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CHAPTER 1 INTRODUCTION 1.1 BRIEF HISTORY Plasma, tion of atoms. the fourth state of matter, positive A plasma ions, state negative can is a collec electrons exist not and only at neutral higher temperatures but also at lower temperatures provided there is a mechanism for ionizing the gas and the density is low enough such essential that recombination is not rapid. The two characteristics of a plasma are its tendency to preserve charge neutrality on a macroscopic scale and the collective behaviour arising out of the presence of 2 long-range Coulomb force which 99Z of particles. More than operates between charged the entire universe is consti tuted by matter in plasma state. I When the electrons in a plasma are displaced from their equilibrium positions, strong el eerie fields are set up between the negatively charged layers and background positive layers. These electric fields restore the particles the more initial neutral condition back to their original mobile electrons positions. oscillate frequency known as the plasma frequency. tions propagate, known as the Langmuir and is we get the wave. by electron It is tend to bringing As with the the a result, a certain If these oscilla plasma wave, also a high-frequency wave el ectrostatic in nature ..A1S0 unmagnetized plasma can support the low-frequency ion-acoustic mode and the highfrequency electromagnetic wave. The presence of a magnetic field, however, greatly increases the number of modes < that the plasma can sustain. 1.2 PLASMA INSTABILITIES AND NONLINEAR EFFECTS The two important characteristics of a plasma are nonlinearity grows to and dispersion. in a plasma, the nonlinear If the amplitude immediately it passes from regime, nonlinear processes come into and as a operation, of a wave the linear result, various leading to the 3 saturation called of of the wave tiie dispersion propagation of a amplitude. relation, wave and where k relation w=w(k) The is w is the wave wave is called dispersive if it contains different wave numbers different phase velocities instability interrelated laboratory or found mag netospheric, Rather, under in these nature or equilibrium free energy gradients Generally, plasmas not in can state such in in density, with two important either created most The the cases fact magnetic equilibrium. assumed to that plasmas found arc Car they may ha'ie some temperature anisotropy field the be laboratory that in and intcrplanatory or thermodynamical in implies as The propagaces plasmas space, equilibrium. created number. (w/^). in the are dynamical and and nonlinearity are terms. frequency a number of modes * having the is and from be the sources of (T^^b: '1' temperature ), (R 7 n , V B, V T) or some kind of beam streaming through the plasmas. 'ITus energy plasma may or be into instability is converted radiation a in a collective small deviation from way. a violent motion electromagnetic where such This leads dynamical a waves. of Plasma conversion to the equilibrium fact the takes that becomes a the further deviation. When grow, of process [dace cause of into the plasma instabilities nonlinear phenomena are that excited appear and modify waves the plasma states. important Ordinarily, when the wave the nonlinear energy density larger than that at the thermal the wave energy density and effects W (W/ becomes equilibrium. the thermal much The ratio of energy 1 become density 1 „,) is used as a measure of turbulence. n0l Generally, nonlinear phenomena can be grouped into two categories Coherent : coherent and nonlinear phenomena the nonlinear development incoherent or turbulent. refer to circumstances where of the system is followed with all due regard to. phase information carried by the waves. Nonlinear examples periodic of waves coherent or soli tons nonlinear are phenomena. nonlinear waves occupy only a small But, obviously coherent space in the spectrum of nonlinear phenomena. Most phenomena in nature are, how ever, found 'turbulent' to when be incoherent applied to a or turbulent. plasma usually The tern refers to circumstances where a large number of collective oscilla tions arc excited by a linear instability. A system can be weakly or strongly turbulent depending on the fluctuations of the particular field quantities. level of 3 1.3 PLASMA-MASER INTERACTION As we have already mentioned, plasmas either created in the laboratory or found in nature are far from the equilibrium state. energy Due for which to the They may have some sources of free instabilities presence of an may occur instability, in the many plasma. nonlinear processes come into operation and the energy is redistri buted over flows from the various degrees the unstable of freedom. inode to the more The damping mechanisms will then extract The stable energy states. the energy from the stable mode and give it to the plasma particles. This results in plasma Finally, a provided the heating, anomalous quasi-steady turbulent sources the and diffusion state sinks is of etc. attained energy are maintained at constant level. Consideration of anomalous radiation from a plasma with enhanced low frequency fluctuations can be treated as • 2-4 a central problem to interpret numerous astrophysics! , viz., Pulsar Auroral Kilometric Radiation etc. and Radiation, laboratory Jupiter plasma Emission, phenomena, viz., Nuclear Fusion. Since the Lawson criterion'1 (Lawson, 1957) for radiation a thermonuclear loss, reactor understanding the depends strongly on radiation mechanism is necessary for the success of nuclear fusion. 6 The principal ionized .plasma moving is charged collision, source of classical particle radiation in a hot, fully bremsstrahl u n g . Whenever suffers acceleration classical bremsstrahl ung occurs. a due to Recently, it I has been shown as Plasma-Maser^, turbulent which that induced bremsstrahlung^, later termed plasma. originates plays a very important It is a new kind of because of the role in a radiation process electron acceleration through the modulation fields. Coupling of electromagnetic or electrostatic turbulence test fields modulation fields electrons, wave produces fields the with low modulation field. nonlincarly interact with causing electrons. The radiated, resulting a strong energy of in the acceleration the resonant the high frequency resonant of electrons frequency These these is test then wave amplitude to grow. This new type of radiation is known as induced bremsstrahl ung. Obviously, it will vanish in absence of the low-frequency turbulence. It is, therefore, termed as anomalous radiation associated with the 1ow-frequency turbulence. At this stage, it will be relevant the basic differences between classical induced bremsstrahlung. Classical to point out bremsstrahlung and bromsstrahlung emission occurs whenever a moving electron suffers acceleration due to collisions. originates On the other hand, because of Che induced nonlinear bremsstrahlung interaction between 7 the resonant electrons and the As mentioned above, these nodulated electric fields. modulation fields appear as a result of the coupling between a high-frequency perturba tion field and the low-frequency fluctuations. Thus it t shows that the origin of acceleration is quite different in bo th cases. The plasma-maser interaction does not require any frequency or satisfied. wave That number is mode-conversion matching why, it processes is like conditions different to from parametric be other interaction, nonlinear scattering etc. According to the (also called quasilinear recent weak theory), turbulence the lowest theory order mode- 2 mode coupling processes are composed of three parts . They are the resonant conditions are Landau damping three-wave interaction^ [the matching +«2 = w^], the nonlinear +k£ = k ^ , [the condition is JL-w = (K-k).V)J and the A r ■*--> *"> , plasma-maser interaction [the conditions are w = k.v; fif= -> •* -> K.VJ. Here w & k are the frequency and wave vector of the low-frequency wave and 1L & K those of the high-frequency wave . This new maser effect in plasma the induced considerable basically brcmsstrahlung attention in turbulence, viz., instability, the past few has years. received This is an energy up-conversion process in which there 8 is a flow of energy from a low-frequency mode in a plasma to a high-frequency high-frequency turbulence mode, mode. is thereby causing The necessary presence for of this growth of the a low-frequency energy up-conversion « process to take place. This maser effect is effective even without the electron population inversion. In plasma this acts as amplitude grows mechanism the the wave. pump low frequency wave The in the high-frequency at the expense of the pump wave The resonant electrons carry effectively wave energy. the energy from the pump wave field to the radiation field. Historically, the growth of the nonresonant through the nonlinear interaction with the resonant mode mode 9 was first pointed out independently Tsytovich et al.^ It has later 2 plasma-maser . The nonlinear effect nonresonant electron modes by been of Natnbu termed the as the resonant and simultaneously on the evolution distribution function is called and the of the inverse pii asma-maser U This anomalous high-frequency radiation in the presence of enhanced low-frequency fluctuations are often reported wave in laboratory excitations from and space ion-sound plasmas. waves were The Langmuir reported by Amagishi 12 . High-frequency whistler mode emissions driven by Jow-f requency ion mode were observed by Fujiyama and 9 Nambu^. The solitons, and the emission of upper hybrid wave solitons from Ohya Langmuir ion waves 15 were wave reported , respectively. emission from by Boswel 1 14 ion-sound and Mori and In Z pinch plasma, the simultaneous observation of ion-sound radiation is reported"^. waves and electromagnetic The plasma wave excitation from MHD modes is observed in Tokamak 17 . In space plasmas, ULL modulated static bursts whistler 18 emissions1 , chorus-related ELF 19 , and turbulence Langmuir wave in solar the emissions wind 20 the electrodriven have by been observed. More recently, the presence of broadband electro static bursts has been reported in the region of Auroral kilometric radiation, suggesting possible link between the electrostatic bursts and the AKR generation^ . Recently, it has been shown 22 523 that the mechanism of plasma-maser can be best understood in terms of a high-frequency nonlinear force. This high-frequency nonlinear force arises as a result of the resonant inter action between the electrons and the modulation fields caused by the coupling between a test high-frequency wave field with the low-frequency turbulence field. This is in contrast to low-frequency the parametric nonlinear interaction force, viz., process the where a ponderomotive force is produced to make a low-frequency wave unstable. On the other hand, in plasma-maser process, the nonlinear force is a high-frequency one and makes the high-frequency 10 wave unstable. The Radiation, related generation mechanisms of Auroral ULF modulated electrostatic electrostatic I bursts in Kilometric waves the and chorus- earth's outer magnetosphere, whistler mode signals in the solar wind and type III solar radio bursts are presented on the basis of t'he theory 2 A . plasma-maser universal also theory^. The extra-ordinary extra 25 stabilization of . The generation mechanism of X-mode presented planets. r.f. drift mode based on the plasma-maser theory has also been proposed is The on basis emission of mode a familiar is The auroral ordinary mode. radiation kilometric radiation extraordinary mode. may 27 of Like and also of of in the the radio radiation is also in the ^ AKR, the are It is probable one plasma-maser wave feature the (bKOM)^ be the electromagnetic kilometric kilometric interaction the the the saturnian broad-band found that Jovian to be in the the plasma-maser probable generation mechanisms of the X-mode from the radio planets. In space the turbulent frequency modes wave etc. processes All and astrophysical fluctuation energy such as MHD wave, of the previously plasmas, is the contained drift wave, studied most in of low- ion-sound mode-coupling show the energy down-conversion from the high- frequency mode to the low-frequency mode. Accordingly, the 11 standard mode-mode coupling processes may not play a signi ficant role in astrophysical plasma. On Che other hand, the most important characteristic of the plasma-maser is the to energy up-conversion from the low-frequency mode t the high-frequency mode. Thus, the plasma-maser proces may play an important role in space and astrophysical p, 3a sm as24 in the 1ow-frequency either or interaction because plasma-maser of the the is value function resonant hangniui r waves ion-cyclotron low theory, is assumed of interaction But the and such waves is toe at the the to contain waves. between electrons electron distribution However, of turbulence generally ion-acoustic resonant small study slope resonant between of the velocity. electrons and Ia rge because of the sufficient! y high value of the slope of the electron distribution function at the resonant velocity. Thus the pi asma~maser inter action between Langmuir waves and electrons may give rise lu s ign if ic an L‘1y enhanced radiation. This closely related accelerated physical nonlinear by to mechanism the random process viz., by introduced by Tsytovich 30 which low-frequency mode for the plasma-maser . plasma-maser particles oscillation. interaction was is are The first 12 Recently, effective in particle flow without open and for supply, (plasma-maser) may is is system type originate of plasma-maser where the For supply There open the 31 ’32 . state new that systems particle plateau^. However, shown available turbulent quasi-1 inear particle is plasma is energy stationary loss. it energy closed from no with enhanced with the the the radiation energy mode-mode spontaneously and systems outside, realized is and couplings as anomalous radiation. Some of the input energy is dissipated through the nonlinear turbulance forces'^. comes from New the dynamic state interaction of of plasma a given stationary plasma turbulence with its surroundings. Quite energy recently, conservation Nambu has sho w n ^ relation between that the total particle kinetic energy and wave energy is satisfied for the plasma-maser process. The ManJ ey-Ruwe relation^ among, plasma waves is l violated and as a result an efficient energy up-conversion from the low-frcquency mode to the high-frequency mode is possible even for a normal unreversed population in plasma tu rbulonce. The plasmn-maser process always co-exists with the cjuasiJ inear process between electrons mode. The new mode-mode coupling comes tivc nonlinear force 37 . The standard and the resonant from the dissipaquasi!inear theory 13 neglects the validity phase of the order assumption approximation foundation of the 2 which plasma to the 1.4 second in is linear clarified 31. ref. field This response (E 2) • under the result theory The random gives of a the turbulent » neglects l ow f r e q u e n c y the second o r d e r e l e c t r i c field due turbulences. A HR IMF DESCRIPTION OF THE. THESIS The p r i n c i p a l gate some aspects theory. pi a s i n a - ma s e r is which there purpose o f of plasma-maser in electric this As this new wc ma s e r have an e n e r g y is of energy to presence of low-frequency for energy up-conversion process It is high-frequency now w i d e l y effect, f r om mode this viz., the already, the a field process low-frequency radiation turbulent accepted to i n v e s t i up-eonversion resonant a a is me n t i o n e d basically n flow study field. is The essential to take p l a c e . that p I as 111 a-m as e r c a n be ( best understood in terms force^’^ . This a result the re s o n a n t the of modulated turbulence nonlinear and the a high-frequency fields field force of with or e l e c t r o m a g n e t i c nonlinear interaction caused a test accelerates accelerated high-frequency electrons waves. or by force arises between e l e c t r o n s coupling high-frequency decelerates can nonlinear t h e n e mi t between field. the as and the This electrons electrostatic In considered the the second emission nonlinear chapter of force of this thesis electromagnetic discussed waves above in a we have caused plasma by with Langmuir turbulence 38 . The Langmuir turbulence is excited I by a weak electron beam drifting through plasma of Maxwellian electrons and ions. a background The growth rate of the electromagnetic wave through the plasma-maser inter action lias been calculated. The expression for the growth rate contains direct two coup I ing parts; one contribution part corresponds while the other to the part the polarization contribution. These results fully agree with 3 c) those obtained irom the standard formulation method' . The essential feature of the present formulation is that the nonlinear force is explicitly calculated and is shown to drive the high-frequency instability. In gene rat ion the of third electromagnetic mode in a magnetized turbulence chapter through plasma the we wave have in the studied the extraordinary in the presence of 'Langmuir p 1asma~ma sor interaction^’. The nonlinear dispersion relation ofthe X-mode in the presence of Langmuir turbulence has been calculated and the growth rate then coupling not that obtained. term in the contribute the growth to The results show that nonlinear dielectric the growth of the is wholly derived direct [unction X-inode. from the This does means the polarization ■ontribution. This is markedly different from the results 15 obtained in the case of electromagnetic unmagnetizecl plasma 3 9 or in radiation a magnetized in contributed both by the case 31 plasma the direct emission of in ordinary where coupling the as an mode growth is well as the abundance of the * polarization terms. electromagnetic planets, the generation view of in the emission present applications. plasma-maser In It study is mechanisms here of X-mocle seems probable considered the that may in to the emission radio have useful mechanism be one of X-mode the of the probable from Lho radio planets. One of the primary conditions necessary for this mechanism to be effective is the presence oL a turbulence Held from which energy can be transferred to the radiation field via the resonant electrons. In studied Lho fourth chapter the generation l.angmuir turbulence plasma-maser polarized of in their this electron a magnetized 40 . interaction with of The electric thesis, we have Bernstain waves from plasma Bernstein vector nearly through ' modes field. They propagate 41 are parallel the wave vector and perpendicular to the external neous magnetic the to homoge in frequency ranges that lie between harmonics of the cyclotron frequency. The nonlinear dispersion waves the in calculated and relation presence its of growth of the Langmuir rate is electron turbulence then Bernstein has obtained, been it is 16 observed that the contribution flrom the direct coupling in the nonlinear dispersion relation vanishes and the growth rate is wholly derived from the polarization contribution. The emission of electromagnetic ^4 - ordinary and extraordinary inodes^ from the nonlinear respectively, turbulence in nonlinear between the field Langmuir wave force present in fie Id driven arising electrons and and sixth the system are the the presented c h ap te rs . is by a we ak e 1e c iron outof in in a magnetized plasma consideration fifth forces 2 waves the resonant modulated '['he again the beam. The interaction fields caused by coupling between the high frequency O-mode and X-mode test Tit'ids respectively with the Langmuir tu lnilence have been calculated. The nonlinear forces thus obtained are then used in their respective fluid equations to obtain finally their growths. Then the results are compared with those obtained earlier from the standard formulation. « Lastly, have in the seventh chapter of the thesis, summarized the results obtained in the we previous cha pte rs. Before clear one the concluding thing interaction nonresonant high more. this chapter we would We have considered between resonant frequency wave. Langmuir like in this wave Considerable to thesis and the attention 17 has aJready betwecMi waves, been paid resonant the the ion-sound considering through to and the growth resonant plasma-maser non-resonant rate of interaction interaction the between Langmuir Langmuir wave electrons and « ion-sound electrons where waves. and w,k and Lon-sound wave The ion-sound v£ are number resonant waves the is interaction weak between because ion-sound w/k<<v , frequency, anti the electron thermal the velocity, respectively. Then the growth rate of the Langmuir wave is sina I1 . On the interaction other between hand, the we consider resonant Lhe Langmuir plasma-maser wave and a non-resonant high frequency wave. As because the resonant interaction between the electrons and the Langmuir wave is strong, 1a rge. the growth rate of the high frequency wave is IS RKKKRKNCKS 1. A. Hasegawa, Plasma Instabilities and Nonlinear (Springcr-Ver1a g , New York, 1975). Effects 2. M. Nambu, Laser and Particle Beams 1, 427 (1983). 3. M. Nambu, Phys. Fluids 25, 1196 (1982). 4. D.A. Gurnctt, J. Geophys. Res. Warwick, 204, J.B. 995 Pearce (1979); Sutherland, and M.A. Astrophys. J. 79, 4227 A.C. (1974); J.W. Riddle, Ruderman 196, 51 Science and P.G. (1975); N.C. Wehrlin, J. Geophys. Res. 86, 1365 (1981). 5. J.D. Lawson, Proc. Phys. Soc. London Ser. B70, 6 (195 7 ). 6. M. Nambu and P.K. Shukla, Phys. Rev. 20A, 2498 (1979). 7 . V .N . Oraevsky and R.7 . Sagdeev, Sov . Phys-Tech. Phys . 7, 955 (1963). 8 . M.N. Rosenbluth, B. Coppi and R.N. Sudan, Ann. Phys . 55, 248 (1969). 9. M. Nambu, Phys. Rev. Letters 34, 387 (1975) . Ni. 1he 1ms son , Phys . L. Stenflo and 11. 1 10. V .N . Tsytovich, Scripta 11, 251 (1975). I1 . V.S. Krivitsky and 1 3 .V . V 1ad im i rov , J . PI asm a Phys . 46, 209 (1991). 12 . Y. AmagishL, J. Phys. Soc. J pn . 29, 764 (1970). 13. H. Fujiyama and M. Nambu, Phys. Letters 105A, 295 ( 1.984) . 14. R.W. Boswell, Geophys . Res. Letters 11, 1015 (1984). 15. I. Mori, and K . Ohya , Phys. Rev. Letters 59, 1825 (1987). 16. K.H. Finken and U. Achmann, Physica 113B, 135 (1982). 19 .17. l.H. Hutchinson and S.K. Kissel , Phys. Fluids 26, 310 (1983 ). 18. N. Corni 11eau-Wehr1 in, J. Geophys. Res. 86, 1365 (1981 ). 19. L.A. Reinlditner, U.A. Gurnett, and T.E. Feist man, J. Geophys. Res. 88, 3079 (1983). 20. C.F. Kennel, H.F. Petschek, F.V. Coronity, K.W. Fredricks, D.A. Gurnett and F.J. Smith, Geophys. Res. Fetters 7, 129 (1980). 21. R. Pottelettc, M. Malingre, A. Bahnsen and M. despersen, Geophys. Res. Fetters 16, 5.15 (1987). 22. M. Nambu and H. Akama, Nuovo Cimento 87B, 176 (1985). 2 3 . S. Bujarbarua, 29A, 2171 S.N. Sarma and M. Nambu, Phy s . R e v . (1984) . 24. M. Nambu, Space Sci. Rev. 44, 357 (1986). 25. M. Nambu, Phys. Rev. 35A, 1953 (1987). 26 . S.N. Sarma , K .K . Sarma and M. Nambu, J. P 1asma , 1 IMiys . 46, 331 (1991). 27. M.F. Kaiser, M.FG Desch, J.W. Warwick and .1.B . Pea rce , Science 209, 1238 (1980). 1 28. .J.W . Wa rwick , .1.B. Pearce, D.R. Fvans, T.D . Carr, J .J . Schauble, J.K. Alexander, M.F. Kaiser, M.I). Desch, M. Pederson, A. Fecacheux, G. Daigne, A. Boischat and C.ll. Barrow, Science 212, 239 ( 1981 ) . 29. V. Fehlane and G. Daigne, J. Geophys. Res. 90 , 12073 ( I98 5). 30. V.N. Tsytovieh, Sov. Phys. JFTP 6 2 , 483 (1985). 31. M. Nambu, T. llada , S.N. Sarma and S. Bujarbarua, Phys. Soc. Jpn. 6 0 , 3004 (1991). J. 20 32. V .N . Tsytovich and V.N. Krivitsky, Comments. Plasma Phys. Controlled Fusion 1.1, 119 (19(37). 33. W. F. Drummond and D. Pines, Nucl . Fusion Suppl . 3, 1049 (1962); A. A. Vedenov, H.P. Velikhov and K.Z., Sagdeev, Nucl . Fusion Suppl . Pt. 2, 465 (1962 ) . 34. M. Nambu, J. Phys. Soe. Jpn. 53, 1594 (1934). 35. M. Nambu, Phys. Rev. betters (Submitted). 36 . J .M. Manley and II. K. Rowe, Proc. oi 1RF 44, 904 (1956) 37. M. Nambu, Phys. Fluids 31, 1296 (198,3). 33 . K ..K. Sariiia, S. N. Rev. 43A, 39. M. Nambu, S.N. Sarma, M. Nambu anti '!'. Ilada, Phy s . 5555 (1991). Sarma and S. Bujarbarua, Phys. FI uids B2, 302 (1990). 40. M. Nambu, S.N. Sarma anti K.K. Sarma, Phys. Rev . 4 5 A , 7456 (1992). 41 . 1 .B. Bernstein, Phys. Rev. 109, 10 (1958). 42. M. N am bu , S.N. Sarma, K.K. Sarma and U .N . Das, Rev A (submitted). Phys .