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  • 1
    Electronic Resource
    Electronic Resource
    Self-sustained magnetic islands (1996)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Plasmas 3 (1996), S. 4628-4636 
    Details
    ISSN: 1089-7674
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Numerical simulations of a single magnetic island evolution are presented in the regime where the island width is smaller than an ion Larmor radius. It is shown that the island rotation is controlled by particle diffusion due to collisions or a background of microturbulence. More precisely, for vanishing density gradient, the sign of rotation frequency is determined by the off-diagonal diffusion term, i.e., by the coefficient of the temperature gradient in the particle flux. As expected from the theory of a stationary island, there exist cases where linearly stable magnetic perturbations are nonlinearly self-sustained. This situation corresponds to large poloidal beta and temperature gradient. The drive is due to diamagnetic frequency effects. However, this situation is not generic, and islands can also decay. It is found that a magnetic island is self-sustained for a negative off-diagonal diffusion coefficient. This case occurs in a tokamak if the inward particle pinch is due to the temperature gradient. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.871586
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  • 2
    Electronic Resource
    Electronic Resource
    Quasistatic heat front and delocalized heat flux (1985)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 28 (1985), S. 835-845 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: New results concerning the mathematical properties of the Fokker–Planck equation describing the electron distribution function are presented. The validity of the approximations obtained by using a finite number of Legendre polynomials to describe the electron distribution function is discussed. It is shown that, due to the Landau form of the electron-ion collision operator, it is sufficient to use two or three Legendre polynomials in problems of interest. The theory is applied to the classical albedo problem as a test, and is also applied to determine the distribution and the heat flux in a heat front typical of laser plasma experiments. It is shown that the heat flux can be expressed as a sort of convolution of the Spitzer–Härm heat flux by a delocalization function. The convolution formula leads in a physically relevant way to the saturation and the delocalization of the heat flux.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865052
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  • 3
    Electronic Resource
    Electronic Resource
    Field line stochasticity during the m=1 reconnection (1993)
    New York, NY : American Institute of Physics (AIP)
    Physics of Fluids 5 (1993), S. 1213-1226 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A full three-dimensional nonlinear magnetohydrodynamic (MHD) simulation using a high number of modes supports a model of the m=1 asymmetric resistive reconnection in tokamaks. The current sheet associated with the internal kink mode exhibits a toroidal modulation mainly due to a finite toroidal pressure effect that leads to an asymmetric m=1 magnetic island. The main effect of the modulation is to drive the growth of (m±1,m) magnetic islands in the plasma on a time scale imposed by the m=1 reconnection process. As the reconnection proceeds, different magnetic island chains with m of order 10 overlap, leading to an annular stochastic region around the m=1 separatrix. The diffusion in this stochastic layer depends exponentially on the current state of the reconnection, and can reach a value high enough to expel the electronic temperature in less than about 100 μsec if the modulation is greater than about 1.0, that is, for low-shear and/or high-pressure gradient equilibrium values on the q=1 surface.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.860911
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  • 4
    Electronic Resource
    Electronic Resource
    An improvement of the nonlocal heat flux formula (1988)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 31 (1988), S. 711-713 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: A new heat flux formula valid in strong inhomogeneous laser-produced plasmas has been derived from the Fokker–Planck equation. The nonlocal treatment of Luciani et al. [Phys. Rev. Lett. 51, 1664 (1983); Phys. Fluids 28, 835 (1985)] is improved by taking into account the electric potential effect. A simple and reliable phenomenological formula is proposed, which is in good agreement with numerical Fokker–Planck computations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866806
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  • 5
    Electronic Resource
    Electronic Resource
    Collisional effects and dispersion relation of magnetic field structures (1987)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 30 (1987), S. 1353-1361 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The local dispersion relation of weak magnetic modes for an arbitrary wavelength ranging from collisional to collisionless cases is derived. The convection velocity and the growth rate are explicitly computed. The convection effects are emphasized and a significant departure from collisional Nernst law is shown to occur even for rather low wavenumbers. In laser plasma experiments, this prevents the convection of intermediate scale magnetic structures generated near the critical layer toward high densities. An explicit convection velocity formula is proposed that is directly usable for numerical purposes. The mathematical tools used in this work are continuous fractions arising naturally from the Fokker–Planck equation with a Landau collisional operator, so that this method can be used to study collisional effects on other plasma modes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.866249
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  • 6
    Electronic Resource
    Electronic Resource
    Electron acceleration in localized plasma waves (1986)
    [S.l.] : American Institute of Physics (AIP)
    Physics of Fluids 29 (1986), S. 3407-3414 
    Details
    ISSN: 1089-7666
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Particle acceleration in a localized electrostatic wave packet is studied. A weak field regime and a strong field regime are displayed. In the weak field limit a quasilinear relation for the velocity perturbation is derived. When the particles cross the accelerating field several times, a quasilinear equation for the distribution function is established. The theory is illustrated by numerical results from a model of resonance absorption of laser light by a plasma. Finally a model of electron reheating in resonance absorption including collisions is presented, leading to a nearly Maxwellian behavior for the hot component of the electron distribution function, f∼exp−(v/v0)8/3.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.865857
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  • 7
    Electronic Resource
    Electronic Resource
    RECONSTRUCTING THE SOLAR CORONAL MAGNETIC FIELD AS A FORCE-FREE MAGNETIC FIELD (1997)
    Springer
    Solar physics 174 (1997), S. 129-149 
    Details
    ISSN: 1573-093X
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present some preliminary results on different mathematical problems encountered in attempts to reconstruct the coronal magnetic field, assumed to be in a force-free state, from its values in the photosphere. We discuss the formulations associated with these problems, and some new numerical methods that can be used to get their approximate solutions. Both the linear constant-α and the nonlinear cases are considered. We also discuss the possible use of dynamical 3D MHD codes to construct approximate solutions of the equilibrium force-free equations, which are needed for testing numerical extrapolation schemes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1004966830232
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  • 8
    Electronic Resource
    Electronic Resource
    On diffusion equations for dynamical systems driven by noise (1989)
    Springer
    Journal of statistical physics 54 (1989), S. 971-995 
    Details
    ISSN: 1572-9613
    Keywords: Fokker-Planck equations ; Lyapunov exponents ; localization ; parametric oscillators
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A unified formalism is presented to study Hamiltonian linear systems driven by noise. With this formalism, the phase averaging approximation, valid at weak noise, is easily performed. Already known results are straightforwardly recovered and new ones are obtained. After introducing this formalism on the exactly solvable one-degree-of-freedom problem with uncorrelated noise, one studies the corresponding exponentially correlated case. The validity of the approximate results thus obtained is considered by investigating the systematic weak-disorder expansion beyond the quasilinear approximation. In particular, it is argued that this expansion behaves uniformly for weak and large correlation time. The two-degrees-of-freedom problem is completely solved at the low-disorder approximation and this result is applied to the two-channel Anderson localization problem. The invariant measure and the two positive Lyapunov exponents are computed at all coupling between the channels. For systems withn degree of freedom the phase averaging leads to a Fokker-Planck equation for the measure in action space describing the system. However, it is argued that it is not solvable except in a special case which is explicitly displayed and solved. Nevertheless, in the large-n limit, it is possible to compute the largest Lyapunov exponent. Moreover, generalized Lyapunov exponents are calculated in this limit, and they do not exhibit a dispersion: in particular, log〈ℰ〉/〈logℰ〉∼1, where ℰ is the energy of the system and where the brackets denote averaging over the noise. On the other hand, it is possible to compute at weak noise the sum of all the positive Lyapunov exponents. Taking into account all these results allows more insight on the whole spectrum of Lyapunov exponents.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01019784
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  • 9
    Electronic Resource
    Electronic Resource
    Bistability driven by correlated noise: Functional integral treatment (1988)
    Springer
    Journal of statistical physics 50 (1988), S. 567-597 
    Details
    ISSN: 1572-9613
    Keywords: Stochastic equations ; non-Markovian effects ; functional integral
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A complete study of non-Markovian effects induced by correlated noise applied to a bistable dynamical system is presented. Starting from the exact functional integral solution of the stochastic equation, it is possible to show that the customary expansion in powers of the characteristic correlation time gives wrong asymptotic results. Other approaches based on a Fokker-Planck equation with a modified diffusion coefficient also fail in reproducing the right long-time behavior of the system. Using a generalized version of instanton calculus of functional integrals, explicit expressions of the invariant measure and transition time between stable fixed points are obtained, in the limit of small noise intensity but arbitrary correlation time. In particular, an original method for extracting the collective degrees of motion has been developed. These analytical results fit, for a large range of parameters, with numerical calculations, giving confidence in the formalism employed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01026491
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  • 10
    Electronic Resource
    Electronic Resource
    Resummation methods of the Chapman-Enskog expansion for a strongly inhomogeneous plasma (1986)
    Springer
    Journal of statistical physics 43 (1986), S. 281-302 
    Details
    ISSN: 1572-9613
    Keywords: Transport theory ; Chapman-Enskog expansion ; Padé approximants ; Borel-Padé approximant ; resummation methods ; non-equilibrium plasma ; strong temperature gradients
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We present a two-fold approach for strongly inhomogeneous plasmas for which the Chapman-Enskog asymptotic expansion breaks down: First, a heuristic one: we solve the kinetic equation by an iterative algorithm, and obtain a non-local response to the local gradients of the local maxwellian distribution function. The other approach consists in resummation methods of the Chapman-Enskog expansion for the distribution function or for its velocity moments: we use Padé or Borel-Padé approximants, and obtain with the simplest ones delocalization formulas similar to those obtained by using the iterative algorithm. These formulas are of great potential use in any situation where strong temperature gradients occur (laser plasma interaction, stellar winds, cloud evaporation).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01010582
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