NG21B-0515
Energy spectra stemming from interactions of Alfvén waves and turbulent eddies
Direct numerical simulations of three-dimensional magnetohydrodynamic turbulence at a Taylor Reynolds number of 1100 on a grid of 15363 points are reported (arXiv:0707.3620 astro-ph, submitted to Phys. Rev. Lett.). The flow is incompressible and decaying in time, and the initial condition is a superposition of large scale ABC Beltrami flows for wavenumbers k ≤ 4 and random noise at small scales with a k-3 spectrum, with negligible correlation between the velocity and the magnetic field (ρC~ 10-4) and equal kinetic and magnetic energies; finally, no uniform magnetic field is imposed. At peak of dissipation, current and vorticity sheets have formed within which strong correlations between the velocity and the magnetic field are found. Dissipation of energy appears independent of Reynolds number, and the energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectrum compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfvén waves and leading to a ~ k-3/2 law; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k\perp-2 spectrum, the perpendicular direction referring to the local quasi-uniform magnetic field. Whether such results are universal is not clear, for example because of the importance of nonlocal interactions between widely separated scales in MHD. Several parameters may play a role, such as ρC or the amount of magnetic helicity in the flow. Thus, high-resolution parametric studies are needed in order to understand in detail the interactions of turbulent eddies and Alfvén waves.
NG21B-0516
Subcritical Shocks With Kinematic Relaxation
Ion heating in quasi-perpendicular collisionless shocks is due to ion gyration just behind the ramp. The gyrating distribution gyrotropizes due to kinematic gyrophase mixing. This collisionless relaxation occurs in high Mach number and low Mach number shocks as well. In low Mach number low beta shocks the relaxation is slow and the downstream ion pressure oscillates in space. The pressure oscillations cause magnetic field oscillations which should be observed as a periodic series of overshoots and undershoots.
NG21B-0517
Highly Nonlinear Features of Electron Diffusion Region
Using a fully three-dimensional Particle-in-cell code and real ion to electron mass ratio of 1836 in a hydrogen plasma, we simulated electrodynamics in an extremely thin current sheet (CS) with and without a guide field. Simulations reveal several highly nonlinear features of electron diffusion region as measured from satellites in magneto-tail and magnetopause regions. These features include: (i) ion acceleration by the Hall electric field like in a ion thruster, (ii) bifurcated current sheet by current disruption (iii) fine-scale step-like structure in the CS magnetic field profile, (iv) strong clumping of electrons and ions in the midst of the CS, (v) spiky perpendicular electric fields confined within the CS, (vi) generation of current layers parallel to the reconnecting magnetic field in the presence of a guide field, (vii) strong modification in the spatial distribution of the guide field across the CS, and (viii) electron acceleration to relativistic energies by the electromagnetic turbulence. Results from the satellite observations and simulations are compared quantitatively.
NG21B-0518
MHD simulation of intermittent turbulence
Space observations indicate that the dynamical processes in the space plasma environment generally entail anisotropic and localized intermittent fluctuations. Results from two-dimensional incompressible MHD simulations are presented to demonstrate the formation of coherent structures and the intermittent turbulence. Several characteristics of intermittent fluctuations, such as non-Gaussian probability distribution functions, the spottiness of the small-scale fluctuations and the multifractal nature, are obtained in the simulations and will be reported.
NG21B-0519
The role of zonal flows in laboratory and space plasmas1
Zonal flows are one-dimensional potential flows excited by primary instabilities in plasmas and fluids. They in turn play a significant role in determining the amplitude level of the primary instability. Zonal flows saturate the primary instability by effectively shearing the primary vortices. The basic secondary instability that leads to the excitation of zonal flows is a modulational instability. We will present two examples, a laboratory plasma and high latitude ionospheric plasma where the turbulent structures lead to generation of zonal flows which in turn regulates the level of the flow and the associated level of anomalous particle transport. 1 Work supported by NSF and DOE
NG21B-0520
Integrable, Nonlinear Travelling Waves and Whistler Oscillitons in Two-Fluid, Electron-Proton Plasmas
A Hamiltonian formulation of oblique travelling waves in a two-fluid, charge-neutral, electron-proton plasma shows that the transverse electron and proton momentum equations are exactly integrable if the total transverse momentum flux integrals in the de-Hoffman Teller frame are zero. The integrable travelling waves are investigated by using the Hamiltonian trajectories in phase-space, and by using the structure equation for the common, longitudinal fluid velocity component of the electron and proton fluids. Numerical examples of travelling waves in a cold plasma, including oscillitons are used to illustrate the physics. The transverse electron and proton fluid velocity components exhibit complex, rosette type patterns. The role of the separatrices in the phase-space, the rotational integral, and the longitudinal structure equation on the different wave forms are discussed.
NG21B-0521
Nonlinear finite-Larmor-radius effects in reduced fluid models
The polarization and magnetization effects associated with the process of dynamical reduction leading to nonlinear gyrokinetic theory [1] are shown to introduce nonlinear finite-Larmor-radius (NFLR) effects into nonlinear reduced-fluid equations [2]. These intrinsically nonlinear FLR effects, which are associated with the transformation from guiding-center phase-space dynamics to gyrocenter phase-space dynamics, are different from standard FLR corrections, which are associated with the transformation from particle phase-space dynamics to guiding-center phase-space dynamics. The reduced fluid equations with NFLR corrections are derived from a variational principle and, thus, automatically possess an exact energy conservation law. Simulation results show agreement with linear theory, nonlinear energy conservation, and mode coupling of Alfven and sound waves.
NG21B-0522
Chaotic Magnetic Fields due to Asymmetric Current Configurations - Modeling Cross-Field Diffusion of Charged Particles in Cosmic Rays
The observed cross-field diffusion of charged particles in cosmic ray transport is assumed to be due to chaotic nature of the interplanetary/intergalactic magnetic fields. The particles are accelerated and energized by the temporal fluctuations of the magnetic field. The generation of chaotic magnetic fields is ad hoc and the characteristics of the fields are chosen to satisfy the observations. We consider simple current configurations consisting of circular loops and straight wires that generate asymmetric, nonlinear, steady-state magnetic fields in three spatial dimensions. These magnetic fields are completely deterministic, and, for certain range of parameters, chaotic. We will present analytical and numerical studies on the generation of chaotic magnetic fields and the nature of these fields. The motion of charged particles in the nonlinear and in the chaotic magnetic fields can be described by the Lorentz equation. An analysis of the particle motion will be presented. A particle moving in chaotic magnetic field superposed on a uniform background magnetic field is found to undergo spatial transport. This shows that chaotic magnetic fields can produce cross-field diffusion. This work is supported by DoE Grant DE-FG02-91ER-54109.
NG21B-0523
A new Differential Equation for Anomalous Diffusion with Potential Applications to Nonlinear Space Plasmas
Since the 1960s Mandelbrot has advocated the use of fractals for the description of the non-Euclidean geometry of many aspects of nature. In particular he proposed two kinds of model to capture persistence in time (his Joseph effect, common in hydrology and with fractional Brownian motion as the prototpe) and/or prone to heavy tailed jumps (the Noah effect, typical of economic indices, for which he proposed Lévy flights as an exemplar). Both effects are now well demonstrated in space plasmas, notably in indices quantifying Earth's auroral currents and in the turbulent solar wind. Models have, however, typically emphasised one of the Noah and Joseph parameters (the Lévy exponent μ and the temporal exponent β) at the other's expense. I will describe recent work [1] in which we studied a simple self-affine stable model-linear fractional stable motion, LFSM, which unifies both effects. I will discuss how this resolves some contradictions seen in earlier work. Such Noah-Joseph hybrid ("ambivalent" [2]) behaviour is highly topical in physics but is typically studied in the paradigm of the continuous time random walk (CTRW) [2,3] rather than LFSM. I will clarify the physical differences between these two pictures and present a recently-derived diffusion equation for LFSM. This replaces the second order spatial derivative in the equation of fBm [4] with a fractional derivative of order μ, but retains a diffusion coefficient with a power law time dependence rather than a fractional derivative in time (c.f. [2,3]). Intriguingly the self-similarity exponent extracted from the CTRW differs from that seen in LFSM. In the CTRW it is the ratio of μ to a temporal exponent, in LFSM it is an additive function of them. I will also show work in progress using an LFSM model and simple analytic scaling arguments to study the problem of the area between an LFSM curve and a threshold-related to the burst size measure introduced by Takalo and Consolini into solar- terrestrial physics and further studied by Freeman et al [5,6]. The extension of our new LFSM results to the related class of multifractals will be discussed. 1. Watkins et al, Space Sci. Rev. 121, 271, 2005. 2. Brockmann et al, Nature 439, 462, 2006. 3. Zaslavsky et al, Physica A, 373, 11, 2007. 4. Wang and Lung, Phys. Lett. A 151, 119, 1990. 5. Freeman et al, Geophys. Res. Lett. 27, 1367, 2000. 6. Freeman et al, Phys. Rev. E 62, 8794, 2000.
NG21B-0524
Laboratory experiments on whistler instabilities and triggered emissions
Strong electron energization is observed (3 to 30 eV) in propagating whistler spheromaks and stationary relaxing field-reversed configurations [http://www.iop.org/EJ/abstract/0741-3335/49/5A/S02]. It is ascribed to the free electron acceleration by an inductive electric field along the toroidal null line (separator). Non-Maxwellian distributions are observed, and temperature anisotropies are likely. These can give rise to whistler instabilities. Spontaneous excitation of whistler modes with Bwave \ll B0 are observed (ω/2 π ≈ 7~MHz, vphase ~eq 1.3× 106~m/s). These magnetic oscillations detach from the whistler spheromak and propagate along and oblique to the ambient magnetic field. Their space-time dependence, polarization, spectra and parameter dependence have been measured. In order to measure the spatial growth rate, small amplitude whistler waves are excited from a separate antenna. It is observed that these trigger a stronger whistler emission at an upshifted frequency. Both convective wave growth against drifting electrons is seen as well as temporal growth in the current layer. Thus the source region exhibits absolute and convective instability mechanisms. These observations are relevant to triggered whistler emissions in the ionosphere and magnetosphere. Work supported by NSF/DOE.
NG21B-0525
Observation of Gendrin modes in a laboratory plasma
Gendrin or constant velocity modes are whistlers with oblique phase velocity and parallel group velocity. They exist for ω< ωc/2, have an angle \cos θG = 2ω/ ωc, parallel phase and group velocities vgr=vph =(c/2)ωc/ωp and a frequency-independent wavelength λ=c/fp. The modes are important for wave particle interactions in the ionosphere and magnetosphere since even without ducting they have no energy spread along \mathbf B0, hence provide for long interaction lengths. We have excited Gendrin modes in a large laboratory plasma with a magnetic loop antenna of diameter D~eq λ at ω~eq 0.3 ωc. The linear waves develop a conical phase front whose surface normal \mathbf{k} makes an angle θ =52° ~eq θG. A conical surface is not a plane wave but a superposition of all Gendrin modes on the 3-D refractive index surface. The cones translate along \mathbf{B}0 with little change indicating a parallel energy flow. By integrating the energy density over a cross section transverse to \mathbf{B}0, the wave damping is obtained and normalized to ki/kr~eq 0.03 which shows that both collisional and Landau damping are small. Since the phase velocity is close to the thermal velocity, this implies that the parallel electric field is small, i.e., the inductive electric field is opposed by a space charge electric field. Work supported by NSF/DOE.
NG21B-0526
Spontaneous Generation of Self-Organized Solitary Wave Structures at the Magnetopause
Spontaneous formation of solitary wave structures has been observed in the Earth's magnetopause, and is shown to be caused by the break-up of a zonal flow by the action of drift wave turbulence. Here we show matched observations and modeling of coherent, large-scale solitary electrostatic structures, generated during the interaction of short-scale drift wave turbulence and zonal flows at the Earth's magnetopause. An analytical model demonstrating the growth rate of broadband drift mode turbulence driving zonal flows based on the wave kinetic treatment is presented. The observations were made by the Cluster spacecraft and the numerical modeling was performed using the wave-kinetic approach to drift wave-zonal flow interactions. Good agreement between observations and simulations has been found, thus explaining the emergence of the observed solitary structured as well as confirming earlier theoretical predictions of their existence. The connection to zonal flows in Tokamak fusion reactors is also presented showing synergy between the two areas and demonstrating that the magnetopause is a transport barrier.
NG21B-0527
Initial Experimental Results of a Laboratory Mini-Magnetosphere for Astronaut Protection
Radiation is a major scientific and technological challenge for manned missions to Mars. With an interplanetary flight time of months to years there is a high probability of Solar Energetic Particle events during the flight. Radiation damage to human tissue could result in acute sickness or death of the occupants of an unprotected spacecraft. Thus there is much interest in techniques to mitigate the effects of these events and of the exposure to cosmic rays. The experimental and modelling work presented here concerns one of several innovative "Active Shield" solutions being proposed [1]. The idea of generating an artificial magnetosphere to recreate the protective shield of the Earth's magnetic field for space craft travelling to the Moon or Mars was considered seriously in the 1960's during the Apollo era. With most of the space agencies around the world setting their sights returning to the Moon and then on to Mars, the idea of some sort of active field solution is experiencing a resurgence. Results from the laboratory experiment to determine the effectiveness of a mini-magnetosphere barrier to be able to expel a flowing energetic "solar wind" plasma will be presented. This is compared to a 3D hybrid simulation code that has been successfully compared to other astrophysical situations e.g. AMPTE artificial comet releases [2]. The experiment and modelling comparisons will demonstrate the scalability between the laboratory and astrophysical scale. [1] Adams, J.H. et al., "Revolutionary Concepts of Radiation Shielding for Human Exploration of Space", NASA/TM- 2005-213688, March 2005. [2] Gargate, L.; Bingham, R.; Fonseca, R. A.; Silva, L. O., "dHybrid: A massively parallel code for hybrid simulations of space plasmas", Computer Physics Communications, Volume 176, Issue 6, Pages 419-425, 15 March 2007, doi:10.1016/j.cpc.2006.11.013
NG21B-0528
Characterisation of edge turbulence in relation to edge magnetic field configuration in L-mode plasmas in the Mega Amp Spherical Tokamak.
Almost all astrophysical and magnetically confined fusion plasmas are turbulent. Here, we examine ion saturation current (Isat) measurements of edge plasma turbulence for three MAST L-mode plasmas that differ primarily in their edge magnetic field configurations. First, absolute moments of the coarse grained data are examined to obtain accurate values of scaling exponents. The dual scaling behaviour is identified in all samples, with the temporal scale τ \! ≈ \!40\!-\!60 μs separating the two regimes. Strong universality is then identified in the functional form of the probability density function (PDF) for Isat fluctuations, which is well approximated by the Fréchet distribution on temporal scales τ ≤ 40μs. For temporal scales τ > 40μs, the PDFs appear to converge to the Gumbel distribution, which has been previously identified as a universal feature of many other complex phenomena. The optimal fitting parameters k=1.15 for Fréchet and a=1.35 for Gumbel provide a simple quantitative characterisation of the full spectrum of fluctuations. We conclude that, to good approximation, the properties of the edge turbulence are independent of the edge magnetic field configuration.
NG21B-0529
Depression of Nonlinearity in the Isotropic MHD Turbulence
Magnetohydrodynamic (MHD) turbulence evolves in response to a complex set of mechanical and electromagnetic stresses that drive couplings across spatial scale, leading to a cascade in which there is a net transfer of energy to small scales. Two important features of MHD turbulence, the production of spatial intermittency and the appearance of distinctive states associated with turbulent relaxation, have generally been studied independently. We show, by using decaying direct numerical simulations, that MHD turbulence generates coherent spatial correlations of several types. These are associated to the tendency of the system to develop local Beltrami fields. Moreover, a self-organization process produces anti-alignments in the magnetic and kinetic components of the acceleration. Each of these effects suppresses the nonlinearity to levels lower than the strengths obtained from "Gaussianized" fields. We conclude that this complex picture of correlations causes a local rapid cancellation of mechanical and electromagnetic forces, leading to a reduction of turbulent fluctuations. The result is the production of intermittent spatial patches.
NG21B-0530
Nonlinear Processes in the Damping of Alfven Solitons
The dynamics of Alfven solitons in the presence of weak resistive damping is investigated numerically using the derivative nonlinear Schrodinger (DNLS) equation. The solitons studied here represent one-dimensional, weakly nonlinear and weakly dispersive Alfven waves traveling at a small angle to an ambient magnetic field. There are three types of solitons allowed in this case: the two-parameter soliton and the one-parameter bright soliton, which are both compressive, along with the one-parameter dark soliton, which is rarefactive. It is found for a bright soliton and also a normal ( v > vA) two-parameter soliton that with weak resistive damping these solitons have a brief increase in amplitude, speed and energy even though the total wave energy is decreasing. Accompanying this is the formation of one or more dark solitons. A two-parameter soliton will subsequently lose amplitude and speed and eventually disperse away. It is found that a bright soliton will eventually coalesce with the first dark soliton formed during its initial damping to yield a two-parameter soliton. The implication of these processes is that a wide class of initial wave profiles, in the presence of weak resistive damping, will result in a leading train of dark solitons.