Force-free Condition Research Articles

Three-Dimensional Metallic Surface Micropatterning through Tailored Photolithography-Transfer-Plating.

Precise micropatterning on three-dimensional (3D) surfaces is desired for a variety of applications, from microelectronics to metamaterials, which can be realized by transfer printing techniques. However, a nontrivial deficiency of this approach is that the transferred microstructures are adsorbed on the target surface with weak adhesion, limiting the applications to external force-free conditions. We propose a scalable "photolithography-transfer-plating" method to pattern stable and durable microstructures on 3D metallic surfaces with precise dimension and location control of the micropatterns. Surface patterning on metallic parts with different metals and isotropic and anisotropic curvatures is showcased. This method can also fabricate hierarchical structures with nanoscale vertical and microscale horizontal dimensions. The plated patterns are stable enough to mold soft materials, and the structure durability is validated by 24 h thermofluidic tests. We demonstrate micropatterned nickel electrodes for oxygen evolution reaction acceleration in hydrogen production, showing the potential of micropatterned 3D metallic surfaces for energy applications.

Jet formation model from accretion disks of electron-ion-photon gas

The problem of Astrophysical Jet formation from relativistic accretion disks through the establishment of relativistic disk-powerful jet equilibrium structure is studied applying the Beltrami-Bernoulli equilibrium approach of Shatashvili and Yoshida 2011; Arshilava et al. 2019. Accretion disk is weakly magnetized consisting of fully ionized relativistic electron-ion plasma and photon gas strongly coupled to electrons due to Thompson Scattering. Analysis is based on the generalized Shakura-Sunyaev α-turbulent dissipation model for local viscosity (being the main source of accretion), in which the contributions from both the photon and ion gases are taken into account. Ignoring the self-gravitation in the disk we constructed the analytical self-similar solutions for the equilibrium relativistic disk-jet structure characteristic parameters in the field of gravitating central compact object for the force-free condition. It is shown, that the magnetic field energy in the Jet is several orders greater compared to that of accretion disk, while jet-outflow is locally Super-Alfvénic with local Plasma-beta <1 near the jet-axis. The derived solutions can be used to analyze the astrophysical jets observed in binary systems during the star formation process linking the jet properties with the parameters of relativistic accretion disks of electron-ion-photon gas.

A kinetic study of black hole activation by local plasma injection into the inner magnetosphere

ABSTRACT An issue of considerable interest in the theory of jet formation by the Blandford–Znajek mechanism, is how plasma is being supplied to the magnetosphere to maintain force-free conditions. Injection of electron–positron pairs via annihilation of MeV photons, emitted from a hot accretion flow, has been shown to be a viable possibility, but requires high enough accretion rates. At low accretion rates, and in the absence of any other form of plasma supply, the magnetosphere becomes charge-starved, forming intermittent spark gaps that can induce intense pair-cascades via interactions with disc radiation, enabling outflow formation. It is often speculated that enough plasma can penetrate the inner magnetosphere from the accretion flow through some rearrangement of magnetic field lines preventing the formation of spark-gaps. To address this question, we conducted a suite of 2D axisymmetric general-relativistic particle-in-cell simulations, in which plasma is injected into specified regions at a predescribed rate. We find that when pair-production is switched off, nearly complete screening is achieved when plasma is injected at the entire region inside the outer light cylinder at a high enough rate. Injection outside this region results in either, the formation of large vacuum-gaps, or coherent, large-amplitude oscillations of the magnetosphere, depending on the injection rate. Within our allowed dynamical range, we see no evidence for the system to reach a steady-state at high injection rates. Switching on pair-production results in nearly complete screening of the entire magnetosphere in all cases, with a small fraction of the Blandford–Znajek power dissipated as TeV gamma-rays.

Equilibriums of extremely magnetized compact stars with force-free magnetotunnels

We present numerical solutions for stationary and axisymmetric equilibriums of compact stars associated with extremely strong magnetic fields. The interior of the compact stars is assumed to satisfy ideal magnetohydrodynamic (MHD) conditions, while in the region of negligible mass density the force-free conditions or electromagnetic vacuum are assumed. Solving all components of Einstein's equations, Maxwell's equations, ideal MHD equations, and force-free conditions, equilibriums of rotating compact stars associated with mixed poloidal and toroidal magnetic fields are obtained. It is found that in the extreme cases the strong mixed magnetic fields concentrating in a toroidal region near the equatorial surface expel the matter and form a force-free toroidal magnetotunnel. We also introduce a new differential rotation law for computing solutions associated with force-free magnetosphere, and present other extreme models without the magnetotunnel.

Mechanochemical subcellular-element model of crawling cells.

Constructing physical models of living cells and tissues is an extremely challenging task because of the high complexities of both intra- and intercellular processes. In addition, the force that a single cell generates vanishes in total due to the law of action and reaction. The typical mechanics of cell crawling involve periodic changes in the cell shape and in the adhesion characteristics of the cell to the substrate. However, the basic physical mechanisms by which a single cell coordinates these processes cooperatively to achieve autonomous migration are not yet well understood. To obtain a clearer grasp of how the intracellular force is converted to directional motion, we develop a basic mechanochemical model of a crawling cell based on subcellular elements with the focus on the dependence of the protrusion and contraction as well as the adhesion and de-adhesion processes on intracellular biochemical signals. By introducing reaction-diffusion equations that reproduce traveling waves of local chemical concentrations, we clarify that the chemical dependence of the cell-substrate adhesion dynamics determines the crawling direction and distance with one chemical wave. Finally, we also perform multipole analysis of the traction force to compare it with the experimental results. Our present work sheds light on how intracellular chemical reactions are converted to a directional cell migration under the force-free condition. Although the detailed mechanisms of actual cells are far more complicated than our simple model, we believe that this mechanochemical model is a good prototype for more realistic models.

Breakdown of force-free electrodynamics in electric zones

Abstract It is shown that force-free electrodynamics (FFE) breaks down in regions where B2 − E2 &amp;lt; 0 (electric zones) even if ${\boldsymbol E}\cdot {\boldsymbol B} =0$. Spontaneous creation of such regions will inevitably lead to plasma oscillations that will subsequently decay over a few periods via anomalous heating and, under certain conditions, emission of high-energy quanta, until the system relaxes to a state in which B2 − E2 ≲ 0. For M87, assuming pair plasma, the inverse Compton cooling time is estimated to be shorter than the dynamical time when E2/B2 − 1 &amp;gt; (104/σ)2 roughly, where σ is the magnetization. If the electric zone is weak, the global system will maintain a nearly force-free state, however, the force-free condition, FμνJν = 0, will be broken at the order of the excess electric field and cannot describe wave dynamics. Our analysis does not support recent claims, that creation of electric zones can trigger a transition to force-free turbulence which, when generated in the ergosphere of a Kerr black hole, can lead to extraction of the black hole rotational energy. Whether some secondary electromagnetic modes produced in the decaying electric zone can extract the BH energy is yet an open question.

Models for calculation of the sideways force due to the kink modes in tokamaks

The solution of the sideways force problem is finally needed for the ITER project. The task became urgent when the extreme danger of such a force was perceived. The predictions were based on the so-called Noll's formula derived under some simplifications. One of them was the prescription of the plasma motion without testing its compatibility with the force balance condition. Later, an alternative approach has been proposed [D. V. Mironov and V. D. Pustovitov, Phys. Plasmas 24, 092508 (2017)], where the key element was the absence of an integral electromagnetic force on the plasma. Another important improvement was a proper treatment of the vacuum vessel wall. Now the extensions of the previously developed models leading to or supporting Noll's formula are proposed with the resistive wall reaction similarly incorporated. The main attributes of those approaches, the plasma displacements, are kept the same as in the original versions. Precisely, these are the plasma tilt or the (1,1) kink mode. Two forces are calculated with such displacements: on the plasma and on the vacuum vessel wall. The former is shown to be far from zero in the analyzed cases, violating thereby the force-free condition. This does not happen when this constraint goes first. It becomes a selection rule for allowable perturbations. These roughly resemble the tilt and (1,1) mode but differ from them, which changes the result dramatically. The maximal force that can be produced by such kink-like modes compatible with the force balance cannot reach even one tenth of Noll's force. The quantitative comparisons of the competing models are provided.

General relativistic calculation of magnetic field and power loss for a misaligned pulsar

In this study, we model a pulsar as a general relativistic oblique rotator, where the oblique rotator is a rotationally deformed neutron star whose rotation and magnetic axis is inclined at an angle. The oblique rotator spins down, losing rotational energy through the magnetic poles. The magnetic field is assumed to be dipolar; however, the star has a non-zero azimuthal component due to the misalignment. The magnetic field induces an electric field for a force-free condition. The magnetic field decreases as the misalignment increases and is minimum along the equatorial plane of the star. In contrast, the electric field remains almost constant initially but decreases rapidly at a high misalignment angle. The charge separation at the star surface is qualitatively similar to that of Newtonian calculation. We find that the power loss for a general relativistic rotator is minimum for either an aligned or an orthogonal rotator, which is in contrasts with Newtonian approach of calculation where the power loss increases with an increase in the misalignment angle.

Diffusivity in force-free simulations of global magnetospheres

ABSTRACT Assuming that the numerical diffusivity triggered by violations of the force-free electrodynamics constraints is a proxy for the physical resistivity, we examine its impact on the overall dynamics of force-free aligned pulsar magnetospheres endowed with an equatorial current sheet (ECS). We assess the constraint violations as a diffusivity source. The effects of modifications on electric fields used to restore force-free conditions are not confined to the ECS, but modify the magnetospheric dynamics on time-scales shorter than the pulsar rotational period. These corrections propagate especially via a channel that was unexplored, namely, changes induced to the electric charge density, ρ. We quantify the global consequences of diffusivity by comparing different techniques to model ρ. By default, we combine a conservative ρ-evolution with hyperbolic/parabolic cleaning of inaccuracies in the Maxwell equations. As an alternative, we enforce a constrained evolution, where ρ is directly computed as the electric field divergence. The conservative approach reduces the Poynting flux dissipated in the ECS by an order of magnitude, along with an increase of the pulsar luminosity driven by a shift of the Y-point location. The luminosity changes according to LY ∝ α0.11, where α is the ratio of diffusion to advection time-scales, controlling the amount of (numerical) diffusivity. Our models suggest interpreting the luminosity dependence on the Y-point location as differences in resistivities encountered at the ECS. Alternatively, they could be interpreted in terms of the pair formation multiplicity, κ, smaller diffusion being consistent with κ ≫ 1.

Scanning ion-conductance microscopy with a double-barreled nanopipette for topographic imaging of charged chromosomes.

Scanning ion conductance microscopy (SICM) is useful for imaging soft and fragile biological samples in liquids because it probes the samples' surface topography by detecting ion currents under non-contact and force-free conditions. SICM acquires the surface topographical height by detecting the ion current reduction that occurs when an electrolyte-filled glass nanopipette approaches the sample surface. However, most biological materials have electrically charged surfaces in liquid environments, which sometimes affect the behavior of the ion currents detected by SICM and, especially, make topography measurements difficult. For measuring such charged samples, we propose a novel imaging method that uses a double-barrel nanopipette as an SICM probe. The ion current between the two apertures of the nanopipette desensitizes the surface charge effect on imaging. In this study, metaphase chromosomes of Indian muntjac were imaged by this technique because, owing to their strongly negatively charged surfaces in phosphate-buffered saline, it is difficult to obtain the topography of the chromosomes by the conventional SICM with a single-aperture nanopipette. Using the proposed method with a double-barrel nanopipette, the surfaces of the chromosomes were successfully measured, without any surface charge confounder. Since the detailed imaging of sample topography can be performed in physiological liquid conditions regardless of the sample charge, it is expected to be used for analyzing the high-order structure of chromosomes in relation to their dynamic changes in the cell division.

Torsional waves with force-free magnetic fields in solar plasma structures

ABSTRACT The aim here is to model torsional waves in homogeneous and expanding twisted flux tubes of solar coronal magnetic plasma structures. For the sake of simplicity, a force-free condition applicable to solar magnetic structures is presented to determine the existing three-dimensional equilibrium magnetic fields. The determined magnetic field is implemented to study the effects of the magnetic twist parameter on the eigenvalues and eigenfunctions of torsional waves. Solenoidal and force-free conditions are applied to find the three-dimensional components of the magnetic field with respect to the numerical flux function. The obtained differential equation is linear where the technique of the separation of variables is implemented in order to solve it. The equilibrium magnetic field components and appropriate vector potential are extracted. Using the provided components in the magnetohydrodynamic theory, a differential equation that governs the frequency dependence of the torsional wave is obtained, whereby the differential transform method is solved. Both eigenvalues and eigenfunctions of torsional waves are calculated numerically. The obtained values for the frequency of the fundamental mode and its first harmonic, together with appropriate functions, exhibit a fine consistency with observations, with regards to the ratio of ω2/ω1, which is estimated to be around 2. At a fixed distance from the tube axis, the ratio increases with the increase of the twist parameter. The higher the applied twist parameter, the more variations of the ω2/ω1 ratio are observed. We cannot find significant variations of the eigenfunctions of torsional waves due to the twist parameter. The consistency between analytical results and observations proves adequate for implementing a force-free equilibrium magnetic field subject to conditions in solar plasma structures regarding torsional wave propagation.

Mechanochemical generation of acid-degradable poly(enol ether)s.

In an effort to develop polymers that can undergo extensive backbone degradation in response to mechanical stress, we report a polymer system that is hydrolytically stable but unmasks easily hydrolysable enol ether backbone linkages when force is applied. These polymers were synthesized by ring-opening metathesis polymerization (ROMP) of a novel mechanophore monomer consisting of cyclic ether fused bicyclohexene. Hydrogenation of the resulting polymers led to significantly enhanced thermal stability (Td > 400 °C) and excellent resistance toward acidic or basic conditions. Solution ultrasonication of the polymers resulted in up to 65% activation of the mechanophore units and conversion to backbone enol ether linkages, which then allowed facile degradation of the polymers to generate small molecule or oligomeric species under mildly acidic conditions. We also achieved solid-state mechano-activation and polymer degradation via grinding the solid polymer. Force-induced hydrolytic polymer degradability can enable materials that are stable under force-free conditions but readily degrade under stress. Facile degradation of mechanically activated polymechanophores also facilitates the analysis of mechanochemical products.

Mean-Field Dynamo Model in Anisotropic Uniform Turbulent Flow with Short-Time Correlations

The mean-field model is one of the basic models of the dynamo theory, which describes the magnetic field generation in a turbulent astrophysical plasma. The first mean-field equations were obtained by Steenbeck, Krause and Rädler for two-scale turbulence under isotropy and uniformity assumptions. In this article we develop the path integral approach to obtain mean-field equations for a short-correlated random velocity field in anisotropic streams. By this model we analyse effects of anisotropy and show the relation between dynamo growth and anisotropic tensors of helicity/turbulent diffusivity. Considering particular examples and comparing results with isotropic cases we demonstrate several mean-field effects: super-exponential growth at initial times, complex dependence of harmonics growth on the helicity tensor structure, when generation is possible for near-zero component or near-zero helicity trace, increase of the averaged magnetic field inclined to the initial current density that leads to effective Lorentz back-reaction and violation of force-free conditions.

Mechanochemical coupling of formin-induced actin interaction at the level of single molecular complex.

Formins promote actin assembly and are involved in force-dependent cytoskeletal remodeling. However, how force alters the formin functions still needs to be investigated. Here, using atomic force microscopy and biomembrane force probe, we investigated how mechanical force affects formin-mediated actin interactions at the level of single molecular complexes. The biophysical parameters of G-actin/G-actin (GG) or G-actin/F-actin (GF) interactions were measured under force loading in the absence or presence of two C-terminal fragments of the mouse formin mDia1: mDia1Ct that contains formin homology 2 domain (FH2) and diaphanous autoregulatory domain (DAD) and mDia1Ct-ΔDAD that contains only FH2. Under force-free conditions, neither association nor dissociation kinetics of GG and GF interactions were significantly affected by mDia1Ct or mDia1Ct-ΔDAD. Under tensile forces (0-7pN), the average lifetimes of these bonds were prolonged and molecular complexes were stiffened in the presence of mDia1Ct, indicating mDia1Ct association kinetically stabilizes and mechanically strengthens bonds of the dimer and at the end of the F-actin under force. Interestingly, mDia1Ct-ΔDAD prolonged the lifetime of GF but not GG bond under force, suggesting the DAD domain is critical for mDia1Ct to strengthen GG interaction. These data unravel the mechanochemical coupling in formin-induced actin assembly and provide evidence to understand the initiation of formin-mediated actin elongation and nucleation.

Three-dimensional Dissipative Pulsar Magnetospheres with Aristotelian Electrodynamics

Abstract A good compromise between the resistive model and the particle-in-cell model is Aristotelian electrodynamics, which can include the back-reaction of the radiative photons onto particle motion and allow for a local dissipation where the force-free condition is violated. We study the dissipative pulsar magnetosphere with Aristotelian electrodynamics where particle acceleration is fully balanced by radiation. The expression for the current density is defined by introducing a pair multiplicity. The 3D structure of the pulsar magnetosphere is then presented by solving the time-dependent Maxwell equations using a pseudo-spectral algorithm. It is found that the dissipative magnetosphere approaches the force-free solution and the dissipative region is more restricted to the current sheet outside the light cylinder (LC) as the pair multiplicity increases. The spatial extension of the dissipative region is self-consistently controlled by the pair multiplicity. Our simulations show the high magnetospheric dissipation outside the LC for the low pair multiplicity.

Generalization of Bantilan-Ishi-Romatschke flow to magnetohydrodynamics

We present a generalization of the Bantilan-Ishi-Romatschke (BIR) solution of relativistic hydrodynamics to relativistic magnetohydrodynamics (RMHD). Using the symmetries of the boundary of the Kerr-AdS5 black hole, and certain simplifying assumptions we solve the equations of RMHD on this boundary for a highly conductive fluid. We then transform the resulting solution to the flat spacetime. Furthermore, we show that the force-free condition causes the magnetic field to become singular at particular points and propose a regularization process for removing the singularities. The regularization process reveals the importance of non-vanishing electrical current in RMHD.

Interplanetary flux ropes of any twist distribution

Context. Recent investigations indicate that the magnetic field configuration in interplanetary flux ropes is in contrast with the common magnetic field models that are used to fit them, namely constant-alpha force-free fields, whose twist increases without limits toward the flux-rope boundary. Therefore, magnetic field configurations with a constant twist are now being employed in fits. Aims. Real flux ropes have varying twist. Therefore, analytical magnetic field configurations with prescribed twist distributions are searched for in cylindrical geometry. Methods. Equations for the field solenoidality and for the force-free condition are solved for case when a twist profile is prescribed. Results. A model of a force-free magnetic field configuration with an arbitrarily given twist distribution in a cylinder and its relative helicity per unit length are presented. It is applied to a core-envelope model recently suggested in studies of twist in magnetic clouds.

1D Magnetodynamic Simulations of Force-free Fields around a Rapidly Rotating Black Hole via Nonradial Magnetic Surfaces along the Equatorial Plane

Abstract Numerical simulations of 1D force-free magnetodynamics (FFMD) by Koide and Imamura showed details of the energy extraction mechanism around a rapidly spinning black hole under the force-free condition in the case of a radial magnetic surface along the equatorial plane. The energy is transported like a tsunami from the ergosphere and spreads to the outside. In this paper, we perform 1D FFMD simulations with nonradial magnetic surfaces along the equatorial plane, which are more general magnetic surface configurations. Using the results of simulations and analytic solutions of the steady-state force-free magnetic field, we find that, except in the case of a radial magnetic surface at infinity, the tsunami induced at the neighborhood of the horizon damps gradually and energy flux along the equatorial plane vanishes after a long period of time or at infinity. This suggests the energy extracted from the spinning black hole through the nonradial magnetic field is transported toward the high latitude around the axis of the black hole and is converted to the kinetic energy of the jet or outflow.

Solar and Galactic Magnetic Halo Structure: Force-Free Dynamos?

Magnetic fields may relax dissipatively to the minimum energy force-free condition whenever they are not constantly created or distorted. We review the axially symmetric solutions for force-free magnetic fields, especially for the non-linear field. A new formulation for the scale invariant state is given. Illustrative examples are shown. Applications to both stellar coronas and galactic halos are possible. Subsequently we study whether such force-free fields may be sustained by classical magnetic dynamo action. Although the answer is `not indefinitely’, there may be an evolutionary cycle wherein the magnetic field repeatedly relaxes to the minimum energy condition after a period of substantial growth and distortion. Different force-free dynamos may coexist at different locations. Helicity transfer between scales is studied briefly. A dynamo solution is given for the temporal evolution away from an initial linear force-free magnetic field due to both α 2 and ω terms. This can be used at the sub scale level to create a `delayed’ α effect.

Helical Twisting Number and Braiding Linkage Number of Solar Coronal Loops

Abstract Coronal loops in active regions are often characterized by quasi-circular and helically twisted (sigmoidal) geometries, which are consistent with dipolar potential field (PF) models in the former case, and with nonlinear force-free field models with vertical currents in the latter case. Alternatively, Parker-type nanoflare models of the solar corona hypothesize that a braiding mechanism operates between unresolved loop strands, which is a more complex topological model. In this study we use the vertical-current approximation of a nonpotential magnetic field solution (that fulfils the divergence-free and force-free conditions) to characterize the number of helical turns N twist in twisted coronal loops. We measure the helical twist in 15 active regions observed with Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager/SDO (Solar Dynamic Observatory) and find a mean nonpotentiality angle (between the potential and nonpotential field directions) of μ NP = 15° ± 3°. The resulting mean rotational twist angle is φ = 49° ± 11°, which corresponds to N twist = φ/360° = 0.14 ± 0.03 turns with respect to the untwisted PF, with an absolute upper limit of N twist ≲ 0.5, which is far below the kink instability limit of . The number of twist turns N twist corresponds to the Gauss linkage number N link in braiding topologies. We conclude that any braided topology (with ) cannot explain the observed stability of loops in a force-free corona, nor the observed low twist number. Parker-type nanoflaring can thus occur in non-force-free environments only, such as in the chromosphere and transition region.