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DOE OSTI2011

Double tearing modes in the presence of internal transport barrier

The linear characteristics of double tearing modes (DTMs) in the presence of internal transport barrier (ITB) are investigated in a cylindrical tokamak plasma. A simple model describing density profile of ITB is suggested. Combining the safety factor profile given by Bierwage et al.[Phys. Plasmas 12, 082504 (2005); 14, 022107 (2007)], the DTMs spectra, scaling laws, and relationships between growth rate and density profile factor in the presence of ITB are studied, respectively. The results show that the resistive drift instability occurs in the case of high poloidal mode numbers. A transition from DTMs to the resistive drift instability is observed, and the dependence of DTMs growth rate on the magnetic Reynolds number has changed greatly due to the presence of ITB. In addition, the linear growth rates of the modes including those with low and high poloidal mode number increase when the plasma density profile steepens in the presence of ITB whatever the inter-resonant distance is smaller or larger.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

SHEAR-DRIVEN DYNAMO WAVES IN THE FULLY NONLINEAR REGIME

Large-scale dynamo action is well understood when the magnetic Reynolds number ( Rm ) is small, but becomes problematic in the astrophysically relevant large Rm limit since the fluctuations may control the operation of the dynamo, obscuring the large-scale behavior. Recent works by Tobias and Cattaneo demonstrated numerically the existence of large-scale dynamo action in the form of dynamo waves driven by strongly helical turbulence and shear. Their calculations were carried out in the kinematic regime in which the back-reaction of the Lorentz force on the flow is neglected. Here, we have undertaken a systematic extension of their work to the fully nonlinear regime. Helical turbulence and large-scale shear are produced self-consistently by prescribing body forces that, in the kinematic regime, drive flows that resemble the original velocity used by Tobias and Cattaneo. We have found four different solution types in the nonlinear regime for various ratios of the fluctuating velocity to the shear and Reynolds numbers. Some of the solutions are in the form of propagating waves. Some solutions show large-scale helical magnetic structure. Both waves and structures are permanent only when the kinetic helicity is non-zero on average.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2011

Global Hall-MHD simulations of magnetorotational instability in a plasma Couette flow experiment

Global MHD and Hall-MHD numerical simulations relevant to the Madison plasma Couette flow experiment (MPCX) have been performed using the extended MHD code NIMROD. The MPCX has been constructed to study the magnetorotational instability (MRI) in a plasma. The two-fluid Hall effect, which is relevant to some astrophysical situations such as protostellar disks, is also expected to be important in the MPCX. Here, we first derive the local Hall dispersion relation including viscosity, extending earlier work by Balbus and Terquem [Astrophys. J. 552, 235 (2001)]. The predictions of the local analysis are then compared with nonlocal calculations of linear stability of the MRI for a parameter range relevant to the MPCX. It is found that the MHD stability limit and mode structure are altered by the Hall term, and nonlocal analysis is necessary to obtain quantitatively reliable predictions for MPCX. Two-fluid physics also significantly changes the nonlinear evolution and saturation of the axisymmetric MRI. Both the Reynolds and Maxwell stresses contribute significantly to momentum transport. In the Hall regime, when the magnetic field is parallel to the rotation axis, the Maxwell stress is larger than the Reynolds stress (similar to the MHD regime). However, when the magnetic field is antiparallel to the rotation axis in the Hall regime, the Reynolds stress is much larger than the Maxwell stress. To further study the role of non-axisymmetric modes, we have also carried out fully nonlinear MHD computations. Non-axisymmetric modes play an increasingly important role as the magnetic Reynolds number increases and grow to large amplitudes in a saturated turbulent state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2016

Fast ignition realization experiment with high-contrast kilo-joule peta-watt LFEX laser and strong external magnetic field

A petawatt laser for fast ignition experiments (LFEX) laser system [N. Miyanaga et al., J. Phys. IV France 133, 81 (2006)], which is currently capable of delivering 2 kJ in a 1.5 ps pulse using 4 laser beams, has been constructed beside the GEKKO-XII laser facility for demonstrating efficient fast heating of a dense plasma up to the ignition temperature under the auspices of the Fast Ignition Realization EXperiment (FIREX) project [H. Azechi et al., Nucl. Fusion 49, 104024 (2009)]. In the FIREX experiment, a cone is attached to a spherical target containing a fuel to prevent a corona plasma from entering the path of the intense heating LFEX laser beams. The LFEX laser beams are focused at the tip of the cone to generate a relativistic electron beam (REB), which heats a dense fuel core generated by compression of a spherical deuterized plastic target induced by the GEKKO-XII laser beams. Recent studies indicate that the current heating efficiency is only 0.4%, and three requirements to achieve higher efficiency of the fast ignition (FI) scheme with the current GEKKO and LFEX systems have been identified: (i) reduction of the high energy tail of the REB; (ii) formation of a fuel core with high areal density using a limited number (twelve) of GEKKO-XII laser beams as well as a limited energy (4 kJ of 0.53-μm light in a 1.3 ns pulse); (iii) guiding and focusing of the REB to the fuel core. Laser–plasma interactions in a long-scale plasma generate electrons that are too energetic to efficiently heat the fuel core. Three actions were taken to meet the first requirement. First, the intensity contrast of the foot pulses to the main pulses of the LFEX was improved to >10{sup 9}. Second, a 5.5-mm-long cone was introduced to reduce pre-heating of the inner cone wall caused by illumination of the unconverted 1.053-μm light of implosion beam (GEKKO-XII). Third, the outside of the cone wall was coated with a 40-μm plastic layer to protect it from the pressure caused by imploding plasma. Following the above improvements, conversion of 13% of the LFEX laser energy to a low energy portion of the REB, whose slope temperature is 0.7 MeV, which is close to the ponderomotive scaling value, was achieved. To meet the second requirement, the compression of a solid spherical ball with a diameter of 200-μm to form a dense core with an areal density of ∼0.07 g/cm{sup 2} was induced by a laser-driven spherically converging shock wave. Converging shock compression is more hydrodynamically stable compared to shell implosion, while a hot spot cannot be generated with a solid ball target. Solid ball compression is preferable also for compressing an external magnetic field to collimate the REB to the fuel core, due to the relatively small magnetic Reynolds number of the shock compressed region. To meet the third requirement, we have generated a strong kilo-tesla magnetic field using a laser-driven capacitor-coil target. The strength and time history of the magnetic field were characterized with proton deflectometry and a B-dot probe. Guidance of the REB using a 0.6-kT field in a planar geometry has been demonstrated at the LULI 2000 laser facility. In a realistic FI scenario, a magnetic mirror is formed between the REB generation point and the fuel core. The effects of the strong magnetic field on not only REB transport but also plasma compression were studied using numerical simulations. According to the transport calculations, the heating efficiency can be improved from 0.4% to 4% by the GEKKO and LFEX laser system by meeting the three requirements described above. This efficiency is scalable to 10% of the heating efficiency by increasing the areal density of the fuel core.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2015

Exact solutions of the incompressible dissipative Hall magnetohydrodynamics

By using analytical method, the exact solutions of the incompressible dissipative Hall magnetohydrodynamics (MHD) equations are derived. It is found that a phase difference may occur between the velocity and magnetic field fluctuations when the kinetic and magnetic Reynolds numbers are both very large. Since velocity and magnetic field fluctuations are both circular polarized, the phase difference makes them no longer parallel or anti-parallel like that in the incompressible ideal Hall MHD.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

A NUMERICAL TREATMENT OF ANISOTROPIC RADIATION FIELDS COUPLED WITH RELATIVISTIC RESISTIVE MAGNETOFLUIDS

We develop a numerical scheme for solving fully special relativistic, resistive radiation magnetohydrodynamics. Our code guarantees conservation of total mass, momentum, and energy. The radiation energy density and the radiation flux are consistently updated using the M-1 closure method, which can resolve an anisotropic radiation field, in contrast to the Eddington approximation, as well as the flux-limited diffusion approximation. For the resistive part, we adopt a simple form of Ohm's law. The advection terms are explicitly solved with an approximate Riemann solver, mainly the Harten-Lax-van Leer scheme; the HLLC and HLLD schemes are also solved for some tests. The source terms, which describe the gas-radiation interaction and the magnetic energy dissipation, are implicitly integrated, relaxing the Courant-Friedrichs-Lewy condition even in an optically thick regime or a large magnetic Reynolds number regime. Although we need to invert 4 Multiplication-Sign 4 matrices (for the gas-radiation interaction) and 3 Multiplication-Sign 3 matrices (for the magnetic energy dissipation) at each grid point for implicit integration, they are obtained analytically without preventing massive parallel computing. We show that our code gives reasonable outcomes in numerical tests for ideal magnetohydrodynamics, propagating radiation, and radiation hydrodynamics. We also applied our resistive code to the relativistic Petschek-type magnetic reconnection, revealing the reduction of the reconnection rate via radiation drag.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2011

Nonlocality and the critical Reynolds numbers of the minimum state magnetohydrodynamic turbulence

Magnetohydrodynamic (MHD) systems can be strongly nonlinear (turbulent) when their kinetic and magnetic Reynolds numbers are high, as is the case in many astrophysical and space plasma flows. Unfortunately these high Reynolds numbers are typically much greater than those currently attainable in numerical simulations of MHD turbulence. A natural question to ask is how can researchers be sure that their simulations have reproduced all of the most influential physics of the flows and magnetic fields? In this paper, a metric is defined to indicate whether the necessary physics of interest has been captured. It is found that current computing resources will typically not be sufficient to achieve this minimum state metric.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2011

A weighted reverse Cuthill-McKee procedure for finite element method algorithms to solve strongly anisotropic electrodynamic problems

This paper presents a technique for improving the convergence rate of a generalized minimum residual (GMRES) algorithm applied for the solution of a algebraic system produced by the discretization of an electrodynamic problem with a tensorial electrical conductivity. The electrodynamic solver considered in this work is a part of a magnetohydrodynamic (MHD) code in the low magnetic Reynolds number approximation. The code has been developed for the analysis of MHD interaction during the re-entry phase of a space vehicle. This application is a promising technique intensively investigated for the shock mitigation and the vehicle control in the higher layers of a planetary atmosphere. The medium in the considered application is a low density plasma, characterized by a tensorial conductivity. This is a result of the behavior of the free electric charges, which tend to drift in a direction perpendicular both to the electric field and to the magnetic field. In the given approximation, the electrodynamics is described by an elliptical partial differential equation, which is solved by means of a finite element approach. The linear system obtained by discretizing the problem is solved by means of a GMRES iterative method with an incomplete LU factorization threshold preconditioning. The convergence of the solver appears to be strongly affected by the tensorial characteristic of the conductivity. In order to deal with this feature, the bandwidth reduction in the coefficient matrix is considered and a novel technique is proposed and discussed. First, the standard reverse Cuthill-McKee (RCM) procedure has been applied to the problem. Then a modification of the RCM procedure (the weighted RCM procedure, WRCM) has been developed. In the last approach, the reordering is performed taking into account the relation between the mesh geometry and the magnetic field direction. In order to investigate the effectiveness of the methods, two cases are considered. The RCM and WRCM procedures has successfully improved the convergence rate of the GMRES solver. For strong anisotropies, the WRCM procedure appears to have a higher convergence rate. The same behavior is shown when applying the methods to the rebuilding of an hypersonic MHD experiment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

EFFECTS OF LARGE-SCALE NON-AXISYMMETRIC PERTURBATIONS IN THE MEAN-FIELD SOLAR DYNAMO

We explore the response of a nonlinear non-axisymmetric mean-field solar dynamo model to shallow non-axisymmetric perturbations. After a relaxation period, the amplitude of the non-axisymmetric field depends on the initial condition, helicity conservation, and the depth of perturbation. It is found that a perturbation that is anchored at 0.9 R{sub ⊙} has a profound effect on the dynamo process, producing a transient magnetic cycle of the axisymmetric magnetic field, if it is initiated at the growing phase of the cycle. The non-symmetric, with respect to the equator, perturbation results in a hemispheric asymmetry of the magnetic activity. The evolution of the axisymmetric and non-axisymmetric fields depends on the turbulent magnetic Reynolds number R{sub m}. In the range of R{sub m} = 10{sup 4}–10{sup 6} the evolution returns to the normal course in the next cycle, in which the non-axisymmetric field is generated due to a nonlinear α-effect and magnetic buoyancy. In the stationary state, the large-scale magnetic field demonstrates a phenomenon of “active longitudes” with cyclic 180° “flip-flop” changes of the large-scale magnetic field orientation. The flip-flop effect is known from observations of solar and stellar magnetic cycles. However, this effect disappears in the model, which includes the meridional circulation pattern determined by helioseismology. The rotation rate of the non-axisymmetric field components varies during the relaxation period and carries important information about the dynamo process.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2014

Quenching and anisotropy of hydromagnetic turbulent transport

Hydromagnetic turbulence affects the evolution of large-scale magnetic fields through mean-field effects like turbulent diffusion and the α effect. For stronger fields, these effects are usually suppressed or quenched, and additional anisotropies are introduced. Using different variants of the test-field method, we determine the quenching of the turbulent transport coefficients for the forced Roberts flow, isotropically forced non-helical turbulence, and rotating thermal convection. We see significant quenching only when the mean magnetic field is larger than the equipartition value of the turbulence. Expressing the magnetic field in terms of the equipartition value of the quenched flows, we obtain for the quenching exponents of the turbulent magnetic diffusivity about 1.3, 1.1, and 1.3 for Roberts flow, forced turbulence, and convection, respectively. However, when the magnetic field is expressed in terms of the equipartition value of the unquenched flows, these quenching exponents become about 4, 1.5, and 2.3, respectively. For the α effect, the exponent is about 1.3 for the Roberts flow and 2 for convection in the first case, but 4 and 3, respectively, in the second. In convection, the quenching of turbulent pumping follows the same power law as turbulent diffusion, while for the coefficient describing the Ω×J effect nearly the same quenching exponent is obtained as for α. For forced turbulence, turbulent diffusion proportional to the second derivative along the mean magnetic field is quenched much less, especially for larger values of the magnetic Reynolds number. However, we find that in corresponding axisymmetric mean-field dynamos with dominant toroidal field the quenched diffusion coefficients are the same for the poloidal and toroidal field constituents.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Generation of X-points and secondary islands in 2D magnetohydrodynamic turbulence

We study the time development of the population of X-type critical points in a two-dimensional magnetohydrodynamic model during the early stages of freely decaying turbulence. At sufficiently high magnetic Reynolds number Re{sub m}, we find that the number of neutral points increases as Re{sub m}{sup 3/2}, while the rates of reconnection at the most active sites decrease. The distribution of rates remains approximately exponential. We focus in particular on delicate issues of accuracy, which arise in these numerical experiments, in that the proliferation of X-points is also a feature of under-resolved simulations. The 'splitting' of neutral points at high Reynolds number appears to be a fundamental feature of the cascade that has important implications for understanding the relationship between reconnection and turbulence, an issue of considerable importance for the Magnetospheric Multiscale and Solar Probe missions as well as observation of reconnection in the solar wind.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2012

MAGNETIC RECONNECTION, HELICITY DYNAMICS, AND HYPER-DIFFUSION

We examine the influence of noise and Alfven wave turbulence on magnetic reconnection in a reduced magnetohydrodynamics model. We focus on the dynamics of magnetic helicity density. Helicity conservation is then used to calculate the global reconnection rate in terms of the helicity density flux. Two specific scenarios are explored-noisy reconnection and Alfven wave turbulent reconnection. For noisy reconnection, the current sheet is assumed to sit in a noisy state, marginal to plasmoid formation instability. The scaling of the reconnection rate in the presence of noise is proportional to (S {sup 2}{sub 0}/V{sub A}L {sup 2}){sup 1/11}, where S {sup 2}{sub 0}/V{sub A}L {sup 2} is the relative amplitude of the noise. We obtain this prediction using a symmetry analysis of the helicity density flux. For Alfven wave turbulent reconnection, a mean field closure scheme is applied. A reconnection rate proportional to (< B-tilde {sup 2}>/ {sup 2}){sup 1/8} is obtained, where < B-tilde {sup 2}>/ {sup 2} and (B) are the relative energy of Alfven wave turbulence and the reconnecting field. The constraint on reconnection rate enforced mean-square magnetic potential conservation is reexamined. A critical magnetic Reynolds number R{sub m,c} is identified. For R{sub m} >> R{sub m,c}, the reconnection rate becomes independent of Spitzer resistivity and thus can be higher than the Sweet-Parker model prediction. Both cases exhibit a weak dependence of the reconnection rate on the amplitude of the turbulence. Therefore, even noise or weak turbulence can trigger fast reconnection if the system is marginally stable. The important distinction between turbulent reconnection and turbulent dissipation of magnetic energy is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Reconnection-driven energy cascade in magnetohydrodynamic turbulence

Magnetohydrodynamic turbulence regulates the transfer of energy from large to small scales in many astrophysical systems, including the solar atmosphere. We perform three-dimensional magnetohydrodynamic simulations with unprecedentedly large magnetic Reynolds number to reveal how rapid reconnection of magnetic field lines changes the classical paradigm of the turbulent energy cascade. By breaking elongated current sheets into chains of small magnetic flux ropes (or plasmoids), magnetic reconnection leads to a previously undiscovered range of energy cascade, where the rate of energy transfer is controlled by the growth rate of the plasmoids. As a consequence, the turbulent energy spectra steepen and attain a spectral index of -2.2 that is accompanied by changes in the anisotropy of turbulence eddies. The omnipresence of plasmoids and their consequences on, for example, solar coronal heating, can be further explored with current and future spacecraft and telescopes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1993

Magnetic reconnection with large separatrix angles

The magnetic reconnection process is studied here using incompressible MHD simulations with different inflow boundary conditions and different magnetic Reynolds numbers R(m). The angle between the magnetic separatrices is in steady state reconnection depends mainly on the normal magnetic field on the inflow boundary. In steady state nonuniform reconnection with large separatrix angles, field-aligned plasma jets appear slightly downstream of the magnetic separatrices. The field-aligned plasma jet are stronger when R(m) is larger. Each field-aligned plasma jet consists of two parts: a slow shock and a fast-mode compressional wave. The slow shock converts the magnetic energy into plasma kinetic energy by acceleration and heating. The fast-mode compressional wave decelerates the plasma to a smaller outflow speed and heats it further. Nearly all the magnetic energy flowing into the diffusion region is converted into other forms. The length and width of the diffusion region depend on the values of the reconnection rate, R(m), and the normal magnetic field on the inflow boundary.

Yan, M.↗

DOE OSTI2022

High repetition rate exploration of the Biermann battery effect in laser produced plasmas over large spatial regions

Abstract In this paper we present a high repetition rate experimental platform for examining the spatial structure and evolution of Biermann-generated magnetic fields in laser-produced plasmas. We have extended the work of prior experiments, which spanned over millimeter scales, by spatially measuring magnetic fields in multiple planes on centimeter scales over thousands of laser shots. Measurements with magnetic flux probes show azimuthally symmetric magnetic fields that range from 60 G at 0.7 cm from the target to 7 G at 4.2 cm from the target. The expansion rate of the magnetic fields and evolution of current density structures are also mapped and examined. Electron temperature and density of the laser-produced plasma are measured with optical Thomson scattering and used to directly calculate a magnetic Reynolds number of $1.4\times {10}^4$ , confirming that magnetic advection is dominant at $\ge 1.5$ cm from the target surface. The results are compared to FLASH simulations, which show qualitative agreement with the data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2013

MAGNETIC WREATHS AND CYCLES IN CONVECTIVE DYNAMOS

Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global three-dimensional magnetohydrodynamic simulations with the anelastic spherical harmonic code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3 {Omega}{sub Sun }), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1982

Anisotropy in MHD turbulence due to a mean magnetic field

The development of anisotropy in an initially isotropic spectrum is studied numerically for two-dimensional magnetohydrodynamic turbulence. The anisotropy develops due to the combined effects of an externally imposed dc magnetic field and viscous and resistive dissipation at high wave numbers. The effect is most pronounced at high mechanical and magnetic Reynolds numbers. The anisotropy is greater at the higher wave numbers.

Shebalin, J. V.↗

NASA NTRS1983

Anisotropy in MHD turbulence due to a mean magnetic field

Shebalin, J. V.↗