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Basics of Laser-Plasma Interaction: A Selection of Topics

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Laser-Driven Sources of High Energy Particles and Radiation

Part of the book series: Springer Proceedings in Physics ((SPPHY,volume 231))

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Abstract

A short, tutorial introduction to some basic concepts of laser-plasma interactions at ultra-high intensities is given. The selected topics include (a) elements of the relativistic dynamics of an electron in electromagnetic fields, including the ponderomotive force and classical radiation friction; (b) the “relativistic” nonlinear optical transparency and self-focusing; (c) the moving mirror concept and its application to light sail acceleration and high harmonic generation, with a note on related instabilities; (d) some specific phenomena related to the absorption of energy, kinetic momentum and angular momentum from the laser light.

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Notes

  1. 1.

    In fact, in classical electrodynamics the ratio between the amount of energy and of momentum modulus in a wavepacket is c, thus this relation must be conserved if the wavepacket is totally absorbed by a medium. In a quantum picture, one may think of the absorption of a given number of photons, each having energy \(\mathcal{E}=\hbar \omega \) and momentum modulus \(\mathcal{E}/c\).

  2. 2.

    We stress that we define the PF as a cycle-averaged approximation of the Lorentz force. However, in the literature sometimes the term “oscillating PF” has been used [8] to refer to oscillating nonlinear terms in the Lorentz force (such as the \(\mathbf{v}\times \mathbf{B}\) term which has a \(2\omega \) component). This definition is inconsistent with the whole idea of separating the “slow” and “fast” scales in the motion.

  3. 3.

    Notice that in (2.9)–(2.10) \(\partial _\mathbf{r}(\dot{\mathbf{r}}_af_a)=\dot{\mathbf{r}}_a\partial _\mathbf{r}f_a\) and \(\partial _\mathbf{p}(\dot{\mathbf{p}}_af_a)=\dot{\mathbf{p}}_a\partial _\mathbf{p}f_a\), as it is usual to write for the Vlasov equation. However, if the LL force is added to the Lorentz force, \(\partial _\mathbf{p}(\dot{\mathbf{p}}_af_a)\ne \dot{\mathbf{p}}_a\partial _\mathbf{p}f_a\). This is not an issue for the standard PIC algorithms which provide a solution of the general kinetic equation (2.9).

  4. 4.

    In principle also low-frequency, coherent radiation which is resolved in the simulation contributes to the RF effect, thus there is some double counting of such radiation in the force since it is included both in the Lorentz and in the LL terms. However, for highly relativistic electrons with \(\gamma \gg 1\) the contribution of the low-frequency part is negligible with respect to that of the dominant frequencies in the radiation spectrum.

  5. 5.

    This estimate for the electron energy is commonly referred to as “ponderomotive scaling”; probably, the name originates from the questionable definition of nonlinear oscillating forces as “ponderomotive” (Sect. 2.2.2).

  6. 6.

    This is analogous to the absence of high-frequency longitudinal motion in a CP wave, Sect. 2.2.1.

  7. 7.

    Note that \(\rho _m\ell \) in (2.30) is formally equivalent to \(\sigma \) in (2.29), but here in (2.30) \(\rho _m\ell \) refers to the total mass of the mirror, i.e. including the ions.

  8. 8.

    https://en.wikipedia.org/wiki/Faraday_wave.

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Authors and Affiliations

  1. National Institute of Optics, National Research Council (CNR/INO), Adriano Gozzini laboratory, via Giuseppe Moruzzi 1, 56124, Pisa, Italy

    Andrea Macchi

  2. Enrico Fermi Department of Physics, University of Pisa, largo Bruno Pontecorvo 3, 56127, Pisa, Italy

    Andrea Macchi

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  1. Andrea Macchi
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Correspondence to Andrea Macchi .

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Editors and Affiliations

  1. Area della Ricerca del CNR, Istituto Nazionale di Ottica, Pisa, Italy

    Leonida Antonio Gizzi

  2. Forschungszentrum Helmholtz-Gemeinschaft, Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

    Ralph Assmann

  3. Area della Ricerca del CNR, Istituto Nazionale di Ottica, Pisa, Italy

    Petra Koester

  4. Area della Ricerca del CNR, Istituto Nazionale di Ottica, Pisa, Italy

    Antonio Giulietti

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Macchi, A. (2019). Basics of Laser-Plasma Interaction: A Selection of Topics. In: Gizzi, L., Assmann, R., Koester, P., Giulietti, A. (eds) Laser-Driven Sources of High Energy Particles and Radiation. Springer Proceedings in Physics, vol 231. Springer, Cham. https://doi.org/10.1007/978-3-030-25850-4_2

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