Disk Dynamo Research Articles

On the role of numerical diffusivity in MHD simulations of global accretion disc dynamos

Observations, mainly of outbursts in dwarf novae, imply that the anomalous viscosity in highly ionized accretion discs is magnetic in origin and requires that the plasma ${\beta \sim 1}$ . Until now, most simulations of the magnetic dynamo in accretion discs have used a local approximation (known as the shearing box). While these simulations demonstrate the possibility of a self-sustaining dynamo, the magnetic activity generated in these models saturates at $\beta \gg 1$ . This long-standing discrepancy has previously been attributed to the local approximation itself. There have been recent attempts at simulating magnetic activity in global accretion discs with parameters relevant to the dwarf novae. These too find values of $\beta \gg 1$ . We speculate that the tension between these models and the observations may be caused by numerical magnetic diffusivity. As a pedagogical example, we present exact time-dependent solutions for the evolution of weak magnetic fields in an incompressible fluid subject to linear shear and magnetic diffusivity. We find that the maximum factor by which the initial magnetic energy can be increased depends on the magnetic Reynolds number as ${\mathcal {R}}_{m}^{2/3}$ . We estimate that current global numerical simulations of dwarf nova discs have numerical magnetic Reynolds numbers around six orders of magnitude less than the physical value found in dwarf nova discs of ${\mathcal {R}}_{m} \sim 10^{10}$ . We suggest that, given the current limitations on computing power, expecting to be able to compute realistic dynamo action in observable accretion discs using numerical MHD is, for the time being, a step too far.

Adaptive integral alternating minimization method for robust learning of nonlinear dynamical systems from highly corrupted data

This paper proposes an adaptive integral alternating minimization method (AIAMM) for learning nonlinear dynamical systems using highly corrupted measured data. This approach selects and identifies the system directly from noisy data using the integral model, encompassing unknown sparse coefficients, initial values, and outlier noisy data within the learning problem. It is defined as a sparse robust linear regression problem. An adaptive threshold parameter selection method is proposed to constrain model fitting errors and select appropriate threshold parameters for sparsity. The robustness and accuracy of the proposed AIAMM are demonstrated through several numerical experiments on typical nonlinear dynamical systems, including the van der Pol oscillator, Mathieu oscillator, Lorenz system, and 5D self-exciting homopolar disc dynamo. The proposed method is also compared to several advanced methods for sparse recovery, with the results indicating that the AIAMM demonstrates superior performance in processing highly corrupted data.

Helical and non-helical large-scale dynamos in thin accretion discs

ABSTRACT The dynamics of accreting and outgoing flows around compact objects depends crucially on the strengths and configurations of the magnetic fields therein, especially of the large-scale fields that remain coherent beyond turbulence scales. Possible origins of these large-scale magnetic fields include flux advection and disc dynamo actions. However, most numerical simulations have to adopt an initially strong large-scale field rather than allow them to be self-consistently advected or amplified, due to limited computational resources. The situation can be partially cured by using sub-grid models where dynamo actions only reachable at high resolutions are mimicked by artificial terms in low-resolution simulations. In this work, I couple thin-disc models with local shearing-box simulation results to facilitate more realistic sub-grid dynamo implementations. For helical dynamos, detailed spatial profiles of dynamo drivers inferred from local simulations are used, and the non-linear quenching and saturation is constrained by magnetic helicity evolution. In the inner disc region, saturated fields have dipole configurations and the plasma β reaches ≃0.1 to 100, with correlation lengths ≃h in the vertical direction and ≃10 h in the radial direction, where h is the disc scale height. The dynamo cycle period is ≃40 orbital time scale, compatible with previous global simulations. Additionally, I explore two dynamo mechanisms which do not require a net kinetic helicity and have only been studied in shearing-box set-ups. I show that such dynamos are possible in thin accretion discs, but produce field configurations that are incompatible with previous results. I discuss implications for future general-relativistic magnetohydrodynamics simulations.

Realization of Bullard’s disc dynamo

We report experimental results from three successful runs of a Bullard-type homopolar disc dynamo. The set-up consisted of a copper disc with a radius of 30 cm and thickness of 3 cm which was placed co-axially beneath a flat, multi-arm spiral coil of the same size and connected to it electrically at the centre and along the circumference by sliding liquid-metal contacts. The magnetic field was measured using Hall probes which were fixed on the top face of the coil. We measured also the radial voltage drop across the coil. When the disc rotation rate reached Ω ≈ 7 Hz , the magnetic field increased steeply approaching B 0 ≈ 40 mT in the central part of the coil. This field was more than two orders of magnitude stronger than the background magnetic field. In the first two runs, the electromagnetic torque braking the disc in the dynamo regime exceeded the breakdown torque of the electric motor driving the disc. As a result, the motor stalled and the dynamo was interrupted. Stalling did not occur in the third run when the driving frequency was set higher and increased faster. We also propose an extended disc dynamo model which qualitatively reproduces the experimental results.

Optimizing disc dynamo

We present an optimized design of our recently realized disc dynamo. Like the original set-up, the optimized dynamo consists of a flatmulti-arm spiral coil and a co-axially placed disc which is connected to the former by sliding liquid metal contacts. In contrast to the original set-up, the disc and the coil in the optimized design have different sizes. This allows the disc to capture more of the high-density magnetic flux generated in the inner part of the coil and to avoid the reverse flux in the outer part of the coil. By optimizing the coil and dics radii, the critical magnetic Reynolds number can be reduced from ≈ 34.6 when the disc and the coil have equal inner and outer radii with the ratio ri/ro ≈ 0.36 to Rm ≈ 11.6. This lowest possible disc dynamo threshold is attained when the disc and the coil have relatively narrow widths. Using a slightly suboptimal but more practical set-up with the inner and outer radii of the disc and coil equal to to (0.3,0.9) and (0.74,1), respectively, self-excitationis expected at Rm ≈ 14.6. Figs 7, Refs 10.

Jets from Accretion Disk Dynamos: Consistent Quenching Modes for Dynamo and Resistivity

Astrophysical jets are launched from strongly magnetized systems that host an accretion disk surrounding a central object. The origin of the magnetic field, which is a key component of the launching process, is still an open question. Here we address the question of how the magnetic field required for jet launching is generated and maintained by a dynamo process. By carrying out nonideal MHD simulations (PLUTO code), we investigate how the feedback of the generated magnetic field on the mean-field dynamo affects the disk and jet properties. We find that a stronger quenching of the dynamo leads to a saturation of the magnetic field at a lower disk magnetization. Nevertheless, we find that, while applying different dynamo feedback models, the overall jet properties remain unaffected. We then investigate a feedback model that encompasses a quenching of the magnetic diffusivity. Our modeling considers a more consistent approach for mean-field dynamo modeling simulations, as the magnetic quenching of turbulence should be considered for both a turbulent dynamo and turbulent magnetic diffusivity. We find that, after the magnetic field is saturated, the Blandford–Payne mechanism can work efficiently, leading to more collimated jets, which move, however, with slower speed. We find strong intermittent periods of flaring and knot ejection for low Coriolis numbers. In particular, flux ropes are built up and advected toward the inner disk thereby cutting off the inner disk wind, leading to magnetic field reversals, reconnection and, the emergence of intermittent flares.

On integrability of the segmented disc dynamo: the effect of mechanical friction

On integrability of the segmented disc dynamo: the effect of mechanical friction

Segmented disc dynamo with symmetric multidirectional patterns of multiscroll chaotic attractors

Rather than adopting the common approach that the multiscroll attractors are obtained through reconstruction of nonlinear functions, this work presents a systematic mechanism for designing multidirectional symmetric multiscroll patterns of chaotic attractors. The present scheme is based on the multilevel signal that work with the nonlinearities and state variables of chaotic system to generate symmetric multidirectional patterns of multiscroll chaotic attractors (MPMCA). To illustrate the mechanism of this systematic approach, the coefficients of quadratic terms of segmented disc dynamo are modified and designed a chaotic system that generates a chaotic attractor consisting of two pairs of symmetrical attractors. The state variables under the multilevel signal are transformed and then combined the symmetric attractors to generate a complete family of symmetric MPMCA in multi directions (including one directional (1D), two directional (2D) and three directional (3D) symmetric patterns of multiscroll chaotic attractors). Chaotic dynamical characteristics of symmetric MPMCA are analysed​ by means of equilibrium points distribution and phase portraits. Matlab simulations results obtained in this work are consistent well with our theoretical analysis verifying the effectiveness of the presented scheme.

Jacobi stability analysis and impulsive control of a 5D self-exciting homopolar disc dynamo

<p style='text-indent:20px;'>In this paper, we make a thorough inquiry about the Jacobi stability of 5D self-exciting homopolar disc dynamo system on the basis of differential geometric methods namely Kosambi-Cartan-Chern theory. The Jacobi stability of the equilibria under specific parameter values are discussed through the characteristic value of the matrix of second KCC invariants. Periodic orbit is proved to be Jacobi unstable. Then we make use of the deviation vector to analyze the trajectories behaviors in the neighborhood of the equilibria. Instability exponent is applicable for predicting the onset of chaos quantitatively. In addition, we also consider impulsive control problem and suppress hidden attractor effectively in the 5D self-exciting homopolar disc dynamo.</p>

Synchronization and Chaos Control Using a Single Controller of Five Dimensional Autonomous Homopolar Disc Dynamo

The electronic implementation, synchronization, and control of hyperchaos in a five-dimensional (5D) autonomous homopolar disc dynamo are investigated in this paper. The hyperchaotic behavior is found numerically using phase portraits and time series in 5D autonomous homopolar disc dynamo is ascertained on Orcad-PSpice software. The synchronization of the unidirectional coupled 5D hyperchaotic system is also studied by using the feedback control method. Finally, hyperchaos found in 5D autonomous homopolar disc dynamo is suppressed thanks to the designed single feedback. Numerical simulations and electronic implementation reveal the effectiveness of the single proposed control.

Relativistic Outflows from a GRMHD Mean-field Disk Dynamo

Abstract In this work, we present simulations of thin accretion disks around black holes, in order to investigate a mean-field disk dynamo, using our resistive GRMHD code, which is able to produce a large-scale magnetic flux. We consider a weak seed field in an initially thin disk, a background (turbulent) magnetic diffusivity, and the dynamo action itself. A standard quenching mechanism is applied to mitigate an otherwise exponential increase in the magnetic field. Comparison simulations of an initial Fishbone–Moncrief torus suggest that reconnection may provide another quenching mechanism. The dynamo-generated magnetic flux expands from the disk interior into the disk corona, becomes advected by disk accretion, and fills the axial region of the domain. The dynamo leads to an initially rapid increase in magnetic energy and flux, while for later evolutionary stages the growth stabilizes. Accretion toward the black hole depends strongly on the type of magnetic-field structure that develops. The radial field component supports extraction of angular momentum, and thus accretion. It also sets the conditions for launching a disk wind, initially from the inner disk area. When a strong field engulfs the disk, strong winds are launched, predominantly driven by the pressure gradient of the toroidal field. For rotating black holes, we identify a Poynting flux-dominated jet, driven by the Blandford–Znajek mechanism. This axial Poynting flux is advected from the disk, and therefore accumulates at the expense of the flux carried by the disk wind, which is itself regenerated by the disk dynamo.

A comparative study of the dynamics of a three-disk dynamo system with and without time delay

The disk dynamo plays an important role in studying the geodynamo and much research works have been devoted to the understanding of dynamo dynamics. This paper further investigates an extended disk dynamo system having three coupled conducting disks and incorporates the interaction-induced time delay in the dynamic governing equations. By carrying out a comparative analysis, the dynamic behaviors of the coupled three-disk dynamo system with and without time delay are studied to explore novel and complex nonlinear dynamic phenomena in the coupled delayed dynamo system. It is found that the double Hopf bifurcations can be induced in the time-delayed dynamo system. Three different topological structures of the unfolding are obtained under different time delays. Accordingly, it is shown that the novel dynamic behaviors, including quasi-periodic torus, three-dimensional torus and the coexistence of multiple attractors, can appear in the time-delayed dynamo system. Furthermore, by performing the continuation analysis on the periodic orbit generated from the Hopf bifurcation of equilibrium, some new coexistence patterns, e.g., the coexistence of periodic orbits and chaos, the coexistence of quasi-periodic orbits and chaos, are observed in the dynamo system with time delay. Based on the obtained results, it is believed that the inclusion of time delay in the modelling of the three-disk dynamo system is necessary and meaningful for developing an in-depth understanding of dynamo dynamics. Finally, the results of theoretical analyses are verified by the numerical simulations.

Hopf bifurcation and synchronization of a five-dimensional self-exciting homopolar disc dynamo using a new fuzzy disturbance-observer-based terminal sliding mode control

Having found hidden hyperchaos in a 5D self-exciting homopolar disc dynamo, we study the existence of a Hopf bifurcation, which leads to unstable limit cycles bifurcating from a stable equilibrium. Hidden chaos with only stable equilibria can be observed from the Hopf bifurcation: a typical way to enable hidden attractors to be located. We then provide a new fuzzy controller, and a fast fuzzy disturbance observer, based on terminal sliding mode control for synchronization of the hyperchaotic system. Fuzzy inference is considered to weaken the chattering phenomena. Using Lyapunov stability theory, the stability of the closed-loop system is proved. Finally, simulations of synchronization are illustrated to show the efficient performance of the designed control method via external disturbances and dynamic uncertainties.

Jacobi analysis of a segmented disc dynamo system

In this paper, Jacobi stability of a segmented disc dynamo system is geometrically investigated from viewpoint of Kosambi–Cartan–Chern (KCC) theory in Finsler geometry. First, the geometric objects associated to the reformulated system are explicitly obtained. Second, the Jacobi stability of equilibria and a periodic orbit are discussed in the light of deviation curvature tensor. It is shown that all the equilibria are always Jacobi unstable for any parameters, a Lyapunov stable periodic orbit falls into both Jacobi stable regions and Jacobi unstable regions. The considered system is not robust to small perturbations of the equilibria, and some fragments of the periodic orbit are included in fragile region, indicating that the system is extremely sensitive to internal parameters and environment. Finally, the dynamics of the deviation vector and its curvature near all the equilibria are presented to interpret the onset of chaos in the dynamo system. In a physical sense, magnetic fluxes and angular velocity can show irregular oscillations under some certain cases, these oscillations may reveal the irregularity of magnetic field’s evolution and reversals.

Control and synchronization of the hyperchaotic attractor for a 5-D self-exciting homopolar disc dynamo

The control of the novel five-dimensional hidden attractors hyperchaotic system is investigated. We suggest an approach to change the model of its hyperchaotic behavior to an unpredictable trivial fixed point employing the stability principle. We are also researching the synchronization of the same system, focusing on the stability theory. Numerical simulations show that effective control and synchronization results are obtained with the control method.

Magnetohydrodynamic Accretion–Ejection: Jets Launched by a Nonisotropic Accretion-disk Dynamo. II. A Dynamo Tensor Defined by the Disk Coriolis Number

Abstract Astrophysical jets are launched from strongly magnetized systems that host an accretion disk surrounding a central object. Here we address the question of how accretion-disk magnetization and the field structure required for jet launching are generated. We continue our work from Mattia & Fendt (Paper I) by considering a nonscalar accretion-disk mean-field α 2Ω dynamo in the context of large-scale disk-jet simulations. We now investigate a disk dynamo that follows analytical solutions of the mean-field dynamo theory, essentially based only on a single parameter, the Coriolis number. We thereby confirm the anisotropy of the dynamo tensor acting in accretion disks, allowing both the resistivity and mean-field dynamo to be related to the disk turbulence. Our new model recovers previous simulations by applying a purely radial initial field while allowing for a more stable evolution for seed fields with a vertical component. We also present correlations between the strength of the disk dynamo coefficients and the dynamical parameters of the jet that is launched, and discuss their implications for observed jet quantities.

Global Dynamics of the Chaotic Disk Dynamo System Driven by Noise

The disk dynamo system, which is capable of chaotic behaviours, is obtained experimentally from two disk dynamos connected together. It models the geomagnetic field and is used to explain the reversals in its polarity. Actually, the parameters of the chaotic systems exhibit random fluctuation to a greater or lesser extent, which can carefully describe the disturbance made by environmental noise. The global dynamics of the chaotic disk dynamo system with random fluctuating parameters are concerned, and some new results are presented. Based on the generalized Lyapunov function, the globally attractive and positive invariant set is given, including a two-dimensional parabolic ultimate boundary and a four-dimensional ellipsoidal ultimate boundary. Furthermore, a set of sufficient conditions is derived for all solutions of the stochastic disk dynamo system being global convergent to the equilibrium point. Finally, numerical simulations are presented for verification.

Absolute control of chaotic responses in Robbins disc dynamo

Chaotic responses of Robbins disc dynamo are considered through boundedness and Lyapunov exponents to specify the place where the controller needed to be applied. In order to get the beneficial aspects in engineering of the Robbins disc dynamo, controller is calculated by using the concept of Lie derivative which is the most significant facet of control analytical technique. The necessary and sufficient conditions are confirmed, and a single input function controller u is constructed for linear and nonlinear output function. Robbins disc dynamo system is totally controlled for the required goals in both cases. To show the effectiveness of proposed control technique, a comparison with other techniques is presented in this article. Numerical simulation results confirm our analytical results.

一个四维混沌的广义发电机系统的动力学分析

一个四维混沌的广义发电机系统的动力学分析

Multistability and bifurcations in a 5D segmented disc dynamo with a curve of equilibria

Multistability, i.e., coexisting attractors, is one of the most exciting phenomena in dynamical systems. This paper presents a new category of coexisting hidden attractor: five-dimensional (5D) systems with a curve of equilibria. Based on the segmented disc dynamo, a new 5D hyperchaotic system is proposed. The paper studies not only coexisting self-excited attractors but also coexisting hidden attractors in the new system with four types of equilibria: a curve of equilibria, a line equilibrium, a stable equilibrium, and no equilibria. Furthermore, the paper proves that the degenerate Hopf and pitchfork bifurcations occur in the system. Numerical simulations demonstrate the emergence of the two bifurcations.