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Relativistic Laser–Atom Physics

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Strong Field Laser Physics

Part of the book series: Springer Series in Optical Sciences ((SSOS,volume 134))

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Notes

  1. 1.

    For a constant amplitude field \(E(t) = E_{0} \sin(\omega t)\), one has \(I_{L} = \frac{1}{2}\sqrt{\frac{\epsilon_{0}}{\mu_{0}}}|E_{0}|^2\).The fictitious intensity associated to the atomic unit of electric field strength \(E_{\rm at} = \frac{e}{(4\pi\epsilon_{0})a_{b}^2}\) experienced by an electron on the first Bohr orbit in hydrogen is \({ I_{\rm at} \approx 3.5\times 10^{+16}\ {\rm W\ cm}^{-2}}\).

  2. 2.

    See note 1.

  3. 3.

    For a laser field from a Nd:Yag laser with photon energy \(\hbar \omega \approx 1.17\ {\rm eV}\) and intensity \(I = 10^{18}\ {\rm W\ cm}^{-2}\), the ponderomotive energy \(U_{\rm p} \approx 105\ {\rm keV}\).

  4. 4.

    For a laser field from a Nd:Yag laser with photon energy \(\hbar \omega \approx 1.17\ {\rm eV}\) and intensity \(I = 10^{18}\ {\rm W\ cm}^{-2}\), the number N of photons contained in a \(V = \lambda^3\) coherence volume (with \(\lambda = 1.06\ \upmu {\rm m}\)) is \(N = \frac{I\:V}{c\:\hbar\omega} \approx 2 \times 10^{14}\).

  5. 5.

    The relevant time scale in the relativistic domain is the natural unit of time: \(t_{0} = \frac {\hbar}{mc^2} \approx 1.29 \times 10^{-21}\ {\rm s}\), associated to the inverse of the electon’s rest mass energy. In order to describe processes induced by an infrared laser, one has to propagate the solutions over several cycles with durations in the femtosecond range, corresponding to propagation times \(\tau \geq 10^7 \times t_{0}\).

  6. 6.

    See note 5.

  7. 7.

    See note 5.

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Acknowledgments

Part of our work mentioned here is the result of fruitful collaborations with C.H. Keitel, P.L. Knight and C. Szymanowski. Also, we would like to acknowledge very helpful discussions with R. Grobe and C.J. Joachain.

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    Alfred Maquet

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Maquet, A., Taïeb, R., Véniard, V. (2008). Relativistic Laser–Atom Physics. In: Brabec, T. (eds) Strong Field Laser Physics. Springer Series in Optical Sciences, vol 134. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34755-4_20

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