旺
ARMONIC GENERATION AND PARAMETRIC INSTABILITIES IN LASER PRODUCED PLASMAS
K. RAMACHANDRAN Department of Physics
Thesis submitted in ffi' 第 iment of the requirement of the degree of
Doctor of Philosop 如
to the
INDIAN INSTITUTE OF TECHNOLOGY. DELHI
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奮撫 7 。タ鷺鼠二ぐ 1 ッ・ 9ツ
1 ぐ、令 M －甘
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1J 'し且馬A,
CERTIFICATE
This is to certify that the thesis entitled, "Harmonic Generation and Parametric Instabilities in Laser Produced Plasmas", being submitted by Mr. K. Ramachandran to the I.I.T.,Delhi, for the award of the degree of Doctor of Philosophy, is a record of bonafide research work carried out by him.
Mr. K. Ramachandran has worked under my guidance and supervision and has fuiffihled the requirements for the submission of this thesis, which to my knowledge, has reached the requisite standard. The results contained in 山i。山esis have notk en submitted, in part or in full, to any other U血versity or Institute, for the award of any degree or diploma.
Professor
Department of Physics
To 物 Parents
bite K. R ．玉 rishnamoo 九 hy Rao and
Late K. Laxmi Bai
ACKNOWLEGEMENTS
It was the blessing by山e God to have chosen me to work under the guidance of Prof. V.K. Tripathi. With the indepth knowledge in the subject and an amazing analytical ability , he has motivated and cultivated in me, a very deep interest and an ability to understand plasma physics. I would like to humbly mention here that I have learnt a true Gandhian way of life from Prof. V.K. Tripa山i. :i am de叩ly indebted to Prof. Tripathi and his family for their constant encouragement and support at all the stages of this work. I really enjoyed my stay in his group.
My sincere and heartfelt thanks are due to Prof. P .K.0 . Pillai and his family,Dr.
A・K・Sharma and his family for their help, encouragement and affection towards me and my wife . They are few of the nicest pe叩le I have come across.
I take this opportunity to thank Dr. H.D. Pandey for his constant encouragement and along with him, Prof. S.K. Dash and Prof. S.K. Dube for their kindness to offer me a job just after completion of the Ph.D work.
I am i ndebted to my seniors and colleagues, Dr. J. Parashar, Dr. K.K. Pant, Dr・ Anamika Shanna, Dr. Lalitha, Dr. Litty, Dr. R.N. Aggarwal, Dr, S.0 . Sharma, Mr・ Rashid, Mr. N.K, Ja如an and Mr. S. Shibu for their encouragement and interaction to keep the reasearch atmosphere very active and alive.
I personally want to thank my near and dear friends, Sridhar, Vijay, Venkat, Sandeep, Rajesh, Rakesh, Mac, G.K.,Seenu, Siva and others for keeping me a good company and making the life more joyful. I had a great time with them・
いst but not the least, J would like to acknowledge the blessings of my grand father and grand mother. Sri. R. B. Chani, Smt. Padmavathi Bai, and the love and affection of my brothers, sisters, my in-laws and their families. The patience and tolerence of my dear wife Sashi needs special mentioning here.
ABSTRACT
The present thesis focuses on two basic problems of laser plasma interaction' vi..
harmonic generation and parametric instabilities. ln the area of harmonic generation. WC have explored the possibility of resonant second harmonic generation in an underdense plasma・lt is seen that a magnetic wiggler could provide additional momentum to the second harmonic photon to satisfy energy and momentum conservations. This greaily enhances the efficiency of the harmonic process. We have also studied three hall harmonic generation in a plasma channel. In the area of parametric instabilities. our studies have been motivated by recent ex芦rinients. We attempted the theory ol' stimulated Raman scattering (SRS) to second harmoniと SRS. We also examined oscillating two stream and deca）・instahiJities in plasma channels, as they are relevant to wake field accelerator and laser－んsion plasmas. A chapterwise summary of the thesis iト given as follows.
In (he second chapter. a viggler magnetic field is used in the generation of second harmonic, mainly to produce a transverse second harmonic current 了22< 。， and to providビ an additional momentum， もえ to the second harmonic photon, thereby making thC second harmonic generation, a resonant process. A high power millimetre wave
（い，,k1) propagating through a magnetized plasma in the presence of a wiggler magnetic fleld (O，長w) produces density pe血rhations at （い」，王，＋長w). The density perturbations couple with the oscillatoi・y velocity at （い1,k1) to produce a nonlinear current at (2い1,2k1+kw) driv i ng second-harmonic electromagnetic radiation・A statiじ magnetic field B。乞 is used to enhance the amplitude of the generated wave via cyclotron resonance.
In the third chapter, we study the three half harmonic generation in a plasma channel. The Langmuir mode, generated in a two plasmon decay process. could couple nonlinearly M・iti) the laser pump to produじe three half harmonic in a plasma channel. Thじ channel could he a prefて）rmed OflC or created by the ponderomotive force of the laser．・
The density perturbations associated with the Langmuir wave couple with the oscillators
velocity due to the pump e1ectrornagnetic wave to produce nonlinear current density al three half harmonic. Since the axial extent of theいngmuir wave is limi1ed. the region of nonlinear interaction is also limited
In the fourth chapter, we propose a theory for the observed shif1 in frequency ol the order of plasma frequency in the generated second harmonic in the experinlen(s conducted at Naval Researchいboratory, Washigton DC.,in recent years. This could be due io the second harmonic SRS of laser radiation in the plasma. A high power linearly polarized laser propagating through a plasma produces oscillatory electron velocity at the second harmonic due to the マ ×B force. This velocity couples a いngmuir wave （い，k) a面 an electromagnetic wave （い1,k1). where い．－い－2いo，長1 ．で－2凡 and い。，馬 are frequency and wave vector of the laser pump, causing second harmonic Raman scattering. The growth rate is maximum for side scattering. This process can occur above the quarter critical density, unlike the first harmonic stimulated Raman scattering which occurs below the quarter critical density
Jn chapter 5, we study the nonlocal theory of the oscillating two stream instability (OTSI) of a plasma wave in a plasma channel. A long wavelength レngmuir wa＼・e
（い。，ち）,propagating through a parabolic plasma density channel, can decay into a low frequency mode （い，k) and two short wavelength レngmuir wave sidebands
（い，.2,k1ュ）,via two stream instability, where い，.2－い 1いo and k1,-k 7 凡・
Depending on the mode number n, the growth rate maximizes in the range Ym,，αO. iい，;-0.4い＿;for the range of k from O
、．■一n ド■ ". 一
and vh are the oscillatory and thermal velocities
iーとい． to O. い
2」 for VO'Vth,where v0
Cs Cs
of electrons，いpi 15 the lort plasma frequency on the axis, cs is the sound speed. The growth rate increases with the width a of the plasma density. channel. It decreases with the mode number. The instability maき be relevant to laser based charged particle accelerators.
In Chapter 6, we study the nonlocal theory of the decay instability in a paraho]ic plasma density channel. Near the critical layer, a large amplitude laser beam、creates
theory of the process is developed,for a parabolic density profile. The growth rate of the instability is significantly reduced due to the nonlocal effects. This instability may he relevant 如 the design of inertial confinement fusion devices.
CONTENTS
Chapter Page
i. Introduction
2. Millimetre-Wave Second-Harmonic Generation in an Underdense Magnetoplasma in the Presence of a Magnetic Wiggler
2. 1 Introduction
2.2 Pump Wave Propagation 23 Nonlinear Cunent Density 2.4 Second-Harmonic Field 2.5 Discussion
1-17 18-28 0八 （U ヘコ くJ lノ『ーA うL つー つー つ山
イ11 つ一 「つ 〔つ （つ 4 （『一 （『】
Three Half Harmonic Generation in a Plasma Channel
Introduction
Nonlinear Current Density Three Half Harmonic Field Discussion
29-38 0ノ 111 「つ OU つ一 （つ （つ （つ
11
4 4
Second Harmonic Stimulated Raman Scattering of
いser Radiation in a Plasma Introduction
3 9-47 9一 n（「一 4 4
00 CU 00 d什 一へ一 く」 11 つーぐJ く」
Oscillating Two Stream Instability of a Plasma
Wave in a Plasma Channel 48-58
Introduction
Oscillating Two Steam Instability 5.3 Conclusion
11 つ一 一
6 6 6.3 6.4
Decay Instability in a Plasma Channel Introduction
Pump Wave
Instability Analysis Conclusion
59-68 nソ 11ょ つ1 nろ 一へ一 AU 6 6
REFERENCES 69-7)
APPENDIX 1(>
