7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Ultrafast observation of the Lorentz transformation around a relativistic
electron beam

Koichi Kan1, Masato Ota2, Tatsunosuke Matsui3, and Makoto Nakajima41
National Institutes for Quantum Science and Technology (QST), Japan, 2 National Institute forFusion Science (NIFS), Japan, 3 Department of Electrical and Electronic Engineering, Mie
University, Japan, 4 Institute of Laser Engineering (ILE), Osaka University, Japane-mail (speaker): kan.koichi@qst.go.jp
Femtosecond electron bunches are helpful for thedevelopment of high-quality and intense X-ray and lightsources for applications in accelerator physics, such as
free-electron lasers. Short electron bunches can also be
applied to time-resolved pump-probe experiments
involving ultrafast electron diffraction and pulse
radiolysis to improve time resolutions. Electro-optic(EO) monitors are one of the techniques for analyzing
the time profile of the femtosecond electron bunch [1-3]because femtosecond electron bunches generate theCoulomb field as terahertz (THz) electric fields.
Diagnostics of electrons or neutrons with picosecond or
femtosecond time resolution based on EO sampling
would also be applied to analyze electric field and fusion
reaction history [4]. Such scheme for ultrafast detectionof THz electromagnetic waves can be applied to plasma
diagnostics and radiations from gyrotrons orsynchrotrons. EO sampling is also used in THz detection
and THz applications for materials and structures [5,6].
In this presentation, demonstration of single-shot
spatio-temporal detection of THz electric field around a
relativistic electron beam with an energy of 35 MeV [7]with sub-millimeter and sub-picosecond resolutions
based on electro-optic sampling will be reported.
Furthermore, a transition between the Liénard–Wiechert
potentials (LWPs) and the Lorentz transformation (LT)was demonstrated using the THz measurement system
for the first time. By passing the electron beam through ametallic foil, an electric field around the electron beam
was screened. After the passage of the metallic boundary,
the Coulomb field was born around the electron beam,and propagated with a spherical wavefront as explainedby the LWPs. In the far propagation length of ~200 mm,
the wavefront forms a plane, which indicates the the LT
as shown in Fig. 1. At the same time, the measurement
was not for the radiation field, but the Coulomb field.
Our ultrafast spatio-temporal measurement of a
relativistic electric field will pave the way forexperimental study of special relativity, electromagnetic
radiations, and relativistic charged particle beams. Thismeasurement scheme could also be applied to plasma
diagnostics which include fields of special relativity,
electromagnetic radiations, and relativistic chargedparticle beams.

Figure 1: Comparison of the spatio-temporal profiles of(a) the experimental result and (b) numerical simulationof the LT. Axes of Z is longitudinal direction for theelectron beam. The origins correspond to the beam center.
Reprinted with changes from an open access reference[2].
References[1] G. Berden, et al., “Benchmarking of Electro-Optic
Monitors for Femtosecond Electron Bunches”, Phys.
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[2] M. Ota et al., “Ultrafast visualization of an electricfield under the Lorentz transformation”, Nat. Phys.
18, 1436, 2022.
[3] M. Ota, et al., “Longitudinal and transverse spatialbeam profile measurement of relativistic electron
bunch by electro-optic sampling”, Appl. Phys.
Express, 14, 026503, 2021.
[4] Y. Arikawa, et al., “The conceptual design of 1-pstime resolution neutron detector for fusion reaction
history measurement at OMEGA and the National
Ignition Facility”, Rev. Sci. Instrum., 91, 063304
2020.
[5] K. Makino, et al., “Significant Volume Expansion asa Precursor to Ablation and Micropattern Formationin Phase Change Material Induced by Intense
Terahertz Pulses”, Scientific Reports, 8, 2914, 2018.
[6] V. C. Agulto, et al., “Anisotropic complex refractive
index of b-Ga2O3 bulk and epilayer evaluated byterahertz time-domain spectroscopy”, Appl. Phys.
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[7] K. Kan, et al., “Time-domain measurement ofcoherent transition radiation using a photoconductive
antenna with micro-structured electrodes”, AIP
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