The Radiation Reaction Effect on Electrons at

The Radiation Reaction Effect on Electrons at SuperHigh Laser Intensities with Application to Ion Acceleration N. M. Naumova, I. V. Sokolov, V. T. Tikhonchuk, T. Schlegel, J. A. Nees et al. Citation: AIP Conf. Proc. 1153, 130 (2009); doi: 10.1063/1.3204517 View online: http://dx.doi.org/10.1063/1.3204517 View Table of Contents: http://proceedings.aip.org/dbt/dbt.jsp?KEY=APCPCS&Volume=1153&Issue=1 Published by the AIP Publishing LLC.

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The Radiation Reaction Effect on Electrons at Super-High Laser Intensities with Application to Ion Acceleration N. M. Naumova*, I. V. Sokolovt, V. T. Tikhonchuk**, T. Schlegel^ J. A. Nees§, C. Labaune^, V. P. Yanovsky§ and G. A. Mourou'l *Lahoratoire d'Optique Appliques, UMR 7639 ENSTA, Ecole Polytechnique, CNRS, 91761 Palaiseau, France '' Space Physics Research Laboratory, University of Michigan, Ann Arbor, MI 48109, USA **Centre Lasers Intenses et Applications, Universite Bordeaux 1 - CEA - CNRS, 33405 Talence Cedex, France ^ GSI Helmholtzzentrum fiir Schwerionenforschung GmbH, Planckstasse 1, D-64291 Darmstadt, Germany § Center for Ultrafast Optical Science and FOCUS Center, University of Michigan, Ann Arbor, MI 48109, USA '^Laboratoirepour rUtilisation des Lasers Intenses, CNRS - CEA - Ecole Polytechnique Universite Pierre et Marie Curie, 91128 Palaiseau Cedex, France ''Institut de la Lumiere Extreme, UMS 3205 ENSTA, Ecole Polytechnique, CNRS, 91761 Palaiseau, France Abstract. At super-high laser intensities the radiation back reaction on electrons becomes so significant that its influence on laser-plasma interaction cannot be neglected while simulating these processes with particle-in-cell (PIC) codes. We discuss a way of taking the radiation effect on electrons into account and extracting spatial and frequency distributions of the generated highfrequency radiation. We also examine ponderomotive acceleration of ions in the double layer created by strong laser pulses and we compare an analytical description with PIC simulations as well. We discuss: (1) non-stationary features found in simulations, (2) electron cooling effect due to radiation losses, and (3) the limits of the analytical model. Keywords: radiation force, laser-plasma interaction, ion acceleration PACS: 52.38.-r, 41.60.-m, 52.50.Jm, 52.75.Di

INTRODUCTION Recent achievements in laser intensity [1] and future perspective of the development of the Extreme Light Infrastructure (ELI) project [2] have boosted a research in the specific area of laser-plasma interactions at intensities of 10^^ -^ 10^^ W/cm^. In this regime, the radiation pressure allows one to use laser pulse energy to accelerate a plasma with a high conversion efficiency. This plasma acceleration process involves the following important elements. First, electrons entrained forward by the laser light create a very strong charge separation field capable of driving ions up to relativistic velocities. Second, ions drag electrons back via the same field and accelerate them towards the laser pulse, which provides electron cooling and facilitates the propagation of the laser pulse through the plasma. CPl 153, Laser-Driven Relativistic Plasmas Applied to Science, Industry and Medicine - The 2 International Symposium edited by P. R. Bolton, S. V. Bulanov, and H. Daido ® 2009 American Institute of Pliysics 978-0-7354-0690-2/09/$25.00

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In this paper we discuss a method that can be used to account for radiation back reaction on electrons simulated with particle-in-cell (PIC) codes and to collect the consequent high-frequency radiation, with the angular and energy spectra of the emitted photons. We revisit an analytical model of a laser piston, representing a double layer driven by laser pressure. We discuss the model predictions with respect to ion acceleration in bulk targets. We validate the model against PIC simulations. We also analyze the non-stationary effects observed in the simulation results, such as: the oscillation of the piston velocity about some average value and electron cooling due to radiation losses. The paper reviews our recent work and related publications.

A WAY TO SIMULATE THE RADIATION BACK REACTION ON THE ELECTRON MOTION An accelerated electron in a strong laser field emits high-frequency radiation [3, 4, 5, 6, 7, 8, 9]. Its back-reaction on the electron motion can not be neglected, if in the frame where the electron is initially at rest, the energy radiated during the interaction time is comparable with mc^: ^ fE^cdt > m(?, where or = -^^^ and E is the electric field. A covariant condition for the radiation reaction to be significant is as follows: ^ —>-^ An

•

(1)

£ — cpx

Here £ and p are the particle energy and momentum and the wave is assumed to propagate along the x-axis. A high value of the integral in (1) may be reached, in principle, at the cost of higher intensity only, '~ 10^^ W/cm^. In the course of the ELI project (see [2]) a laser is expected to reach focusable pulse energy of 1.5 kJ at A « 0.8//m, so the radiation effects will be dominant: the condition (1) is fulfilled. Another opportunity may be realized while a strong laser pulse interacts with energetic electrons, which move oppositely to the direction of the pulse propagation. In this case £ — pxC ^2£^ mcP, facilitating the fulfillment of Ineq.(l). In such a geometry, powerful X-ray radiation is generated in the direction of the electron momentum [10]. The condition (1) determines the regime, in which the energy is efficiently converted to X-ray or 7 bursts. In the course of a strong laser pulse interaction with a dense plasma the counterpropagating electrons may be accelerated in a backward direction by a charge separtion field (see, e.g., [11]). At moderate intensities the generation of short pulses of higherfrequency radiation [12, 13, 14] may be interpreted as the reflection of the laser pulse from these bunches as from a reflecting medium: the frequency of the reflected wave is upshifted: w(r) '-^ lfm)^o, if the reflector moves with a Lorentz-factor of 7(,„) > 1 towards an incident wave. Here we consider such high laser intensities that emission frequencies are upshifted to the hard X-ray and 7 range. At realistic electron density, N^ < lO^^'cm^^, the averaged field approximation of the reflecting medium is not applicable for emitted photon energies exceeding 10 keV, because N^{c/bj(^))'^ !)• The agreement is less satisfactory for lower density plasma. Nevertheless for sufficiently high intensity it is still possible to keep an efficient laser piston regime of ion acceleration, as is shown in Ref. [44] for OQ = 100 and a deuterium plasma of density 20nc, but the ion energy spectrum becomes broader. We observe a qualitative change for the density lOn-c while keeping the same laser amplitude. Some electrons penetrate the charge separation layer, are accelerated there and lose a great portion of their energy during interaction with the light. The disbalance between electrons and ions allows for the laser pulse to penetrate the plasma in front of the piston, as a result electrons and ions are accelerated in a much wider region directly by the laser pulse and arising charge separation fields. Only a portion of ions is able to be ahead of the laser pulse. For this simulation the energy conversion for ions is 34% instead of expected 51 %, and about 6% for electrons. The reduced laser piston performance is also supported by increasing radiation losses that consume 43% of laser energy.

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In simulations for linear polarized light, the penetration of electrons into the charge separation layer becomes even easier due to the oscillation of the ponderomotive force. As a result the performance of the laser piston acceleration changes similarly to a lower density plasma case. CONCLUSION Future experiments at super-high intensities demanding more sophisticated tools need to be designed with very high precision. The role of PIC simulations taking into account the radiation back reaction on electrons and related X-ray and 7-ray production is significant in this research. The challenges at super-high intensities are related to high efficiency processes of the production of high energy photons and ions. The developed laser piston model verified with PIC simulations has allowed the proposal of a competitive scheme for the fast ignition by using super-intense laser pulses [42]. This reserach is in the main stream of the ELI and HiPER projects. ACKNOWLEDGMENTS This work was coordinated by the Institute Lasers et Plasmas and by the Institut de la Lumiere Extreme. It is supported by the ANR under the contract No. BLAN07-3186728, by the Region Aquitaine under project No. 34293, and by the HiPER and ELI European projects. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

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