Supersonic micro-jets and their application to few cycle laser driven electron acceleration [Elektronische Ressource] / vorgelegt von Karl Schmid

Karl Schmid

Sujets

• Physik

Informations

• Publié par: ludwig-maximilians-universitat_munchen
• Publié le: 01 janvier 2009
• Nombre de lectures: 16
• Langue: English
• Poids de l'ouvrage: 16 Mo

Extrait

SupersonicMicro-Jets
AndTheirApplicationto
Few-CycleLaser-Driven
ElectronAcceleration
KarlSchmid
München2009SupersonicMicro-Jets
AndTheirApplicationto
Few-CycleLaser-Driven
ElectronAcceleration
KarlSchmid
Dissertation
an der Fakultät für Physik
der Ludwig–Maximilians–Universität
München
vorgelegt von
Karl Schmid
aus Wien
München, den 30. Juni 2009Erstgutachter: Prof. Dr. Ferenc Krausz
Zweitgutachter: Prof. Dr. Toshiki Tajima
Tag der mündlichen Prüfung: 23. Juli 2009Contents
Contents v
List of Figures ix
List of Tables xiii
Abstract xv
Introduction 1
I Supersonic Micro-Jets 13
1 Theory of Compressible Fluid Flow 15
1.1 One Dimensional Theory of Compressible Fluid Flow . . . . . . . . . . . 15
1.1.1 Equation of State and the First Principal Law . . . . . . . . . . . 15
1.1.2 Changes of State . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.1.3 Compressible Gas Flow in 1D - Perturbations and Shocks . . . . 18
1.1.4 Continuous Flows in Nozzles . . . . . . . . . . . . . . . . . . . 24
1.1.5 Cluster Formation in Supersonic Gas Jets . . . . . . . . . . . . . 32
2 Numeric Flow Simulation 35
2.1 Flow Models for Computational Fluid Dynamics . . . . . . . . . . . . . 35
2.1.1 Parameterization of de Laval Nozzles . . . . . . . . . . . . . . . 36
2.1.2 Size Eects and Eects of low Pressure . . . . . . . . . . . . . . 37
2.1.3 Boundary Layers . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
2.2.1 Supersonic Flows and the de Laval Nozzle . . . . . . . . . . . . 41
2.2.2 Optimal Nozzle Shape . . . . . . . . . . . . . . . . . . . . . . . 44vi CONTENTS
2.2.3 Influence of the Nozzle Geometry on the Flow Parameters . . . . 45
2.2.4 Eects of Nozzle Size and Varying Backing Pressure . . . . . . . 56
2.2.5 Eects of Non-Negligible Background Pressure . . . . . . . . . . 65
2.2.6 Gas Targets with Additional Degrees of Freedom . . . . . . . . . 65
3 Experimental Characterization of Gas Jets 69
3.1 Setup for Characterizing Gas Jets . . . . . . . . . . . . . . 69
3.2 Numerical Evaluation of Experimental Data . . . . . . . . . . . . . . . . 71
3.3 Experimental Results on Gas Jets . . . . . . . . . . . . . . . . . . . . . . 72
3.4 Shock Fronts in Supersonic Gas Jets . . . . . . . . . . . . . . . . . . . . 75
II Few-Cycle Laser-Driven Electron Acceleration 79
4 Electron Acceleration by Few-Cycle Laser Pulses: Theory and Simulation 81
4.1 Introduction to Relativistic Laser-Plasma Physics . . . . . . . . . . . . . 81
4.1.1 Non-Relativistic Cold Collisionless Plasmas . . . . . . . . . . . . 81
4.1.2 Relativistic Threshold Intensity . . . . . . . . . . . . . . . . . . 85
4.1.3 Relativistic Single Electron in EM Field . . . . . . . . . . . . . . 85
4.1.4 Relativistic Cold Collisionless Plasma Equations . . . . . . . . . 88
4.1.5 Electromagnetic Waves – Self-Focusing . . . . . . . . . . . . . . 90
4.1.6 Electrostatic Waves - Wave breaking . . . . . . . . . . . . . . . . 92
4.1.7 Laser Wakefield Acceleration and Scaling Laws . . . . . . . . . . 95
4.2 Results of Particle-In-Cell Simulations . . . . . . . . . . . . . . . . . . . 100
5 Experimental Setup 105
5.1 The Light Source: Light Wave Synthesizer 10 . . . . . . . . . . . . . . . 105
5.2 Setup of the Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 110
6 Experimental Results on Electron Acceleration 115
6.1 Performance and Stability of the Electron Accelerator . . . . . . . . . . . 115
6.2 Multiple Accelerated Electron Bunches . . . . . . . . . . . . . . . . . . 125
6.3 Discussion of the Experimental Results . . . . . . . . . . . . . . . . . . 127
7 Next Steps for Optimizing the Accelerator 131
Conclusion 139Table of Contents vii
A Numeric setup of the fluid flow simulations 143
A.0.1 The Optimal Mesh . . . . . . . . . . . . . . . . . . . . . . . . . 144
A.0.2 Comparison of Numeric Flow Models . . . . . . . . . . . . . . . 148
B Nozzle designs 153
Bibliography 161
Publications by the Author 179
Curriculum Vitae 181
Acknowledgements 185viii Table of ContentsList of Figures
1 Electron acceleration in the bubble regime . . . . . . . . . . . . . . . . . 5
2 Threshold of the Bubble Regime . . . . . . . . . . . . . . . . . . . . . . 7
3 Sketch of a typical de Laval nozzle . . . . . . . . . . . . . . . . . . . . . 10
1.1 Rankine-Hugoniot curve for the perfect gas . . . . . . . . . . . . . . . . 21
1.2 Shock in a perfect gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3 Normalized flow density within a de Laval nozzle . . . . . . . . . . . . . 27
1.4 Flow parameters inside a de Laval nozzle - 1D model . . . . . . . . . . . 28
1.5 Flow state at the exit of a de Laval . . . . . . . . . . . . . . . . . 31
1.6 Clustering in Ar and He jets . . . . . . . . . . . . . . . . . . . . . . . . 33
2.1 Parameterization of de Laval Nozzles . . . . . . . . . . . . . . . . . . . 37
2.2 Knudsen number for dierent pressures . . . . . . . . . . . . . . . . . . 37
2.3 Line-outs normal to flow direction inside a de Laval nozzle . . . . . . . . 39
2.4 On-axis line-outs inside a de Laval nozzle . . . . . . . . . . . . . . . . . 41
2.5 Divergence of gas jets produced by subsonic and supersonic nozzles . . . 42
2.6 Density profiles of gas jets produced by subsonic and supersonic nozzles . 43
2.8 Geometry study: free jet propagation . . . . . . . . . . . . . . . . . . . 49
2.9 study: displacement thickness . . . . . . . . . . . . . . . . . . 50
2.10 Geometry study: gradient width . . . . . . . . . . . . . . . . . . . . . . 53
2.11 study: density gradient width. Linear dependence on L d =d 54C E
2.12 Geometry study: flat top quality . . . . . . . . . . . . . . . . . . . . . . 54
2.13 study: density peak-to-peak fluctuations . . . . . . . . . . . . 55
2.14 Pressure and size study: Knudsen numbers of pressure and size series . . 56
2.15 and size study: gas jet divergence . . . . . . . . . . . . . . . . . 57
2.16 Pressure and size study: flow displacement . . . . . . . . . . . . . . . . . 58
2.17 and size study: thickness at nozzle exit . . . . . . 59
2.18 Pressure and size study: density gradient width . . . . . . . . . . . . . . 60
2.19 and size study: at the nozzle exit . . . . . . . . 60x LIST OF FIGURES
2.20 Pressure and size study: density and Mach number at nozzle exit . . . . . 61
2.21 and size study: exit density vs. backing pressure for dierent
nozzle sizes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
2.22 Pressure and size study: density peak-to-peak fluctuations . . . . . . . . . 63
2.23 Influence of background pressure . . . . . . . . . . . . . . . . . . . . . . 65
2.24 Double nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.25 Shock fronts produced by knife-edge in the supersonic gas jet. . . . . . . 67
3.1 Mach-Zehnder interferometer . . . . . . . . . . . . . . . . . . . . . . . . 70
3.2 Abel inversion sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.3 Gas jet characterization for 150m nozzle . . . . . . . . . . . . . . . . . 73
3.4 Measured on axis density and stability . . . . . . . . . . . . . . . . . . . 75
3.5 Supersonic shock front measurement . . . . . . . . . . . . . . . . . . . . 77
4.1 Artist’s conception of a plasma bubble . . . . . . . . . . . . . . . . . . . 96
4.2 PIC simulation: physical state of plasma . . . . . . . . . . . . . . . . . . 101
4.3 PIC Simulation: Electron Spectrum . . . . . . . . . . . . . . . . . . . . 103
5.1 Layout of LWS-10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5.2 Measured pulse duration and focal spot of LWS-10 . . . . . . . . . . . . 108
5.3 Peak-to-background contrast of LWS-10 . . . . . . . . . . . . . . . . . . 109
5.4 Photograph of the Experimental Chamber . . . . . . . . . . . . . . . . . 110
5.5 Experimental layout of electron accelerator . . . . . . . . . . . . . . . . 111
5.6 Simulated magnetic field map of electron spectrometer . . . . . . . . . . 113
6.1 Low background energy spectra . . . . . . . . . . . . . . . . . . . . . . 117
6.2 Typical electron spectrum (Lanex) . . . . . . . . . . . . . . . . . . . . . 119
6.3 Electron energy fluctuation . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.4 Density and spot size variation . . . . . . . . . . . . . . . . . . . . . . . 122
6.5 Gas jet position scan . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
6.6 Shot series of 27 monoenergetic electron spectra . . . . . . . . . . . . . . 125
6.7 Reproducible electron spectra with 150m gas jet . . . . . . . . . . . . . 126
6.8 Electron spectrum showing multiple bunches . . . . . . . . . . . . . . . 126
6.9 High energy electron spectra showing multiple bunches . . . . . . . . . . 127
7.1 Wake field at density transition . . . . . . . . . . . . . . . . . . . . . . . 133
7.2 Ratio between plasma wave period and mean free path . . . . . . . . . . 136
A.1 Shock fronts in a nozzle with smaller radii . . . . . . . . . . . . . . . . . 144
A.2 Mesh quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146