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Context. For magnetically driven events, the magnetic energy of the system is the prime energy reservoir that fuels the dynamical evolution. In the solar context, the free energy (i.e., the energy in excess of the potential field energy) is one of the main indicators used in space weather forecasts to predict the eruptivity of active regions. A trustworthy estimation of the magnetic energy is therefore needed in three-dimensional (3D) models of the solar atmosphere, e. g., in coronal fields reconstructions or numerical simulations.
Aims. The expression of the energy of a system as the sum of its potential energy and its free energy (Thomson's theorem) is strictly valid when the magnetic field is exactly solenoidal. For numerical realizations on a discrete grid, this property may be only approximately fulfilled. We show that the imperfect solenoidality induces terms in the energy that can lead to misinterpreting the amount of free energy present in a magnetic configuration.
Methods. We consider a decomposition of the energy in solenoidal and nonsolenoidal parts which allows the unambiguous estimation of the nonsolenoidal contribution to the energy. We apply this decomposition to six typical cases broadly used in solar physics. We quantify to what extent the Thomson theorem is not satisfied when approximately solenoidal fields are used.
Results. The quantified errors on energy vary from negligible to significant errors, depending on the extent of the nonsolenoidal component of the field. We identify the main source of errors and analyze the implications of adding a variable amount of divergence to various solenoidal fields. Finally, we present pathological unphysical situations where the estimated free energy would appear to be negative, as found in some previous works, and we identify the source of this error to be the presence of a finite divergence.
Conclusions. We provide a method of quantifying the effect of a finite divergence in numerical fields, together with detailed diagnostics of its sources. We also compare the efficiency of two divergence-cleaning techniques. These results are applicable to a broad range of numerical realizations of magnetic fields.
The general electromagnetic fluctuation theory is a powerful tool to analyze the magnetic fluctuation spectrum of a plasma. Recent works utilizing this theory for a magnetized non-relativistic isotropic Maxwellian electron-proton plasma have demonstrated that the equilibrium ratio of vertical bar delta B vertical bar/B-0 can be as high as 10(-12). This value results from the balance between spontaneous emission of fluctuations and their damping, and it is considerably smaller than the observed value vertical bar delta B vertical bar/B-0 in the solar wind at 1 au, where 10(-3) less than or similar to vertical bar delta B vertical bar/B-0 less than or similar to 10(-1). In the present manuscript, we consider an anisotropic bi-Maxwellian distribution function to investigate the effect of plasma instabilities on the magnetic field fluctuations. We demonstrate that these instabilities strongly amplify the magnetic field fluctuations and provide a sufficient mechanism to explain the observed value of vertical bar delta B vertical bar/B-0 in the solar wind at 1 au.
In order to explain the variance of the solar rotation law during the activity minima and maxima, the angular momentum transport by rotating magnetoconvection is simulated in a convective box penetrated by an inclined azimuthal magnetic field. Turbulence-induced kinetic and magnetic stresses and the Lorentz force of the large-scale magnetic background field are the basic transporters of angular momentum. Without rotation, the sign of the magnetic stresses naturally depends on the signs of the field components as positive (negative) B theta B phi transport the angular momentum poleward (equatorward). For fast enough rotation, however, the turbulence-originated Reynolds stresses start to dominate the transport of the angular momentum flux. The simulations show that positive ratios of the two meridional magnetic field components to the azimuthal field reduce the inward radial as well as the equatorward latitudinal transport, which result from hydrodynamic calculations. Only for B theta B phi>0 (generated by solar-type rotation laws with an accelerated equator) does the magnetic-influenced rotation at the solar surface prove to be flatter than the nonmagnetic profile together with the observed slight spin-down of the equator. The latter phenomenon does not appear for antisolar rotation with polar vortex as well as for rotation laws with prevailing radial shear.
Observations of radio halos and relics in galaxy clusters indicate efficient electron acceleration. Protons should likewise be accelerated and, on account of weak energy losses, can accumulate, suggesting that clusters may also be sources of very high energy (VHE; E > 100 GeV) gamma-ray emission. We report here on VHE gamma-ray observations of the Coma galaxy cluster with the VERITAS array of imaging Cerenkov telescopes, with complementing Fermi Large Area Telescope observations at GeV energies. No significant gamma-ray emission from the Coma Cluster was detected. Integral flux upper limits at the 99% confidence level were measured to be on the order of (2-5) x 10(-8) photonsm(-2) s(-1) (VERITAS, >220 GeV) and similar to 2 x 10(-6) photonsm(-2) s(-1) (Fermi, 1-3GeV), respectively. We use the gamma-ray upper limits to constrain cosmic rays (CRs) and magnetic fields in Coma. Using an analytical approach, the CR-to-thermal pressure ratio is constrained to be < 16% from VERITAS data and <1.7% from Fermi data (averaged within the virial radius). These upper limits are starting to constrain the CR physics in self-consistent cosmological cluster simulations and cap the maximum CR acceleration efficiency at structure formation shocks to be <50%. Alternatively, this may argue for non-negligible CR transport processes such as CR streaming and diffusion into the outer cluster regions. Assuming that the radio-emitting electrons of the Coma halo result from hadronic CR interactions, the observations imply a lower limit on the central magnetic field in Coma of similar to(2-5.5) mu G, depending on the radial magnetic field profile and on the gamma-ray spectral index. Since these values are below those inferred by Faraday rotation measurements in Coma (for most of the parameter space), this renders the hadronic model a very plausible explanation of the Coma radio halo. Finally, since galaxy clusters are dark matter (DM) dominated, the VERITAS upper limits have been used to place constraints on the thermally averaged product of the total self-annihilation cross section and the relative velocity of the DM particles, <sigma nu >.
We quantitatively address the conjecture that magnetic helicity must be shed from the Sun by eruptions launching coronal mass ejections in order to limit its accumulation in each hemisphere. By varying the ratio of guide and strapping field and the flux rope twist in a parametric simulation study of flux rope ejection from approximately marginally stable force-free equilibria, different ratios of self- and mutual helicity are set and the onset of the torus or helical kink instability is obtained. The helicity shed is found to vary over a broad range from a minor to a major part of the initial helicity, with self helicity being largely or completely shed and mutual helicity, which makes up the larger part of the initial helicity, being shed only partly. Torus-unstable configurations with subcritical twist and without a guide field shed up to about two-thirds of the initial helicity, while a highly twisted, kink-unstable configuration sheds only about one-quarter. The parametric study also yields stable force-free flux rope equilibria up to a total flux-normalized helicity of 0.25, with a ratio of self- to total helicity of 0.32 and a ratio of flux rope to external poloidal flux of 0.94. These results numerically demonstrate the conjecture of helicity shedding by coronal mass ejections and provide a first account of its parametric dependence. Both self- and mutual helicity are shed significantly; this reduces the total initial helicity by a fraction of ∼0.4--0.65 for typical source region parameters.
It has been suggested that coronal mass ejections (CMEs) remove the magnetic he-licity of their coronal source region from the Sun. Such removal is often regarded to be necessary due to the hemispheric sign preference of the helicity, which inhibits a simple annihilation by reconnection between volumes of opposite chirality. Here we monitor the relative magnetic he-licity contained in the coronal volume of a simulated flux rope CME, as well as the upward flux of relative helicity through horizontal planes in the simulation box. The unstable and erupting flux rope carries away only a minor part of the initial relative helicity; the major part remains in the volume. This is a consequence of the requirement that the current through an expanding loop must decrease if the magnetic energy of the configuration is to decrease as the loop rises, to provide the kinetic energy of the CME.
The architecture of exoplanetary systems is often different from the solar system, with some exoplanets being in close orbits around their host stars and having orbital periods of only a few days. In analogy to interactions between stars in close binary systems, one may expect interactions between the star and the exoplanet as well. From theoretical considerations, effects on the host star through tidal and magnetic interaction with the exoplanet are possible; for the exoplanet, some interesting implications are the evaporation of the planetary atmosphere and potential effects on the planetary magnetism. In this review, several possible interaction pathways and their observational prospects and existing evidence are discussed. A particular emphasis is put on observational opportunities for these kinds of effects in the high-energy regime.
A conducting Taylor-Couette flow with quasi-Keplerian rotation law containing a toroidal magnetic field serves as a mean-field dynamo model of the Tayler-Spruit type. The flows are unstable against non-axisymmetric perturbations which form electromotive forces defining a effect and eddy diffusivity. If both degenerated modes with m = +/- 1 are excited with the same power then the global a effect vanishes and a dynamo cannot work. It is shown, however, that the Tayler instability produces finite alpha effects if only an isolated mode is considered but this intrinsic helicity of the single-mode is too low for an alpha(2) dynamo. Moreover, an alpha Omega dynamo model with quasi-Keplerian rotation requires a minimum magnetic Reynolds number of rotation of Rm similar or equal to 2000 to work. Whether it really works depends on assumptions about the turbulence energy. For a steeper-than-quadratic dependence of the turbulence intensity on the magnetic field, however, dynamos are only excited if the resulting magnetic eddy diffusivity approximates its microscopic value, eta(T) similar or equal to eta. By basically lower or larger eddy diffusivities the dynamo instability is suppressed.
Magnetic agnetic field generation in core-sheath jets via the kinetic Kelvin-Helmholtz instability
(2014)
We have investigated magnetic field generation in velocity shears via the kinetic Kelvin-Helmholtz instability (kKHI) using a relativistic plasma jet core and stationary plasma sheath. Our three-dimensional particle-in-cell simulations consider plasma jet cores with Lorentz factors of 1.5, 5, and 15 for both electron-proton and electron-positron plasmas. For electron-proton plasmas, we find generation of strong large-scale DC currents and magnetic fields that extend over the entire shear surface and reach thicknesses of a few tens of electron skin depths. For electron-positron plasmas, we find generation of alternating currents and magnetic fields. Jet and sheath plasmas are accelerated across the shear surface in the strong magnetic fields generated by the kKHI. The mixing of jet and sheath plasmas generates a transverse structure similar to that produced by the Weibel instability.