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Journal articles on the topic 'Plasma turbulence; Nonlinear theories'

Author: Grafiati

Published: 6 September 2023

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1

Bandyopadhyay, Riddhi, Ramiz A. Qudsi, S. Peter Gary, William H. Matthaeus, Tulasi N. Parashar, Bennett A. Maruca, Vadim Roytershteyn, et al. "Interplay of turbulence and proton-microinstability growth in space plasmas." Physics of Plasmas 29, no. 10 (October 2022): 102107. http://dx.doi.org/10.1063/5.0098625.

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Numerous prior studies have shown that as proton beta increases, a narrower range of proton temperature anisotropy values is observed. This effect has often been ascribed to the actions of kinetic microinstabilities because the distribution of observational data aligns with contours of constant instability growth rates in the beta-anisotropy plane. However, the linear Vlasov theory of instabilities assumes a uniform background in which perturbations grow. The established success of linear-microinstability theories suggests that the conditions in regions of extreme temperature anisotropy may remain uniform for a long enough time so that the instabilities have the chance to grow to sufficient amplitude. Turbulence, on the other hand, is intrinsically nonuniform and nonlinear. Thin current sheets and other coherent structures generated in a turbulent plasma may quickly destroy the uniformity. It is, therefore, not a-priori obvious whether the presence of intermittency and coherent structures favors or disfavors instabilities. To address this question, we examined the statistical distribution of growth rates associated with proton temperature-anisotropy driven microinstabilities and local nonlinear time scales in turbulent plasmas. Linear growth rates are, on average, substantially less than the local nonlinear rates. However, at the regions of extreme values of temperature anisotropy, near the “edges” of the populated part of the proton temperature anisotropy-parallel beta plane, the instability growth rates are comparable or faster than the turbulence time scales. These results provide a possible answer to the question as to why the linear theory appears to work in limiting plasma excursions in anisotropy and plasma beta.

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2

Schertzer, D., and E. Falgarone. "MFGA-IDT2 workshop: Astrophysical and geophysical fluid mechanics: the impact of data on turbulence theories." Nonlinear Processes in Geophysics 3, no. 4 (December 31, 1996): 229–30. http://dx.doi.org/10.5194/npg-3-229-1996.

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Abstract. 1 Facts about the Workshop This workshop was convened on November 13-15 1995 by E. Falgarone and D. Schertzer within the framework of the Groupe de Recherche Mecanique des Fluides Geophysiques et Astrophysiques (GdR MFGA, Research Group of Geophysical and Astrophysical Fluid Mechanics) of Centre National de la Recherche Scientifique (CNRS, (French) National Center for Scientific Research). This Research Group is chaired by A. Babiano and the meeting was held at Ecole Normale Superieure, Paris, by courtesy of its Director E. Guyon. More than sixty attendees participated to this workshop, they came from a large number of institutions and countries from Europe, Canada and USA. There were twenty-five oral presentations as well as a dozen posters. A copy of the corresponding book of abstracts can be requested to the conveners. The theme of this meeting is somewhat related to the series of Nonlinear Variability in Geophysics conferences (NVAG1, Montreal, Aug. 1986; NVAG2, Paris, June 1988; NVAG3, Cargese (Corsica), September, 1993), as well as seven consecutive annual sessions at EGS general assemblies and two consecutive spring AGU meeting sessions devoted to similar topics. One may note that NVAG3 was a joint American Geophysical Union Chapman and European Geophysical Society Richardson Memorial conference, the first topical conference jointly sponsored by the two organizations. The corresponding proceedings were published in a special NPG issue (Nonlinear Processes in Geophysics 1, 2/3, 1994). In comparison with these previous meetings, MFGA-IDT2 is at the same time specialized to fluid turbulence and its intermittency, and an extension to the fields of astrophysics. Let us add that Nonlinear Processes in Geophysics was readily chosen as the appropriate journal for publication of these proceedings since this journal was founded in order to develop interdisciplinary fundamental research and corresponding innovative nonlinear methodologies in Geophysics. It had an appropriate editorial structure, in particular a large number of editors covering a wide range of methodologies, expertises and schools. At least two of its sections (Scaling and Multifractals, Turbulence and Diffusion) were directly related to the topics of the workshop, in any case contributors were invited to choose their editor freely. 2 Goals of the Workshop The objective of this meeting was to enhance the confrontation between turbulence theories and empirical data from geophysics and astrophysics fluids with very high Reynolds numbers. The importance of these data seems to have often been underestimated for the evaluation of theories of fully developed turbulence, presumably due to the fact that turbulence does not appear as pure as in laboratory experiments. However, they have the great advantage of giving access not only to very high Reynolds numbers (e.g. 1012 for atmospheric data), but also to very large data sets. It was intended to: (i) provide an overview of the diversity of potentially available data, as well as the necessary theoretical and statistical developments for a better use of these data (e.g. treatment of anisotropy, role of processes which induce other nonlinearities such as thermal instability, effect of magnetic field and compressibility ... ), (ii) evaluate the means of discriminating between different theories (e.g. multifractal intermittency models) or to better appreciate the relevance of different notions (e.g. Self-Organized Criticality) or phenomenology (e.g. filaments, structures), (iii) emphasise the different obstacles, such as the ubiquity of catastrophic events, which could be overcome in the various concerned disciplines, thanks to theoretical advances achieved. 3 Outlines of the Workshop During the two days of the workshop, the series of presentations covered many manifestations of turbulence in geophysics, including: oceans, troposphere, stratosphere, very high atmosphere, solar wind, giant planets, interstellar clouds... up to the very large scale of the Universe. The presentations and the round table at the end of the workshop pointed out the following: - the necessity of this type of confrontation which makes intervene numerical simulations, laboratory experiments, phenomenology as well as a very large diversity of geophysical and astrophysical data, - presumably a relative need for new geophysical data, whereas there have been recent astrophysical experiments which yield interesting data and exciting questions; - the need to develop a closer intercomparison between various intermittency models (in particular Log-Poisson /Log Levy models). Two main questions were underlined, in particular during the round table: - the behaviour of the extremes of intermittency, in particular the question of divergence or convergence of the highest statistical moments (equivalently, do the probability distributions have algebraic or more rapid falloffs?); - the extension of scaling ranges; in other words do we need to divide geophysics and astrophysics in many small (nearly) isotropic subranges or is it sufficient to use anisotropic scaling notions over wider ranges? 4 The contributions in this special issue Recalling that some of the most useful insights into the nature of turbulence in fluids have come from observations of geophysical flows, Van Atta gives a review of the impacts of geophysical turbulence data into theories. His paper starts from Taylor's inference of the nearly isotropy of atmospheric turbulence and the corresponding elegant theoretical developments by von Karman of the theory of isotropic turbulence, up to underline the fact that the observed extremely large intermittency in geophysical turbulence also raised new fundamental questions for turbulence theory. The paper discusses the potential contribution to theoretical development from the available or currently being made geophysical turbulence measurements, as well as from some recent laboratory measurements and direct numerical simulations of stably stratified turbulent shear flows. Seuront et al. consider scaling and multiscaling properties of scalar fields (temperature and phytoplankton concentration) advected by oceanic turbulence in both Eulerian and Lagrangian frameworks. Despite the apparent complexity linked to a multifractal background, temperature and fluorescence (i.e. phytoplankton biomass surrogate) fields are expressed over a wide range of scale by only three universal multifractal parameters, H, \\alpha and C_l. On scales smaller than the characteristic scale of the ship, sampling is rather Eulerian. On larger scales, the drifting platform being advected by turbulent motions, sampling may be rather considered as Lagrangian. Observed Eulerian and Lagrangian universal multifractal properties of the physical and biological fields are discussed. Whereas theoretical models provide different scaling laws for fluid and MHD turbulent flows, no attempt has been done up to now to experimentally support evidence for these differences. Carbone et al. use measurements from the solar wind turbulence and from turbulence in ordinary fluid flows, in order to assess these differences. They show that the so-called Extended Self-Similarity (ESS) is evident in the solar wind turbulence up to a certain scale. Furthermore, up to a given order of the velocity structure functions, the scaling laws of MHD and fluids flows axe experimentally indistinguishable. However, differences can be observed for higher orders and the authors speculate on their origin. Dudok de Wit and Krasnosel'skikh present analysis of strong plasma turbulence in the vicinity of the Earth's bow shock with the help of magnetometer data from the AMPTE UKS satellite. They demonstrate that there is a departure from Gaussianity which could be a signature of multifractality. However, they point out that the complexity of plasma turbulence precludes a more quantitative understanding. Finally, the authors emphasise the fact that the duration of records prevents to obtain any reliable estimate of structure functions beyond the fourth order. Sylos Labini and Pietronero discuss the problem of galaxy correlations. They conclude from all the recently available three dimensional catalogues that the distribution of galaxies and clusters is fractal with dimension D ~ 2 up to the present observational limits without any tendency towards homogenization. This result is discussed in contrast to angular data analysis. Furthermore, they point out that the galaxy-cluster mismatch disappears when considering a multifractal distribution of matter. They emphasise that a new picture emerges which changes the standard ideas about the properties of the universe and requires a corresponding change in the related theoretical concepts. Chilla et al. investigate with the help of a laboratory experiment the possible influence of the presence of a large scale structure on the intermittency of small scale structures. They study a flow between coaxial co-rotating disks generating a strong axial vortex over a turbulent background. They show that the cascade process is preserved although strongly modified and they discuss the relevance of parameters developed for the description of intermittency in homogeneous turbulence to evaluate this modification.

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3

Itoh, Sanae-I., and Kimitaka Itoh. "Kinetic Description of Nonlinear Plasma Turbulence." Journal of the Physical Society of Japan 78, no. 12 (December 15, 2009): 124502. http://dx.doi.org/10.1143/jpsj.78.124502.

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4

van Milligen, B. Ph, C. Hidalgo, and E. Sánchez. "Nonlinear Phenomena and Intermittency in Plasma Turbulence." Physical Review Letters 74, no. 3 (January 16, 1995): 395–98. http://dx.doi.org/10.1103/physrevlett.74.395.

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5

LEVICH, E. "NEW DEVELOPMENTS AND CLASSICAL THEORIES OF TURBULENCE." International Journal of Modern Physics B 10, no. 18n19 (August 30, 1996): 2325–92. http://dx.doi.org/10.1142/s0217979296001057.

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In this paper we review certain classical and modern concepts pertinent for the theory of developed turbulent flows. We begin by introducing basic facts concerning the properties of the Navier-Stokes equation with the emphasis on invariant properties of the vorticity field. Then we discuss classical semiempirical approaches to developed turbulence which for a long time have constituted a basis for engineering solutions of turbulent flows problems. We do it for two examples, homogeneous isotropic turbulence and flat channel turbulent flow. Next we discuss the insufficiency of classical semi-empirical approaches. We show that intermittency is an intrinsic feature of all turbulent flows and hence it should be accounted for in any reasonable theoretical approach to turbulence. We argue that intermittency in physical space is in one to one correspondence with certain phase coherence of turbulence in an appropriate dual space, e.g. Fourier space for the case of homogeneous isotropic turbulence. In the same time the phase coherence has its origin in invariant topological properties of vortex lines in inviscid flows, modified by the presence of small molecular viscosity. This viewpoint is expounded again using the examples of homogeneous isotropic turbulence and channel flow turbulence. Finally we briefly discuss the significance of phase coherence and intermittency in turbulence for the fundamental engineering challenge of turbulence control.

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6

Belli, E. A., G. W. Hammett, and W. Dorland. "Effects of plasma shaping on nonlinear gyrokinetic turbulence." Physics of Plasmas 15, no. 9 (September 2008): 092303. http://dx.doi.org/10.1063/1.2972160.

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7

Hidalgo, C., R. Balbín, B. Brañas, T. Estrada, I. García-Cortés, M. A. Pedrosa, E. Sánchez, and B. van Milligen. "Nonlinear phenomena and plasma turbulence in fusion plasmas." Physica Scripta 51, no. 5 (May 1, 1995): 624–26. http://dx.doi.org/10.1088/0031-8949/51/5/013.

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8

YAGI, Masatoshi, Sanae-I. ITOH, Kimitaka ITOH, Masafumi AZUMI, Patrick H. DIAMOND, Atsushi FUKUYAMA, and Takayuki HAYASHI. "Nonlinear Drive of Tearing Mode by Microscopic Plasma Turbulence." Plasma and Fusion Research 2 (2007): 025. http://dx.doi.org/10.1585/pfr.2.025.

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9

Li-Fang, Dong, Fan Wei-Li, Wang Hui-Juan, Zhang Qing-Li, and Wang Long. "Nonlinear Interaction and Coherent Structure in Tokamak Plasma Turbulence." Chinese Physics Letters 23, no. 11 (October 26, 2006): 3007–9. http://dx.doi.org/10.1088/0256-307x/23/11/034.

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10

Qian, S., Y. C. Lee, and H. H. Chen. "A study of nonlinear dynamical models of plasma turbulence." Physics of Fluids B: Plasma Physics 1, no. 1 (January 1989): 87–98. http://dx.doi.org/10.1063/1.859109.

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11

Friedman, B., T. A. Carter, M. V. Umansky, D. Schaffner, and I. Joseph. "Nonlinear instability in simulations of Large Plasma Device turbulence." Physics of Plasmas 20, no. 5 (May 2013): 055704. http://dx.doi.org/10.1063/1.4805084.

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12

Howes, G. G. "A dynamical model of plasma turbulence in the solar wind." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2041 (May 13, 2015): 20140145. http://dx.doi.org/10.1098/rsta.2014.0145.

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A dynamical approach, rather than the usual statistical approach, is taken to explore the physical mechanisms underlying the nonlinear transfer of energy, the damping of the turbulent fluctuations, and the development of coherent structures in kinetic plasma turbulence. It is argued that the linear and nonlinear dynamics of Alfvén waves are responsible, at a very fundamental level, for some of the key qualitative features of plasma turbulence that distinguish it from hydrodynamic turbulence, including the anisotropic cascade of energy and the development of current sheets at small scales. The first dynamical model of kinetic turbulence in the weakly collisional solar wind plasma that combines self-consistently the physics of Alfvén waves with the development of small-scale current sheets is presented and its physical implications are discussed. This model leads to a simplified perspective on the nature of turbulence in a weakly collisional plasma: the nonlinear interactions responsible for the turbulent cascade of energy and the formation of current sheets are essentially fluid in nature, while the collisionless damping of the turbulent fluctuations and the energy injection by kinetic instabilities are essentially kinetic in nature.

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13

Meyrand, Romain, Anjor Kanekar, William Dorland, and Alexander A. Schekochihin. "Fluidization of collisionless plasma turbulence." Proceedings of the National Academy of Sciences 116, no. 4 (January 4, 2019): 1185–94. http://dx.doi.org/10.1073/pnas.1813913116.

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In a collisionless, magnetized plasma, particles may stream freely along magnetic field lines, leading to “phase mixing” of their distribution function and consequently, to smoothing out of any “compressive” fluctuations (of density, pressure, etc.). This rapid mixing underlies Landau damping of these fluctuations in a quiescent plasma—one of the most fundamental physical phenomena that makes plasma different from a conventional fluid. Nevertheless, broad power law spectra of compressive fluctuations are observed in turbulent astrophysical plasmas (most vividly, in the solar wind) under conditions conducive to strong Landau damping. Elsewhere in nature, such spectra are normally associated with fluid turbulence, where energy cannot be dissipated in the inertial-scale range and is, therefore, cascaded from large scales to small. By direct numerical simulations and theoretical arguments, it is shown here that turbulence of compressive fluctuations in collisionless plasmas strongly resembles one in a collisional fluid and does have broad power law spectra. This “fluidization” of collisionless plasmas occurs, because phase mixing is strongly suppressed on average by “stochastic echoes,” arising due to nonlinear advection of the particle distribution by turbulent motions. Other than resolving the long-standing puzzle of observed compressive fluctuations in the solar wind, our results suggest a conceptual shift for understanding kinetic plasma turbulence generally: rather than being a system where Landau damping plays the role of dissipation, a collisionless plasma is effectively dissipationless, except at very small scales. The universality of “fluid” turbulence physics is thus reaffirmed even for a kinetic, collisionless system.

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14

Nakata, M., T. H. Watanabe, and H. Sugama. "Nonlinear entropy transfer via zonal flows in gyrokinetic plasma turbulence." Physics of Plasmas 19, no. 2 (February 2012): 022303. http://dx.doi.org/10.1063/1.3675855.

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15

Shukla, P. K., Arshad M. Mirza, and R. T. Faria. "Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma." Physics of Plasmas 5, no. 3 (March 1998): 616–24. http://dx.doi.org/10.1063/1.872776.

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16

Viana, R. L., E. C. Da Silva, T. Kroetz, I. L. Caldas, M. Roberto, and M. A. F. Sanjuán. "Fractal structures in nonlinear plasma physics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1935 (January 28, 2011): 371–95. http://dx.doi.org/10.1098/rsta.2010.0253.

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Fractal structures appear in many situations related to the dynamics of conservative as well as dissipative dynamical systems, being a manifestation of chaotic behaviour. In open area-preserving discrete dynamical systems we can find fractal structures in the form of fractal boundaries, associated to escape basins, and even possessing the more general property of Wada. Such systems appear in certain applications in plasma physics, like the magnetic field line behaviour in tokamaks with ergodic limiters. The main purpose of this paper is to show how such fractal structures have observable consequences in terms of the transport properties in the plasma edge of tokamaks, some of which have been experimentally verified. We emphasize the role of the fractal structures in the understanding of mesoscale phenomena in plasmas, such as electromagnetic turbulence.

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17

de OLIVEIRA, L. P. L., F. B. RIZZATO, and A. C. L. CHIAN. "Intrinsic modulational Alfvénic turbulence." Journal of Plasma Physics 58, no. 3 (October 1997): 441–53. http://dx.doi.org/10.1017/s0022377897005837.

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The nonlinear dynamics of a finite-amplitude Alfvén wave in a dispersive modulational regime is analysed. Use is made of a conservative model to show that turbulence may arise via deterministic chaos. The behaviour of the system is studied as one varies the initial amplitude of the pump Alfvén wave, the dispersion parameter and the plasma parameter β.

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18

Yoon, Peter H. "Two-fluid approach to weak plasma turbulence." Plasma Physics and Controlled Fusion 63, no. 12 (November 3, 2021): 125012. http://dx.doi.org/10.1088/1361-6587/ac2e40.

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Abstract Weakly turbulent processes that take place in plasmas are customarily formulated in terms of kinetic theory. However, owing to an inherent complexity associated with the problem, thus far the theory is fully developed largely for unmagnetized plasmas. In the present paper it is shown that a warm two fluid theory can successfully be employed in order to partially formulate the weak turbulence theory in spatially uniform plasma. Specifically, it is shown that the nonlinear wave-wave interaction, or decay processes, can be reproduced by the two-fluid formalism. The present finding shows that the same approach can in principle be extended to magnetized plasmas, which is a subject of future work.

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19

Erofeev, V. I. "Weak Plasma Turbulence Theory and Some Other Items of Plasma Kinetics." Australian Journal of Physics 51, no. 5 (1998): 843. http://dx.doi.org/10.1071/p97080.

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A new approach to a plasma kinetic description is discussed, the beginnings of which were published recently (Erofeev 1997a). It is shown that calculations of the three-wave collision integral following this approach confirm the intensity and structure of the three-wave collision integral obtained in the traditional theory. The reported kinetics extend the area of applicability for the weak plasma turbulence theory: apart from waves it properly accounts for the effect of various other plasma nonlinear structures of the type of solitons, drift vortices, collapsing cavities and so on. Some directions for further studies are also discussed.

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20

Morad, Adel M., S. M. A. Maize, A. A. Nowaya, and Y. S. Rammah. "A New Derivation of Exact Solutions for Incompressible Magnetohydrodynamic Plasma Turbulence." Journal of Nanofluids 10, no. 1 (March 1, 2021): 98–105. http://dx.doi.org/10.1166/jon.2021.1765.

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The objective of this paper is to study the propagation of nonlinear, quasi-parallel, magnetohydrodynamic waves of small-amplitude in a cold Hall plasma of constant density. Magnetohydrodynamic equations, along with the cold plasma were expanded using the reductive perturbation method, which leads to a nonlinear partial differential equation that complies with a modified form of the derivative nonlinear evolution Schrödinger equation. Exact solutions of the turbulent magnetohydrodynamic model in plasma were formulated for the physical quantities that describe the problem completely by using the complex ansatz method. In addition, the complete set of equations was used taking into account the magnetic field, which can be considered to be constant in the x-direction to create stable vortex waves. Vortex solutions of the modified nonlinear Schrödinger equation (MNLS) were compared with the solutions of incompressible magnetohydrodynamic equations. The obtained equations differ from the standard NLS equation by one additional term that describes the interaction of the nonlinear waves with the constant density. The behavior of both the velocity profile and the waveform of pressure were studied. The results showed that there are clear disturbances in the identity of the velocity and thus pressure. The identity of both velocity and pressure results from that a magnetic field is formed.

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21

Balikhin, M. A., I. Bates, and S. Walker. "Identification of linear and nonlinear processes in space plasma turbulence data." Advances in Space Research 28, no. 5 (January 2001): 787–800. http://dx.doi.org/10.1016/s0273-1177(01)00515-4.

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22

Sarma, S. N., K. K. Sarma, and M. Nambu. "Plasma maser theory of the extraordinary mode in the presence of Langmuir turbulence." Journal of Plasma Physics 46, no. 2 (October 1991): 331–46. http://dx.doi.org/10.1017/s0022377800016159.

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The emission of extraordinary mode radiation in a plasma with Langmuir turbulence driven by an electron beam is considered. The process of emission considered in this paper is the plasma maser effect, which is essentially an energy up-conversion process. The energy necessary for the growth of the extraordinary mode is derived from the Langmuir turbulence. The nonlinear dispersion relation of the extraordinary mode in the presence of Langmuir turbulence is obtained and its growth rate calculated. The scope of application of the results to space-plasma observation is then stressed.

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23

DEKA, P. N., and A. BORGOHAIN. "On unstable electromagnetic radiation through nonlinear wave–particle interactions in presence of drift wave turbulence." Journal of Plasma Physics 78, no. 5 (February 27, 2012): 515–24. http://dx.doi.org/10.1017/s0022377812000207.

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AbstractA study on the generation of unstable electromagnetic wave through nonlinear wave–particle interactions in an inhomogeneous plasma has been presented. Drift wave turbulence, which is one of the common features of inhomogeneous plasma, is found to be strongly in phase relation with thermal particles. The plasma particles, accelerated by drift wave turbulence field, may transfer their energy to electromagnetic O-mode through a modulated field. This process has been described by Vlasov Maxwell system of equations. From the nonlinear dispersion relation for O-mode the growth rate has been estimated. It has been observed that growth of unstable O-mode may predict magnetospheric electromagnetic radiation phenomena.

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24

Shaikh, D., and P. K. Shukla. "Spectral properties of electromagnetic turbulence in plasmas." Nonlinear Processes in Geophysics 16, no. 2 (March 12, 2009): 189–96. http://dx.doi.org/10.5194/npg-16-189-2009.

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Abstract. We report on the nonlinear turbulent processes associated with electromagnetic waves in plasmas. We focus on low-frequency (in comparison with the electron gyrofrequency) nonlinearly interacting electron whistlers and nonlinearly interacting Hall-magnetohydrodynamic (H-MHD) fluctuations in a magnetized plasma. Nonlinear whistler mode turbulence study in a magnetized plasma involves incompressible electrons and immobile ions. Two-dimensional turbulent interactions and subsequent energy cascades are critically influenced by the electron whisters that behave distinctly for scales smaller and larger than the electron skin depth. It is found that in whistler mode turbulence there results a dual cascade primarily due to the forward spectral migration of energy that coexists with a backward spectral transfer of mean squared magnetic potential. Finally, inclusion of the ion dynamics, resulting from a two fluid description of the H-MHD plasma, leads to several interesting results that are typically observed in the solar wind plasma. Particularly in the solar wind, the high-time-resolution databases identify a spectral break at the end of the MHD inertial range spectrum that corresponds to a high-frequency regime. In the latter, turbulent cascades cannot be explained by the usual MHD model and a finite frequency effect (in comparison with the ion gyrofrequency) arising from the ion inertia is essentially included to discern the dynamics of the smaller length scales (in comparison with the ion skin depth). This leads to a nonlinear H-MHD model, which is presented in this paper. With the help of our 3-D H-MHD code, we find that the characteristic turbulent interactions in the high-frequency regime evolve typically on kinetic-Alfvén time-scales. The turbulent fluctuation associated with kinetic-Alfvén interactions are compressive and anisotropic and possess equipartition of the kinetic and magnetic energies.

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25

Weatherall, James C. "Numerical study of the radio microstructure associated with the plasma turbulence emission model." International Astronomical Union Colloquium 160 (1996): 205–8. http://dx.doi.org/10.1017/s0252921100041476.

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AbstractRecent observational data of short time-scale fluctuations in the radio emission of pulsars offer the opportunity for new tests of proposed emission models. For this purpose, the existing models must be developed to make predictions regarding the temporal characteristics of the emission. A computer solution of the time evolution of plasma wave turbulence details the properties of the nonlinear plasma emission mechanism. As a consequence of ponderomotive nonlinearity in the plasma medium, two-stream growing modes develop modulational instability, leading to the onset of strong, two-dimensional plasma turbulence. The turbulence exhibits explosive spatial collapse of regions of high electric field, and the escape of bursts of radiation.

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Rosa, Reinaldo R., Mauricio J. A. Bolzan, Francisco C. R. Fernandes, H. S. Sawant, and Marian Karlický. "Nonlinear analysis of decimetric solar bursts." Proceedings of the International Astronomical Union 5, S264 (August 2009): 279–81. http://dx.doi.org/10.1017/s174392130999278x.

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AbstractThe solar radio emissions in the decimetric frequency range (above 1 GHz) are very rich in temporal and spectral fine structures due to nonlinear processes occurring in the magnetic structures on the corresponding active regions. In this paper we characterize the singularity spectrum, f(α), for solar bursts observed at 1.6, 2.0 and 3 GHz. We interpret our findings as evidence of inhomogeneous plasma turbulence driving the underlying plasma emission process and discuss the nonlinear multifractal approach into the context of geoeffective solar active regions.

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27

MARSCH, ECKART, and DANIEL VERSCHAREN. "On nonlinear Alfvén-cyclotron waves in multi-species plasma." Journal of Plasma Physics 77, no. 3 (September 24, 2010): 385–403. http://dx.doi.org/10.1017/s0022377810000541.

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AbstractLarge-amplitude Alfvén waves are ubiquitous in space plasmas and a main component of magnetohydrodynamic (MHD) turbulence in the heliosphere. As pump waves, they are prone to parametric instability by which they can generate cyclotron and acoustic daughter waves. Here, we revisit a related process within the framework of the multi-fluid equations for a plasma consisting of many species. The nonlinear coupling of the Alfvén wave to acoustic waves is studied, and a set of compressive and coupled-wave equations for the transverse magnetic field and longitudinal electric field is derived for waves propagating along the mean-field direction. It turns out that slightly compressive Alfvén waves exert, through induced gyro-radius and kinetic-energy modulations, an electromotive force on the particles in association with a longitudinal electric field, which has a potential that is given by the gradient of the transverse kinetic energy of the particles gyrating about the mean field. This in turn drives electric fluctuations (sound and ion-acoustic waves) along the mean magnetic field, which can nonlinearly react back on the transverse magnetic field. Mutually coupled Alfvén-cyclotron--acoustic waves are thus excited, a nonlinear process that can drive a cascade of wave energy in the plasma, and may generate compressive microturbulence. These driven electric fluctuations might have consequences for the dissipation of an MHD turbulence and, thus, for the heating and acceleration of particles in the solar wind.

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CAMBON, CLAUDE, N. N. MANSOUR, and F. S. GODEFERD. "Energy transfer in rotating turbulence." Journal of Fluid Mechanics 337 (April 25, 1997): 303–32. http://dx.doi.org/10.1017/s002211209700493x.

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The influence of rotation on the spectral energy transfer of homogeneous turbulence is investigated in this paper. Given the fact that linear dynamics, e.g. the inertial waves regime found in an RDT (rapid distortion theory) analysis, cannot affect a homogeneous isotropic turbulent flow, the study of nonlinear dynamics is of prime importance in the case of rotating flows. Previous theoretical (including both weakly nonlinear and EDQNM theories), experimental and DNS (direct numerical simulation) results are collected here and compared in order to give a self-consistent picture of the nonlinear effects of rotation on turbulence.The inhibition of the energy cascade, which is linked to a reduction of the dissipation rate, is shown to be related to a damping of the energy transfer due to rotation. A model for this effect is quantified by a model equation for the derivative-skewness factor, which only involves a micro-Rossby number Roω=ω′/(2Ω) – ratio of r.m.s. vorticity and background vorticity – as the relevant rotation parameter, in accordance with DNS and EDQNM results.In addition, anisotropy is shown also to develop through nonlinear interactions modified by rotation, in an intermediate range of Rossby numbers (RoL<1 and Roω>1), which is characterized by a macro-Rossby number RoL based on an integral lengthscale L and the micro-Rossby number previously defined. This anisotropy is mainly an angular drain of spectral energy which tends to concentrate energy in the wave-plane normal to the rotation axis, which is exactly both the slow and the two-dimensional manifold. In addition, a polarization of the energy distribution in this slow two-dimensional manifold enhances horizontal (normal to the rotation axis) velocity components, and underlies the anisotropic structure of the integral length-scales. Finally a generalized EDQNM (eddy damped quasi-normal Markovian) model is used to predict the underlying spectral transfer structure and all the subsequent developments of classic anisotropy indicators in physical space. The results from the model are compared to recent LES results and are shown to agree well. While the EDQNM2 model was developed to simulate ‘strong’ turbulence, it is shown that it has a strong formal analogy with recent weakly nonlinear approaches to wave turbulence.

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Krommes, John A. "Systematic statistical theories of plasma turbulence and intermittency: current status and future prospects." Physics Reports 283, no. 1-4 (April 1997): 5–48. http://dx.doi.org/10.1016/s0370-1573(96)00052-x.

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30

HELLER, M. V. A. P., I. L. CALDAS, A. A. FERREIRA, E. A. O. SAETTONE, and A. VANNUCCI. "Tokamak turbulence at the scrape-off layer in TCABR with an ergodic magnetic limiter." Journal of Plasma Physics 73, no. 3 (June 2007): 295–306. http://dx.doi.org/10.1017/s0022377806004569.

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AbstractThe influence of an ergodic magnetic limiter (EML) on plasma turbulence is investigated in the Tokamak Chauffage Alfvén Brésilien (TCABR), a tokamak with a peculiar natural superposition of the electrostatic and magnetic fluctuation power spectra. Experimental results show that the EML perturbation can reduce both the magnetic oscillation and the electrostatic plasma turbulence. Whenever this occurs, the turbulence-driven particle transport is also reduced. Moreover, a bispectral analysis shows that the nonlinear coupling between low- and high-frequency electrostatic fluctuations increases significantly with the EML application.

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31

Wang, B. B., G. P. Zank, L. Adhikari, and L. L. Zhao. "On the Conservation of Turbulence Energy in Turbulence Transport Models." Astrophysical Journal 928, no. 2 (April 1, 2022): 176. http://dx.doi.org/10.3847/1538-4357/ac596e.

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Abstract Zank et al. developed models describing the transport of low-frequency incompressible and nearly incompressible turbulence in inhomogeneous flows. The formalism was based on expressing the fluctuating variables in terms of the Elsässar variables and then taking “moments” subject to various closure hypotheses. The turbulence transport models are different according to whether the plasma beta regime is large, of order unity, or small. Here, we show explicitly that the three sets of turbulence transport models admit a conservation representation that resembles the well-known WKB transport equation for Alfvén wave energy density after introducing appropriate definitions of the “pressure” associated with the turbulent fluctuations. This includes introducing a distinct turbulent pressure tensor for 3D incompressible turbulence (the large plasma beta limit) and pressure tensors for quasi-2D and slab turbulence (the plasma beta order-unity or small regimes) that generalize the form of the WKB pressure tensor. Various limits of the different turbulent pressure tensors are discussed. However, the analogy between the conservation form of the turbulence transport models and the WKB model is not close for multiple reasons, including that the turbulence models express fully nonlinear physical processes unlike the strictly linear WKB description. The analysis presented here both serves as a check on the validity and correctness of the turbulence transport models and also provides greater transparency of the energy dissipation term and the “turbulent pressure” in our models, which is important for many practical applications.

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32

Chian, Abraham C. L. "Order and Chaos in Accretion Disks of Active Galactic Nuclei." International Astronomical Union Colloquium 163 (1997): 663–66. http://dx.doi.org/10.1017/s0252921100043359.

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AbstractLangmuir turbulence plays an important role in electron heating and generation of plasma emission in accretion disks of active galactic nuclei. The nonlinear dynamical behavior of Langmuir turbulence and its relevance in the interpretation of AGN variability is discussed. In particular, we study nonlinear saturation of the Langmuir stimulated modulational instability, for which the low-frequency mode is a resonant ion-acoustic wave. The nonlinear system of coupled wave equations is shown to undergo transition from order to chaos via the route of quasiperiodicity. The periodic, quasiperiodic and chaotic variabilities in AGN emissions may be the electromagnetic signatures of the ordered and chaotic states of Langmuir turbulence in accretion disks or jets of AGN.

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33

Buti, B. "Chaos and Turbulence in Solar Wind." International Astronomical Union Colloquium 154 (1996): 33–41. http://dx.doi.org/10.1017/s0252921100029936.

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AbstractLarge amplitude waves as well as turbulence has been observed in the interplanetary medium. This turbulence is not understood to the extent that one would like to. By means of techniques of nonlinear dynamical systems, attempts are being made to properly understand the turbulence in the solar wind, which is essentially a nonuniform streaming plasma consisting of hydrogen and a fraction of helium. We demonstrate that the observed large amplitude waves can generate solitary waves, which in turn, because of some propagating solar disturbance, can produce chaos in the medium. The chaotic fields thus generated can lead to anomalously large plasma heating and acceleration.Unlike the solitary waves in uniform plasmas, in nonuniform plasmas we get accelerated solitary waves, which lead to electromagnetic as well as electrostatic (e.g. ion acoustic) radiations. The latter can be a very efficient source of plasma heating.

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34

Ghosh, Sanjoy, and Tulasi N. Parashar. "Linear vs. nonlinear acceleration in plasma turbulence. I. Global versus local measures." Physics of Plasmas 22, no. 4 (April 2015): 042302. http://dx.doi.org/10.1063/1.4916975.

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35

van Milligen, B. Ph, C. Hidalgo, E. Sánchez, M. A. Pedrosa, R. Balbı́n, I. Garcı́a-Cortés, and G. R. Tynan. "Statistically robust linear and nonlinear wavelet analysis applied to plasma edge turbulence." Review of Scientific Instruments 68, no. 1 (January 1997): 967–70. http://dx.doi.org/10.1063/1.1147727.

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36

Hamabata, Hiromitsu. "Modulational instability produced by Alfvénic turbulence in a collisionless plasma." Journal of Plasma Physics 46, no. 2 (October 1991): 319–30. http://dx.doi.org/10.1017/s0022377800016147.

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Using first-order smoothing theory, Fourier analysis and perturbation methods, we obtain the evolution equation of the wave spectrum as well as the nonlinear forces generated by Alfvénic turbulence in a finite-β plasma with dispersion and phenomenological Landau-damping effects. The stability of Alfvénic turbulence is then analysed by solving the derived mean-field equations. It is shown that parallel-propagating turbulent Alfvén waves with dispersion can be modulationally unstable, leading to amplification of large-scale Alfvén waves and acoustic waves when Landau-damping effects are strong and weak respectively.

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37

Porporato, Amilcare, Milad Hooshyar, Andrew D. Bragg, and Gabriel Katul. "Fluctuation theorem and extended thermodynamics of turbulence." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (November 2020): 20200468. http://dx.doi.org/10.1098/rspa.2020.0468.

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Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker–Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.

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38

Katou, K. "Early onset of dissipative electrostatic drift-wave turbulence." Journal of Plasma Physics 40, no. 3 (December 1988): 567–78. http://dx.doi.org/10.1017/s0022377800013520.

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The nonlinear dynamics of a low-frequency electrostatic dissipative inhomogeneous plasma in an external magnetic field is studied for conditions above the critical point. The diffusion flux and the saturation level are self-consistently calculated from first principles, i.e. from the Braginskii equation.

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39

Singh, Indraj, P. K. Gupta, R. Uma, and R. P. Sharma. "Spatiotemporal nonlinear evolution of the laser pulse and turbulence generation in laser produced plasmas." Physics of Plasmas 29, no. 4 (April 2022): 042114. http://dx.doi.org/10.1063/5.0085724.

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This study presents a model to understand the behavior of the turbulence generated in the magnetic field of mega gauss order during high-intensity laser interaction with magnetized plasma. The modified nonlinear Schrödinger (MNLS) equation is developed by contemplating the effect of the group velocity dispersion, diffraction, and nonlinearity induced by the relativistic variation of electron mass and the nonlinear ponderomotive force. Numerical simulation is carried out to solve the dimensionless MNLS equation. The simulation results show the generation of the solitary wave type coherent structures in the nonlinear spatiotemporal evolution of the laser pulse at the early stage, but subsequent turbulence generation has also been observed. The ensemble-averaged turbulent power spectrum has been studied and the power-law scaling is approximately ∼ [Formula: see text](a solid red line of scaling [Formula: see text] is given for reference). To get insight into the spatiotemporal nonlinear development of the laser pulse, while propagating in the plasma medium, a semi-analytical model has also been presented. The present study could be substantial in replicating astrophysical scenarios by laboratory simulations along with understanding the underlying quintessential physics of magnetic turbulence.

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Shalchi, A. "Perpendicular Diffusion of Energetic Particles: A Complete Analytical Theory." Astrophysical Journal 923, no. 2 (December 1, 2021): 209. http://dx.doi.org/10.3847/1538-4357/ac2363.

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Abstract Over the past two decades scientists have significantly improved our understanding of the transport of energetic particles across a mean magnetic field. Due to test-particle simulations, as well as powerful nonlinear analytical tools, our understanding of this type of transport is almost complete. However, previously developed nonlinear analytical theories do not always agree perfectly with simulations. Therefore, a correction factor a 2 was incorporated into such theories with the aim to balance out inaccuracies. In this paper a new analytical theory for perpendicular transport is presented. This theory contains the previously developed unified nonlinear transport theory, the most advanced theory to date, in the limit of small Kubo number turbulence. New results have been obtained for two-dimensional turbulence. In this case, the new theory describes perpendicular diffusion as a process that is sub-diffusive while particles follow magnetic field lines. Diffusion is restored as soon as the turbulence transverse complexity becomes important. For long parallel mean-free paths, one finds that the perpendicular diffusion coefficient is a reduced field line random walk limit. For short parallel mean-free paths, on the other hand, one gets a hybrid diffusion coefficient that is a mixture of collisionless Rechester & Rosenbluth and fluid limits. Overall, the new analytical theory developed in the current paper is in agreement with heuristic arguments. Furthermore, the new theory agrees almost perfectly with previously performed test-particle simulations without the need of the aforementioned correction factor a 2 or any other free parameter.

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41

Rönnmark, K., and T. Biro. "Phase-space description of plasma waves. Part 2. Nonlinear theory." Journal of Plasma Physics 47, no. 3 (June 1992): 479–89. http://dx.doi.org/10.1017/s0022377800024363.

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A representation of the physical fields as functions on (k, ω, r, t) phase space can be based on Gaussian windows and Fourier transforms. Within this representation, we obtain a very general formula for the second-order nonlinear current J(k, ω, r, t) in terms of the vector potential A(k, ω, r, t). This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasmas, including the effects of inhomogeneous turbulence, wave convection and refraction.

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42

Soucek, J., T. Dudok de Wit, V. Krasnoselskikh, and A. Volokitin. "Statistical analysis of nonlinear wave interactions in simulated Langmuir turbulence data." Annales Geophysicae 21, no. 3 (March 31, 2003): 681–92. http://dx.doi.org/10.5194/angeo-21-681-2003.

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Abstract. We present a statistical analysis of strong turbulence of Langmuir and ion-sound waves resulting from beam-plasma interaction. The analysis is carried out on data sets produced by a numerical simulation of one-dimensional Zakharov’s equations. The nonlinear wave interactions are studied using two different approaches: high-order spectra and Volterra models. These methods were applied to identify two and three wave processes in the data, and the Volterra model was furthermore employed to evaluate the direction and magnitude of energy transfer between the wave modes in the case of Langmuir wave decay. We demonstrate that these methods allow one to determine the relative importance of strongly and weakly turbulent processes. The statistical validity of the results was thoroughly tested using surrogated data set analysis.Key words. Space plasma physics (wave-wave interactions; experimental and mathematical techniques; nonlinear phenomena)

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Janhunen, Salomon, Gabriele Merlo, Alexey Gurchenko, Evgeniy Gusakov, Frank Jenko, and Timo Kiviniemi. "Simulation of transport in the FT-2 tokamak up to the electron scale with GENE." Plasma Physics and Controlled Fusion 64, no. 1 (November 26, 2021): 015005. http://dx.doi.org/10.1088/1361-6587/ac318c.

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Abstract Prior experimental work on the FT-2 tokamak has observed electron density fluctuations at electron Larmor radius scales using the enhanced scattering (ES) diagnostic (Gusakov et al 2006 Plasma Phys. Control. Fusion 48 A371–6, Gurchenko and Gusakov 2010 Plasma Phys. Control. Fusion 52 124035). Gyrokinetic GENE simulations of conditions at the upper hybrid resonance layer probed by the ES diagnostic show the presence of the anticipated turbulence from the electron temperature gradient (ETG) driven instability in linear and nonlinear simulations. Ion-scale turbulence is responsible for majority of the transport via trapped electron modes, while impurities act to merge the spectrum of the ion and the electron scale instabilities into a continuum. The linear spectrum at electron scales is characterized by maximal growth rate at a significant ballooning angle θ 0, and at ion scales the turbulence is broad in the ballooning angle distribution. The neoclassical shearing rate obtained from GENE breaks symmetry in nonlinear simulations of ETG turbulence, which manifests itself as an asymmetric turbulence spectrum. The electron density fluctuation spectrum obtained with GENE corresponds well to the ES measurement at electron scales, as do the fluxes obtained from the ion-scale simulations.

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44

Meinecke, Jena, Petros Tzeferacos, Anthony Bell, Robert Bingham, Robert Clarke, Eugene Churazov, Robert Crowston, et al. "Developed turbulence and nonlinear amplification of magnetic fields in laboratory and astrophysical plasmas." Proceedings of the National Academy of Sciences 112, no. 27 (June 22, 2015): 8211–15. http://dx.doi.org/10.1073/pnas.1502079112.

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The visible matter in the universe is turbulent and magnetized. Turbulence in galaxy clusters is produced by mergers and by jets of the central galaxies and believed responsible for the amplification of magnetic fields. We report on experiments looking at the collision of two laser-produced plasma clouds, mimicking, in the laboratory, a cluster merger event. By measuring the spectrum of the density fluctuations, we infer developed, Kolmogorov-like turbulence. From spectral line broadening, we estimate a level of turbulence consistent with turbulent heating balancing radiative cooling, as it likely does in galaxy clusters. We show that the magnetic field is amplified by turbulent motions, reaching a nonlinear regime that is a precursor to turbulent dynamo. Thus, our experiment provides a promising platform for understanding the structure of turbulence and the amplification of magnetic fields in the universe.

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45

Gkioulekas, Eleftherios. "On the elimination of the sweeping interactions from theories of hydrodynamic turbulence." Physica D: Nonlinear Phenomena 226, no. 2 (February 2007): 151–72. http://dx.doi.org/10.1016/j.physd.2006.11.012.

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46

Hnat, Bogdan, and Nicholas Walkden. "Amplitude Modulation And Nonlinear Self-Interactions of the Geodesic Acoustic Mode at the Edge of MAST." Plasma 2, no. 2 (May 8, 2019): 168–78. http://dx.doi.org/10.3390/plasma2020013.

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We studied the amplitude modulation of the radial electric field constructed from the Langmuir probe plasma potential measurements at the edge of the mega-ampere spherical tokamak (MAST). The Empirical Mode Decomposition (EMD) technique was applied, which allowed us to extract fluctuations on temporal scales of plasma turbulence, the Geodesic Acoustic Mode (GAM), and those associated with the residual poloidal flows. This decomposition preserved the nonlinear character of the signal. Hilbert transform (HT) was then used to obtain the amplitude modulation envelope of fluctuations associated with turbulence and with the GAM. We found significant spectral coherence at frequencies between 1–5 kHz, in the turbulence and the GAM envelopes and for the signal representing the low frequency zonal flows (LFZFs). We present the evidence of local and nonlocal, in frequency space, three wave interactions leading to coupling between the GAM and the low frequency (LF) part of the spectrum.

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47

Deka, P. N., and S. Gogoi. "The Wave Energy Up Conversion of Plasma Wave in Inhomogeneous Ionosphereic Plasma." Journal of Scientific Research 11, no. 3 (September 1, 2019): 339–50. http://dx.doi.org/10.3329/jsr.v11i3.40982.

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Different types of instabilities are observed in the thermodynamically nonequilibrium Earth's ionosphere. Effective energy exchange process among waves may takes place through nonlinear interaction modes because of availability of free energy. We consider gradients in density and magnetic field is present in the system which support drift wave turbulence. In this study we concern on the wave energy up conversion of electrostatic nonresonant lower hybrid wave through plasma maser instability in the mid-altitude ionospheric region. We have formulated the growth rate of lower hybrid wave by Vlasov-Poisson mathematical frame and estimated its value by observational data.

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48

Roytershteyn, Vadim, and Gian Luca Delzanno. "Nonlinear coupling of whistler waves to oblique electrostatic turbulence enabled by cold plasma." Physics of Plasmas 28, no. 4 (April 2021): 042903. http://dx.doi.org/10.1063/5.0041838.

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49

Kono, Mitsuo. "A route to turbulence in nonlinear development of an ion beam–plasma instability." Physics of Fluids 28, no. 5 (1985): 1494. http://dx.doi.org/10.1063/1.864983.

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50

Chiu, J. S., and A. K. Sen. "Experimental Determination of a Nonlinear Dynamic Model of Plasma Turbulence Using Feedback Control." Physical Review Letters 83, no. 26 (December 27, 1999): 5503–6. http://dx.doi.org/10.1103/physrevlett.83.5503.

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