Coherent Transition Radiation from Bunches of Charged Particles

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Form factors for bunches of charged particles largely determine the characteristics of the emitted coherent radiation. Transition radiation is emitted when a charged particle passes through an inhomogeneity such as a boundary between two different media. In this Demonstration, the boundary is between a vacuum and a metal target with infinite electrical conductance. The form factor can be used to determine the output radiation spectra, a solution of the inverse problem of determining the configuration of the charged particle beam from the emitted radiation.


The plots show form factors versus the wavelength or frequency of the coherent transition radiation, for varying parameters. Beneath the graph is a diagram showing the motion of the wave train and the geometry of the interaction. The target is shown as a green plate, the detector is shown as a yellow square and the charged-particle bunches are shown as red spheres. You can choose the target tilt angle, detector position and other parameters. All bunches are assumed to be of equal size.


number of bunches: number of bunches in the train

energy of particles: electron energy in the train (in MeV)

spacing: distance between bunches (in mm)

: size of bunches along axis (in mm)

: size of bunches along axis (in mm)

: size of bunches along axis (in mm)

tilt angle: tilt angle of target to train trajectory (in degrees)

: detector position along axis (in degrees)

: detector position along axis (in degrees)

: left value in graph (in mm)

: right value in graph (in mm)

: left value in graph (in THz)

: right value in graph (in THz)

plot points: number of plot points in graph curve

maximum recursion: option for plotting accuracy

target size: dimension of square target

distance: distance between target and detector (in mm)

movement of bunches: position of train on axis in diagram

parameter 1, 2, 3: position of camera used to view objects


Contributed by: Dmitry Shkitov and Marzhan Toktaganova (December 2020)
Based on an idea from: Dmitry Shkitov
Open content licensed under CC BY-NC-SA



Snapshot 1: one-electron bunch in train

Snapshot 2: three-electron bunches in train

Snapshot 3: four-electron bunches in train


[1] G. A. Naumenko, "Form-Factors of Relativistic Electron Bunches in Polarization Radiation," Advanced Materials Research, 1084, 2015 pp. 138–146. doi:10.4028/

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