Laser plasma interaction and terahertz (THz) radiation

LASER PLASMA INTERACTION AND TERAHERTZ (THz) RADIATION

RAM KISHOR SINGH

CENTRE FOR ENERGY STUDIES

INDIAN INSTITUTE OF TECHNOLOGY DELHI

©Indian Institute of Technology Delhi (IITD), New Delhi, 2016

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Acknowledgements

I wish to express my sincere gratitude to my supervisor Prof. R. P. Sharma, Centre for Energy Studies, IIT Delhi, for his systematic guidance, cool temperament, valuable suggestions, support, advice and constant encouragement throughout the course of my research work. The critical comments rendered by him during the discussions are deeply appreciated. I could not have imagined having a better advisor and mentor for my Ph.D. work. It is because of his deep knowledge of the subject that this work has taken the present shape. I hope that I could be as lively, enthusiastic and energetic as him. I could not be prouder of my academic roots and hope that I can in turn pass on the research values and the dreams that he has given to me.

I am deeply obliged to Prof. A.D. Rao, Prof. T. S. Bhatti, Dr. R. Uma, Dr.

Ramesh Narayna, and all faculty members of CES for their valuable suggestions, advices and approval of my thesis work. I thank to other staff members of Center for Energy studies, IIT Delhi for their kind help and cooperation during my research work.

I am particularly thankful to all my group members, Dr. Monika Singh, Dr.

Naveen Kumar Dwivedi, Dr. Kalpesh modi, Dr. Nitin Yadav, Dr. Nidhi Sharma, Dr.

Alok ji, Nilesh Kumar Pathak, Ravindra, Sangita, Anju, Ashis, Swati, Dr. Motilal Rinawa, Subodh Kumar, Prachi, Pradeep and Saba for their cooperation, and support during my research work. Last but not least special thanks go to my friends Deepanshu, Eshwar, Sanjay, Madhu Sudan, Piyush, Manish, and Manoj Kumar for

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their wonderful cooperation, positive criticism and selfless help during my research work at IIT Delhi.

This acknowledgement would remain incomplete without expressing my sincere feelings towards my parents and other family members for their patience, and understanding during my research work. I owe it deeply to them for their encouragement and support, which gave me courage and confidence to materialize this research work.

I also wish to express my gratefulness to University Grants Commission (U.G.C.), India for financial support of the work.

Finally, I solicit blessings of God for progress and prosperity.

Ram Kishor Singh

Abstract

The present thesis is an attempt to understand parametric decay processes (stimulated Raman and Brillouin back scattering) and mechanisms of terahertz (THz) radiation generation in the course of laser plasma interaction. The study includes the analytical modeling and numerical simulations for different cases of laser plasma interaction in paraxial ray approximation.

In the parametric decay, stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) processes have unique place because these processes arise during high power laser plasma interaction and are undesirable in laser induced fusion. The laser beam imparts an oscillatory velocity to the plasma species.

A nonlinear current density arises at beat frequency when this nonlinear oscillatory velocity couples with the pre-existing density perturbation. This nonlinear current density is responsible for the SRS and SBS processes. The charge species in plasma also experiences a nonlinear force, known as ponderomotive force that arises due to non-uniform intensity profile of the laser beam. This nonlinear force expels the electron from maximum irradiance position to lower irradiance region. The dielectric constant change according to plasma density and therefore plasma behaves like a converging lens. A propagating high power laser beam gets self focused and beam intensity enhances many fold at the focused region. At the focused position the nonlinear processes also get affected which in turn enhance back scattered light through SRS and SBS processes. From experimental point of view, the high power laser beam may not have a Gaussian intensity profile but have superimposed spike or

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ring ripple which has irradiance maximum far from the axis. The ring ripple intensity profile can be written in the form of hollow Gaussian laser beam (HGB). The laser beam having HGB intensity profile can get self focused and excite the electron plasma wave and ion acoustic wave with similar spatial profile.

Plasma has also been used as a nonlinear medium for the high power electromagnetic radiation in THz region because it can sustain high power. A wave in THz region can be excited by various methods with the help of laser plasma interaction though the beat wave mechanism is more popular. Nonlinear mixing of laser frequencies in plasma arises due to collisional, ponderomotive and relativistic nonlinearity which are set up in different time scales. In collisional nonlinearity, electrons acquire nonlinear oscillatory velocities at beat wave frequency due to temperature dependent collisional frequency and externally applied static electric field perpendicular to the direction of propagation. This nonlinear oscillatory velocity couples with the pre-existing density ripple and gives rise to nonlinear current density which is the source of THz radiation generation. In the case of ponderomotive nonlinearity, electrons experiences a ponderomotive force at beat wave frequency in the direction perpendicular to the direction of two copropagating laser beams having non-uniform intensity profiles. This ponderomotive force causes the nonlinear oscillatory velocity of electrons which couples with the pre-existing ripple density and gives rise to transient current density. Besides the beat wave frequency generation method, one can also generate THz wave by amplitude modulated laser beam having modulation frequency in THz region. The electrons experience a nonlinear oscillatory velocity which arises on the account of ponderomotive force at modulation frequency.

A source for THz radiation can be achieved if this nonlinear oscillatory velocity couples with the pre-existing density ripple.

The second chapter deals with back SRS process and third chapter with SBS process in filamented HGB. The back reflectivities get significantly affected in self focused HGB and have maximum reflectivity around the maximum irradiance. In the fourth chapter of the thesis, excitation of the THz radiation has been proposed by beating of two copropagating laser beams having cosh-Gaussian intensity profile in a periodic density plasma considering ponderomotive nonlinearity. Fifth chapter deals with excitation of the THz radiation by the beating of two cross focused laser beams having Gaussian intensity profile in periodic density plasma, considering collisional nonlinearity and externally applied static electric field. Cross focusing effects of two spatial-Gaussian laser beams in the presence of externally applied magnetic field on the generation of THz radiation has been discussed in chapter six, considering ponderomotive nonlinearity. In the seventh chapter of thesis, excitation of the THz radiation has been proposed by self focusing of amplitude modulated Gaussian laser in magnetized plasma, considering ponderomotive nonlinearity. Studies show that cross focusing, externally applied static magnetic and electric field enhance the THz yield significantly.

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Contents

Certificate i

Acknowledgements ii

Abstract iv

Contents vii

List of Figures xi

Chapter 1 Introduction 1-27 1.1 Background 1

1.2 Self focusing of laser beam 6

1.2.1 Collisional nonlinearity 7

1.2.2 Ponderomotive nonlinearity 7

1.2.3 Relativistic nonlinearity 8

1.3 Stimulated Raman scattering 9

1.4 Stimulated Brillouin scattering 10

1.5 THz sources based on laser plasma interaction 11

1.5.1 Effect of the external static electric field 12

1.5.2 Effect of the external static magnetic field 12

1.5.3 Effect of laser beam focusing 13

1.5.4 Importance of density ripples 13

1.6 Methodology 14

1.7 Objective and outline of the thesis 15

Chapter wise summary of the thesis 18

References 22

Chapter 2 Stimulated Raman back scattering of filamented hollow Gaussian beam 28-46 2.1 Introduction 28

2.2 Propagation of hollow Gaussian laser beam and excitation of 30

electron plasma wave 2.3 Stimulated Raman scattering 36

2.4 Results and Discussion 39

2.5 Conclusion 41

References 45

Chapter 3 Stimulated Brillouin back scattering of filamented hollow Gaussian beam 47-65 3.1 Introduction 47

3.2 Propagation of hollow Gaussian laser beam and excitation of 49

ion acoustic wave 3.3 Stimulated Brillouin scattering 55

3.4 Results and discussion 58

3.5 Conclusion 60

References 64

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Chapter 4 THz generation by cosh-Gaussian lasers in a rippled density

plasma 66-82

4.1 Introduction 66

4.2 Evaluation of nonlinear current density 68

4.3 Result and discussion 71

References 80

Chapter 5 Terahertz generation by two cross focused laser beams in collisional plasmas 83-101 5.1 Introduction 83

5.2 Propagation of Gaussian laser beams in collisional plasma 85

5.3. Generation of THz radiation 88

5.4 Results and discussion 91

5.5 Conclusion 93

References 99

Chapter 6 Terahertz generation by two cross focused Gaussian laser beams in magnetized plasma 102-120 6.1 Introduction 102

6.2 Cross-focusing of laser beams 105

6.3 Generation of THz radiation 108

6.4 Results and discussion 110

6.5 Conclusion 113

References 118

Chapter 7 Terahertz radiation by self focused amplitude modulated Gaussian laser beam in magnetized ripple density plasma 121-136

7.1 Introduction 121

7.2 Self focusing of amplitude modulated laser beam 123

7.3 Terahertz (THz) radiation 126

7.4 Results and discussion 128

7.5 Conclusion 130

References

¹³⁵

Chapter 8 Summary and future prospects 137

List of research publications 139

Bio-data of the author 142

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List of Figures

Figure Number

Description Page

2.1 Normalized intensity distribution for order 1. (a) HGB and EPW at ξ=0, (b) HGB at first focal point, (c) EPW at first focal point, (d) Back SRS at first focal point.

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2.2 Normalized intensity distribution for order 2. (a) HGB and EPW at ξ=0, (b) HGB at first focal point, (c) EPW at first focal point, (d) Back SRS at first focal point.

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2.3 Normalized intensity distribution for order 3. (a) HGB and EPW at ξ=0, (b) HGB at first focal point, (c) EPW at first focal point, (d) Back SRS at first focal point.

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2.4 Variation of back reflectivity against normalized distance of propagationξ.

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3.1 Normalized intensity distribution for order 1. (a) HGB and IAW at ξ=0, (b) HGB at first focal point, (c) IAW at first focal point, (d) Back SBS at first focal point.

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3.2 Normalized intensity distribution for order 2. (a) HGB and IAW at ξ=0, (b) HGB at first focal point, (c) IAW at first focal point, (d) Back SBS at first focal point.

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3.3 Normalized intensity distribution for order 3. (a) HGB and IAW at ξ=0 , (b) HGB at first focal point, (c) IAW at first focal point, (d) Back SBS at first focal point.

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3.4 Variation of back reflectivity against normalized distance of propagationξ.

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4.1a

Normalized cosh-Gaussian laser field amplitude and intensity vs.

normalized transverse distance



x/w0



for 0 b 1. Dashed line, solid line is respectively for normalized intensity and normalized amplitude. Whenw =.05mm0 ,ω =2.4×10 rad/sec, 1 ¹⁴

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ω =2.1×10 rad/sec2 and ω =2×10 rad/sec. p ¹³

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4.1b Normalized cosh-Gaussian field amplitude and intensity vs. x w0

for1 b 2. Normalized intensity and normalized amplitude are represented by dashed line, solid line respectively.

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4.2 Variation of normalized emitted radiation amplitude vs. ω ω_p for different values of n nα 0 0.1, 0.3 and 0 b 1. All laser plasma parameters are same as in Fig. (4.1).

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4.3a Variation of normalized THz radiation field amplitude vs. x w for ₀ 0 b 1 and n n_{α 0} 0.1 for the same parameters as in Fig. (4.1).

ω1=2.4×10 rad/sec,¹⁴ ω ₂ =2.1×10 rad/sec¹⁴ .

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4.3b Normalized THz radiation field and vs. x/w for ₀ 1 b 2 of two 78

xiii lasers in rippled density plasma.

4.4 Efficiency of THz radiation generation vs. normalized beating frequency for 0 b 1. Dashed lines, solid lines are respectively for x w0 2 3,1 2 andn nα 0 0.1 for the same parameters as in Fig. (4.1).

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5.1 Variation of first laser beam intensity with normalized distance in radial (normalized byr ) and propagation wave direction ₁₀ (normalized byR_d) in collisional plasma forν =1ns . ₀ ^-1

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5.2 Variation of first laser beam intensity with normalized distance in radial (normalized byr₁₀) and propagation wave direction (normalized byR_d) in collisional plasma forν =1.3ps . ₀ ^-1

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5.3 Schematic representation for THz radiation generation in the presence of external static field and ripple density plasma.

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5.4 Normalized THz amplitude forν =1ns , (a) ₀ ^-1 E =0.5kVcm with _dc ^-1 cross focusing of laser beams (b) E =0.5kVcm without cross _dc ^-1 focusing of laser beams (c) E =1kVcm with cross focusing of _dc ^-1 laser beams (d) E =1kVcm without cross focusing of laser beams. _dc ^-1

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5.5 Normalized THz amplitude forν =1.3ps , (a) ₀ ^-1 E =0.5kVcm with _dc ^-1 cross focusing of laser beams (b) E =0.5kVcm without cross _dc ^-1 focusing of laser beams (c) E =1kVcm with cross focusing of _dc ^-1

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laser beams (d) E =1kVcm without cross focusing of laser beams. _dc ^-1 5.6 Power spectra of THz radiation with and without cross focusing of laser beams for external static electric field E =0.5kVcm and _dc ^-1

-1

E =1kVcm respectively, whendc r r =0₁₀ andν =1ns₀ ^-1.

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6.1 Variation of dimensionless beam width parameters of laser beams with varying electron cyclotron frequency; ω =0.1ω ,0.3ω _{c p p} and0.5ω_p. The solid lines show the variation of dimensionless beam width parameter f₁while dotted lines show for f₂ with normalized distance of propagation, when both laser beams are present. The dash lines show the variation of beam width parameter f₁in the absence of the second laser beam.

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6.2 Normalized Intensity variation of (a) first laser beam (b) second laser beam with normalized distance of propagation forω =0.5ω_{c p}.

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6.3 Schematic representation for THz radiation generation in externally applied static magnetic field in ripple density plasma.

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6.4 Normalized THz amplitude variation with and without cross focusing of laser beams for ω =0.1ω ,0.3ω_{c p p} and0.5ω . The solid _p line shows the variation of Normalized THz amplitude with cross focusing while dotted line shows without cross focusing against the normalized radial direction

 

y/r1 .

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6.5 Power spectra of THz radiation with cross focusing (solid line) and without cross focusing (dotted line) of laser beams aty r =0.4 for ₁

c p p

ω =0.1ω ,0.3ω and0.5ω_p.

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7.1 Variation of beam dimensionless width parameters with normalized distance.

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7.2 Schematic diagram for the THz radiation in magnetized ripple density plasma.

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7.3 Variation of THz radiation amplitude with normalized distance around the maximum irradiance (y/r =0.4, z=0₀ ) for (a)

c p

ω =0.1ω and (b) ω =0.6ω_{c p} forn =0.2n_{q 0}.

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7.4 Variation of THz radiation amplitude with radial distance y/r₀ of the laser beam forn =0.2n_{q 0}.

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7.5 Power spectra of THz radiation with cross focusing (solid line) and without cross focusing (dotted line) of laser beams aty r =0.4 for ₁ (a) ω =0.1ω_{c p} and (b)ω =0.6ω_{c p} forn =0.2n_{q 0}.

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