Shigeaki Uchida- The Effects of Resonantly Enhanced Fields in Picosecond Laser Produced Plasmas

8/3/2019 Shigeaki Uchida- The Effects of Resonantly Enhanced Fields in Picosecond Laser Produced Plasmas

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THE EFFECTS OF RESONANTLY ENHANCED FIELDS INPICOSECOND LASER PRODUCED PLASMAS

by

Shigeaki Uchida

Submitted in Partial Fulfillmentof the

Requirements for the D e w

DOCTOR OFPHILOSOPHY

Supervised by Professor David D. MeyerhoferDepartment of Mechanical EngineeringCollege of Engineering and Applied Science

University of RochesterRochester, New York


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CURRICULUM VITAEShigeaki Uchida was born on April 10, 1959 in Osaka, Japan. He attended Osaka

University in 1979 where he received a Bachelor of Science degree in ElectricalEngineering and a Master of Science in Electromagnetic Energy Engineering in 1983and 1985, respectively. From 1986 to 1992 he attended the University of Rochester asa graduate student in the department of mechanical engineering where he was therecipient of an exchange student fellowship from Japanese Ministry of Education and aCollege Fellowship. After obtaining a Master of Science in May 1989, he wassupported by a Research Fellowship of the Laboratory for Laser Energetics (LLE) andperformed his thesis research under the supervision of David D. Meyerhofer.


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AcknowledgementsI am deeply grateful to my thesis advisor, Professor David Meyerhofer for his

insightful suggestions and guidance regarding to the experiments and the interpretationof the data. His continuous encouragement throughout the course of the research isvery much appreciated.

I would like to thank Dr. Martin Richardson who initiated the ultra short laserplasma experiments at the LLE. He provided many useful suggestions andencouragement. I would also llke to thank Dr. Leonard Goldrnan and Professor AlbertSimon who I owe very much in my early period of graduate study in U of R andresearch at the LLE.

This project would not have been successful without the support andencouragement from my fellow (former) graduate students. My special thanks go toDr. Yung-Ho Chuang who improved the laser system to desirable and stable condition,Dr. Steven Augst who coded an excellent data acquisition program and Hong Chen fornumerous discussions and help on image data analysis. I appreciate the careful readingof this work by Steve Gutstein. The help and friendship of Justin Peatross, ChrisMoore, Brian Buerke and Mark Adarns are also greatly appreciated.

I would like to thank Dr. Jaque Delettrez for helpful discussion and simulations,Drs. Tom Boehly, Robert Kremens, Oscar Lopez-Raffo, Samuel Letzring, and SteveBatha for their supports regarding the plasma diagnostics and target chamber apparatus,and Dr. Hyo-gun Kim and the staff of Target Fabrication Laboratory at the LLE forproviding high quality targets. I also acknowledge the technical support of RaymondBahr, Gregory Pien, Charles Hestdalen, Dick Fellows, and G. Raffaele-Addamo andother staff at LLE.

Finally I would like to thank my thesis committee chair-person, Professor JosephEberly, for his various comments and suggestion. I would also like to thank the other


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members of my thesis committee, Professor Adrian Melissinos and Professor ColinMckinsme.

This work was supported by the U.S.Department of Energy Office of InertialConfinement Fusion under agreement No. DE-FC03-85DP40200 and by the LaserFusion Feasibility Project at the Laboratory for Laser Energetics, which is sponsoredby the New York StateEnergy Research and Development Authority and the Universityof Rochester.


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AbstractPicosecond laser-plasma interactions have been studied experimentally using a 1-

ps, 1-pm laser interacting with solid targets. The experiments have been conductedwith a detailed knowledge of the laser pulse shape. High intensity contrast laser pulsesensure that no preformed plasma exists before the arrival of the main picosecond pulsein an intensity range where nonlinear processes start to dominate the laser absorptionnamely from 1014 to 1016 ~ / c m 2 .

When no preformed plasma exists, the resonantly oscillating field at the criticalsurface can be significantly enhanced and can accelerate plasma particles tosuperthermal energies. This field enhancement was studied in terms of the amplitude ofp-polarized (laser electric field vector component parallel to the plane of incidence)component through an extensive characterization of the ion blowoff including the ioncurrent, angular dismbution, ion charge state as a function of velocity and velocitydismbution. Two primary findings from this characterization are: 1) the ion blowoffcharacteristics depend entirely on the p-polarized component of laser and not on thelaser energy, and 2) the nonthermal electrons driving the plasma expansion are highlymonoenergetic. These findings are supported by several other plasma diagnosticswhich include laser energy absorption, continuum and Ka x-ray measurements.

It is suggested from the experimental observation that the electrons are acceleratedby the ponderomotive force in the resonantly oscillating field. The intensityenhancement at the critical surface was calculated based on the ponderomotive pictureusing experimentally measured electron kinetic energy. The experimental values arecompared with theoretical values that include plasma-wave dispersion effects on theresonantly oscillating field strength. The ponderomotive acceleration mechanism iscompared to wavebreaking as an explanation for the nonthermal electron acceleration.


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Table of contents.....................................................................able of contents vi...........................................................................ist of figures vu

................................................................................reface 1.....................................................................EFERENCES - 3.............................................hort and long pulse laser-produced plasmas 6.....................................................................-1 Introduction - 6....................................................-2 Overview of previous work 7

1-3 The novel aspects of the present work in ultra-short laser...........................................................nteraction studies 12......................................................................EFERENCES 16.....................................................................heoretical background -21.....................................................................1-1 Introduction 21

.......................1-2 EM wave propagation in a short scale length plasma 22............................1-3 Elecmc field enhancement at the critical surface 30

11-4 The ponderomotive potential and wavebreaking for energetic........................................................lectron acceleration 39

..............................................1-5 Isothermal expansion of Plasma 43......................................................................EFERENCES 46...................................................................................xperiments 50

..................................................................11-1 Laser system -50111-2 Target and irradiation system................................................ 52III-3 Pulse characteristics........................................................... 54............................................................11-4 Plasma diagnostics 60REFERENCES ......................................................................8.........................................................................................esults 82

....................................................V-1 Absorption measurements 82


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. .IV-2 X-ray emission............................................................... 85............................................................V-3 Ion measurements 8 8...................................................................V-4 emission 103

..................................................V-5Super high energy electrons 105REFERENCES ................................................................... 106

Analysis and discussion...................................................................... 108.....................................................................- 1 Lntroduction 108

V -2 Plasma density scale length....................................................109............-3 Calculation of the intensity enhancement at the critical surface 111

...............-4 Resonance field amplitude and p-polarized light absorption 113..............................-5 Monoenergetic feature of accelerated electrons 117V-6 Ponderomotive acceleration and wavebreaking for producing.......................................................he energetic particles 121V-7 Thermal component of high contrast s-polarized light

....................................................................nteraction 123V-8 The plasma depletion in the critical density and a density cavity.......... 124

......................................................................EFERENCES 128..........................................................................oncluding remarks 130

VI-1 Summary ...................................................................... 30...........................................................I-2 Future investigation 13 2

........................................................................EFERENCE 132


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Fig. 1-1Fig. 1-2Fig.2- 1

Fig.2-2

Fig.2-3Fig.2-4Fig.2-5Fig.3- 1Fig.3-2Fig.3-3Fig. 3-4Fig.3-5Fig. 3-6Fig. 3-7Fig. 3-8Fig. 3-9Fig 3- 10

List of figures .............................he y-z plane defines the laser plane of incidence 14..........................onderomotive acceleration of high energy particles 16

An EM wave propagation obliquely incident in an inhomogeneousplasma and two important locations. the turning point and the.....................................................................ritical surface - 2 4Oblique incidence (angle of incidence 80)of an EM wave on aplanar plasma density profile (density merit parailel to the z-.....................................xis) Vacuum-plasma boundary is at z=0 26

..........................aser electric field profile around the critical surface 30Laser electric field profile obliquely incident on an expanding.........lasma showing anAiry swelling and a resonance enhancement - 3 2...................vertaking of electron fluid oscillation in resonance fie1. 34Schematic of the glass laser system with CPAC used for the.........................................................................xperiments 51........................................arget alignment and irradiation system 54..............................aser pulse shape measured by an autocorrelator 56Image of focused laser spot taken inside of the target chamber..............58Target irradiation geometry at the best focus of the laser.....................59Horizontal view of the integrating sphere used in the absorption.....................................................................easurements - 6 2Back wall correction of the integrating sphere.................................64Schematic of charge collector showing magnetic filter. bias meshand honeycomb structure for reducing electron noises........................ 66

.................................................lecmstatic ion charge analyzer 67Calculated signal reduction on ion current trace as a function ofbias voltage for ion velocity 1x 108 d s e c .................................... 8


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Fig. 3-11

Fig. 3- 12

Fig 3-13

Fig. 3- 14

Fig 3-15

Fig 3-16Fig. 4- 1

Fig. 4-2Fig. 4-3

Fig. 4-4Fig. 4-5

Fig. 4-6

Fig. 4-7

Fig. 4-8

The magnetic electron analyzer detects discrete electron energydistribution. ........................................................................0The location of three detectors of the magnetic electron analyzerand the corresponding electron energies. ...................................... .71X-ray transmission of the filters used for continuummeasurements. .................................................................... -72One channel of k-edge filtered scintillator photomultiplier (PMT)x-ray detector is shown. .......................................................... 74Expected x-ray spectrum calculated for each filter combination atT, = 10keV. ...................................................................... 75Spectral response of the K, detector........................................... 77Incident angle dependence of laser energy absorption measured bythe integrating sphere..............................................................5X-ray signal ratios as a function of hot electron tempe am. . . ............. 87Ion current traces from low and high contrast pulse interactions

....................................................etected at the target normal. .91..........................-polarized intensity Ip dependence of ion current. .93

Comparison of two ion current traces obtained from different totallaser intensity but a similar p-polarized intensity (Ip = 1015WIcm2)..............................................................................4Ion velocity distribution calculated from the ion current trace andion charge measurement. ........................................................ .95Electron temperature as a function of p-polarized intensity, Ipdeduced from the velocity distribution using an isothermalexpansion model..................................................................96

...................................on velocity distribution of ion charge state. 98


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Fig. 4-9

Fig. 4-10

Fig. 4-11

Fig. 4-12

Fig. 4- 13Fig. 5-1

Fig. 5-2

Fig. 5-3

Fig. 5-4

Fig. 5-5

Fig. 5-6

Fig. 5-7

Fig. 5-8

Comparison of the experimental data and model calculation on.....................................................easured ion charge states. . 9 9

Angular distribution of ion blowoff shows interaction pulse.............................................................onaast dependence.. 101

Electron kinetic energy accelerated by ponderomotive potential in. . .......................................................esonantly oscrllating fields 102X-ray signal in all solid angles measured by an Al-filtered Ka

............................................................................etector.. 104...........-polarized intensity dependence of 250 keV electron production 106Plasma density scale length, L=(VnJn,)-l, calculated from the

..............................................otal number of fast ion component 111Comparison of intensity enhancement factors estimated from

.........xperiments and calculated using plasma wave convection effects. 113Thermal component of ion current of p-polarization is extracted bysubtracting the fast ion component from the ion current trace

................................................................hown in Fig. 4-3. 115Comparison of p-polarized intensity and the pure p-polarizedabsorption (p-polarization minus s-polarization)..........................116Shifted (the solid line) and unshifted Maxwellian (the brokenline).................................................................................. 117Comparison of measured Ka ignal and calculated signal using

............................................onoenergetic electron distribution. 118Cold plasma wavebreaking region and warm plasma-wavecoupling region determined by Eq. 2-23....................................... 123Relativistic electron energy accelerated in the cavity enhanced fieldas a function of the cavity enhancement factor.. ...............................127


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PrefaceWhen intense laser pulses (exceeding the breakdown threshold of solids) irradiate

solid materials, the absorption of the laser energy creates a system of high temperatureionized matter. This system is called a plasma because the particles in the systemrespond to external or induced fields collectively depending on the temperature anddensity. This collective behavior of plasma is the source of a wide range of laser-plasma interaction phenomena such as the excitation of plasma waves and theirinstabilities, energy transport and hydrodynamic motion. These phenomena have beeninvestigated primarily in the context of laser fusion feasibility research since the late1960's.' Therefore, the interaction time scale at the focus of attention has been from afew tens of picoseconds to a few nanoseconds that is determined by the hydrodynamicsof plasmas.

However, the recent development of ultra-short pulse (< 1 ps) laser systems 2-56using techniques such as a chirped pulse amplification and compression (CPAC) has

opened the opportunities of studying laser-matter (plasma) interactions with time scalesof order of or less than one picosecond. Much interest in studying short-pulse laser-plasma interactions has been driven by the possibility of producing ultra-short x-raypulses. 7-1 These pulses can be used to study the structure and electronic states ofmatter with extremely high temporal resolution. These x-rays can also be used as acalibration source for temporal measurements.7' '* l2 The interaction of a short laserpulse with a plasma itself provides unique physical conditions such as high temperaturesolid density material, l3 steep density gradient plasmas, 14' l 5 and recombination x-ray lasers l 6 from a rapidly cooling plasma. The systematic development of theapplications and study of these kinds of plasmas are based on understanding themechanism of the ultra-short laser-plasma interaction.


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Recent investigations have revealed that the absorption of a short-pulse laser isconsistent with the FresneVDrude models for moderate laser intensities (up to mid 1014Wlcm*). They have also inferred the scale length, L, 2 (Vn$&)-l, of plasmas usingthe dependence of absorption on laser incident angle and polarization. On the otherhand, the occurrence of non-linear processes at higher intensities, which has beenindicated by several authors,17' l8 remains to be explored. The present work dealswith this intensity regime. In particular, it has been found that resonantly enhancedlaser electric fields play a significant role in the absorption processes at the criticalsurface where the electron plasma frequency equals the incident laser frequency. It isshown that the field enhancement is determined by plasma-wave dispersion effects 19'20 by comparing the experimental results and theoretical calculations. The concomitanthigh energy electron acceleration by the enhanced ponderomotive force is consistentwith the experimental observations presented in this thesis.

This investigation is based on a series of experimental observations of plasmascreated by l-pm, I-ps laser pulses incident on solid A1 planar targets. Since it isdesirable to incorporate as many plasma diagnostics as possible to investigate theinteraction processes in detail, extensive plasma characterizations have been carried outon laser absorption and the emission of ions, electrons and x-rays. The importantresults are the measurement of the laser intensity enhancement at the critical surface andthe characterization of concomitant high energy electron and ion production. Theexperimental results are interpreted by a theory that couples electromagnetic wavepropagation in a short scale length plasma with resonantly oscillating plasma waves atthe critical density. The resulting ponderomotive potential is used to explain thegeneration of high energy electrons (16 keV) and ions (S100 keV). The picture ofponderomotive acceleration is examined against the conventional wavebreakingmechanism for high energy particle production and found to be consistent with thepresent experimental conditions.


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In studying ultra-short laser interaction, it is very important to control the level ofprepulse or satellite emission. Several improvements have been made for the CPACsystem in the Laboratory for Laser Energetics to suppress the prepulse to an intensitybelow 10-5 of the main pulse.21 Having control over the intensity contrast allowscomparison of interaction characteristics with and without the existence of preformedplasmas. In the present work, the temporal laser pulse shape is measured with adynamic range of the five orders of magnitude ensuring that a high contrast 1-ps pulseinteracts with solid material. In fact significant changes in interaction characteristicsfrom the low contrast to the high contrast pulse interaction have been observed andparticular emphasis is put on the characterization of the high contrast interactions.

The thesis consists of six chapters. An overview of previous work on plasmainteractions with short-pulse lasers as well as long pulse lasers is given in chapter I todefine and clarify the boundary of the present work in the context of existing work.Chapter I1 contains a review of theoretical work that is vital to this work such aselectromagnetic wave propagation in plasma, laser electric field enhancement at theresonance point (critical surface) and its limiting mechanisms, and an isothermal plasmaexpansion model on which the ion measurements are based. Experimental proceduresand diagnostics are described in chapter I11 followed by the experimental results inchapter IV. Chapter V covers further discussion of the results and comparison withtheoretical models. Finally, chapter VI summarizes the work

REFERENCES

W. Kruer, The Physics of Laser Plasma Interactions (Addison-Wesley,Redwood City, 1987).

R. L. Fork, C. V. Shank and R. T. Yen, "Amplification of 70-fs optical pulsesto gigawatt powers," Appl. Phys. Lett. 41,223 (1982).


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C. Rolland and P. B. Corkurn, "Generation of 130-fsec midinfrared pulses." J.Opt. Soc. Am. B 3, 1625 (1986).

J. H. Glownia, J. Misewich and P. P. Sorokin, "160-fsec XeCl excimeramplifier system," J. Opt. Soc. Am . B 4, 1061 (1987).

N. Sarukura, Y. Ishida, H. Nakano and Y. Yamamoto, "cw passive modelocking of a Ti:sapphire laser," Appl. Phys. Lett. 56, 814 (1990).

D. Strickland and G. Mourou, "Compression of amplified chirped opticalpulses," Optics Cornrn. 56 ,2 19 (1985).

D. Kiihlke, U. Herpers and D. von der Linde, "Soft x-ray emission fromsubpicosecond laser-produced plasmas," Appl. Phys. L ett. 50, 1785 (1987).

0. L. Landen, E. M. Campbell and M. D. Perry, "X-ray characterization ofpicosecond laser plasmas," Optics Comm. 6 3, 25 3 (1987).

D. G. Steams, 0.L. Landen, E. M. Cam pbell and J. H. Scofield, "Generationof ultrashort x-ray pulses," Phys. Rev. A 37, 1684 (1988).

l o J. A. Cobble, G. A. Kyrala, A. A. Hauer, A. J. Taylor, C. C. Gomer, N. D.Delamater and G. T. Schappert, "Kilovolt x-ray spectroscopy of asubpicosecond -laser-excited source," Phys. Rev. A 39 ,4 54 (1989).

J. D. K metec, C. L. Gordon, I. J. J. Macklin, B. E. Lemoff. G. S. Brown andS. E. Hanis, "MeV x-ray generation with a femtosecond laser," Phys. Rev.Lett. 68, 1527 (1992).

l 2 M. M. Mum ane, H. C. Kapteyn and R. W. Falcone, "X-ray streak camera with2 ps response," Appl. Phys. Lett. 56, 1948 (1990).

l 3 H. M. Milchberg, R. R. Freem an, S. C. Davey and R. M. More, "Resistivityof a simple metal from room temp erature to lo 6 K," Phys. Rev. Len. 61 ,2364 (1988).


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l 4 I. C. Kieffer, et al., "Short-pulse laser absorption in very steep plasma densitygradients," Phys. Rev. Lett. 62, 760 (1989).

l 5 0. L. Landen, D. G. Steams and E. M. Campbell, "Measurement of theexpansion of picosecond laser-produced plasmas using resonance absorptionprofile spectroscopy," Phys. Rev. Lett. 63, 1475 (1989).

l 6 G . J. Pert and S. A. Ramsden, "Population inversion in plasmas produced bypicosecond laser pulses," Optics Cornrn. 1 1,2 70 (197 4).

l7 R. Fedosejevs, R. Ottrnann, R. Sigel, G. Kiihnle, S. Szatmiki and F. P.Schiifer, "Absorption of subpicosecond ultraviolet laser pulses in high-densityplasma," Appl. Phys. B 50, 79 (1990).

l8 M. Chaker, I. C. Kieffer, I. P. Matte. H. PCpin, P. Audebert, P. Maine, D.Strickland,P. Bado and G. Mourou, "Interaction of a 1 psec laser pulse withsolid matter," Phys. Fluids B 3, 167 (1991).

l9 V. L. Ginrburg, "Section 20. A special characteristic of an electromagneticwave field propagating in an inhomogeneous isotropic plasma. The interactionof electrom agne tic and plasma waves," in Propagation of ElecrromagneticWaves in P lasma, edited by W .L. Sadowski and D. M. Gallik. (Gordon andBreach, 1961) p. 377-403.

20 D. D. Meyerhofer, "The interaction of high intensity lasers with short scale-length plasmas," in the Abstracts of 21st Annual Anomalous AbsorptionConference, (Banff, Alberta, Canada, 1991).

21 Y.-H. Chuang, D. D. Meyerhofer, S. Augst, H. Chen, J. Peatross and S.Uchida, "Suppression of the pedestal in a chirped-pulse-amplification aser,"J. Opt. Soc. Am. B 8, 1226 (1991).


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CHAPTER IShort and long pulse laser-produced plasmas

1-1 IntroductionBecause of the transient nature of laser produced plasmas, the basic parameters such astemperature and density have significant spatial variations within an expanding plasma.This variation is usually represented by scale lengths such as the density- andtemperature-scale length of the plasma. For example the electron density scale length isdefined Ln = (Vn,/n,)-1. The temperature scale length is usually longer than that ofelectron density due to the long electron heat conduction range. Of the two scalelengths, the density scale length Ln plays an important role in the interaction of lightwith plasmas since, for example, it controls the rate of light absorption or dispersion ofunstable modes of plasma instabilities. Earlier work has dealt mostly with plasmaswith L,, longer than the interacting laser wavelength, h ~ .or the short-pulse plasmas,on the other hand, the scale length is expected to be shorter than hL. This is the newfeature of the short-pulse laser-plasma interaction.

Although the interaction mechanisms in the short-pulse plasmas are expected to bedifferent from those of long-pulse plasmas, much about short-pulse plasmas can belearned from the comparison of these two kinds of plasmas. There have been a numberof studies done for short-pulse laser-plasma interactions covering a wide range of laserintensity (1011- 1016 WIcm2) and pulse width (160 fs - 1 ps) as well as laser wavelength (0.25 pm - 1 pm). The interaction characteristics of these studies varydepending on the experimental conditions. It is helpful to know what has been learnedabout short-pulse interactions to clarify the present work boundary. Therefore, thepresent chapter is devoted to a review of recent short-pulse plasma investigations aswell as previous work on long-pulse plasmas.


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1-2 Overview of previous workI-2-a Short-pulse laser interaction studies

Previous experimental work of short-pulse laser-plasma interaction can be dividedinto four categories: 1)absorption (reflectivity) measurements, 2) plasma expansioncharacterizations, 3) interaction of solid state matter with intense laser light and 4) shortx-ray pulse generation and its characterization. They are further divided into twogroups in terms of laser pulse width used for the experiments: 1 ps and less than 0.5PS.

Absorption measurements have been done at 1 ps l3 and 250 fs lo ' 'with 1-pmand 0.25-pm pulses, respectively, incident on metal targets such as Al, Cu and Au.With 250 fs pulses and intensity < 1014 ~ / c m 2 ,he measured absorption has beenfound to be consistent with the FresneVDrude model or linear metal optics.10 Themodel is valid in the limit of no hydrodynamic motion (expansion) of the plasma thatcauses a significant penetration of the incident laser field into the overdense or soliddensity plasma. The absorption is attributed to electron-ion collisions driven by laserelectric fields. A very steep (


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depending on the laser pulse width. These numbers will be compared with the resultsof the present work.

Unique experiments have been done on high temperature solid matter interactionswith short-pulse lasers.2 The resistivity of A1 up to lo6 'K has been obtained bymeasuring the temperature rise of the laser heated surface. The resistivity saturates attemperatures above Te = 40 eV corresponding to a minimum electron mean free path.The thermal response of metals has been investigated in terms of electron thermalconductivity and electron-lattice energy exchange. 9 l5 The relaxation time for whichthermal conductivity dominates the relaxation process and the optical damage thresholdof metals is determined. Since the response of metals to ultra-short pulses determinesthe initial formation of plasma on targets, the results of these investigations are offundamental importance for short-pulse laser-plasma interaction studies.

There have been a number of studies of x-ray conversion efficiency both forcontinuum and line emission.17 Kiihlke's explanation for the low x-ray conversionefficiency in higher density plasmas is the weaker coupling efficiency. However, thisdoesn't seem to be the case because high absorption has been observed in a highconmt interaction. The simulations performed by Chakerer al. l3 suggest that a highplasma temperature (higher than 1keV) lasts for a shorter period without a prepulsebecause of the expansion cooling of higher density plasmas. A recent experiment 18with 1~-1018Wlcm2 of 120 fs pulses irradiating heavy metals has observed beyond 1MeV of x-ray photons with energy conversion efficiencies up to 0.3%. The radiation isattributed to the bremsstrahlung emission of very energetic electrons traveling through asolid target resulting in unique short-pulse duration and small source size. However,the mechanism producing the energetic electrons has not been clarified.

From a theoretical viewpoint, four mechanisms are considered to be important tothe absorption of short-pulse laser light by matter: 1) collisional absorption 2, 8, 10,13, 2) "vacuum heating," 19-213) skin effects 22' 23, and 4jresonance absorption.


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Any pararnemc instabilities,24 which occur in long-scale-length plasma interactions.can not be supported by a short-pulse generated plasma because of the small spatialextent of the plasma. Most of the existing experimental studies have been performedwith intensities up to 10'5 ~ / c m 2nd are compatible with the collisional (classical)models. In the range of intensity above 1016 w/cm2 and for small scale lengths,L&I 0.1, the vacuum heating starts dominating the absorption of p-polarized light. Thismechanism was fust described by Brunel l9 and further investigated by Gibbon er al .for an extensive range of plasma This process is most efficient when theelectron quiver amplitude is larger than the plasma scale length so that the electronsacquire the oscillating energy in the vacuum electric field. If the interacting pulse issufficiently short so that the plasma can be considered as homogeneous within a skindepth in terms of density and temperature, the skin effect might play an important rolein absorption.22' 23 However, in a light material such as A1 with a picosecond pulseduration, Rozmus er al. 22 have showed that the occurrence of a skin effect isprevented by hydrodynamic expansion. When the plasma scale length is longer thanthe electron quiver amplitude, the resonantly oscillating elecmc field at the criticaldensity is expected to be important. Much of the theoretical work on resonanceabsorption can be found in the context of long-scale-length plasma interaction studiesthat are reviewed in the next section since the mechanism is most relevant to the presentinvestigation.

I-2-b Long pulse laser interaction studiesLaser interactions with plasmas have been the primary focus of laser fusion

feasibility research because these processes influence the energy coupling between thelaser and fusion targets. These processes include inverse bremsstrahlung, resonanceabsorption and parametric instabilities among which the latter two have been studied inconjunction with high energy particle_production. Inverse bremsstrahlung is significant


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when the electron temperature is not very high. This process entirely depends onelectron-ion collisions and exhibits no polarization dependence nor high energy particleproduction. Parametric instabilities require relatively long-scale-length plasmas to beefficient and are expected not to be supported by ultra-short laser produced plasmas.Resonance absorption, on the other hand, depends on the density scale length and thepolarization of the interacting pulse so it is most relevant to the present study.

As the laser power increases, the oscillatory electron energy increases and thedensity gradient around the critical surface steepens, which leads to a short distancebetween the turning point and the critical surface. These two effects together lead to astronger resonance field and more efficient resonance absorption. Therefore, resonanceabsorption becomes a crucial coupling mechanism at higher laser intensity ( 1 ~ h ~ > 1 0p m 2 ~ 1 c m 2 here IL and h are the intensity and wavelength of laser). Since theelectron oscillatory energy is proportional to laser wavelength, this is especially the casefor relatively long wavelength lasers (h = 1- 10pm) for which most extensive studieshave been done.

Numerous experimental and theoretical studies have been done on C02-laser-plasma interactions (h = 10 pm) with a primary focus being paid to the connectionbetween resonance absorption and high energy electron generation. Since the electronoscillatory energy is proportional to ILh2, the long wavelength C02 laser has been apreferable system for resonance absorption studies. The CO.2 laser systems had beenone of the candidates for an ICF driver because of their high conversion efficiency fromelecmc to light energy. However, the high yield hot electrons from C@ laser plasmascause preheat of the fusion target (fuel) making target compression to a desirabledensity difficult. Therefore, the clarification of the characteristics and mechanisms ofhot electron production were the primary focus of investigation to assess the feasibilityof CO.2 laser ICF. Since the hot electron production depends on the laser intensity, aglass laser (1 pm) system might also be problematical especially when the laser


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intensity exceeds 1016 ~ / c m ~ . ~ ~herefore, hot elecwns generated from glass-laserproduced plasmas have also been studied extensively.

Ih2 scaling of hot electron temperature has been an important signature for theidentification of nonlinear processes occurring in the laser-plasma interaction. Forinstance, theories based on a flux limitation with stochastically heated electrons at thecritical surface 26' 27 predict TH- (ILh2)m,whereas resonance absorption is shownto depend on either (1~h2)lE8' 29 or ( 1 ~ h 2 ) l n . ~ ~xperimentally obtained TH by x-ray measurements is compatible with resonance absorption showing an (ILh2)1/3dependence.30-33 Similar results of x-ray measurements also have been found withglass laser systems (h= 1 pm) where the dependence varies: (ILh2)0.25-0.41.5, 34,35These results are further supported by fractional absorption measurements,36bremsstrahlung emission dependence on the polarization and incident angle,37,38 andthe studies of the energy and angular anisotropy of the fast ions.35, 39, 40 Thesestudies show the incident angle dependence of absorption on p-polarized light, which isparticular for resonance absorption, as well as the enhancement of absorption, x-raybrernsstrahlung, and fast ion emission in the case of p-polarized light interaction.

Other characteristics of long-pulse-laser produced plasmas that are relevant to thepresent investigation include (1) density steepening at the critical region, and (2) self-generated azimuthal coronal magnetic fields due to the currents induced by hotelectrons.

In those plasmas, a scale length less than the laser wavelength, < 1, occursnear the critical surface even for relatively long pulse duration (typically subnanosecondto a few nanoseconds) due to the ponderomotive forces in the critical region.41,42However, this steep density step is accompanied by an extended expanding underdenseplasma 43 giving raise to parametric instabilities such as SRS (Stimulated RamanScattering), which needs to be distinguished from the processes occurring at the criticalsurface. A longer pulse duration leads to a hydrodynamic modificition of density


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profile 42 and makes simple interpretation of phenomena difficult. Ultra-short-pulseexperiments, on the other hand, can make this point clearer since the critical surfacewith a steep density gradient is directly adjacent to vacuum and the number of processesis reduced. For instance, parametric instabilities whose thresholds are determined bythe balance between the incident pumping and plasma wave convection cannot grow inthe steep density gradient. Furthermore, the short distance between the laser turningpoint (reflecting point) and the critical surface results in the large enhancement ofresonantly oscillating laser electric fields because the decay of p-polarized field isminimized. Thus the resonantly oscillating fields and resulting phenomena are expectedto dominate the short-pulse interactions.

1-3 The novel aspects of the present work in ultra-short laserinteraction studies

This thesis describes an experimental characterization of high intensity contrast 1-pslaser produced plasma at 1-pm wave length. Although there has been much work donefor ultra-short laser-plasma interactions, very few reports have compared high contrastwith low contrast interactions. Here high contrast interactions are those where thecontrast between the main picosecond pulse and a prepulse is high enough that nopreformed plasma exists before the arrival of the main pulse. In the case of the lowcontrast interaction condition the main picosecond pulse interacts with a preformedplasma. The dominant interaction mechanism among various processes depends on thesize and scale length of plasma in which the laser light propagates. The present study

has found significant changes in interaction phenomena between the low contrast andhigh contrast interactions. Although the primary focus of the investigation in this studyis the high contrast picosecond laser-plasma interactions, a comparison between the twocontrast cases makes the high contrast interaction characteristics clearer. Therefore,


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experimental observations from low contrast pulse interactions are also presented asnecessary to contrast the characteristics of high contrast pulse interactions.

Most of the previous work characterizing ultra-short laser-plasma interactions hasbeen done by comparing measured absorption with the solutions of Maxwell'sequations employing a phenomenological collision frequency (damping rate). Thismethodology becomes inadequate when detailed interaction mechanisms are to beexplored and nonlinear processes begin to play an important role. As described in theprevious section, the interaction processes in the range of laser intensity of the presentinterest (loi4- 1016Wlcm2) are expected to be dominated by nonlinear mechanisms thatproduce high energy particles. Although the direct measurements of high energyparticles have not previously been used as diagnostics in picosecond interactionexperiments, these measurements become inevitable as the nonlinear processes begin todominate. In this study, high energy electron and ion emissions as well as absorptionand x-ray measurements are used to characterize the interaction mechanisms in thepicosecond laser plasmas. Inparticular, ion blowoff has been extensively characterizedand used to estimate various plasma parameters.

The target plasma is generated on smooth solid A1 plates where the plasma has astrong inhomogeneity (density gradient) along the target normal. Under such plasmaconditions, the laser elecmc field component along the density gradient (p-polarizedfield) can excite plasma waves resonantly while another component (perpendicular tothe gradient) has no effects on the plasma wave excitation. The excitation of plasmawaves by a p-polarized light is depicted in Fig. 1-1. The transverse electromagneticwaves have elecmc field components along the density gradient at the turning point andexcite longitudinal electrostatic waves. Since electron plasma waves oscillate at theplasma natural frequency which is a function of plasma density, the electrostatic wavebecomes resonant at the critical surface where the plasma frequency equals the laser


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frequency. Thus the p-polarized transverse electromagnetic wave energy is convertedto the longitudinal electrostatic wave energy.

plasma wavesII

Vne4- I

waves

I I 1 b z"a ~ ~ 0 ~ 2 0

Critical surface Turning point k, =0

Fig. 1 1 The y-z plane defines the laser plane of incidence. For p-polarizedEM waves, the electric field vector lies in this plane and it is in the z-direction (parallel to the density gradlent) at the turning point.

Therefore, the polarization of obliquely incident laser electric fields has significanteffects on the interaction characteristics and is chosen as one of the primaryexperimental parameters. The effects of polarization are examined by independentlyaltering the total laser intensity and p-polarized electric field component (electric fieldslying in the plane of incidence or along the density gradient). The characteristics ofhigh energy electrons and ions have been found to depend on the p-polarizedcomponent alone.

Previously in long scale length plasmas the high energy electron generation fromthe critical surface has been attributed to wavebreaking acceleration or electron trappingin plasma waves. The high energy electrons produced from the short scale length


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plasmas, on the other hand, exhibit a fairly monoenergetic spectrum and consist ofalmost the entire population of electrons in the resonance region. These features are notexpected from wavebreaking or electron trapping. Therefore, a new mechanism for theobserved electron acceleration from the resonance region has been introduced, that is,the ponderomotive acceleration.

The determining processes of enhanced p-polarized field that accelerates the highenergy electrons by its ponderomotive force have been examined. Various processesare compared in terms of their limiting effects on the resonantly oscillating fields. Theenhanced fields have been determined experimentally and found to be best described byplasma-wave dispersion effects.

Based on the experimental observations and comparisons with theoreticalestimations, the following physical picture for high energy particle acceleration hasbeen drawn. Figure 1-2 illustrates the process showing the enhanced laser field alongwith the plasma density profile. When an obliquely incident laser pulse has a p-polarized electric field component at the turning point in a plasma, the field penetratesto the critical surface and drives electrons resonantly. These oscillating electrons buildan electrostatic wave and enhance the incident laser field. In a short scale-lengthplasma, the enhancement is limited by plasma-wave dispersion effects. Since theresonance field is highly localized, the ponderomotive force that is proportional to thegradient of the field is significant. This ponderomotive force mainly acts on theelectrons in the resonance region and accelerates them to its potential energy. Theelectrons accelerated toward vacuum leave immobile ions behind and build up anambipolar field. This ambipolar field then accelerates the ions. Eventually the ionscatch up with the electron motion and expand together. During this process, almost theentire energy initially residing in the electrons is transferred to the ion kinetic energy.


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) lectrons\\ Electric field

E l m n/pdensityCritical

Incident laser

surface pointFig. 1-2 Ponderomotive acceleration of high energy particles. The spatial

profile of the lase r electric field (solid line) and the electron density(broken line) are shown.

REFERENCES

0. . Landen, E. M. Campbell and M. D. Perry, "X-ray characterization ofpicosecond laser plasmas," O ptics Comrn. 63 ,2 53 (1987 ).

H. M. Milchberg. R. R. Freeman, S. C. Davey and R. M. More. "Resistivityof a simple metal from room temperature to l o6 K," Phys. Rev. Lett. 61.2364 (1988).

P. B. Corkum. F. Brunel, N. K. Sherman and T.Srinivasan-Rao. 'Thermalresponse of metals to ultrashort-pulse laser excitation," Phys. Rev. Lett. 61,2886 (1988).

0. L. Landen. D. G. Stearns and E. M. Campbell. "Measurement of theexpansion of picosecond laser-produced plasmas using resonance absorptionprofile spectroscopy," P hys. Rev. Lett. 63, 1475 (1989).

M. M. Murnane. H. C. Kapteyn and R. W. Falcone, "High-density plasmasproduced by ultrafast laser pulses," Phys. Rev. Lett. 62, 155 (1989).


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M. M. Murnane, H. C. Kapteyn and R. W. Falcone, "Generation andapplication of ultrafast x-ray sources," IEEE J. Quantum Electron. 25,2417(1989).

J. C. Kieffer, et al., "Short-pulse laser absorption in very steep plasma densitygradients," Phys. Rev. Lett. 62, 760 (1989).

J. C. Kieffer, et al., "Absorption of an ultrashort laser pulse in very steepplasma density gradients," IEEE J. Quantum Electron. 25,2640 (1989).

H. M. Milchberg and R. R. Freeman, "Expansion-induced Doppler shifts fromultrashort-pulse laser-produced plasmas," Phys. Rev. A 41,221 1 (1990).

lo R. Fedosejevs, R. Ottmann, R. Sigel, G. Kiihnle, S. SzatmM and F. P.Schiifer, "Absorption of subpicosecond ultraviolet laser pulses in high-densityplasma," Appl. Phys. B 50, 79 (1990).

R. Fedosejevs, R. Ottmann, R. Sigel, G. Kiihnle, S. Szatmhi and F. P.Schiifer, "Absorption of femtosecond laser pulses in high-density plasma,"Phys. Rev. Lett. 64, 1250 (1990).

l2 T.Engers, W. Fendel, H. Schiiler, H. Schulz and D. von der Linde, "Second-harmonic generation in plasmas produced by femtosecond laser pulses,"Phys. Rev. A 43,4564 (1991).

l3 M. Chaker, J. C. Kieffer, J. P. Matte, H. Pepin, P. Audebert, P. Maine, D.Smckland, P. Bado and G. Mourou, "Interaction of a 1 psec laser pulse withsolid matter," Phys. Fluids B 3, 167 (1991).

l4 H. M. Milchberg and R. R. Freeman, "Light absorption in ultrashort scalelength plasmas," J. Opt. Soc. Am. B 6, 1351 (1989).

H. E. Elsayed-Ali and J. W. Herman, "Picosecond time-resolved surface-latticetemperature probe," Appl. Phys. Lett. 57, 1508 (1990).


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l6 D. Kiihlke, U. Herpers and D. von der Linde, "Soft x-ray emission fromsubpicosecond laser-produced plasmas," Appl. Phys. Lett. 50, 1785 (1987).

l7 J. A. Cobble. G. T. Schappert, L. A. Jones. A. I. Taylor, G. A. K yrala and R.D. Fu lton, "The interaction of a irradiance, subpicosecond laser pulse withaluminum: T he effects of the prepulse on x-ray production," J. Appl. P hys.69, 3369 (1991).

l8 J. D. Kmetec, C. L. Gordon, I. J. J. Macklin, B. E. Lemoff, G. S. Brown andS. E. Harris, "MeV x-ray generation with a femtosecond laser," Phys. Rev.Lett. 68, 1527 (1992).

l9 F. Brunel. "Not-so-resonant, resonant absorption," Phys. Rev. Lett. 59, 52(1987).20 P. Gibbon and A. R. Bell, "Collisionless absorption in sharp-edged plasmas,"

Phys. Rev. Lett. 68, 1535 (1992).21 G. Bonnaud , P. Gibbo n, J. Kindel and E. W illiams, "Laser interaction with a

sharp-edged overdense plasma," Laser Part. Beams 9, 3 3 9 (1991).

22 W. Rozm us and V. T. Tikhonchuk, "Skin effect and interaction of short laserpulses with dense plasmas," Phys. Rev. A 42,7401 (1990).23 E. G. Gamaliy and R. Dragila, "Interaction of ultrashort laser pulses at

relativistic intensit ies with solid targets: Relativistic skin effect," Phys. Rev. A42,929 (1990).

24 C. S. Liu, "Parametric instabilities in an inhomogeneous unmagnetizedplasmas," in Advances in Plasma Physics, edited by A. Simon and W. B.Thomson. (Wiley, New York, 1976) 6: p.121-176.

25 K. R. Manes, H. G. Ahlstrom, R. A. Haas and J. F. Holnichter, "Light-plasma interaction studies with high-power glass laser," J. Opt. Soc. Am.67 ,71 7 (1977).


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26 R. L. Morse and C. W. Neilson, "Occurrence of high-energy electrons andsurface expansion in laser-heated target plasmas," Phys. Fluids 16, 909(1973).

27 H. H. Klein and W. M. Manheimer, "Effect of plasma inhomogeneity on theproduction of energetic electrons," Phys. Rev. Lett. 33, 353 (1974).

28 D. W . Forslund, J. M. Kindel, K. Lee, E. L. Lindman and R. L. Morse,"Theory and simulation of resonant absorption in a hot plasma," Phys. Rev.A 11, 679 (1975).

29 K. G. Estabrook, E. J. Valeo and W. L. Kruer, "Two-dimensional relativisticsimulations of resonance absorption," Phys. Fluids 18, 1151 (1975).

30 D. W. Forslund, J. M. Kindel and K. Lee, "Theory of hot-electron spectra athigh laser intensity," Phys. Rev. Lett. 39, 284 (1977).

31 G. D. Enright, N. H. Burnett and M. C. Richardson, "X-ray emissioncharacteristics of plasmas created by a high-intensity C 02 laser," Appl. Phys.Lett 31,494 (1977).

32 G. D. Enright, M. C. Richardson and N. H. Burnett, "Superthermal x-rayemission from C02-laser-produced plasmas," J. Appl. Phys. 50, 3909

33 H. Pepin, B. Grek and F. Rheault, "X-ray emission measurements from C02-laser-created plasmas," J. Appl. Phys. 48 , 3312 (1977).

34 R. A. Haas, H. D. Shay, W. L. Kruer, M. J. Boyle, D. W. Phillion, F.Rainer, V. C. Rupert and H. N. Kornblum, "Interaction of 1.06-pm laserradiation with planar targets," Phys. Rev. Lett. 39, 1533 (1977).

35 B. Luther-Davies, "X-ray bremsstrahlung and fast-ion measurements frompicosecond laser-produced plasmas," Optics Cornm. 23,98 (1977).


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36 K. R. Manes, V. C. Rupert, J. M. Auerbach, P. Lee and J. E. Swain,"Polarization and angular dependence of 1.06-pm laser-light absorption byplanar plasmas," Phys. Rev. Lett. 39, 28 1 (1977).

37 B. Luther-Davies, "Evidence of resonance absorption in laser-producedplasmas from the polarization and angular dependence of high-energy x-raybremsstrahlung emission," Appl. Phys. Lett. 32,209 (1978).

38 1. E. Balmer and T. P. Donaldson, "Resonance absorption of 1 . 0 6 ~aserradiation in laser-generated plasma," Phys. Rev. Lea 39, 1084 (1977).

39 1. S. Pearlman, J. I. Thomson and C. E. Max, "Polarization-dependentabsorption of laser radiation incident on dense-plasma planar targets," Phys.Rev. Lett. 38, 1397 (1977).

P. WPgli and T. P. Donaldson, "Fast-ion emission and resonance absorption inlaser-generated plasma," Phys. Rev. Lett. 40, 875 (1978).

41 R. Fedosejevs, M. D. J. Burgess, G. D. Enright and M. C. Richardson, .'Theelectron density structure of the plasma produced on glass microballoons by10.6 pm radiation," Phys. Fluids 24, 537 (1981).

42 D. R. Bach, et al., "Intensity-dependent absorption in 10.6-pm laser-illuminated spheres," Phys. Rev. Lett. 50,2082 (1983).

43 A. Raven and 0. Willi, "Electron-density strucnues in laser-produced plasmasat high irradiances," Phys. Rev. Lett. 43, 278 (1979).


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CHAPTER I1Theoretical background

11-1 IntroductionThere are several physical concepts that need to be covered to characterize and

understand the plasma conditions under investigation. These include,1. Electromagnetic (EM) wave propagation in a short-scale-length plasma2. Electric field enhancement at the critical surface by plasma oscillation3. The ponderomotive potential in plasma4 . Isothermal plasma expansionThe behavior of an EM wave in an underdense plasma has been well characterized

by the WKB approximation. This is valid when the fields vary slowly in space sincethe method solves the wave equations by each order of derivative assuming a higherorder derivative is negligible compared to a lower order.' However, for picosecondlaser plasmas where L, is shorter distance than the laser wavelength or for sharplypeaked resonance fields at the critical surface, the fields vary in distances shorter thanwavelength and the slowly varying approximation breaks down. Maxwell's equationsthen have to be solved numerically.

When laser light has a p-polarized component, linear mode coupling of the EMwave to the electrostatic plasma wave takes place at the resonance region where theplasma frequency nearly equals the laser frequency (see Fig. 1-1). Such a modeconversion could be very efficient in a short-scale-length plasma where incident wavesreach the resonance region before being strongly attenuated. The amplitude of theresonantly oscillating fields in short scale-length plasmas is then determined by thebalance between the enhancement of the plasma wave through the mode conversion andconvection of the wave out of the resonance region.


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The enhanced elecmc field leads to the acceleration of plasma particles tosuprathermal energies. The mechanism of the acceleration varies depending on theplasma temperature and driving laser electric field amplitude. In a cold plasma, theelectron fluid oscillates harmonically in the driving field. As the oscillation develops,the plasma wave breaks when one fluid element overtakes another. The resonantlyoscillating field can no longer keep electron harmonic motion thus the oscillation energyis abruptly converted to an electron random energy. The strength of the oscillation isthen limited to the wavebreaking amplitude. When a plasma has a very steep densitygradient, on the other hand, the plasma wave dispersion takes energy out of theresonance region and determines the steady state wave amplitude when the dispersionbalances the input energy flux. The ponderomotive acceleration of the suprathermalelectrons from the resonantly enhanced field is the consistent picture with theexperimental results. This mechanism is examined against the wavebreakingmechanism. The amplitude of the resonantly enhanced field is inferred from the ionkinetic energy through the ponderomotive potential.

One proven technique to characterize the suprathermal electrons from the resonantlyenhanced field is an ion measurement. An isothermal expansion model of ion (plasma)provides a means of estimating plasma temperature. The velocity distribution of ionsexhibits a high energy tail that can be well described by the model and determines theplasma temperature. The velocity distribution of ions reflects the characteristics ofelectrons that accelerate ions through an ambipolar electric field. The ion kinetic energyis used to estimate the ponderomotive potential of the resonance fields and show thatthe accelerated electrons have a fairly monoenergetic spectrum.

11-2 EM wave propagation in a short scale length plasmaThe understanding of EM wave propagation in a plasma is of primary importance

for the investigation of short-pulse laser-plasma interactions. In short-pulse laser-


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plasma interactions, the EM wave interacts with a highly inhomogeneous plasma wherethe plasma scale length,

is much shorter than the wavelength of laser. When laser light is obliquely incident onsuch plasmas, the interaction exhibits a strong dependence on the laser polarization andthe angle of incidence.

When an EM wave propagates in plasma obliquely to the density gradient, twolocations become important, turning point and the critical surface. Figure 2- 1 depictsthese two locations with the spatial variation of p-polarized laser electric field. Sinceplasmas are dispersive, EM waves propagating obliquely to the axis of inhomogeneitytowards high density region deflect and eventually reflect from the plasma region. Thepoint where the EM waves turn around is called the turning point. Beyond the turningpoint, the field strength decays exponentially and a finite amount of field penetratesthrough the higher density region, the electric field tunneling. If the tunneling field hasa component along the density gradient, it excites electron plasma oscillations. Theseoscillations become resonant at the critical surface where the local plasma frequency~ p eequals the laser frequency oo. Because of the resonant nature of the oscillation, theamplitude of electric fields can be driven to much larger values than that of drivingelectric fields and accelerate electrons to very high energies. To examine EM waveinteraction with plasmas, the modification of the propagating EM fields in the plasmaneeds to be known. In this section the propagation of an EM wave in a plasma is

2reviewed emphasizing the solution for p-polarized light to give a basis for an estimateof field structure in plasma.


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P-polarized laser field envelope

Incident laser

Fig. 2-1 An EM wave propagation obliquely incident in an inhomogeneousplasma and two important locations, the tuming point and the criticalsurface. The spatial variation of p-polarized laser electric field isalso shown.

The wave equations of laser light with a frequency o ropagating in a plasma canbe developed from Faraday's law and Ampere's law,

The displacement current is neglected compared with the conduction current. Theconductivity of plasma o (J = oE) s calculated from a linearized force equation ofelectron fluid,


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where ve is the velocity of the electron fluid and Vei is the collision frequency. Theplasma current density is

where ~ p es the plasma frequency, ~ p eAmpere's law (2-2) becomes

%2where E(Z)= 1 - is the dielectric function of the plasma. From theW(O + ivei)

equations (2- 1) and (2-3)' the wave equations for E and B are02V ~ E V(V*E) +- ( z ) = 0c2

The second term of Eq. 2-4 leads to an important consequence of the resonantlyenhanced laser field at the critical surface. When this term is zero, the wave is purelyelectromagnetic and no mode conversion from EM wave to electrostatic (ES) wavestakes place. This term corresponds to an ES mode of the incident laser field and only


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exists for the case of p-polarization. Poisson's equation gives V*(&(z)E)= 0 whichcan be expanded to yield

The divergence of E exhibits a resonant response at the critical surface where Re(&)=0. The existence of this term introduces additional complexity in solving the waveequation and makes the B-field (Eq. 2-5) a preferable choice as described in the nextsection. Equations 2-4 and 2-5 are redundant and the choice between E and B dependson the polarization of the EM wave propagating in an inhomogeneous plasma. Inshort-pulse laser interactions, the plasma density profile can be considered as onedimensional (planar expansion), since the plasma expands a distance much less than itsdiameter (= 1%). Therefore, without loss of generality, Cartesian coordinates can bedefined as shown in Fig. 2-2.

Critical surface, z, C (Z )=0s,Turning point - -,plasmavacuum

Fig. 2-2 Oblique incidence (angle of incidence 80) of an EM wave on aplanar plasma density profile (density gradient parallel to the z-axis).Vacuum-plasma boundary is at z=0. Wave k-vector is a function ofz and turns around at sin%^.


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Here the z-axis is in the direction of the plasma density gradient (dnddz> 0), i.e.,target normal, and the y-z plane is the plane of incidence. The above assumptionensures that the wave is independent of x coordinate. The plasma-vacuum boundary isset to be at z=0 plane, i.e., %=O for ze0. The angle of incidence 80 is defined as anangle between the wave k vector in vacuum and the z-axis perpendicular to target.

For p-polarized light, the elecmc field vector has two components that transformEq. (2-4) into

These are coupled equations for Ey and EZso it is convenient to work with Eq. (2-5)which yields a single wave equation for p-polarized light where theB field has only thexcomponent Bx,

Equation (2-6) can be solved by expressing Bx as B"(z)exp(-ikay)where

and

Here 8(z) is the instantaneous angle between k-vector and z-axis and B" is the complexmagnetic field along x. Substituting this expression into Eq. (2-6) yields


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The fact that the left-hand side is independent of y requires both sides be equal to zero,i.e.,

and letting the real and imaginary parts of the right hand side be independently zerogives

Here vei/o


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Here,

and

Equations 2-9 and 2-10 are integrated from the overdense region to the underdenseregion to calculate the value at the critical density. The overdense region was chosen asa starting point of integration to match the boundary condition of evanescent waves.The electric field at the critical surface is a sum of the electromagnetic driving field,&,and the resonantly enhanced electrostatic field supported by the plasma oscillations.The electrostatic field will be discussed in the next section. With Ampere's law and thelaw of refraction, the electric field& can be expressed in terns of vacuum electric fieldand decay factor through the critical surface,

where Bd is the corresponding magnetic field penetrating through the critical surface.Note that Ed is not the resonantly oscillating elecmc field but the laser elecmc field thattunnels through from the turning point to the resonance point and drives the plasmawave resonantly at the critical density. The resonantly oscillating field at the resonancesurface is derived in next section by coupling this field with plasma oscillations.

Figure 2-3 shows the example of laser electric field pmfle calculated, according toEqs. 2-9 and 2-10, for n(z)=nee% where Ln= 1 5 ~ Ahat is assumed to be constant


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across the region. The laser elecmc field strength is normalized to its maximum value(at 5000A) and the distance is measured relative to the critical density. In this examplethe laser elecmc field decays to -20% of its vacuum value at the critical density. Thedecay factor qt varies from 23% to 17% as the scale length increases from l000A to2000A.

Distance from the critical surface (A )Fig. 2-3 Laser electric field profile around the critical surface. The field

strength is normalized to the maximum value and the distance isrelative to the critical surface. The broken line indicates the plasmadensity profile used in the calculation.

11-3 Electric field enhancement at the critical surfaceThe tunneling elecmc fields of p-polarized light at the critical surface drive the

electrons along the density gradient and resonantly drives electron plasma wave. Thisleads to the enhancement of electric field strength as shown in Fig. (2-4). There aretwo types of field "swelling" appearing in this figure near the resonance surface. One

5of them is so called Airy swelling whose cause can be understood by noting that the


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energy flux of light is conserved and the group velocity of light. vg = ce(n,)ln,becomes minimum at the turning point. Since this swelling is due to the conservationof energy alone. it can exist for either s- or p-polarization. An other swelling, which isthe primary interest in this thesis, is the field enhancement at the critical surface causedby the resonance response of plasma oscillation to incident fields. When the laserelectric field oscillate s the plasma elec trons along the density g radient the laser light hasa p-polarized component, it creates a charge separation because ions are immobile.This charge separation then drives the plasma oscillation at a plasma frequencydepending on the local density. The driving is resonant where the local plasmafrequency matches the incident laser frequency. This oscillation does not occur for ans-polarized field component.


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&--I-TResonanceenhancement

Incident wave Airy swelling

Resonance surface

Incident wave Airy swelling

Resonance surface

Fig. 2-4 Laser electric field profile obliquely incident on an expanding plasmashowing an Airy swelling and a resonance enhancement. The Airyswelling is due to the decrease of group velocity whereas theresonance enhancement is due to the resonance response of plasmaat the critical surface. The horizontal and vertical scale do notnecessary reflect the real scaling.

Because of the resonance feature of this oscillation the enhancement could beinfinite if no process takes energy out of the region or broadens the resonance region.In the long scale length plasma, electron-ion collisions determine the width of theresonant region and thus the maximum enhancement. As the scale length becomesshorter, the width of the resonant region becomes narrower and the enhancementfurther develops. When the width becomes smaller than electron oscillation amplitudeor the Debye length, either one of these dimensions determines the width of theresonance. The electron oscillation in the resonant field averages the field strength andbroadens the width; thus the enhancement is lower than that predicted by collisionaleffects. The Debye length determines the range in which collective plasma responsehas an effect, i.e., the width of resonantly oscillating field when limitd by a plasma


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7wave convection. ti These two limiting processes can be related m wavebreaking andthe ponderomotive acceleration of electrons and are described in some detail in thissection.

When the resonant field width is larger than the Debye length or electron oscillatingamplitude, the field enhancement is determined by the ratio of the laser frequency,wgand the elecuon-ion collision frequency, vc at the critical surface. This is derived bysolvingEM wave equations for p-polarized case and calculates the electric field at thecritical surface. 6' The laser intensity enhancement is given by

where 8inc and k are an angle of incidence and a laser wave vector. The width of thevcfield, 6 s then given by -Ln. When the plasma scale length is short enough so that6%

the field width becomes shorter than the electron oscillating amplitude, x,, or theDebye length, hD,, the resonant field begins to be broadened by the field averagingeffects due to the electron oscillation or the plasma pressure perturbation (plasma wavedispersion).

Wavebreaking is a process in which neighboring electron fluid elements overtakeeach other in a harmonic motion driven by an external field.99 lo Through thisprocess, the oscillating electron energy is abruptly transferred to electron kineticenergies and accelerates electrons out of the resonance region. The mechanism ofwavebreaking can be examined by considering the equation of electron motion andPoisson's equation. When external electric field, Ed,drives plasma electrons around itscritical density in the direction of density inhomogeneity, the charge separation betweenelectrons and immobile ions induces a resonance field which in turn drives the electronoscillation and enhances itself. The enhancement is strongest at the exact resonance (orcritical density), whereas neighboring oscillations ark dephased from the driver due to


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their different natural frequency. Therefore, the amplitude of electron oscillation islargest at the resonance surface leading to the overtaking between the neighboring fluidcomponent as the oscillation develops. This process is illustrated in Fig. 2-5 where theabscissa and ordinate correspond to the initial and present positions of electrons,respectively. The fluid overtaking occurs where dz/dzg =0 he region indicated by thesquare. It has been shown that the electron fluid elements satisfying this overtakingcondition that consists of a few percent of electron population traverse the resonanceregion in phase with the field and escape it.7, 11

Before overtaking

Fig. 2-5. Overtaking of electron fluid oscillation in resonance field y) nd zcorrespond to initial and present positions, respectively. Overtakingoccurs when more than two fluid components occupy the sameposition. Only the fluid components in the overtaking region areaccelerated and escape the region.

Themaximum energy that electrons can obtain from the resonance field is estimatedby analyzing the electron plasma wavebreaking. The dynamics of wavebreaking wasfust analyzed by Dawson and further developed by Albritton and Koch. 7, 10, 12Before wavebreaking takes place, the electron motion can be described by a harmonic


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oscillation equation with Poisson's equation. This description is valid as long as thefluid elements do not cross each other. As the oscillation develops, one can impose anovertaking condition to the electron fluid trajectory and calculate the electron energy atthat moment This energy gives the estimate of the accelerated electron energy and thusenergy dissipation through wavebreaking.

The motion of an oscillating electron near the critical density is convenientlydescribed via Lagrangian variables where the position z of a electron fluid is expressedin terms of its initial position y) nd time t,

The analysis assumes that 1) the ion fluctuations are negligible, 2) the driving electricfield Ed is uniform over the oscillation, 3) density gradient, Ln around the resonance islinear, and 4) o


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Referring to Fig. 2-30 and Eq.2-12, the overtaking (or orbit crossing) occurs whenfluid elements from different initial positions take the same position simultaneously,that is, azlay) = 1 + ao/ay) = 0. With Eq.2- 13, the overtaking time is tb = ( 8 / ~ ) 1 / 2 / ~and thus the maximum velocity is

where vd a eE&w the electron quiver velocity in the driving field. This velocity isused to determine the maximum electron energy from overtaking.

When a plasma has a steep density gradient, the plasma dispersion relation obtainsan additional convective term. This can be seen by solving equations of continuity andmotion of electrons with keeping a derivative of the unperturbed electron density.Since it suffices to consider an electron motion in the direction of the density gradient(in the z direction) alone, the governing equations are

and

All the quantities have a standard meaning regarding to electrons. Assuming that only- - - Nthe density has an unperturbed term, that is, ne = no + ne,Ve = Ve, E = E, and Pe = Pelinearizes Eqs. 2- 15 and 2- 16.


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where the products of the perturbed terms are neglected. Using Fe Te ,Eq. 2- 18becomes,

Equations 2-18, 2-19 and Poisson's equation give a complete set of couplingequations,

Combining these three equations yields

i kT T 1term has been dropped compared to kZ sinceLn> ; .Lme m,At the critical surface, w =9,gives the plasma wave decay factor due to the steepdensity gradient,

the result given by GinzburgP Here hDe s the electron Debye length defined as

. This decay factor gives an estimate of the spatial width of the resonantly enhancedfield at the critical surface, ( L ~ ~ ~ L ~ ) " .omparing this width with the scale length( ~ r .s discussed in the next paragraph,ields the field enhancement factor of -the energy deposited into the resonance region is dissipated by the wave convection.


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A similar result can be obtained by estimating the elecmc field amplitude of theharmonic oscillation of the electrons at the critical density driven by the p-polarizedcomponent of the incident laser elecmc field. As discussed in the previous section thez component of elecmc field Ez can be estimated by Ampere's law, Eq. 2-3 and the law

0of refraction, Eq.2-8: k(z)sinl(z)= ky= sin&).

Here Ed is the component of laser field that drives electrons along the density gradient.From the result of the previous section, Ed =qt%, the elecmc field of laser in vacuum.The penetration strength q is approximately 0.2 (see Fig. 2-3). Without a limitingmechanism Ez could grow infinitely at the critical surface where Re(&)=0. Since thedriven electric field Ez is proportional to electron displacement, Ez can replace theplasma electron density in a forced harmonic (plasma wave) equation. Ez can then becalculated by solving a plasma wave equation.

Wave convection is particularly important in the case of short scale length plasmas.Here ve is the electron thermal velocity and the plasma density gradient is approximatedto be locally linear. The left and right hand sides correspond to a natural harmonicoscillation of the plasma and the driving force due to the incident laser field,respectively. As can be seen from the plasma wave dispersion relation, Eq. 2-20,plasma waves decay as they propagate out of the resonance region. Therefore, aphysically acceptable solution 18 is evanescent as z +f 0 and given by


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with

where x i (o02/3ve2h)1/' and x = 2.6 gives the maximum value of I = 1.7. Thus thepeak electxic field Ep is

Ep = 1 2(%)m& = 1.2( ) Ed.AD2The Eq. 2-22 gives the am plitude of the enhanced electrostatic field that is limited

by the plasma w ave dispersion and can be compared w ith the field strength given bywaveb reaking, Eq. 2- 14. Com paring Eqs. 2-14 and 2-22 and using the driving fieldamplitude in term s of the vacuum field amp litude obtained in the previous section,& =qtEg, the criterion for the cold plasma wavebreaking is

Equation 2-23 gives the threshold laser intensity of the plasma wave convectionlimit at a given electron temperature. When the plasma wave convection limits theamplitude of enhanced field, the ponderomotive force due to the sharp field gradientaccelerates the electron s to its potential. Th e number of electron accelerated in theprocesses also distinguishes the mechanism. The ponderomotive force accelerated theentire population of electrons to its potential energy, while wavebreaking onlyaccelerated those electrons in the overtaking region.

11-4 The ponderomotive potential and wavebreaking for energeticelectron acceleration

In the study of laser-plasma interactions, two types of forces are of interest andimportant to various phenom ena in plasma. They are thermokinetic forces due to


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gasdynamic pressure of plasmas and electrodynamic forces of a nonlinear type. Thelatter has direct importance to laser-plasma interactions. This nonlinear electrodynamicforce is, when exerted on plasmas, commonly called ponderomotive force and exists,either for an electromagnetic or electrostatic field, whenever the field has gradient.Physically this force depends on the spatial variation of the amplitude of the electronoscillations within the field, that is, the (E*V)E term for electrostatic field or VxB termfor elecmmagnetic field.

When an elecmn oscillates in a nonuniform elecmmagnetic or elecmstatic field, itacquires a net drift during many oscillations. Physically the electron is accelerated morein the strongest field region than in weaker field region and does not return to theoriginal position during one oscillation. This displacement accumulates over manyoscillations and results in net drift. The driving force for the drift is proportional to thegradient of the field and expressed in terms of the potential, h n d , by

The electron eventually acquires a kinetic energy equal to the oscillation energy in thefield. This dnft is called ponderomotive acceleration. The electrons oscillating in theresonantly enhanced field are accelerated by this process because of the steep gradientof the field structure.

The ponderomotive acceleration of plasma l 3 due to the resonantly oscillating fieldat the critical density contrasts with wavebreaking heating in terms of the spectra andnumber of electrons produced through the processes. The ponderomotive forceaccelerates an electron to a definite velocity determined by its potential during manyoscillations of the fields; therefore, the electron spectrum due to this process is expectedto be a shifted Maxwellian (beam-like) distribution. The beam-like distribution or abulk acceleration of plasma has been observed in a series of microwave plasma


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interaction experiments 141 l5 and numerical simulations using a particle code on EMwave conversion to ES wave. The wavebreaking process, on the other hand, randomlydistributes the collapsing wave energies among electrons.16 The number of electronsaccelerated in the ponderomotive potential, as the second distinctive point, is muchlarger than that of wavebreaking process since all the particles in the resonance regioncan participate in the process when ~ 2 / 8 l c n , k ~T , 1, the condition for which theoscillatory energy is larger than the thermal energy.

The ponderomotive force can bederived from an electron force equation,17

where E(x, t) is assumed to have a time dependence, ES(x)cosot with Es bearing thespatial variation of E. The first order solution of Eq 2-24 is

and thus

B1 is given by Faraday's law,

Es is expanded, up to second order, about x = xo,

The second order ofEq 2-24 is then


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Substituting Eqs 2-25,2-26, and 2-27 and averaging over one period l / o yield

This is the ponderomotive force per electron that is eventually transferred to ionsthrough ambipolar fields.

The ponderomotive acceleration of electrons, in the present work, is shown to be adominant mechanism in the present plasma condition whereas wavebreaking (electronovertaking) in a resonantly oscillating plasma wave has been regarded as a mechanismfor high energy electron generation from the critical surface in long scale lengthplasmas.7' Therefore, it is necessary to examine some of the features of theelectrons produced by the wavebreaking process to distinguish wavebreaking from theponderomotive acceleration.

A resonantly oscillating plasma wave at the critical surface accelerates an electron tosuperthermal energies. This acceleration is determined by the electric field amplitude ofthe plasma wave. The plasma temperature has important effects on the amplitude of thefield as shown in the previous section. When a plasma is cold, the plasma waveamplitude can grow until wavebreaking occurs and the breaking wave can abruptly giveenergies to electrons and ejects them out of the resonance region. The electrons thatparticipate in wavebreaking take energy away from the resonance region and the growthof the field saturates. The plasma wave amplitude is thus determined by thewavebreaking amplitude, and the number of electrons accelerated is limited to a smallfraction of electrons in the dtical region because, as soon as overtaking occurs, waveenergy is taken away by those accelerated electrons and growth of wave saturates (seeFig. 2-10). When a plasma is w m , on the other hand, thermal convection extends thespatial width of resonantly oscillating field and reduces the field amplitude.11, 19


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Electrons are then accelerated by the ponderomotive force of the plasma wave field.Since electrons are accelerated in the ponderomotive potential as they oscillate in theresonance field, a larger portion of electrons is expected to participate in the process.Therefore, the measurement of the number of electrons accelerated from the resonanceregion can distinguish between wavebreaking and the pondemmotive acceleration.

A number of numerical and theoretical studies 16' 18-20 have shown thatwavebreaking produces near Maxwellian electron distribution superimposed on a coldelectron distribution and so is measured by a continuum x-ray spectroscopy.21-24 onthe other hand, the pondemmotive force accelerates particles during many oscillationsand thus every electron is accelerated to a given energy.

11-5 Isothermal expansion of PlasmaAccelerated electrons lose their energy either by collisional or noncollisional

processes. The efficiency of the collisional process decreases as the electron energyincreases due to the ve-3 (ve is the electron velocity) dependence of the collisionfrequency. Therefore, the high energy electrons tend to leave stationary ions beforelosing energies collisionally and create an ambipolar field due to the charge separation.As this field builds up, the ions are accelerated and energy transfer from the electrons toions occurs. Thus the high energy electrons tend to lose more energy by acceleratingions than by collisions. Through this process, the accelerated ions (so-called fast ions)obtain large fraction of absorbed energy that has been initially absorbed by the highenergy electrons. This ion blowoff can be detected as an ion current (density) andserves as an important plasma diagnostic.

An ion current trace can provide information about the target plasma such as totalparticle number and energy, and the temperature of the electrons that accelerate ions.Estimating the total number and energy is rather straight forward; although, theestimation of electron temperature requires the analysis of the ion-velocity distribution


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based on an isothermal plasma expansion model. The model assumes: (1) isothermalelectron distribution, (2) charge neutrality, (3) two fluid components made of hotelectrons and relatively cold ions (Ti =O), (4) planar one dimensional expansion, (5)negligible collisions, and (6) Boltvnan equilibrium. An isothermal expansion model isphysically plausible because (1)thermal conduction in the plasma is sufficiently rapid tosuppress large temperature gradients and (2) heat conduction into the cold dense plasmaabove critical surface can be significant on the picosecond time scale.25*26 he scalelength of plasma is expected to be longer than Debye length and charge betweenelectrons and ions always balances. The effect of cold electrons on the fast ionacceleration can be neglected since their pressure is much smaller than that of the hotelectrons. The temperature of the ions is also assumed to be low so that their pressurecan be neglected. In the collisionless limit, the analysis is very simple and the plasma isexpected to be collisionless for the high electron energies in present work. Sinceelectron response time l f o p e is much shorter than the time scale of plasma expansion,the electron fluids are always in equilibrium with the electrostatic potential, i.e., aBoltzmann equilibrium.27

The isothermal expansion model was fust developed by Gurevich e r . a ~ . ~ ~nd hasbeen a basic model in various studies.29-32 The analysis uses a set of three equations:continuity and force equations of ion fluids and Boltvnann equation,

8/3/2019 Shigeaki Uchida- The Effects of Resonantly Enhanced F

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Shigeaki Uchida- The Effects of Resonantly Enhanced Fields in Picosecond Laser Produced Plasmas