Early nonlinear regime of MHD internal modes: the resistive case

It is shown that the critical layer analysis, involved in the linear theory of internal modes, can be extended continuously into the early nonlinear regime. For the m=1 resistive mode, the dynamical analysis involves two small parameters: the inverse of the magnetic Reynolds number S and the m=1 mode amplitude A, that measures the amount of nonlinearities in the system. The location of the instantaneous critical layer and the dominant dynamical equations inside it are evaluated self-consistently, as A increases and crosses some S-dependent thresholds. A special emphasis is put on the influence of the initial q-profile on the early nonlinear behavior. Predictions are given for a family of q-profiles, including the important low shear case, and shown to be consistent with recent experimental observations

Kinetic limit of N-body description of wave-particle self- consistent interaction

A system of N particles eN=(x1,v1,...,xN,vN) interacting self-consistently with M waves Zn=An*exp(iTn) is considered. Hamiltonian dynamics transports initial data (eN(0),Zn(0)) to (eN(t),Zn(t)). In the limit of an infinite number of particles, a Vlasov-like kinetic equation is generated for the distribution function f(x,v,t), coupled to envelope equations for the M waves. Any initial data (f(0),Z(0)) with finite energy is transported to a unique (f(t),Z(t)). Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution fN(0)-->f(O) weakly and with Zn(0)-->Z(O) as N tends to infinity, the states generated by the Hamiltonian dynamics at all time 0<t<T are such that (eN(t),Zn(t)) converges weakly to (f(t),Z(t)). Comments: Kinetic theory, Plasma physics.Comment: 18 pages, LaTe

Chaos suppression in the large size limit for long-range systems

We consider the class of long-range Hamiltonian systems first introduced by Anteneodo and Tsallis and called the alpha-XY model. This involves N classical rotators on a d-dimensional periodic lattice interacting all to all with an attractive coupling whose strength decays as r^{-alpha}, r being the distances between sites. Using a recent geometrical approach, we estimate for any d-dimensional lattice the scaling of the largest Lyapunov exponent (LLE) with N as a function of alpha in the large energy regime where rotators behave almost freely. We find that the LLE vanishes as N^{-kappa}, with kappa=1/3 for alpha/d between 0 and 1/2 and kappa=2/3(1-alpha/d) for alpha/d between 1/2 and 1. These analytical results present a nice agreement with numerical results obtained by Campa et al., including deviations at small N.Comment: 10 pages, 3 eps figure

Unveiling the nature of out-of-equilibrium phase transitions in a system with long-range interactions

Recently, there has been some vigorous interest in the out-of-equilibrium quasistationary states (QSSs), with lifetimes diverging with the number N of degrees of freedom, emerging from numerical simulations of the ferromagnetic XY Hamiltonian Mean Field (HMF) starting from some special initial conditions. Phase transitions have been reported between low-energy magnetized QSSs and large-energy unexpected, antiferromagnetic-like, QSSs with low magnetization. This issue is addressed here in the Vlasov N \rightarrow \infty limit. It is argued that the time-asymptotic states emerging in the Vlasov limit can be related to simple generic time-asymptotic forms for the force field. The proposed picture unveils the nature of the out-of-equilibrium phase transitions reported for the ferromagnetic HMF: this is a bifurcation point connecting an effective integrable Vlasov one-particle time-asymptotic dynamics to a partly ergodic one which means a brutal open-up of the Vlasov one-particle phase space. Illustration is given by investigating the time-asymptotic value of the magnetization at the phase transition, under the assumption of a sufficiently rapid time-asymptotic decay of the transient force field

Equilibrium statistical mechanics for single waves and wave spectra in Langmuir wave-particle interaction

Under the conditions of weak Langmuir turbulence, a self-consistent wave-particle Hamiltonian models the effective nonlinear interaction of a spectrum of M waves with N resonant out-of-equilibrium tail electrons. In order to address its intrinsically nonlinear time-asymptotic behavior, a Monte Carlo code was built to estimate its equilibrium statistical mechanics in both the canonical and microcanonical ensembles. First the single wave model is considered in the cold beam/plasma instability and in the O'Neil setting for nonlinear Landau damping. O'Neil's threshold, that separates nonzero time-asymptotic wave amplitude states from zero ones, is associated to a second order phase transition. These two studies provide both a testbed for the Monte Carlo canonical and microcanonical codes, with the comparison with exact canonical results, and an opportunity to propose quantitative results to longstanding issues in basic nonlinear plasma physics. Then the properly speaking weak turbulence framework is considered through the case of a large spectrum of waves. Focusing on the small coupling limit, as a benchmark for the statistical mechanics of weak Langmuir turbulence, it is shown that Monte Carlo microcanonical results fully agree with an exact microcanonical derivation. The wave spectrum is predicted to collapse towards small wavelengths together with the escape of initially resonant particles towards low bulk plasma thermal speeds. This study reveals the fundamental discrepancy between the long-time dynamics of single waves, that can support finite amplitude steady states, and of wave spectra, that cannot.Comment: 15 pages, 7 figures, to appear in Physics of Plasma

Molecular gas and star formation towards the IR dust bubble S24 and its environs

We present a multi-wavelength analysis of the infrared dust bubble S24, and its environs, with the aim of investigating the characteristics of the molecular gas and the interstellar dust linked to them, and analyzing the evolutionary status of the young stellar objects (YSOs) identified there. Using APEX data, we mapped the molecular emission in the CO(2-1), $^{13}$CO(2-1), C$^{18}$O(2-1), and $^{13}$CO(3-2) lines in a region of about 5'x 5' in size around the bubble. The cold dust distribution was analyzed using ATLASGAL and Herschel images. Complementary IR and radio data were also used.The molecular gas linked to the S24 bubble, G341.220-0.213, and G341.217-0.237 has velocities between -48.0 km sec$^{-1}$ and -40.0 km sec$^{-1}$. The gas distribution reveals a shell-like molecular structure of $\sim$0.8 pc in radius bordering the bubble. A cold dust counterpart of the shell is detected in the LABOCA and Herschel images.The presence of extended emission at 24 $\mu$m and radio continuum emission inside the bubble indicates that the bubble is a compact HII region. Part of the molecular gas bordering S24 coincides with the extended infrared dust cloud SDC341.194-0.221. A cold molecular clump is present at the interface between S24 and G341.217-0.237. As regards G341.220-0.213, the presence of an arc-like molecular structure at the northern and eastern sections of this IR source indicates that G341.220-0.213 is interacting with the molecular gas. Several YSO candidates are found to be linked to the IR extended sources, thus confirming their nature as active star-forming regions. The total gas mass in the region and the H$_2$ ambient density amount to 10300 M$_{\odot}$ and 5900 cm$^{-3}$, indicating that G341.220-0.213, G341.217-0.237, and the S24 HII region are evolving in a high density medium. A triggering star formation scenario is also investigated.Comment: 17 pages, 16 figures. Submitted to A&A. Revised according to the referee repor

Linear theory and violent relaxation in long-range systems: a test case

In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For special cases, exact finite-N linear growth rates have been exhibited, including, in some spatially inhomogeneous case, finite-N corrections. A random matrix approach is then proposed to estimate the finite-N growth rate for some random initial states. Within the continuous, $N \rightarrow \infty$, approach, the growth rates are finally derived without restricting to spatially homogeneous cases. All the numerical simulations show a very good agreement with the different theoretical predictions. Then, these linear results are used to discuss the large-time nonlinear evolution. A simple criterion is proposed to measure the ability of the system to undergo a violent relaxation that transports it in the vicinity of the equilibrium state within some linear e-folding times

Early out-of-equilibrium beam-plasma evolution

We solve analytically the out-of-equilibrium initial stage that follows the injection of a radially finite electron beam into a plasma at rest and test it against particle-in-cell simulations. For initial large beam edge gradients and not too large beam radius, compared to the electron skin depth, the electron beam is shown to evolve into a ring structure. For low enough transverse temperatures, the filamentation instability eventually proceeds and saturates when transverse isotropy is reached. The analysis accounts for the variety of very recent experimental beam transverse observations.Comment: to appear in Phys. Rev. Letter