3D relaxation MHD modeling with FOI-PERFECT code for electromagnetically driven HED systems

<p>Near-Earth solar wind conditions, including disturbances generated by coronal mass ejections (CMEs), are routinely forecast using 3-dimensional, numerical magnetohydrodynamic (MHD) models of the heliosphere. The resulting forecast errors are largely the result of uncertainty in the near-Sun boundary conditions, rather than heliospheric model physics or numerics. Thus ensembles of heliospheric model runs with perturbed initial conditions are used to estimate forecast uncertainty. MHD heliospheric models are relatively cheap in computational terms, requiring tens of minutes to an hour to simulate CME propagation from the Sun to Earth. Thus such ensembles can be run operationally. However, ensemble size is typically limited to ~10<sup>1</sup>-10<sup>2</sup>, which may be inadequate to sample the relevant high-dimensional parameter space. Here, we describe a simplified solar wind model that can estimate CME arrival time in approximately 0.01 seconds on a modest desktop computer and thus enables significantly larger ensembles. It is a 1-dimensional, incompressible, hydrodynamic model, which has previously been used for the steady-state solar wind, but is here used in time-dependent form. This approach is shown to adequately emulate the MHD solutions to the same boundary conditions for both steady-state solar wind and CME-like disturbances. We suggest it could serve as a “surrogate” model for the full 3-dimensional MHD models. For example, ensembles of ~10<sup>5</sup>-10<sup>6</sup> members can be used to identify regions of parameter space for more detailed investigation by the MHD models. Similarly, the simplicity of the model means it can be rewritten as an adjoint model, enabling variational data assimilation with MHD models without the need to alter their code. Model code is available as an Open Source download in the Python language.</p>

Observations of interplanetary scintillation (IPS) provide a set of data that is used in estimating the solar wind parameters with reasonably good accuracy. Various tomography techniques have been developed to deconvolve the line‐of‐sight integration effects ingrained in observations of IPS to improve the accuracy of solar wind reconstructions. Among those, the time‐dependent tomography developed at the University of California, San Diego (UCSD) is well known for its remarkable accuracy in reproducing the solar wind speed and density at Earth by iteratively fitting a kinematic solar wind model to observations of IPS and near‐Earth spacecraft measurements. However, the kinematic model gradually breaks down as the distance from the Sun increases beyond the orbit of Earth. Therefore, it would be appropriate to use a more sophisticated model, such as a magnetohydrodynamics (MHD) model, to extend the kinematic solar wind reconstruction beyond the Earth's orbit and to the outer heliosphere. To test the suitability of this approach, we use boundary conditions provided by the UCSD time‐dependent tomography to propagate the solar wind outward in a MHD model and compare the simulation results with in situ measurements and also with the corresponding kinematic solution. Interestingly, we find notable differences in proton radial velocity and number density at Earth and various locations in the inner heliosphere between the MHD results and both the in situ data and the kinematic solution. For example, at 1 AU, the MHD velocities are generally larger than the spacecraft data by up to 150 km s−1, and the amplitude of density fluctuations is also markedly larger in the MHD solution. We show that the MHD model can deliver more reasonable results at Earth with an ad hoc adjustment of the inner boundary values. However, we conclude that the MHD model using the inner boundary conditions derived from kinematic simulations has little chance to match IPS and in situ data as well as the kinematic model does unless it too is iteratively fit to the observational data and measurements.

In recent years, considerable research has been carried out relative to the electromagnetic (EM) propagation and refraction characteristics in metamaterials with emphasis on the origins of negative refractive index. Negative refractive index may be introduced in metamaterials via different methods; one such is the con- dition whereby the Poynting vector of the EM wave is in opposition to the group velocity in the material. Alternatively, negative refractive index also occurs when the group and phase velocities in the medium are in opposition. The latter phenomenon has been extensively investigated in the literature, including recent work involving chiral metamaterials with material dispersion up to the first order. This paper examines the pos- sible emergence of negative refractive index in dispersive chiral metamaterials with material dispersion up to the second order. The motivation is to determine if using second- as opposed to first-order dispersion may lead to more practical negative index behavior. A spectral approach combined with a slowly time-varying phasor analy- sis is applied, leading to the analytic derivation of EM phase and group velocities, and the resulting phase and group velocities and the corresponding phase and group indices are evaluated by selecting somewhat arbitrary dispersive parameters. The results indicate the emergence of negative index (via negative phase indices along with positive group indices, as reported in the literature) or negative index material (NIM) behavior over infor- mation bandwidths in the low RF range. The second-order results are not significantly better than those for first-order results based on the theoretical analysis; however, greater parametric flexibility exists for the second-order system leading to the higher likelihood of achieving NIM over practical frequency bands. The velocities and indices computed using the Lorentzian and Condon models yield an NIM bandwidth around 200 − 400 Mrad∕sec, about 2 orders of magnitude higher than that for the parametric approach; more impor- tantly, NIM is found not to occur in the first order when using practical models. © 2015 Society of Photo-Optical

Three major cusp models are systematically compared with low-resolution (large-scale) and high-resolution (fine-scale) low-altitude observations. Those models are (a) global magnetohydrodynamics (MHD) models (including MHD+drift models), (b) turbulent/diffusive entry models, and (c) direct flowing entry models. Although low-resolution data are mostly consistent with MHD models, high-resolution data mostly contradicts them. The data instead supports the other models in which the cusp is considered as a local `extra' open region. This is a good lesson to us: past supportive `tests' of MHD cusp models might have essential flaws in the methodology, and high-resolution data is necessary even for large-scale modelings.

In this study, we simulate the Solar Wind Charge Exchange (SWCX) soft X‐ray emissions at dayside magnetosheath and cusps by using magnetohydrodynamic (MHD) and LAtmos TEst Particle (LaTeP) models. MHD models are unable to resolve the particle kinetic effects, such as the different behaviors of ions with different q/m, or distinguish the magnetospheric plasma from the solar wind plasma. We investigate these effects with the LaTeP model. As the LaTeP model does not self‐compute magnetic and electric field, the magnetic and electric field data obtained from Open Geospace General Circulation Model (OpenGGCM) and Lagrangian version of the piecewise parabolic method (PPMLR) MHD model are used as the input to LaTeP model. The soft X‐ray emissivity maps simulated from pure OpenGGCM and PPMLR MHD approaches and from LaTeP‐OpenGGCM and LaTeP‐PPMLR approaches are presented and compared. The results indicate that the LaTeP model can well resolve the kinetic effects and can be used to investigate the individual spectral characteristics. Therefore, the LaTeP model is a complementary approach for simulating the X‐ray emissions near the dayside magnetopause. We also calculate the ratio of integrated OVII/OVIII line intensities, produced by charge exchange of O7+ ions and O8+ ions, respectively. We find a relatively higher ratio at the bow shock compared to the surrounding areas, suggesting that this ratio can be an effective parameter to identify the bow shock location.

A numerical investigation is carried out to analyze forced convection heat transfer in magnetohydrodynamic (MHD) flow past a circular cylinder by considering the penetration of magnetic field inside it. The coupled Navier–Stokes and Maxwell equations are solved along with the energy equation using fourth-order compact finite difference scheme. We have found that the actual decrease in the rate of heat transfer upon the increase in magnetic field is almost double than what is presented in earlier studies where magnetic field is not considered to penetrate inside the cylinder. A non-monotonic behavior of local Nusselt number and mean Nusselt number with interaction parameter is observed which is in good agreement with experimental findings. Validity of heat transfer with quasi static MHD (QSMHD) flow suggests that the heat transfer results of QSMHD flow can be reproduced from our full MHD model in the limit of vanishing magnetic Reynolds number.

Advanced numerical methods based on exponential propagation have been applied to magnetohydrodynamic (MHD) simulations. This recently developed numerical technique evolves the system of nonlinear equations using exponential propagation of the Jacobian matrix. The exponential of the matrix is approximated by projecting it onto the Krylov subspace using the Arnoldi algorithm. The primary advantage of the exponential propagation method is that it allows time steps exceeding the Courant-Friedrichs-Lewy (CFL) limit. Another important aspect is faster convergence of the iteration computing the Krylov subspace projection compared to solving an implicit formulation of the system with similar iterative methods. Since the time scales in the resistive MHD equations are widely separated, the exponential propagation methods are especially advantageous for computing the long term evolution of a low-beta plasma. We analyze several types of exponential propagation methods and highlight important issues in the development of such techniques. Our analysis also suggests new ways to construct schemes of this type. Implementation issues, including scalability properties of exponential propagation methods, and performance are also discussed. In the second part of this work we present numerical MHD models which are constructed using exponential propagation methods and which describe the evolution of the magnetic arcades in the solar corona. Since these numerical methods have not been used before for large evolutionary systems like resistive MHD, we first validate our approach by demonstrating application of the exponential schemes to two existing magnetohydrodynamic models. We simulate the reconnection process resulting from shearing the footpoints of two-dimensional magnetic arcades and compute the three-dimensional linear force-free states of plasma configurations. Analysis of these calculations leads us to new insights about the topology of the solutions. The final chapter of this work is dedicated to a new three-dimensional numerical model of the dynamics of coronal plasma configurations. The model is motivated by observations and laboratory experiments simulating the evolution of solar arcades. We analyze the results of numerical simulations and demonstrate that our numerical approach provides an accurate and stable way to compute the solution to the zero-resistive MHD system. Based on comparisons of the simulation results and the observational data, we offer an explanation for the observed structure of eruptive events in the corona called coronal mass ejections (CME). We argue that the diversity of the images of CMEs obtained by the observational instruments can be explained as two-dimensional projections of a unique three-dimensional plasma configuration and suggest an eruption mechanism.

This thesis primarily focuses on understanding the plasma behavior during the helicity injection stage of a pulsed spheromak experiment. Spheromak formation consists of a series of dynamic steps whereby highly localized plasma near the electrodes evolves toward a Taylor state equilibrium. The dynamical evolution stage has been modeled as a series of equilibrium states in the past. However, the experiments at the Caltech spheromak facility have revealed that unbalanced J x B forces drive non equilibrium Alfvenic flows during these preliminary stages. The Caltech spheromak experiment uses coplanar electrodes to produce a collimated plasma jet flowing away from the electrodes. The jet formation stage precedes the spheromak formation and serves as a mechanism for feeding particles, magnetic helicity, energy, and toroidal flux into the system. Detailed density and flow velocity measurements of hydrogen and deuterium plasma jets have revealed that the jets are extremely dense with β [subscript thermal] ~1. Furthermore, the flow velocity was found to be Alfvenic with respect to the the toroidal magnetic field produced by the axial current within the plasma. An existing magnetohydrodynamics (MHD) model has been generalized to successfully predict the effect of plasma current on the jet's density and flow velocity. The behavior of these laboratory jets is in stark contrast to the often considered model for astrophysical jets describing them as equilibrium configurations with hollow density profiles. Other contributions of this thesis include the following. 1. The thesis presents an analytical proof that resistive MHD equilibrium with closed flux tubes is not feasible. This implies that sustained spheromak experiments cannot maintain helicity while being in a strict equilibrium. 2. The thesis describes measurements to characterize the circuit parameters of the high voltage discharge circuit used in the Caltech spheromak experiment. 3. The thesis also describes the setup of novel He-Ne laser interferometers used to measure the density of plasma jets. The ease of alignment of these interferometers was greatly enhanced by having unequal path lengths of the scene and reference beams. 4. Finally, the thesis details the setup for a soft X-ray (SXR)/Vacuum ultra violet (VUV) imaging system. Some preliminary images of reconnecting flux tubes captured by the imaging setup are also presented.

An adequate modelling of the electromagnetic interaction of the plasma with the surrounding conductors is paramount for the correct reproduction of 3D plasma dynamics. Simulations of the latter provide in turn useful predictions regarding the plasma evolution, the related MHD modes leading to disruptions and the electromagnetic forces acting on the vacuum vessel’s components when said disruptions occur. 
The latest modelling efforts with the 3D FEM non-linear JOREK code have been directed towards the eddy current coupling of a reduced magnetohydrodynamic (MHD) plasma model with thin and volumetric wall codes (STARWALL and CARIDDI). 
In this contribution, we present an eddy current coupling between the full MHD model of JOREK and the STARWALL code; this new coupling scheme describes the full three-dimensional interactions of the plasma with the vacuum region and external conductors, modeled by natural boundary conditions linking the magnetic vector potential A to the magnetic field B. The consistency of the new coupling scheme is validated via benchmarks for axisymmetric Vertical Displacement Events and multi-harmonics simulations of MHD modes.

This work investigates the interaction between high current vacuum arc (HCVA) and the macroparticle (MP) generated from the cathode spots (CS) in the small-size vacuum trigatron. Magnetohydrodynamic (MHD) model is used to describe the arc column. MPs are added into MHD model, which are described by discrete phase model (DPM). The control equations of MPs include charging equation, motion equation and heat transfer equation, in which the evaporation of MPs is also considered. Based on the above model, the effects of MP diameter and arc current on the characteristics of MPs are studied. Simulation results show that MPs leave the interelectrode gap with a deflection angle larger than the initial angle under the influence of plasma. The motion of MPs is similar to that of projectiles. MPs with smaller diameter are influenced by the arc plasma more significantly. MPs can act as a source of the plasma, but these influences are not obvious in HCVA. What may be more harmful to the trigatron is the charging process of MPs during post-arc process.

The dawn‐dusk asymmetry of the magnetopause radial distance under the Parker (and ortho‐Parker) configuration of the interplanetary magnetic field (IMF) is investigated. An extensive data set of about 50,000 magnetopause crossings identified in the data from the THEMIS A‐E, Magion 4, Geotail, and Interball‐1 satellites is used for this purpose. It is shown that the magnetopause radial distances are larger at the side where the IMF is quasi‐parallel to the bow shock normal than at the side where IMF is quasi‐perpendicular to the bow shock normal. The effect is more significant at the flanks than close to the subsolar point. This introduces a significant asymmetry of the magnetopause shape, with the difference in the magnetopause radial distances being as large as about one Earth radius beyond the terminator. The experimental results are confirmed by a global magnetohydrodynamic (MHD) model, demonstrating that the asymmetry can be explained by MHD effects, without considering foreshock transients. This MHD model is further used to investigate the evolution of individual pressure components across the magnetopause and contrast them in quasi‐parallel and quasi‐perpendicular cases.

Ion heating during a substorm on 15 February 2008, starting at 0348 UT, is studied with a new approach recently described in Ashour‐Abdalla et al. (2015). The general conditions of the magnetotail are obtained from a global magnetohydrodynamic (MHD) model and are used to drive a full kinetic particle‐in‐cell (PIC) simulation of a 3‐D region of the tail. Within the kinetic box, the ions, the electrons, and the fields evolve self‐consistently. The large scales are captured by the MHD model and the small scales by the PIC model based on the MHD state. This approach is used to study ion heating. Different heating mechanisms were analyzed by examining the velocity distributions at different locations. In the x direction heating occurs as the reconnection‐generated ion jet interacts with the environment in which it propagates. The heating is found mostly in the separatrices and increases downstream of the reconnection region. In the y direction the heating is less intense and is found near the dipolarization fronts. It occurs as ions become magnetized and gyrotropize the distribution function. In addition, ions can be heated in the y direction by the reconnection electric field near the reconnection site. In the z direction the ions are heated by the formation of beams moving along z between the separatrices.

Based on magnetohydrodynamic (MHD) model of vacuum arc, the computer simulation of vacuum arc was carried out in this paper. In the MHD model, mass conservation equation, momentum conservation equations, energy conservation equations, generalized ohm's law and Maxwell equation were considered. MHD equations were calculated by numerical method, and the distribution of vacuum arc plasma parameters and current density were obtained. Simulation results showed that the magnetic constriction effect of vacuum arc is primarily caused by the Hall effect. In addition, the inhibition of axial magnetic field (AMF) on constriction of vacuum arc was calculated and analyzed.

Fast magnetic reconnection plays a fundamental role in driving explosive\ndynamics and heating in the solar chromosphere. The reconnection time scale of\ntraditional models is shortened at the onset of the coalescence instability,\nwhich forms a turbulent reconnecting current sheet through plasmoid\ninteraction. In this work we aim to investigate the role of partial ionisation\non the development of fast reconnection through the study of the coalescence\ninstability of plasmoids. Unlike the processes occurring in fully ionised\ncoronal plasmas, relatively little is known about how fast reconnection\ndevelops in partially ionised plasmas of the chromosphere. We present 2.5D\nnumerical simulations of coalescing plasmoids in a single fluid\nmagnetohydrodynamic (MHD) model, and a two-fluid model of a partially ionised\nplasma (PIP). We find that in the PIP model, which has the same total density\nas the MHD model but an initial plasma density two orders of magnitude smaller,\nplasmoid coalescence is faster than the MHD case, following the faster thinning\nof the current sheet and secondary plasmoid dynamics. Secondary plasmoids form\nin the PIP model where the effective Lundquist number $S = 7.8 \\cdot 10^3$, but\nare absent from the MHD case where $S = 9.7 \\cdot 10^3$: these are responsible\nfor a more violent reconnection. Secondary plasmoids also form in linearly\nstable conditions as a consequence of the non-linear dynamics of the neutrals\nin the inflow. In the light of these results we can affirm that two-fluid\neffects play a major role on the processes occurring in the solar chromosphere.\n

We evaluate a number of simple, one-point phenomenological models for the decay of energy-containing eddies in magnetohydrodynamic (MHD) and hydrodynamic turbulence. The MHD models include effects of cross helicity and Alfvénic couplings associated with a constant mean magnetic field, based on physical effects well-described in the literature. The analytic structure of three separate MHD models is discussed. The single hydrodynamic model and several MHD models are compared against results from spectral-method simulations. The hydrodynamic model phenomenology has been previously verified against experiments in wind tunnels, and certain experimentally determined parameters in the model are satisfactorily reproduced by the present simulation. This agreement supports the suitability of our numerical calculations for examining MHD turbulence, where practical difficulties make it more difficult to study physical examples. When the triple-decorrelation time and effects of spectral anisotropy are properly taken into account, particular MHD models give decay rates that remain correct to within a factor of 2 for several energy-halving times. A simple model of this type is likely to be useful in a number of applications in space physics, astrophysics, and laboratory plasma physics where the approximate effects of turbulence need to be included.