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Heinrich Hora

Plasmas at HighTemperature and Density

Applications and Implicationsof Laser-Plasma Interaction

Springer-VerlagBerlin Heidelberg NewYorkLondon Paris TokyoHong Kong BarcelonaBudapest

Atsthor

Prof. Dr. Dr. Heinrich HoraCERN, CH-1211 Geneva 23S~itzerland

This book is based on the author's "Physics of Laser Driven Plasmas".

ISBN 3-540-54312-0 Springer-Verlag Berlin Heidelberg New YorkISBN 0-387-54312-0 Springer-Verlag New York Berlin Heidelberg

This work is subject to copyright. All rights are reserved, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, re-use ofillustrations, recitation, broadcasting, reproduction on microfilms or in other ways, andstorage in data banks. Duplication of this publication or parts thereof is only permittedunder the provisions of the German Copyright Law of September 9, 1965, in its currentversion, and a copyright fee must always be paid. Violations fall under the prosecutionact of the German Copyright Law.

© Springer-Verlag Berlin Heidelberg 1991Printed in Germany

Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr.2153/3140-543210 - Printed on acid-free paper

Dedicated to our Grandchildren

Simon McCluskey

Barbara Hora

Alexander McCluskey

Benedikt Hora

Preface

"New physics" is an appealing new keyword, not yet devalued by the ravages of inflation.But what has this to do with such an ugly field as plasma physics, steeped in classical physics,mostly outworn, with all its unsolved and ambiguous technological problems and its messyand open ended numerical studies?

"New physics" is concerned with quarks, Higgs particles, grand unified theory, super­strings, gravitational waves, and the profound basics of cosmology and black holes. It isthe field of astonishing quantum effects, demonstrated by the von Klitzing effect and high­temperature superconductors. But what can plasma physicists offer, after so many years ofexpensive and frustrating research to solve the problem of fusion energy?

One may suggest that the fascinating research of chaos with applications to plasma, or theachievements of statistical mechanics applied to plasmas, has something to offer and shouldbe the subject of attention. However, this is not the aim of this book.

Complementing the traditional aim of physics, which is to interpret the phenomena ofnature by generalizing laws such that exact predictions about new properties and effects canbe drawn, this book demonstrates how new physics has been derived over the last 30 yearsfrom the state of matter which exists at high temperatures (plasma). The advent of the laser,with its very high energy densities and its concentration to extremely small volumes and tovery short time periods, opened up a whole new regime for the interaction of materials andhigh-density plasmas, which enforced the appearance of the "rather new physics".

Here are a few examples:• Who would have expected that optical waves in vacuum have a longitudinal compo­

nent? Thomas Young discovered in 1801 the pure transversality of optical radiation. This wasnot understandable at that time, when it was known that mechanical waves never exist with­out longitudinal components. Maxwell's equation then only revealed solutions of the purelytransverse plane waves in electromagnetism. Against all this traditional knowledge, the recentfindings about the dynamics of electrons driven by laser beams by nonlinear forces led to the~xact derivation of longitudinal optical wave components.

• The same nonlinear force interaction, in view of momentum transfer in experiments,led to the clarification of the angular momentum ofoptical beams and brought about the firstsubstantiation of the photon spin by a macroscopic property.

• The conditions of very high laser intensities led to nonlinear and relativistic gener­alization of the optical response (dielectrics and absorption) with a prediction of relativisticself-focusing to understand how GeV ions are produced by laser irradiation of solid targets.

• The quantum generalization of Coulomb collisions in plasmas at high temperaturesexplains the anomalous resistivity, in agreement with observations where links are givenbetween the simply derived Coulomb collision frequency and quantum electrodynamics, in­cluding stimulated emission.

VIII

• Against the view of the fundamentalists (that plasmas do not have internal electricfields) laser-plasma interaction enforced the derivation of very strong electric fields and dou­ble layers inside plasmas and unexpected properties as a new resonance to explain strangeexperimental results, including widespread second-hannonic emission of the plasma coronaat the site of laser irradiation of solid targets.

• Many attempts to explain very complicated interaction phenomena were erroneouslydirected towards stimulated scattering. After it was confirmed experimentally that this scat­tering does not dominate the energy transfer, it was possible to understand the complicatedphenomena (stuttering interaction) and how these can be overcome experimentally by randomphase plates (RPP) or induced spatial incoherence (lSI).

All these developments merged into the derivation of a new principle of nonlinear physics:that very strange and unexpected phenomena can be predicted beyond well-known linearphysics, and that it is necessary to increase the accuracy of linear physics more and more.Furthermore, exact treatments which avoid neglections are more important in nonlinear physicsthan in linear physics. This opens a fundamentally new era of predictable physics (as distin­guished from chaos) and of formerly unthinkable new phenomena for technological applica­tions.

The immediate applications of laser-plasma interaction physics are well known: the pri­mary goal is to solve the energy problem. The increase in temperature of the atmosphereduring the last 50 years by nearly one degree has been confirmed without any doubt fromtemperature measurements taken at locations remote from human settlements. Furthermore,there is a strong correlation between the recorded rise in temperature and the increase in thecontent of carbon dioxide in the atmosphere, which is linked to the excessive burning of fossilfuels in our modem, industrialised world.

Even if some energy conservation were achieved by the major industrial countries, theever increasing need for energy by the 75% of the world's population located in developingcountries - especially China and India - will result in further increases in overall- energyproduction.

Solar energy and hydroelectric power may provide part of the answer, but experience hasshown that these alternatives, while 'clean', are not likely to produce the quantities of energyrequired at a low enough cost.

Nuclear fission is now considered a possible alternative source for energy production, butthe problems of radioactive waste disposal and the ever present threat of nuclear accidentsrestrict its advantages. If nuclear sources are the solution, then the answer probably rests inthe alternative nuclear fusion.

Energy production from fusion reactions has been the subject of extensive and often frus­trating research over many years, aimed primarily at controlling the overall reaction with mag­netic confinement or inertial confinement. Fusion energy produced by magnetic confinementmay be excluded because it is too expensive, based on the results of Pfirsch and Schmitter,who demonstrated that even with the most ideal assumptions, the cost of producing energythis way will be up to ten times higher than energy produced by the established light waterreactors. Our attention then turns to inertial confinement fusion, especially laser fusion. Evenat this early stage of conceptual development, it appears that by using laser pulses in the MJenergy range, energy can be produced by inertial confinement fusion at costs similar to thoseofoperating a light water reactor. With intense technological development, it is conceivable

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that after the first laser fusion reactors becomt\ available subsequent improvements in physicsand engineering knowledge will result in energy production costing three to five times lessthan that produced by light water reactors.

The application of laser fusion is in need of considerable applied research and shouldunderline the importance of the field of physics to which this book is directed. However, theimportance to physics should not merely be considered in isolation.

The problem of continued human existence is the subject of increasing debate with con­siderable concern being expressed over the emission of carbon dioxide from the burning offossil fuels. The potential for ecological catastrophe as a result of the 'greenhouse effect' isbecoming increasingly clear and the world is in need of developing a method for the large­scale production of 'clean' low-cost energy. It might be possible in the near future to establisha world order without aggression, without suppression of ethnic groups, minorities or indi­viduals, without police states and political prisoners, with justice and freedom and withouteconomic crises. The solution of these problems is difficult but there is hope for a solutionsoon.

The subsequent problem of avoiding pollution of our planet, however, will be, by ordersof magnitude, more difficult than avoiding war, suppression and other problems of humanity.The task before us is to develop a safe, inexhaustible and 'clean' source of energy for thefuture of our civilisation and our planet. This book therefore addresses not only an importantapplication of science, but a key problem concerning the future of mankind.

Other less urgent but nevertheless important applications of laser-plasma interaction relateto new schemes for the acceleration of charged particles to TeV energies as alternatives to theclassical accelerator schemes or advanced combinations of these schemes. The applications tomaterial processing, welding, cutting, surface hardening and microelectronics are of very wideindustrial scale. These applications, but even much more the basic physics being discoverednow, and more dramatically in the future, explain the need for a presentation of this newphysics. However, since the appearance of the author's book Physics oflAser Driven Plasmas(John Wtley, New York, 1981) ten years ago, only one further physics monograph (by W.Kruer) has appeared despite the above-mentioned exciting developments. One reason for thismay be that important phenomena were not clarified before. This situation, however, mayhave changed just within the last few years.

As indicated in my book ten years ago, only the clarified basics of this field were presented.Now that the book is out of print, a reproduction of the established results, together with theaddition of the enormous developments that have taken place during the past 10 years, formthe content of this book. There is little to change from the earlier treatment: almost allfindings remain valid. This is the reason why the unchanged text of Physics ofLaser DrivenPlasmas was used wherever possible with the only changes being corrections of misprints. Theadditional new aspects are then explained in summaries, expansions and updated commentsfor each section. This is the fastest and most efficient way to present this exciting field ofnew physics to newcomers, as well as to stimulate experts.

Thanks are due to my previous publisher (John Wiley and Sons) and to Springer-Verlagfor the arrangement of this book in this special form. The preparation of this book wasmainly completed at the University of New South Wales, Kensington, Sydney, Australia, andrepresents many years of work in this field. The continuous support by the University isgratefully acknowledged. I am further indebted to my numerous co-workers, who in recent

x

years have helped to develop so many fundamental new insights and discoveries that onlythe references to each of these points in the original literature can provide an explanation.Immeasurable thanks for the preparation of this book are due to my secretary, Ms DorisBock, and the editorial assistance in some parts by my son-in-law, Mr. Brian Minikin, isgratefully acknowledged. Further I am grateful for the support by the Gordon Godfrey Fundsfor Theoretical Physics at the University of New South Wales, to the Australian ResearchCouncil for continuous support as well as to overseas collaboratioq, especially with Prof.G.H. Miley at the University of Illinois at Urbana, and with Profs. W.C. Stwalley and G.Knorr at the University of Iowa. I thank numerous colleagues, especially Profs. A. Scharmannand W. Scheid at the University of GieSen, Prof. P. Mulser of the Technological Universityat Darmstadt, Dr. G. Winstel and Dr. E. Krimmel of the Siemens Research Centre Munich­Perlach, all in Germany, Prof. H.P. Weber and Drs. T. Donaldson and J. Balmer at theUniversity of Berne, Switzerland, and the Rockford Technology Corp. in Vancouver, Canada,for their cooperation and support.

Sydney, January 1991 H. Hora

Contents

1 Aim and Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Basic Aspects1.2 Limitations1.3 Lasers1.4 Review of Phenomena and Results1.5 Very High Power Lasers1.6 Further Phenomena and Results

2 Elements of the Microscopic Plasma Theory . . . . . . . . . . . . . . . . . . . . . . . . . . 272.1 Plasma Frequency and Debye Length2.2 Plasmons2.3 Polarization Shift of H-like Lines in Plasmas2.4 Cyclotron Frequency2.5 Collisions2.6 Anomalous Resistivity, Quantum Collisions

and Tokamak Experiments

3 Kinetic Theory 523.1 Distribution Functions3.2 Loss of Information3.3 Derivation of Macroscopic Equations3.4 Landau Damping3.5 Concluding Remarks on Microscopic Theory

4 Hydrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.1 Euler's Equation of Motion4.2 Bernoulli's Stationary Solution4.3 Equation of Continuity4.4 Compressibility4.5 Acoustic Waves4.6 Equation of Energy

5 Self-Similarity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765.1 Hydrodynamic Derivation5.2 Laser Irradiation with Varying Pellet Radius5.3 Numerical Example5.4 Applications to Foils5.5 Introductory Remarks to the Following Three Chapters

XII

6 Plasma Dynamics and Lorentz Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.1 The Two-Fluid Equation of Motion6.2 The Diffusion Equation (Ohm's Law)6.3 Electrodynamic Equations6.4 Refractive Index of Plasma and Its Relation to Absorption6.5 Nonlinear and Relativistic Absorption6.6 Absorption Constant and QED Theory

7 Waves in Inhomogeneous Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.1 WKB Approximation for Perpendicular Incidence7.2 Oblique Incidence and WKB Solution7.3 The Rayleigh Profile7.4 The Airy Profiles

8 Equation of Motion 1328.1 Equivalence to Maxwellian Stress Tensor8.2 Obliquely Incident Plane Waves8.3 Nonponderomotive Collisional Term of the Nonlinear Force8.4 Additional Third-Order Tenns for Perpendicular Incidence8.5 The General Non-Transient Nonlinear Force8.6 The Transient Nonlinear Force8.7 Single Particle Model of Nonlinear Force

and High Internal Electric Fields Inside of Plasmas8.8 Genuine Two Fluid Plasma Model

with Full Description of Internal Electric Fields8.9 Double Layers and Surface Tension of Plasmas

9 Momentum and Instability by the Nonlinear Forces 1779.1 Range of Predominance of the Nonlinear Force9.2 Momentum Transfer to the Plasma Corona and Compression9.3 Energy Transfer by Integration of the Nonlinear Force9.4 Photon Momentum in Plasma (Abraham-Minkowski Problem)9.5 Parametric Instabilities

10 Numerical and Experimental Examples - Solitons10.1 Thennokinetic Forces10.2 Static Case with Nonlinear Forces10.3 Approximative Dynamic Cases10.4 Experimental Examples10.5 Acceleration of Thick Blocks10.6 Solitons

204

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10.7 Numerical Results from the Genuine Two Fluid Modeland Electric Double Layers

10.8 Smoothing of Laser-Plasma Interaction

11 Striated Motion and Resonance Absorption . . . . . . . . . . . . . . . . . . . . . . . . . . . 25511.1 Striated Motion11.2 Resonance Absorption11.3 A New Resonance at Supercritical Density

12 Laser Beams in Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28612.1 Nonlinear Force (ponderomotive) Self-Focusing12.2 Relativistic Self-Focusing12.3 Tenuous Plasmas, Exact Beams, and Free Electron Lasers12.4 Spontaneous Magnetic Fields - Alfven Waves12.5 Conclusions for Medium Laser Intensities12.6 Conclusions for Very High Laser Intensities12.7 Exact Gaussian Beam, Cluster Injection Laser Amplifier,

and Laser Acceleration of Particles in Vacuum

13 Laser Compression of Plasma for Nuclear Fusion 32913.1 Nuclear Fusion Reactions13.2 Adiabatic Volume Compression and Volume Ignition13.3 Solution of Laser Fusion by Spark Ignition

and Indirect Drive13.4 Improvement by Volume Ignition and Direct Drive13.5 Estimations of Future Clean Fuel Fusion13.6 Responsible Politics

a) Need for Energy and Need for Safe Environmentb) Difficulty of Political Decisionsc) Decision About Magnetic Confinement Fusiond) What Can Inertial Confinement Fusion (ICF) Offer?

Appendix A: The Effective Mass .. .. .. .. .. .. . .. .. .. . . . . . . . . . . . . . . . . . . . . 383Appendix B: The Maxwell-Boltzmann Distribution . . . . . . . . . . . . . . . 387Appendix C: Derivation of the General Two-Fluid Equatioos 391Notes Added in Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399List of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 401References (by Numbers) 406References (Alphabetical) 419Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432