# Browsing by Department "Institute for Fusion Studies"

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Item Angular redistribution of nonlinear perturbations: A universal feature of nonuniform flows(2010-06) Horton, W.; Kim, J. H.; Chagelishvili, G. D.; Bowman, J. C.; Lominadze, J. G.; Horton, W.Show more Classically, the net action of nonlinear turbulent processes is interpreted as either a direct or inverse cascade. However, in nonuniform/shear flows the dominant process is a nonlinear redistribution over wave number angle of perturbation spatial Fourier harmonics. We call this process a nonlinear transverse redistribution (NTR). This phenomenon is demonstrated for a simple two-dimensional constant shear (non-normal) flow by numerically simulating the nonlinear dynamics of coherent and stochastic vortical perturbations in the flow. NTR is a general feature of nonlinear processes that should manifest itself in nonuniform engineering, environmental, and astrophysical flows. The conventional characterization of turbulence in terms of direct and inverse cascades, which ignores NTR, appears to be misleading for shear flow turbulence. We focus on the action of nonlinear processes on the spectral energy. NTR redistributes perturbations over different quadrants of the wave number plane and the interplay of this nonlinear redistribution with linear phenomena becomes intricate: it can realize either positive or negative feedback. In the case of positive feedback, it repopulates the quadrants in wave number space where the shear flow induces linear transient growth.Show more Item Asymmetry-driven structure formation in pair plasmas(2009-12) Mahajan, S. M.; Shatashvili, N. L.; Berezhiani, V. I.; Mahajan, S. M.Show more The nonlinear propagation of electromagnetic waves in pair plasmas, in which the electrostatic potential plays a very important but subdominant role of a "binding glue" is investigated. Several mechanisms for structure formation are investigated, in particular, the "asymmetry" in the initial temperatures of the constituent species. It is shown that the temperature asymmetry leads to a (localizing) nonlinearity that is qualitatively different from the ones originating in ambient mass or density difference. The temperature-asymmetry-driven focusing-defocusing nonlinearity supports stable localized wave structures in 1-3 dimensions, which, for certain parameters, may have flat-top shapes.Show more Item Existence Of The Magnetorotational Instability(2008-07) Mahajan, S. M.; Krishan, V.; Mahajan, S. M.Show more By posing and solving a global axisymmetric eigenvalue problem on an infinite domain with modes vanishing at zero and infinity for a differentially rotating MHD plasma, the conditions for the occurrence of a purely growing low-frequency mode known as the magnetorotational instability (MRI) are mapped. It is shown that the MRI criterion drawn from the "local dispersion relation" is at best inadequate and may even be misleading. The physics of the MRI is rather nuanced. It is dictated by the details of the radial profile of the rotation velocity Omega(r) and not just by the sign and the magnitude of its gradient, Omega'. The salient features of the class of profiles for which the MRI-like eigenmodes may occur are given along with the eigenspectrum. For a variety of other profiles, it is shown that an unstable magnetorotational mode is not a valid eigensolution.Show more Item Global Axisymmetric Magnetorotational Instability With Density Gradients(2008-05) Pino, Jesse; Mahajan, S. M.; Pino, Jesse; Mahajan, S. M.Show more We examine global incompressible axisymmetric perturbations of a differentially rotating MHD plasma with radial density gradients. It is shown that the standard magnetorotational instability (MRI) criterion drawn from the local dispersion relation is often misleading. If the equilibrium magnetic field is either purely axial or purely toroidal, the problem reduces to finding the global radial eigenvalues of an effective potential. The standard Keplerian profile including the origin is mathematically ill-posed, and thus any solution will depend strongly on the inner boundary. We find a class of unstable modes localized by the form of the rotation and density profiles, with reduced dependence on boundary conditions.Show more Item A Multivariate Fit Luminosity Function And World Model For Long Gamma-Ray Bursts(2013-04) Shahmoradi, Amir; Shahmoradi, AmirShow more It is proposed that the luminosity function, the rest-frame spectral correlations, and distributions of cosmological long-duration (Type-II) gamma-ray bursts (LGRBs) may be very well described as a multivariate log-normal distribution. This result is based on careful selection, analysis, and modeling of LGRBs' temporal and spectral variables in the largest catalog of GRBs available to date: 2130 BATSE GRBs, while taking into account the detection threshold and possible selection effects. Constraints on the joint rest-frame distribution of the isotropic peak luminosity (L-iso), total isotropic emission (E-iso), the time-integrated spectral peak energy (E-p,E-z), and duration (T-90,T-z) of LGRBs are derived. The presented analysis provides evidence for a relatively large fraction of LGRBs that have been missed by the BATSE detector with E-iso extending down to similar to 10(49) erg and observed spectral peak energies (Ep) as low as similar to 5 keV. LGRBs with rest-frame duration T-90,T-z less than or similar to 1 s or observer-frame duration T-90 less than or similar to 2 s appear to be rare events (less than or similar to 0.1% chance of occurrence). The model predicts a fairly strong but highly significant correlation (rho = 0.58 +/- 0.04) between E-iso and E-p,E-z of LGRBs. Also predicted are strong correlations of L-iso and E-iso with T-90,T-z and moderate correlation between L-iso and E-p,E-z. The strength and significance of the correlations found encourage the search for underlying mechanisms, though undermine their capabilities as probes of dark energy's equation of Stateat high redshifts. The presented analysis favors-but does not necessitate-a cosmic rate for BATSE LGRBs tracing metallicity evolution consistent with a cutoff Z/Z(circle dot) similar to 0.2-0.5, assuming no luminosity-redshift evolution.Show more Item Parametric Amplification Of Laser-Driven Acceleration In A Plasma Channel(2012-06) Arefiev, A. V.; Schollmeier, M.; Khudik, V. N.; Arefiev, Alexey V.; Khudik, Vladimir N.Show more Two-dimensional particle-in-cell simulations are presented for a laser-irradiated solid-density target with and without an underdense preplasma. It is shown that an underdense preplasma can generate an energetic electron tail in addition to the warm electrons generated at the critical surface. Preplasma electrons are accelerated in a quasi-static positively charged channel formed by the laser. At ultra-relativistic laser intensities (a(0) = 10), the acceleration mechanism is not sensitive to the laser polarization. An energetic tail with energies significantly exceeding the energy expected for a single electron in a vacuum is present in simulations with s and p-polarized beams. This suggests that the mechanism of parametric amplification of laser-driven electron acceleration is a likely explanation for the observed phenomenon.Show more Item Particle simulation of Lyapunov exponents in one-component strongly coupled plasmas(1997-03) Ueshima, Y.; Nishihara, K.; Barnett, D. M.; Tajima, T.; Furukawa, H.; Barnett, D. M.; Tajima, T.Show more The Lyapunov exponents and instantaneous expansion rates in a phase space of Coulomb many-body systems are measured with the use of a three-dimensional particle code SCOPE [K. Nishihara, Kakuyugo Kenkyu 66, 253 (1991)]. The code calculates particle dynamics determined by Coulomb forces among individual particles. The Lyapunov exponents normalized by plasma frequency are found to be proportional to Gamma(-25) in the range of 1 less than or equal to Gamma less than or equal to 160, where Gamma is the Coulomb coupling constant of the ion one-component plasma. There is a large jump of the Lyapunov exponent near Gamma similar to 170, which corresponds to the phase transition from the liquid to the solid state in the one-component plasma. In the solid state, the normalized Lyapunov exponents are proportional to Gamma(-6/5) for 170Show more Item Penetration And Scattering Of Lower Hybrid Waves By Density Fluctuations(2014-06) Horton, W.; Goniche, M.; Peysson, Y.; Decker, J.; Ekedahl, A.; Litaudon, X.; Horton, W.Show more Lower Hybrid [LH] ray propagation in toroidal plasma is controlled by a combination of the azimuthal spectrum launched from the antenna, the poloidal variation of the magnetic field, and the scattering of the waves by the density fluctuations. The width of the poloidal and radial RF wave spectrum increases rapidly as the rays penetrate into higher density and scatter from the turbulence. The electron temperature gradient [ETG] spectrum is particularly effective in scattering the LH waves due to its comparable wavelengths and parallel phase velocities. ETG turbulence is also driven by the radial gradient of the electron current density giving rise to an anomalous viscosity spreading the LH-driven plasma currents. The scattered LH spectrum is derived from a Fokker-Planck equation for the distribution of the ray trajectories with a diffusivity proportional to the fluctuations. The LH ray diffusivity is large giving transport in the poloidal and radial wavenumber spectrum in one -or a few passes - of the rays through the core plasma.Show more Item Plasma acceleration and cooling by strong laser field due to the action of radiation reaction force(2008-12) Berezhiani, V. I.; Mahajan, S. M.; Yoshida, Z.; Mahajan, S. MShow more It is shown that for super intense laser pulses propagating in a hot plasma, the action of the radiation reaction force (appropriately incorporated into the equations of motion) causes strong bulk plasma motion with the kinetic energy raised even to relativistic values; the increase in bulk energy is accompanied by a corresponding cooling (intense cooling) of the plasma. The effects are demonstrated through explicit analytical calculations.Show more Item Real Beads On Virtual Strings: Charged Particles On Magnetic Field Lines(2012-11) Breizman, Boris; Khudik, Vladimir; Breizman, Boris; Khudik, VladimirShow more We discuss a similarity between the drift of a charged particle inside a slowly moving solenoid and the motion of a fluid element in an ideal incompressible fluid. This similarity can serve as a useful instructional example to illustrate the concepts of magnetic field lines and magnetic confinement. (C) 2012 American Association of Physics Teachers. [http://dx.doi.org/10.1119/1.4746068]Show more Item Riemann Ellipsoids: Hamiltonian Formulation and Stability Analysis(2015) Benavides, Santiago José; Morrison, Philip J.; Gamba, Irene M.Show more The equilibria and stability of self-gravitating liquid masses has been studied and debated for more than a century by great physicists and mathematicians such as Newton, Maclaurin, Jacobi, Poincaré, Dirichlet, Riemann, and Chandrasekhar, and is still drawing interest from researchers today. Here I present an original approach to formulating the problem in the context of Hamiltonian theory, namely by applying moments of the position and velocity to the constrained Poisson bracket for a fluid. I then study the stability of a certain family of equilibrium ellipsoids with internal flow that depends linearly on the spatial coordinates (Riemann ellipsoids) using this constrained Hamiltonian formulation of the problem. This formulation allows us to use robust stability analysis methods, as well as study the dynamics in a straightforward way. The spectral stability results agree qualitatively with that of Chandrasekhar's, but the parameter value is slightly off, and the nonlinear stability analysis results do not give a definite answer due to the nature of the bifurcation (steady-state). It is still possible to use the Rayleigh-Ritz method to determine whether our system is nonlinearly unstable, but due to time constraints this was not done.Show more Item Self-modulation of nonlinear Alfven waves in a strongly magnetized relativistic electron-positron plasma(2013-08) Lopez, Rodrigo A.; Asenjo, Felipe A.; Munoz, Victor; Chian, Abraham C. L.; Valdivia, J. A.; Asenjo, Felipe A.Show more We study the self-modulation of a circularly polarized Alfven wave in a strongly magnetized relativistic electron-positron plasma with finite temperature. This nonlinear wave corresponds to an exact solution of the equations, with a dispersion relation that has two branches. For a large magnetic field, the Alfven branch has two different zones, which we call the normal dispersion zone (where d omega/dk > 0) and the anomalous dispersion zone (where d omega/dk < 0). A nonlinear Schrodinger equation is derived in the normal dispersion zone of the Alfven wave, where the wave envelope can evolve as a periodic wave train or as a solitary wave, depending on the initial condition. The maximum growth rate of the modulational instability decreases as the temperature is increased. We also study the Alfven wave propagation in the anomalous dispersion zone, where a nonlinear wave equation is obtained. However, in this zone the wave envelope can evolve only as a periodic wave train.Show more Item Self-modulation of nonlinear waves in a weakly magnetized relativistic electron-positron plasma with temperature(2012-04) Asenjo, Felipe A.; Borotto, Felix A.; Chian, Abraham C. L.; Munoz, Victor; Valdivia, J. Alejandro; Rempel, Erico L.; Asenjo, Felipe A.Show more We develop a nonlinear theory for self-modulation of a circularly polarized electromagnetic wave in a relativistic hot weakly magnetized electron-positron plasma. The case of parallel propagation along an ambient magnetic field is considered. A nonlinear Schrodinger equation is derived for the complex wave amplitude of a self-modulated wave packet. We show that the maximum growth rate of the modulational instability decreases as the temperature of the pair plasma increases. Depending on the initial conditions, the unstable wave envelope can evolve nonlinearly to either periodic wave trains or solitary waves. This theory has application to high-energy astrophysics and high-power laser physics.Show more Item Spectrum Of Global Magnetorotational Instability In A Narrow Transition Layer(2009-06) Pino, Jesse; Mahajan, S. M.; Pino, Jesse; Mahajan, S. M.Show more The global magnetorotational instability is investigated for a configuration in which the rotation frequency changes only in a narrow transition region. If the vertical wavelength of the unstable mode is of the same order or smaller than the width of this region, the growth rates can differ significantly from those given by a local analysis. In addition, the nonaxisymmetric spectrum admits overstable modes with a nontrivial dependence on azimuthal wavelength, a feature missed by the local theory. In the limit of vanishing transition region width, the Rayleigh-centrifugal instability is recovered in the axisymmetric case, and the Kelvin-Helmholtz instability in the nonaxisymmetric case.Show more Item Transport Properties in Nontwist Area-Preserving Maps(2009-12) Szezech, J. D.; Caldas, I. L.; Lopes, S. R.; Viana, R. L.; Morrison, P. J.; Morrison, P. J.Show more Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds. (C) 2009 American Institute of Physics. [doi: 10.1063/1.3247349]Show more Item Turbulence and bias-induced flows in simple magnetized toroidal plasmas(2011-05) Li, B.; Rogers, B. N.; Ricci, P.; Gentle, K. W.; Bhattacharjee, A.; Gentle, K. W.Show more Turbulence and bias-induced flows in simple magnetized toroidal plasmas are explored with global three-dimensional fluid simulations, focusing on the parameters of the Helimak experiment. The simulations show that plasma turbulence and transport in the regime of interest are dominated by the ideal interchange instability. The application of a bias voltage alters the structure of the plasma potential, resulting in the equilibrium sheared flows. These bias-induced vertical flows located in the gradient region appear to reduce the radial extent of turbulent structures, and thereby lower the radial plasma transport on the low field side.Show more Item Two-fluid temperature-dependent relativistic waves in magnetized streaming pair plasmas(2010-02) Soto-Chavez, A. R.; Mahajan, S. M.; Hazeltine, R. D.; Soto-Chavez, A. R.; Mahajan, S. M.; Hazeltine, R. D.Show more A relativistic two-fluid temperature-dependent approach for a streaming magnetized pair plasma is considered. Such a scenario corresponds to secondary plasmas created at the polar caps of pulsar magnetospheres. In the model the generalized vorticity rather than the magnetic field is frozen into the fluid. For parallel propagation four transverse modes are found. Two are electromagnetic plasma modes which at high temperature become light waves. The remaining two are Alfveacutenic modes split into a fast and slow mode. The slow mode is cyclotron two-stream unstable at large wavelengths and is always subluminous. We find that the instability cannot be suppressed by temperature effects in the limit of large (finite) magnetic field. The fast Alfveacuten mode can be superluminous only at large wavelengths, however it is always subluminous at high temperatures. In this incompressible approximation only the ordinary mode is present for perpendicular propagation. For oblique propagation the dispersion relation is studied for finite and large strong magnetic fields and the results are qualitatively described.Show more Item Vortex bubble formation in pair plasmas(2013-07) Berezhiani, V. I.; Shatashvili, N. L.; Mahajan, S. M.; Aleksic, B. N.; Mahajan, S. M.Show more It is shown that delocalized vortex solitons in relativistic pair plasmas with small temperature asymmetries can be unstable for intermediate intensities of the background electromagnetic field. Instability leads to the generation of ever-expanding cavitating bubbles in which the electromagnetic fields are zero. The existence of such electromagnetic bubbles is demonstrated by qualitative arguments based on a hydrodynamic analogy, and by numerical solutions of the appropriate nonlinear Schrodinger equation with a saturating nonlinearity.Show more