Thesis presented to obtain the grade of DOCTOR FROM ECOLE POLYTECHNIQUE Speciality : Plasma Physics by Yannick Glinec Propagation of an ultra-intense laser pulse in an under-dense plasma : production of quasi-monoenergetic electron beams and development of applications. defended on September, 22nd 2006 in front of the following committee : Mr. Patrick Mora Chairman Mr.VictorMalka Thesissupervisor Mr. Philippe Martin Referee Mr. Vladimir Tikhonchuk Referee Mme. Sylvie Jacquemot Mr. Henri Videau 3 This document is a translation of the french version of the PhD thesis published at Ecole Polytechnique. This is an interactive document which should evolve in time. De- pending on the improvements done to the document, the relevant figure in the version number will be modified : first digit increases for major modification, second digit for minor corrections (typesetting errors, layout, ...). List of changes made to the document Date Version Listofmodifications 2006-10-30 Beginningoftranslation 2006 1.0 Initial release, translation from the french version Contents Acknowledgments 9 Introduction 11 1 Theory and evolution of electron acceleration using laser-plasma interaction 15 1.1 Propagationofanelectromagneticwave . .... 15 1.1.1 Maxwellequations . .. .. .. .. .. .. .. 15 1.1.2 Laserparameters .......................... 16 1.1.3 Gaussianbeams........................... 16 1.2 Plasmawaves ................................ 18 1.2.1 Plasmaparameters . .. .. .. .. .. .. .. 18 1.2.2 Fluidequations ........................... 19 1.2.3 Unidimensionalmodel of the acceleration of electrons inaplasma wave ................................ 19 1.3 Non-lineareffects.............................. 23 1.3.1 Ponderomotiveforce . 23 1.3.2 Laserself-focusing . 24 1.3.3 Wavebreaking ........................... 25 1.4 Accelerationmechanisms. 26 1.4.1 Linearregime............................ 27 1.4.2 Non-linearregime . .. .. .. .. .. .. .. 28 1.5 Futureofthelaser-basedacceleration . ..... 32 1.5.1 Extension of the bubble regime to higher energies, scalinglaws . 32 1.5.2 Injectionandlinearacceleration . .. 37 1.5.3 Alternativetechniques . 38 2 Quasi monoenergetic spectrum and optimization 41 2.1 Descriptionoftheexperiment . 41 2.1.1 Characteristics of the laser in “salle jaune” at LOA . ...... 41 2.1.2 Experimentalsetup . 42 2.2 Quasimonoenergeticspectra . 44 2.2.1 Improvementofthequalityoftheelectronbeam . ... 44 2.2.2 Experimentalspectra . 45 2.2.3 Comparisonto3DPICsimulations . 46 2.2.4 Absolutecalibrationof thescintillatingscreen and discussion about thecharge.............................. 48 5 6 CONTENTS 2.3 “quasi monoenergetic” regime in a narrow range of parameters ...... 51 2.3.1 Influenceoftheelectrondensity . 51 2.3.2 Influenceofthepulseduration . 52 2.3.3 Influenceoflaserenergy . 54 2.3.4 Influenceoftheapertureofthefocusingoptics . .... 55 2.4 Stability................................... 56 2.4.1 Beampointingstability. 57 2.4.2 Spectralstability . .. .. .. .. .. .. .. 58 3 Structures of the electron beam and propagation of the laser 59 3.1 Oscillationsinthespectrum. .. 59 3.1.1 Experimentalresults . 59 3.1.2 Propagationofanasymmetriclaserpulse . .. 62 3.2 Transitionradiation . .. .. .. .. .. .. .. .. 64 3.2.1 AngularandspatialdistributionoftheOTR . ... 65 3.2.2 Experimentalsetup . 69 3.2.3 Imagingdiagnostic . 69 3.2.4 Spectralanalysis . .. .. .. .. .. .. .. 72 3.2.5 OscillationsintheOTRspectrum . 74 3.2.6 Measurementsintheterahertzrange . 76 3.3 Laserpulseproperties. 79 3.3.1 Originoftemporalshortening . 79 3.3.2 Laserspectrumbroadening. 80 3.3.3 Temporalshorteningofthelaserpulse . .. 80 3.3.4 Transmittedlaserintensity . 85 3.3.5 Thomsonscattering. 86 3.3.6 Interferometry ........................... 88 4 Applications of laser-based electron beams 91 4.1 Applicationtoradiography . 91 4.1.1 Highresolutionradiography . 92 4.1.2 Retrievaloftheinternalprofileoftheobject . ..... 93 4.1.3 Estimation of the γ-raysourcesize. 95 4.2 Applicationtoradiotherapy. .. 97 4.2.1 Simulationparameters . 98 4.2.2 Directirradiation . 99 4.2.3 Convergingelectronbeam . 103 4.2.4 Discussion ............................. 104 4.3 Applicationtofemtolysis . 106 4.4 Application to the generation of X-ray radiation (betatron mechanism) . 109 Conclusion and perspectives 113 A Betatron oscillation model 117 A.1 Analyticalequations .. .. .. .. .. .. .. .. 117 A.2 Optimisationofparameters . 119 CONTENTS 7 B Description of the electron spectrometer 121 B.1 Experimentalsetup ............................. 121 B.2 Analytictrajectory ............................. 122 B.2.1 Forarectangularmagnet . 122 B.2.2 Foracircularmagnet. 123 B.2.3 Adjustment to the magnetic field measured experimentally . 123 B.2.4 Dispersionpower. 124 B.3 Developmentofnewspectrometers. 127 C Determination of the amplitude of the electron spectrum 129 C.1 Simulation of the energy deposition in the scintillator ........... 129 C.2 CalibrationofthescintillatoratElyse . ...... 131 C.3 Absolutecalibration. 134 C.3.1 Conversioninphotonsinthescintillator . 134 C.3.2 Collectionbyoptics . 134 C.3.3 Yieldofthecamera. 134 C.4 Useofanintegratingcurrenttransformer. ...... 135 Acknowledgments I’ve spend three exciting years at Laboratoire d’Optique Appliqu´ee in Palaiseau. This laboratory belongs to three different administrations : ENSTA, Ecole´ Polytechnique and CNRS (UMR 7639). I would like to thank first my PhD supervisor, Victor Malka, vi- sionary and realistic leader, hyperactive but still always available for his students. I re- member having chosen this PhD subject after an interview at the laboratory in 2003. At that time, when most student wanted to start working in the field of cold atoms, i.e. the study of Bose-Einstein condensates, plasma physics was suffering of a lack of clarity. The list of instabilities and the restricted applicability of analytical equations to perturbative assumptions where responsible for my limited understanding of this physics. On the op- posite, the understanding of the physics of condensates obtained at very low temperature was provocative and attractive. Nevertheless, comments from Victor convinced me : the use of an ultra-short laser pulse limited the instability growth and allowed a better energy transfer to kinetic energy of accelerated electrons. The world record of the electron energy was thus obtained in this research group with laser-plasma interaction during the pioneer work carried out during Sven Fritzler’s PhD thesis. At the time, Jerome Faure also became a permanent researcher in this group. During these three years, we have worked together in many experiments during which Jerome taught me everything with a lot of care and patience. I’ve personally really enjoyed the relevance of his thoughts and his temper. Thanks to him, I couldn’t have wished a better formation than the one I was given. The group “Particle Sources by Laser”, in which I’ve been working, contains two research themes : electron acceleration and proton acceleration by laser. This second half of the group, working on the generation of a proton source, is composed of Alain Guemnie Tafo, Mauro Manclossi, Frederike Ewald and Joao Jorge Santos. Recently, Agustin Lifschitz has joined the team for a theoretical and simulation support. I would like to thank the whole team for their kind attention to me. I would like also to point at the impressive work of the laser team working in the laser room (“Salle Jaune”) : Jean-Philippe Rousseau, Fr´ed´eric Burgy, Brigitte Mercier and more recently Amar Tafzi who has just joined this team. I would like to underline their exceptional availability and their patience in front of an aggressive team of never- satisfied-experimentalists. I also remember the support from Dani`ele Hulin during my initial application in the laboratory. And I would like also to thank Olivier Albert for his gentleness and his peda- gogy during my training course in the laboratory as a future engineer because, following this training course, I’ve decided to continue with a PhD thesis. I would like to thank the administration of the laboratory, the director of which is currently G´erard Mourou, the work of the secretaries, the technical staff (the workshop, the maintenance, the multimedia 9 10 CONTENTS staff ...) and more generally all the teams working in the laboratory. But outside the daily work in the lab, the unconditional support of my relatives from Britanny, from Paris and my family are essential support to fulfill these three years of studies. The biggest thank goes for Lina who remained incredibly calm and stoic even when I was bad-tempered. Finally, I also remember all the collaborators I’ve been working with : The team from CEA DAM Ile-de-Franceˆ : Erik Lefebvre, Loic Le Dain, St´ephane • Darbon, B´en´edicte Guilpart. The team from Imperial College working at the Rutherford Appleton Laboratory : I • quote in particular Stuart Mangles and Alec Thomas from this team, who I had the opportunity to meet several times. Alexander Pukhov from the Virtual Laser Plasma Laboratory (VLPL) in Germany. • The laser and plasma group (GoLP) in Portugal : Luis O. Silva and Jorge Vieira. • The German group from DKFZ : Hanitra Szymanowski, Thomas Fuchs and Uwe • Oelfke. The laboratory Solides Irradi´es at Ecole´ Polytechnique : St´ephane Esnouf and Guil- • laume Petite. Guilhem Gallot from laboratory Optique et Biosciences at Ecole´ Polytechnique. • The team at Elyse´ in Orsay : Mehran Mostafavi, Vincent de Waele, Hugues Monard • and J.P. Larbre. Thank you for you help, your advice and all the good time spent together.