# Plasma and Fusion Research

## Volume 7, 2404010 (2012)

# Regular Articles

- Institute of Laser Engineering, Osaka University, 2-6 Yamada-oka, Suita, Osaka 565-0871, Japan
- 1)
- Advanced Beam Technology Division, Japan Atomic Energy Agency, Kyoto 619-0215, Japan

### Abstract

In the near future, the intensity of the ultra-short pulse laser will reach to 10^{22} W/cm^{2}.
When an electron is irradiated by this laser, the electron's behavior is relativistic with significant bremsstrahlung.
This radiation from the electron is regarded as the energy loss of electron.
Therefore, the electron's motion changes because of the kinetic energy changing.
This radiation effect on the charged particle is the self-interaction, called the “radiation reaction” or the “radiation damping”.
For this reason, the radiation reaction appears in laser electron interactions with an ultra-short pulse laser whose intensity becomes larger than 10^{22} W/cm^{2}.
In the classical theory, it is described by the Lorentz-Abraham-Dirac (LAD) equation.
But, this equation has a mathematical difficulty, which we call the “run-away”.
Therefore, there are many methods for avoiding this problem.
However, Dirac's viewpoint is brilliant, based on the idea of quantum electrodynamics.
We propose a new equation of motion in the quantum theory with radiation reaction in this paper.

### Keywords

radiation reaction, laser electron interaction, exawatt laser, LAD equation, advanced potential, retarded potential, Dirac equation, QED

### Full Text

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This paper may be cited as follows:

Keita SETO, Hideo NAGATOMO, James KOGA and Kunioki MIMA, Plasma Fusion Res. 7, 2404010 (2012).