Magnetic Chaos and Transport Paul Terry and Leonid Malyshkin, group leaders with active participation from MST group, Chicago group, MRX, Wisconsin astrophysics I.Understand the dynamics of spectral energy transfer in the inertial range of MHD turbulence (covered by P.Terry) Decorrelation times, anisotropy, and spectra Role of turbulence drive in experiments (large, small scale) Common characteristics: ISM, experimental plasmas Role of Hall effects, reconnection, anisotropies from fields and flows 2.Understand transport of energy and particles resulting from magnetic fluctuations (covered by L.Malyshkin) Role of magnetic fluctuation properties: stochasticity, spectral composition, resonances Role of magnetic field in thermal conduction for galaxy cluster collapse Cosmic ray transport in galactic magnetic field

Presentation overview Understanding the dynamics of spectral energy transfer in the inertial range of MHD turbulence – Three tasks: 1. Characterize turbulence properties in experiment; relation to reconnection and large scale flows and fields 2. Analytic theory and computation: understand properties, model experiment, bridge between expt and astrophysics 3. Effects of Hall terms and rotation Update on some recent work: Role of turbulence/wave interactions on spectrum anisotropy and inverse energy transfer

Use experiments to tackle key unanswered questions about the nature of magnetic turbulence Does mean magnetic field contribute to turbulent decorrelation? Advective nonlinearity Magnetic nonlinearity What is the turbulent spectrum? k -5/3, k -3/2, k -2, something else? What is the anisotropy of spectrum? None, k || =k 2/3, k || =0, something else? What governs energy transfer direction? ( relevant to dynamo, heating) Global invariants, wave dynamics, other? What happens at resonances? (relevant to ion heating, reconnection) Reversal surface, fluctuations in reconnection 1. Characterize turbulent properties in expt

To make connections to astrophysics, experiment must assess inertial range or account for instability and dissipative effects Determine if there is an inertial range Measure turbulence up to hundreds of kHz and characterize turbulent quantities Investigate turbulence for collisional plasmas, compare with less collisional plasmas In inertial range look at: spectrum fall off dependence on mean field anisotropy cascade directions 1. Characterize turbulent properties in expt

Measure turbulent decorrelation to determine role of mean field and anisotropy Devise appropriate techniques to discriminate against linear tearing instability Computational modeling Tearing suppression (ext current drive) Isolation of inertial scales Use bispectral techniques to isolate turbulent decorrelation rate in expt measurement, Mean field scaling, variation with nonlinearity, relation to fluid straining 1. Characterize turbulent properties in expt

Study resonance regions for insight on role of turbulence in other center topics Measure turbulence at resonant surfaces, especially m=0 Resonant surface: k B=0 MST: Anisotropy, spectrum dominated by resonant fluctuations Does this change in smaller scales? Reconnection for stochastic B vs. k =0 Effect of m=0 fluctuations on momentum transport, ion heating Measure structure and fluctuations in reconnection layer in MRX Is reconnection turbulent? What conditions? Role of fluctuations in heating, acceleration assoc with reconnection 1. Characterize turbulent properties in expt

Application of experimental observations to astrophysics requires theory and modeling Derive predictions for observable quantities in MST inertial range Spectrum: role of B 0 (k 0), p, drive, magnetic shear Anisotropy All components of fluctuating flow, field Resonant damping, viscous damping rates Investigate coupling of small scale magnetic turb with large scale tearing fluctuations using DEBS Role of magnetic shear, cross over from driven to inertial range, spectrum slope, dissipation, role of small-scale instability 2. Analytic theory and computation -3/2: Alfvén -2: kinetic Alfvén -5/3

Use new analysis techniques to extract crucial underlying quantities like decorrelation time Derive bispectral formulas for turbulent decorrelation in MHD w/wo mean magnetic field, tearing instability Must treat multiple fields, multiple nonlinearities (recently available) Require modeling of effect of tearing instability on turb decorrelation Examine computationally spectra, decorrelation time, effective turbulent diffusion (FLASH+hydro, or new code) Use special diagnostics (bispectra, infinitesimal response, energy transfer) Develop technique for 3D velocity measurement of interstellar turbulence; test with experiment Infinitesimal Response 2. Analytic theory and computation

Borrow from fluid turbulence understanding to probe MHD anisotropy and cascade Fluids: Rotation breaks symmetry introduces anisotropy anisotropic inertia waves Inverse energy transfer by 3D motions (wave anisotropy, not global invariants, determine transfer direction) large scale structure with wave anisotropy MHD: Lorentz force Coriolis force Anisotropic Alfvén waves MHD anisotropy has anisotropy of Alfvén wave Investigate anisotropy and spectral transfer in MHD using fluid paradigm Evaluate role of helicity conservation when wave anisotropy operating 2. Analytic theory and computation

Study compressible MHD for application to astrophysics Previous work: ISM, molecular clouds New: role of compressibility, intermittency in scaling of scintillation pulse width Gaussian statistics for dn/dr gives Lévy statistics for dn/dr gives Consistent with ray scattering from randomly oriented shock discontinuities Investigate intermittency in compressible MHD Formulate statistics of passively advected scalar in compressible MHD 2. Analytic theory and computation

How magnetic turbulence is dissipated and effect of dissipation is important is astrophysics and lab expts (Relevant to ion heating, reconnection, interpretation of expt spectra) Investigate spectrum and intermittency in turbulence with Braginskii viscosity Anisotropic Braginskii viscosity can have significant effect on spectrum, dynamo, intermittency given anisotropy of field Apply to primordial dynamo theory Investigate role of compressibility in dissipation of magnetic turbulence 2. Analytic theory and computation

Investigation of decaying turbulence and disk coronae provides comparison points to lab plasmas Understand and characterize B-field unfolding in decaying turbulence When forcing is intermittent, turbulence decays Magnetogenesis theories, forcing by supernova shocks Question: on what scales does turbulence survive during unwinding? Relate to relaxation after sawtooth event in MST Formulate MRI theory, dimensional analysis, and spectral transfer analysis for accretion disk coronae Parallels characterization of turbulence in laboratory plasmas (MST) MRI Tearing instability: compare, contrast coupling to smaller scale turbulence, Reynolds stress, Maxwell stress 2. Analytic theory and computation

Study of Hall effects and rotation makes contact with reconnection, angular momentum transport Calculate properties of turbulence in model with Hall physics, in unbounded and bounded geometries Relevant to evolution of fluctuations in reconnection (MRX) Contrast with turbulence of Alfvén, kinetic Alfvén waves (k > ) New types of wave motion, new time scales What does it do to spectra, anisotropy, decorrelation? Examine effect of rotation on anisotropies, spectral energy transfer in MHD using wave/turbulence interaction paradigm Relevant to MRI, large scales in rotating systems Interplay of Alfvén waves, rotational modes Examine types of anisotropies, transport 3. Hall effects and rotation

In plasma, can energy cascade in inverse direction when dynamical invariants indicate forward cascade? Density gradient driven microturbulence (drift waves) Simpler than MHD – study inverse transfer (relevant to dynamo, flow drive) and anisotropy in plasmas 2D System: Linear Behavior: Anisotropic waves: k y V D (k y B, n - symmetry breaking ) Wave are unstable: ~ << Global anisotropy: zonal flows reflecting wave anisotropy – when k y =0 Update on recent work

Interaction of linear waves and nonlinearity alters energy transfer, isotropy to produce global anisotropy Properties of nonlinearity: v n Isotropic Forward cascade (breaks enstrophy invariance, energy conserved) Waves dominate at large scales Wave dispersion in turbulent decorrelation induces inverse, anisotropic transfer via near-resonant triads, excitation of damped eigenmode Update on recent work

Analytic theory describes inverse energy transfer, yields condition for near resonant triads Weak turbulence theory fails to explain inverse transfer when invariants dictate forward transfer (rotating turbulence) Strong turbulence theory based on statistical closure Self-consistent specification of nonlinear damping (not prescribed) Asymptotic expansion in k y V D << 1 unfolds recursion Examine energy transfer rate for rough antisymmetry: Transfer direction change when k k MHD shares many common features: anisotropic waves, anisotropy reflecting wave anisotropy, advective nonlinearity, multiple eigenmodes Does common physics drive inverse energy transfer, global anisotropy? Update on recent work

Conclusion: there are a number of projects in magnetic turbulence linking lab and astrophysics Small scale turbulence in MST - interstellar turbulence Turbulence at resonant layer - reconnection, momentum transport Test 3D velocity measurement technique for interstellar turbulence on experiment Tearing driven turbulence versus MRI driven turbulence B-unfolding in decaying turbulence