Chapter 5
Relativistic Laser-Electron Interactions
5.1 Introduction
For the case when the laser intensity approaches 10
18 W/cm
2 for 1 μm wavelength
lasers, relativistic effect should be taken into account to any of phenomena induced
by laser-matter interaction. In order to obtain electron motion in such laser field,
relativistic electron motion should be solved, and the radiation due to retardation
effect, coming from the finiteness of the speed of light compared to the velocity of
electron, cannot be neglected. Relativistic effect to mass correction of a single
electron is itself nonlinear effect to laser dynamics interacting with an electron.
When electron oscillation velocity approaches the speed of light, the relativistic mass
correction changes the plasma frequency of the matters. Since the magnetic force to
the electron becomes comparable to the electric one, in addition, laser field in matter
can also induce the electrostatic wave through v 3 B force.
In this section, we briefly summarize the important relation of special relativity.
When the relations of relativistic physics are shown without derivation or proof in
what follows, readers are recommended to refer mainly the Chaps. 1, 2, and 3 in the
textbook by Landau and Lifshitz [1] and the Chap. 11 in the book by J. D.
Jackson [2].
5.2 Special Relativity for Electron Motion
Derive the equation of the momentum conservation of electromagnetic field. It is
useful to use the momentum change by coupling with charged particles via Lorentz
force. The momentum change per unit volume is given by
© Springer Nature Switzerland AG 2020
H. Takabe, The Physics of Laser Plasmas and Applications - Volume 1, Springer
Series in Plasma Science and Technology,
https://doi.org/10.1007/978-3-030-49613-5_5
167
Relativistic Laser-Electron Interactions
5.1 Introduction
For the case when the laser intensity approaches 10
18 W/cm
2 for 1 μm wavelength
lasers, relativistic effect should be taken into account to any of phenomena induced
by laser-matter interaction. In order to obtain electron motion in such laser field,
relativistic electron motion should be solved, and the radiation due to retardation
effect, coming from the finiteness of the speed of light compared to the velocity of
electron, cannot be neglected. Relativistic effect to mass correction of a single
electron is itself nonlinear effect to laser dynamics interacting with an electron.
When electron oscillation velocity approaches the speed of light, the relativistic mass
correction changes the plasma frequency of the matters. Since the magnetic force to
the electron becomes comparable to the electric one, in addition, laser field in matter
can also induce the electrostatic wave through v 3 B force.
In this section, we briefly summarize the important relation of special relativity.
When the relations of relativistic physics are shown without derivation or proof in
what follows, readers are recommended to refer mainly the Chaps. 1, 2, and 3 in the
textbook by Landau and Lifshitz [1] and the Chap. 11 in the book by J. D.
Jackson [2].
5.2 Special Relativity for Electron Motion
Derive the equation of the momentum conservation of electromagnetic field. It is
useful to use the momentum change by coupling with charged particles via Lorentz
force. The momentum change per unit volume is given by
© Springer Nature Switzerland AG 2020
H. Takabe, The Physics of Laser Plasmas and Applications - Volume 1, Springer
Series in Plasma Science and Technology,
https://doi.org/10.1007/978-3-030-49613-5_5
167