimes.
  • The enhanced slice method offers superior accuracy for complex, non-ideal charged particle beam systems.
  • These advancements contribute to more precise design and improved performance of particle beam optics.