COLLISIONAL EFFECTS ON THZ RADIATION GENERATED BY LASER
PLASMA INTERACTION
DIVYA SINGH
DEPARTMENT OF PHYSICS
INDIAN INSTITUTE OF TECHNOLOGY DELHI
JULY 2016
©Indian Institute of Technology Delhi (IITD), New Delhi, 2016
COLLISIONAL EFFECTS ON THZ RADIATION GENERATED BY LASER
PLASMA INTERACTION
by
DIVYA SINGH Department of Physics
Submitted
in fulfilment of the requirements of the degree of
Doctor of Philosophy
to the
Indian Institute of Technology Delhi
JULY 2016
Dedicated to
my family and loved ones
&
those
whoever inspired and encouraged me
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Certificate
This is to certify that the thesis entitled “Collisional Effects on THz Radiation Generated by Laser Plasma Interaction” being submitted by Ms. Divya Singh is worthy of consideration for the award of the degree of Doctor of Philosophy and is a record of the original bonafide research work carried out by her under my guidance and supervision, and that the results contained in it have not been submitted in part or full to any other university or institute for award of any degree/ diploma.
I certify that she has pursued the prescribed course of research. I approve the thesis for the award of the degree of Doctor of Philosophy.
Hitendra K. Malik Professor Department of Physics Indian Institute of Technology Delhi INDIA
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Acknowledgements
________________________________________________________________
In the course of this Ph.D. research, I have been blessed with the support of many people.
I feel my heart core indebtedness to my supervisor Professor Hitendra K. Malik for his advice, patience, selfless support and guidance during this entire duration of the course.
His insights remain always enlightening to me. It is very pleasant working with Prof. Malik.
I would like to express my sincere thanks to my parent institution, Rajdhani College, University of Delhi, to provide me No Objection, in order to pursue this Ph.D. research at IIT Delhi.
Every research scholar needs and values the support of their fellow members. I thank all the members of Plasma Waves and Particle Acceleration (PWAPA) Laboratory of Department of Physics, IIT Delhi, for endless hours of useful and useless discussions. I feel very grateful to Dr. Sukhmander Singh for his help in sharing and learning MATLAB software for the Research in initial days. I also thank Dr. Rakhee Malik to help me plotting graphs in MS-Excel software.
Above all, I extend many thanks to my family, my parents, my parents in laws, my loving husband Dr. Saurav Suman and my caring sisters Poorva Singh and Ayushi Dheeraj for their selfless love, support and encouragement that they extended to me all the time, during the course of Ph.D. research. Without their support and understanding, I would not be able to finish it at far.
At last, I express my gratitude, obligations and indebtedness to God for giving me the strength and patience to complete and write my Ph.D. dissertation and also thank for blessing me with such a group of nice fellow members and family.
Divya Singh
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Abstract
_____________________________________________
Electromagnetic radiation in Terahertz range (0.1 – 10 THz) lying between high frequency microwave and low frequency IR region is non-ionizing, non-invasive and intrinsically safe and is an important research tool. That is why THz radiation may be used for bio-inspired research. These numerous applications are medical imaging, material characterisation, chemical engineering systems, instrumentation and pharmaceuticals, communication and wireless data transmission, the THz Time Domain Spectroscopy (THz- TDS) and in security systems. THz radiations can be classified into incoherent radiations, broadband coherent radiations and narrowband coherent radiations. Photoconduction and optical-rectification are two most common approaches for generating broad band THz radiation. The photoconductive materials have been employed to generate relatively large average THz power and bandwidth as high as 4 THz. Optical rectification makes use of inverse of the electro-optic effect. The narrow band THz radiation sources are crucial for high resolution spectroscopy applications like in telecommunications, particularly for extremely high band width intra-satellite links. Traditional laser based THz emitters like electro-optic crystals and photo-conductive antennas are subjected to low conversion efficiencies of THz emission and also to material breakdown at such high powers. This problem is not encountered with plasmas, as the plasma is highly nonlinear and impervious to material breakdown and can sustain very high field. Hence, the damage limit in case of plasmas is negligible.
In the proposed thesis, collisional effects on the mechanism of THz radiation generationare investigated by laser plasma interaction. Generation of THz radiation is theoretically investigated in laser produced plasma based on the approach of development of ponderomotive force and induced nonlinear plasma currents driven by an inhomogeneous laser electric field. In the studies conducted by other researchers, they have largely assumed the Gaussian distribution of the lasers intensity/ field, and obtained low conversion efficiency in the mechanism. However, we have made efforts to enhance the efficiency by wisely choosing the lasers intensity profile and applying external uniform magnetic field or periodic electric field on the plasma electrons. Under this situation, maximum transfer of laser energy take place to the plasma electrons through the coupling of ponderomotive force and nonlinear currents generated in plasma. For the sake of completeness, we consider the collisions between the electrons and neutral atoms in the plasma, which are not taken into account by other workers due to complexity of the problem. Moreover, in the next attempt, we consider the finite temperature of the electrons. The effect of electron thermal motion is found to decay the efficiency if the electron neutral collision frequency is comparable to or greater than 1/10th of plasma frequency; otherwise for lower collisional frequencies, the thermal
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motions help generating stronger nonlinearities in plasma electrons redistribution and the current. On the other hand, we have obtained THz radiation through a different approach of wake field excited in plasma under the application of external magnetic field. In particular, a transverse component of electromagnetic field is generated in presence of perpendicular magnetic field. This field excites the THz radiation. Here, our main focus has been to achieve larger field with the application of stronger magnetic field and different index of super- Gaussian laser pulses. A comparative study of the two mechanisms, i.e. wake field and beating, reveals that the THz of higher field is possible through the laser beating. This is due to the fact that the lasers produce a longitudinal component of wake field in which a part of energy is utilized.
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Table of Contents
_____________________________________________
Page No.
Certificate ... i
Acknowledgements ... ii
Abstract ... iii-iv Table of Contents ... v-viii List of Figures ... ix-xv List of Tables ... xvi
List of Symbols ... xvii - xix List of Abbreviations ... xx
Chapter 1 Introduction and Literature Review ... 1 - 35 1.1 Plasma ... 1
1.1.1 Underdense and overdense plasmas ... 2
1.1.2 Weakly coupled and strongly coupled plasmas ... 3
1.1.3 Collisionless and Collisional plasmas ... 4
1.2 Laser Interaction with Plasma ... 5
1.2.1 Laser field and profile ... 6
1.2.2 Quiver velocity of plasma electrons ... 9
1.2.3 Ponderomotive force ... 11
1.2.4 Beat wave process ... 12
1.2.5 Wake field excitation... 13
1.3 Overview and Scope of THz Radiation ... 14
1.3.1 New research aspect of THz technology ... 15
1.3.1.1 Medical applications ... 16
1.3.1.2 Optical applications ... 17
1.3.1.3 Spectroscopic applications ... 17
1.3.1.4 Other applications ... 19
1.3.2 THz radiation generation and detection ... 19
1.3.2.1 THz by optical rectification ... 20
1.3.2.2 THz by photoconductive antenna ... 22
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1.3.2.3 THz by laser plasma interaction ... 23
1.3.2.4 THz radiation detection ... 29
1.4 Motivation ... 30
1.5 Thesis Organization ... 31
Chapter 2 Laser Beat Wave Excitation and THz Emission ... 37 - 62 2.1 Plasma Electrons Dynamics in Laser Field ... 37
2.1.1 Super-Gaussian laser profile and ponderomotive force ... 38
2.1.2 Excitation of plasma currents ... 39
2.1.3 Resonance and phase matching condition ... 41
2.2 Calculation of THz Radiation field ... 43
2.2.1 Effect of beam width ... 44
2.2.2 Effect of density ripples ... 46
2.2.3 Effect of sG index on critical transverse distance ... 47
2.3 Efficiency of THz Radiation Mechanism ... 48
2.4 Bifocal THz Radiation ... .51
2.4.1 Skew cosh-Gaussian laser ... 52
2.4.2 Excitation of plasma currents ... 52
2.4.3 Emission of THz radiation ... 53
2.4.4 Efficiency of the Mechanism of THz radiation ... 53
2.4.5 Discussions ... 54
2.5 Focii of Bifocal THz Radiation and Role of Skewness Parameter ... 60
2.6 Conclusions ... 62
Chapter 3 THz Emission under External Magnetic Field ... 63 - 80 3.1 Plasma Electron Dynamics in External Magnetic Field ... 63
3.1.1 Nonlinear ponderomotive force ... 64
3.1.2 Excitation of plasma currents ... 65
3.2 Calculation of THz Fields ... 66
3.2.1 Dielectric tensor ... . 66
3.2.2 Resonance and phase matching condition ... 68
3.3 Efficiency of THz Radiation Mechanism ... 69
3.4 Study of THz field amplitude and efficiency ... 69
3.5 Tuning of THz Frequency ... 77
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3.6 Conclusions ... 80
Chapter 4 Effect of Thermal Motion of Electrons on THz Emission ... 81 - 97 4.1 Plasma Electrons Dynamics in Laser Field ... 81
4.1.1 Ponderomotive force for sG laser profile ... 82
4.1.2 Generations of plasma currents ... 83
4.2 Discussion on Modified Resonance and Phase Matching Condition ... 85
4.3 Calculation of THz Radiation Field ... 88
4.3.1 Effect of electron-neutral collision ... 89
4.3.2 Effect of plasma electrons temperature ... 92
4.4 Efficiency of THz Radiation Mechanism ... 94
4.5 Conclusions ... 96
Chapter 5 THz Emission under External Periodic Electric Field ... 99 - 114 5.1 Derivation of electrons Oscillatory Velocity ... 100
5.2 Study of Ponderomotive Force ... 101
5.3 Study of Different Kinds of Plasma Currents ... 103
5.4 Derivation of Phase Matching Condition ... 106
5.5 Evaluation of Different Kinds of THz Radiation Fields ... 107
5.5.1 Comparison of beat wave enabled THz and external field induced THz fields ... 108
5.6 Role of External Periodic Electric Field ... 110
5.7 Efficiency of Scheme ... 111
5.8 Conclusions ... 113
Chapter 6 Plasma Wake Fields and THz Emission ... 115 - 136 6.1 Reductive Perturbation Technique ... 115
6.1.1 Current density for sG laser field profile ... 116
6.1.2 Current density for chG laser field profile ... 119
6.2 Quasistatic Approximation and Excitation of Plasma Wake Field ... 121
6.3 SG Laser Driven THz Radiation and Discussion ... 122
6.4 ChG Laser Driven THz Radiation and Discussion ... 131
6.5 Conclusions ... 136
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Chapter 7 Concluding Remarks and Future Works ... 137 - 142
7.1 Concluding Remarks ... 137
7.2 Future Scope of Work ... 139
7.2.1 The Development of High Power THz Radiation ... 140
7.2.2 Nonlinear Terahertz Effect ... 140
7.2.3 THz Plasmonic Lenses ... 141
7.2.4 Nanomaterial Incorporated THz Technology ... 141
7.2.5 Polarization Control of Emitted THz Radiation ... 141
Research Publications ... 143 - 145 References ... 147 - 157 Brief Bio-data of the Author ... 159
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List of Figures
Fig 1.1 Plasma is 4th and most common state of matter.
Fig 1.2 Different types of plasma in nature and science, the tilted lines denote the Debye length.
Fig 1.3 Profiles of electric field of SG lasers for different index p, when E0L = 5
˟108V/m and bw= 0.01 cm. Here, p = 2 corresponds to the Gaussian laser.
Fig 1.4 Beam profile of incident laser pulses is shown for skew-ChG beams for different orders-n and skewness parameters.
Fig 1.5 Geometry and Schematic of Terahertz Radiation Generation by beating of lasers in plasma where plasma has corrugated density profile along the axis of propagation.
Fig 1.6 THz band in electromagnetic spectrum.
Fig 1.7 THz generation by optical rectification.
Fig 1.8 THz generation by Photo conductive antenna.
Fig 2.1 Variation of normalized wave number of periodic structure of density ripples with normalized electron-neutral collision frequency for different values of laser beat wave frequency.
Fig 2.2 Transverse profile of THz radiation field with different values of sG index p and collision frequency ν, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, bw= 0.01cm and Nα/N0 = 0.3.
Fig 2.3 3D surface plot of variation of normalized THz radiation field with normalized transverse distance yfrom the z-axis and normalised density ripples, for different values of p and ν, ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, and bw= 0.01cm.
Fig 2.4 Dependence of critical transverse distance y0 on different values of SG index.
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Fig 2.5 Variation of efficiency of THz radiation mechanism with beam width bw for different values of p and ν, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, y = 0.8bw and Nα/N0 = 0.4.
Fig 2.6 Variation of efficiency of THz radiation mechanism with bw for different values of collision frequency and Skewness parameter for n=1, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, y = 0.5bw and Nα/N0 = 0.1.
Fig 2.7 Variation of efficiency of THz radiation mechanism with bw for different values of collision frequency and skewness parameter for n=2, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, y = 0.5bw and Nα/N0 = 0.1.
Fig 2.8 Transverse profile of THz radiation field with different values of skewness parameter (below critical parameter) and collision frequency ν, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, bw= 0.01cm and Nα/N0 = 0.1.
Fig 2.9 3D surface plot of variation of normalized THz radiation field with normalized transverse distance yfrom the z-axis and normalised beating frequency (above critical parameter), for different values of s, ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, and bw= 0.01cm.
Fig 2.10 3D contour Plot of variation in the normalized THz radiation field with normalized transverse distance yfrom the z-axis as well as normalised beating frequency (above critical parameters for n=1) for ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/m, and bw= 0.01cm.
Fig 2.11 Variation in the efficiency of THz radiation field with Skewness parameter.
Here other parameters are the same as in Fig 2.10.
xi
Fig 3.1 Variation of nonlinear ponderomotive force with normalised collision frequency when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y
= 0.8bw p = 6 and Nα/N0 = 0.4.
Fig 3.2 Variation of nonlinear oscillatory current with external applied magnetic field for different values of p, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw and Nα/N0 = 0.4.
Fig 3.3 Transverse profile of THz radiation field with different values of SSG index p, collision frequency ν and normalised ripple density Nα/N0, when ω1= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, bw= 0.01cm, ω = 1.15ωp and B = 5T.
Fig 3.4 Variation of normalized THz radiation field with normalized collision frequency for different values of p and external magnetic field, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, ω = 1.15ωp, E0 = 5.0×108 V/cm, Nα/N0 = 0.4, bw= 0.01cm and y/bw= 0.8.
Fig 3.5 Variation of efficiency of THz radiation mechanism with normalised collision frequency for different values of p, ν and B, when ω1 = 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw and Nα/N0 = 0.4.
Fig 3.6 Variation of normalized THz field amplitude and normalized wave number of periodic structure of density ripples with external magnetic field for different values of laser SG index, when the other parameters are the same as used in Fig.3.1.
Fig 3.7 Dependence of THz radiation frequency and average energy flux density of the emitted THz radiation on the external magnetic field for SSG lasers of index p = 6.
xii
Fig 4.1 Variation of normalized ripple wave number with electron temperature for various collision rates of plasma electron with neutrals when ω= 2.4×1014 rad/s andωp= 2.0×1013 rad/s.
Fig 4.2 Variation of normalized ripple wave number with normalised resonant frequency for different electron temperature when ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, p = 6 and y = 0.8bw.
Fig 4.3 Variation of normalized ripple wave number with normalised collision frequency for various plasma resonant frequency when ωp= 2.0×1013 rad/s and Te = 3keV.
Fig 4.4 Variation of normalised magnitude of emitted THz radiation field with electron temperature when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s,ν = 0, E0 = 5.0×108 V/cm, y = 0.8bw, p = 6, and Nα/N0 = 0.4.
Fig 4.5 Comparative variation of normalised magnitude of emitted THz radiation with electron temperature in presence of low or high collisions with sG laser of beam width bw = 0.01 cm when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw and p = 6.
Fig 4.6 Comparative variation of normalised magnitude of emitted THz radiation with electron temperature in presence of collisions with SG laser of beam width bw
= 0.01 cm when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw and p = 6.
Fig 4.7 Effect of Resonant frequency on normalised magnitude of emitted THz radiation at different electron temperatures when ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw p = 6 and ν = 0.05 ωp.
xiii
Fig 4.8 Comparative variation of efficiency of the mechanism of emitted THz radiation with electron temperature in presence of collisions with SG laser of beam width bw = 0.01 cm when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw and p = 6.
Fig 4.9 Variation of efficiency of the mechanism of emitted THz radiation with normalised resonant frequency for different electron temperature when ωp= 2.0×1013 rad/s,ν = 0.05 ωp, E0 = 5.0×108 V/cm, p = 6 and y = 0.8bw.
Fig 5.1 Schematic of THz radiation generation in presence of periodic electric field via laser plasma interaction.
Fig 5.2 Transverse components of ponderomotive force with normalized distance from beam axis when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, p = 6,ν = 0.05ωp, E0= 5.0×108 V/cm,Es= 1.0×103V/cm, bw = 0.01cm; FpNL beating and FpNL EFI represent the first term and resultant of last two terms of Eq. (5.9) respectively.
Fig 5.3 Variation of magnitudes of plasma currentsJ1NLy
and EFI plasma currentsJ2NLy with normalized transverse distance for SG laser whenbw = 0.01cm, ω=
2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, Es= 1.0×103V/cm, p = 6 and ν = 0.05 ωp.
Fig 5.4 Variation of normalized amplitude of emitted THz radiation field (a) beat wave enabled THz radiation and (b) EFI THz radiation with beam width for various sG laser profiles and normalized beat wave frequency, when ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bwand ν = 0.05 ωp.
Fig 5.5 Variation of normalized magnitude of emitted EFI THz radiation field with external periodic electric field for SG laser when ω= 2.4×1014rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bwand ν = 0.05 ωp.
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Fig 5.6 Variation of EFI plasma currents and ponderomotive force with strength of periodic electric field for SG laser of p = 6when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bwandν = 0.05 ωp.
Fig 5.7 Variation of efficiency of the mechanism of the generation of EFI THz radiation field with strength of external electric field for SG laser when ω=
2.4×1014rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bwandν = 0.05 ωp.
Fig 6.1 Transverse profile of longitudinal wakefield with normalised distance from beam axis for various collision frequency when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw p = 8, L = 0.5 λp andξ = -0.25L.
Fig 6.2 Nature of wake field obtained numerically and analytically from Eq.
(6.49),when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw, p = 8, ν = 0.05 ωp,, B = 1 Tesla, L = 1.5 λp and ξ = -0.25L.
Fig 6.3 Variation of amplitude of emitted THz radiation (Ey) and longitudinal wakefield (Ez) with sG laser for bw = 0.01 cm when ω= 2.4×1014 rad/s, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw, p = 8, ν = 0.5 ωp,, B = 1 Tesla, L
= 1.5 λp and ξ = -0.25L.
Fig 6.4 Variation of normalized magnitude of emitted THz radiation field with beam width for various sG laser profiles when ω= 1.15ωp, ωp= 2.0×1013 rad/s, E0 = 5.0×108 V/cm, y = 0.8bw ,ν = 0.5 ωp,, B = 1 Tesla, L = 0.5 λp and ξ = -0.8L.
Fig 6.5 Transverse profile of emitted THz radiation field with normalized transverse distance from beam axis for various collision frequencies when p = 2, 4, 6, ω=
1.45ωp, ωp= 2.0×1013 rad/s,bw=0.01 cm, E0 = 5.0×108 V/cm, y = 0.8bw ,ν = 0.5 ωp,, B = 1Tesla, L = 0.5 λp and ξ = -0.8L.
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Fig 6.6 Variation of normalized amplitude of emitted THz radiation field (Ey/E0) and longitudinal wakefield (Ez/E0) with sG index p for bw=0.01 cm when ω=
1.15ωp, ωp= 2.0×1013 rad/s,bw=0.01 cm, E0 = 5.0×108 V/cm, y = 0.8bw ,ν = 0.05 ωp,, B = 1Tesla, L = 0.5 λp and ξ = -0.8L.
Fig 6.7 Variation of normalized amplitude of emitted THz radiation field with normalized collision frequency for SG index p = 6 when bw=0.01 cm , ω=
1.15ωp, ωp= 2.0×1013 rad/s,bw=0.01 cm, E0 = 5.0×108 V/cm, y = 0.8bw , B = 1Tesla, L = 0.5 λp and ξ = -0.8L.
Fig 6.8 Plot of THz field amplitude with skewness index-‘s’ for skew chG laser in plasma, when ω = 2.4×1014 rad/sec, ωp = 2.0×1013 rad/sec, y = 0.5bw , E0 = 5.0×108 V/m, bw = 0.01cm and L = 0.5λp.
Fig 6.9 3D visualization of dependence of field amplitude of THz radiation with normalized collision frequency and external magnetic field in the plasma for critical skewness parameters (n, s), when ω = 2.4×1014 rad/sec, ωp = 2.0×1013 rad/sec, y = 0.5bw , E0 = 5.0×108 V/m, bw = 0.01cm and L = 0.5λp.
Fig 6.10 3D visualization of dependence of transverse profile of THz field amplitude with normalized frequency and normalized transverse distance from the beam axis of propagation of laser in plasma for skewness parameter set (n, s) when ω = 2.4×1014 rad/sec, ωp = 2.0×1013 rad/sec, y = 0.5bw , E0 = 5.0×108 V/m, bw = 0.01cm and L = 0.5λp.
Fig 7.1 Summary figure of the global market for THz radiation devices and system from 2007-2018.
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List of Tables
Table 1.1 Electron densities in different laser produced plasmas.
xvii
List of Symbols
B External magnetic field
Bw Magnetic plasma wake field EL Laser electric field
ETHz Terahertz electric field
Es External periodic electrostatic field Ew Electric plasma wake field
FpNL Ponderomotive force
J Plasma current density
L Laser pulse length
M Ion mass
ND Number of particles in Debye sphere i.e. Debye Number Ne Plasma electron density
Ni Plasma ion density
N0 Total density
Nα/N0 Normalized ripple density Nʹ Periodic ripples (Nαeiαz) density
P Polarization
Te Electron temperature
Ti Ion temperature
<WL> Energy density of laser
<WTHz> Energy density of THz
a Normalized (eE/mcω) electric field of laser; perturbation expansion parameter bw Beam width of laser
c Speed of light
e Electron charge
xviii k Wave number difference of lasers
kp Plasma wave number
kB Boltzmann’s constant
k1, 2 Wave number of lasers
m Electron mass
n Order of skew ChG laser
p sG laser index
υ Plasma electron velocity
υg Laser group velocity
υp Plasma wave phase velocity
υq Quiver velocity of plasma electrons υth Electron thermal velocity
s Skewness parameter of ChG laser
y Transverse distance from axis of propagation of laser y/ bw Normalized transverse distance
z Propagation distance of laser in plasma in lab frame
α Density ripple wave number
αc/ωp Normalized ripple wave number εr Dielectric constant of plasma ε0 Permittivity of free space
δ Wave number of external periodic electrostatic field
η Efficiency
χe Electrical susceptibility of plasma
λD Debye length
λmfp Mean free path of plasma electrons between the collisions
λp Plasma wave length
Λ Coulomb logarithm
xix µ0 Permeability of free space
ν Collision frequency
ν/ωp Normalized collisional frequency
ω Frequency difference of lasers/ beat wave frequency
ωc Cyclotron frequency
ωp Plasma frequency
ωTHz Frequency of THz radiation
ω1, 2 Frequency of lasers
ω/ωp Normalized beat wave frequency ϕpNL
Ponderomotive potential
τ Mean time between collision of electron with neutral atom ξ Propagation distance of laser in plasma in laser pulse frame
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List of Abbreviations
BBO β-Barium Borate Optic
BW Beat Wave
BWM Beat Wave Mixing
chG Cosh-Gaussian
DARC DC to AC Radiation Converter
DFG Difference Frequency Generation
EFI External Field Induced
EM Electromagnetic
EOC Electro-Optic Crystal
EOS Electro-Optic Sampling
ES Electrostatic
FWM Four Wave Mixing
FTL Flat Top Laser
GL Gaussian Laser
LPP Laser Produced Plasma
NL Non-Linear
OR Optical Rectification
PBWA Plasma Beat Wave Accelerator
PCA Photo Conductive Antenna
PF Ponderomotive Force
PW Plasma Wave
PWFA Plasma WakeField Accelerator
sG Super-Gaussian
SHG Second Harmonic Generation
THz Terahertz
