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Pierre-Louis Sulem

Publications and source records attributed to Pierre-Louis Sulem.

8 recordsLinked to original sources
arXiv2026

Sub-sonic compressible magnetohydrodynamic turbulence I. Alfv\'enic and fast-magnetosonic injection, amplitude dependence, and compressibility effects

We investigate how sub-sonic compressible magnetohydrodynamic (MHD) turbulence properties that are relevant for cosmic-ray (CR) transport in the Galaxy are affected by the nature and amplitude of initial fluctuations, and by the plasma compressibility $\beta$. We perform 3D simulations of decaying compressible ideal-MHD turbulence at $1024^3$ resolution with the PLUTO code. The level of density fluctuations in fully developed turbulence is insensitive to whether this state is reached starting from Alfv\'enic or fast-magnetosonic perturbations. Fast-magnetosonic injection is characterized by an early phase of rapid shock dissipation, followed by a turbulence-dominated decay with a rate comparable to that of the Alfv\'enic case. The contribution of fast-magnetosonic fluctuations in fully developed turbulence remains relevant only when the initial injection consists exclusively of fast modes. Large-amplitude turbulence ($\delta B/B_0>1$) is characterized by a nearly isotropic Kolmogorov or Iroshnikov-Kraichnan spectrum for Alfv\'enic or fast-magnetosonic injection, respectively. At low amplitudes ($\delta B/B_0\ll1$), both initial Alfv\'enic and mixed-wave perturbations lead to strongly anisotropic turbulence with spectra $\propto k_\perp^{-5/3}$ and $\propto k_z^{-2}$ (becoming steeper at $\beta\gg1$), whereas fast-magnetosonic perturbations produce a turbulent state populated by shocks with a nearly isotropic $k^{-2}$ spectrum. Magnetic-field curvature and mirror structures are strongly sensitive to fluctuation amplitude and plasma $\beta$. The predicted -2.5 power-law scaling emerges only in the large-amplitude regime at high $\beta$. This work highlights that features of sub-sonic compressible MHD turbulence that may affect CR transport are sensitive to large-scale conditions and to the plasma $\beta$. Their effect on CR diffusion and field-line random walk is the object of Paper II.

physics.plasm-ph↗
arXiv2024

Impact of pressure anisotropy on the cascade rate of Hall-MHD turbulence with biadiabatic ions

The impact of ion pressure anisotropy on the energy cascade rate of Hall-MHD turbulence with biadiabatic ions and isothermal electrons is evaluated in three-dimensional direct numerical simulations, using the exact (or third-order) law derived in \citet{simon_exact_2022}. It is shown that pressure anisotropy can enhance or reduce the cascade rate, depending on the scales, in comparison with the prediction of the exact law with isotropic pressure, by an amount that correlates well with pressure anisotropy $a_p=\frac{p_\perp}{p_\parallel}\neq1$ that develops in simulations initialized with an isotropic pressure (${a_p}_0=1$). A simulation with initial pressure anisotropy, ${a_p}_0=4$, confirms this trend, exhibiting a stronger impact on the cascade rate, both in the inertial range and at larger scales, close to the forcing scales. Furthermore, a Fourier-based numerical method, to compute exact laws in numerical simulations in the full $(\ell_\perp,\ell_\parallel)$ increment plane, is presented.

physics.plasm-ph↗
arXiv2022

Turbulent regimes in collisions of 3D Alfvén-wave packets

Using 3D gyrofluid simulations, we revisit the problem of Alfven-wave (AW) collisions as building blocks of the Alfvenic cascade and their interplay with magnetic reconnection at magnetohydrodynamic (MHD) scales. Depending on the large-scale nonlinearity parameter $χ_0$ (the ratio between AW linear propagation time and nonlinear turnover time), different regimes are observed. For strong nonlinearities ($χ_0\sim1$), turbulence is consistent with a dynamically aligned, critically balanced cascade--fluctuations exhibit a scale-dependent alignment $\sinθ_k\propto k_\perp^{-1/4}$, a $k_\perp^{-3/2}$ spectrum and $k_\|\propto k_\perp^{1/2}$ spectral anisotropy. At weaker nonlinearities (small $χ_0$), a spectral break marking the transition between a large-scale weak regime and a small-scale $k_\perp^{-11/5}$ tearing-mediated range emerges, implying that dynamic alignment occurs also for weak nonlinearities. At $χ_0<1$ the alignment angle $θ_{k_\perp}$ shows a stronger scale dependence than in the $χ_0\sim1$ regime, i.e. $\sinθ_k\propto k_\perp^{-1/2}$ at $χ_0\sim0.5$, and $\sinθ_k\propto k_\perp^{-1}$ at $χ_0\sim0.1$. Dynamic alignment in the weak regime also modifies the large-scale spectrum, scaling roughly as $k_\perp^{-3/2}$ for $χ_0\sim0.5$ and as $k_\perp^{-1}$ for $χ_0\sim0.1$. A phenomenological theory of dynamically aligned turbulence at weak nonlinearities that can explain these spectra and the transition to the tearing-mediated regime is provided; at small $χ_0$, the strong scale dependence of the alignment angle combines with the increased lifetime of turbulent eddies to allow tearing to onset and mediate the cascade at scales that can be larger than those predicted for a critically balanced cascade by several orders of magnitude. Such a transition to tearing-mediated turbulence may even supplant the usual weak-to-strong transition.

astro-ph.SR↗
arXiv2021

Inverse cascade and magnetic vortices in kinetic Alfvén-wave turbulence

A Hamiltonian two-field gyrofluid model for kinetic Alfvén waves (KAWs) in a magnetized electron-proton plasma, retaining ion finite-Larmor-radius corrections and parallel magnetic field fluctuations, is used to study the inverse cascades that develop when turbulence is randomly driven at sub-ion scales. In the directions perpendicular to the ambient field, the dynamics of the cascade turns out to be nonlocal and the ratio $χ_f$ of the wave period to the characteristic nonlinear time at the driving scale affect some of its properties. For example, at small values of $χ_f$, parametric decay instability of the modes driven by the forcing can develop, enhancing for a while inverse transfers. The balanced state, obtained at early time when the two counter-propagating waves are equally driven, also becomes unstable at small $χ_f$, leading to an inverse cascade. For $β_e$ smaller than a few units, the cascade slows down when reaching the low-dispersion spectral range. For higher $β_e$, the ratio of the KAW to the Alfvén frequencies displays a local minimum. At the corresponding transverse wavenumber, a condensate is formed, and the cascade towards larger scales is then inhibited. Depending on the parameters, a parallel inverse cascade can develop, enhancing the elongation of the ion-scale magnetic vortices that generically form.

physics.plasm-ph↗
arXiv2019

Modeling imbalanced collisionless Alfvén wave turbulence with nonlinear diffusion equations

A pair of nonlinear diffusion equations in Fourier space} is used to study the dynamics of strong Alfvén-wave turbulence, from MHD to electron scales. Special attention is paid to the regime of imbalance between the energies of counter-propagating waves commonly observed in the solar wind (SW), especially in regions relatively close to the Sun. In the collisionless regime where dispersive effects arise at scales comparable to or larger than those where dissipation becomes effective, the imbalance produced by a given injection rate of generalized cross-helicity (GCH), which is an invariant, is much larger than in the corresponding collisional regime described by the usual (or reduced) magnetohydrodynamics. The combined effect of high imbalance and ion Landau damping induces a steep energy spectrum for the transverse magnetic field at sub-ion scales. This spectrum is consistent with observations in highly Alfvenic regions of the SW, such as trailing edges, but does not take the form of a transition range continued at smaller scales by a shallower spectrum. This suggests that the observed spectra displaying such a transition result from the superposition of contributions originating from various streams with different degrees of imbalance. Furthermore, when imbalanced energy injection is supplemented at small scales in an already fully developed turbulence, for example under the effect of magnetic reconnection, a significant enhancement of the imbalance at all scales is observed.

physics.plasm-ph↗
arXiv2018

Fluid and gyrofluid modeling of low-$β_e$ plasmas: phenomenology of kinetic Alfvén wave turbulence

Reduced fluid models including electron inertia and ion finite Larmor radius corrections are derived asymptotically, both from fluid basic equations and from a gyrofluid model. They apply to collisionless plasmas with small ion-to-electron equilibrium temperature ratio and low $β_e$, where $β_e$ indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong, constant and uniform magnetic guide field. The consistency between the fluid and gyrofluid approaches is ensured when choosing ion closure relations prescribed by the underlying ordering. A two-field reduction of the gyrofluid model valid for arbitrary equilibrium temperature ratio is also introduced, and is shown to have a noncanonical Hamiltonian structure. This model provides a convenient framework for studying kinetic Alfvén wave turbulence, from MHD to sub-$d_e$ scales (where $d_e$ holds for the electron skin depth). Magnetic energy spectra are phenomenologically determined within energy and generalized helicity cascades in the perpendicular spectral plane. Arguments based on absolute statistical equilibria are used to predict the direction of the transfers, pointing out that, within the sub-ion range associated with a $k_\perp^{-7/3}$ transverse magnetic spectrum, the generalized helicity could display an inverse cascade if injected at small scales, for example by reconnection processes.

physics.plasm-ph↗
arXiv2009

Arrest of Langmuir wave collapse by quantum effects

The arrest of Langmuir-wave collapse by quantum effects, first addressed by Haas and Shukla [Phys. Rev. E 79, 066402 (2009)] using a Rayleigh-Ritz trial-function method is revisited, using rigorous estimates and systematic asymptotic expansions. The absence of blow up for the so-called quantum Zakharov equations is proved in two and three dimensions, whatever the strength of the quantum effects. The time-periodic behavior of the solution for initial conditions slightly in excess of the singularity threshold for the classical problem is established for various settings in two space dimensions. The difficulty of developing a consistent perturbative approach in three dimensions is also discussed, and a semi-phenomenological model is suggested for this case.

math.AP↗