General Magnetic Field Configurations Research Articles

Histogram of oriented gradients: a technique for the study of molecular cloud formation

We introduce the histogram of oriented gradients (HOG), a tool developed for machine vision that we propose as a new metric for the systematic characterization of spectral line observations of atomic and molecular gas and the study of molecular cloud formation models. In essence, the HOG technique takes as input extended spectral-line observations from two tracers and provides an estimate of their spatial correlation across velocity channels. We characterized HOG using synthetic observations of HI and 13CO (J = 1 → 0) emission from numerical simulations of magnetohydrodynamic (MHD) turbulence leading to the formation of molecular gas after the collision of two atomic clouds. We found a significant spatial correlation between the two tracers in velocity channels where vHI ≈ v13CO, almost independent of the orientation of the collision with respect to the line of sight. Subsequently, we used HOG to investigate the spatial correlation of the HI, from The HI/OH/recombination line survey of the inner Milky Way (THOR), and the 13CO (J = 1 → 0) emission from the Galactic Ring Survey (GRS), toward the portion of the Galactic plane 33°.75 ≤l ≤ 35°.25 and |b| ≤ 1°.25. We found a significant spatial correlation between the two tracers in extended portions of the studied region. Although some of the regions with high spatial correlation are associated with HI self-absorption (HISA) features, suggesting that it is produced by the cold atomic gas, the correlation is not exclusive to this kind of region. The HOG results derived for the observational data indicate significant differences between individual regions: some show spatial correlation in channels around vHI ≈ v13CO while others present spatial correlations in velocity channels separated by a few kilometers per second. We associate these velocity offsets to the effect of feedback and to the presence of physical conditions that are not included in the atomic-cloud-collision simulations, such as more general magnetic field configurations, shear, and global gas infall.

Magnetosphere structure of a Kerr black hole: Marginally force-free equatorial boundary condition

The role of equatorial boundary condition in the structure of a force-free black hole magnetosphere was rarely discussed, since previous studies have been focused on the field lines entering the horizon. However, recent high-accuracy force-free electrodynamics (FFE) simulations \cite{East2018} show that there are both field lines entering the horizon and field lines ending up on the equatorial current sheet within the ergosphere for asymptotic uniform field configuration. For the latter field lines, the equatorial boundary condition is well approximated being marginally force-free, i.e., $B^2-E^2\approx 0$, where $B$ and $E$ are the magnetic and electric field strength, respectively. In this paper, we revisit the uniform field solution to the Kerr BH magnetosphere structure and investigate the role of the marginally force-free equatorial boundary condition. We find this boundary condition plays an important role in shaping the BH magnetosphere in various aspects, including the shape of the light surface, the near-horizon field line configuration and the source of the Poynting flux. We also propose an algorithm for numerically solving the Grad-Shafranov equation and self-consistently imposing the marginally force-free equatorial condition. As a result, we find a good agreement between our numerical solutions and the high-accuracy FFE simulations. We also discuss the applicability of the marginally force-free boundary condition and the numerical algorithm proposed in this paper for general magnetic field configurations.

SPATIAL DISTRIBUTION OF PAIR PRODUCTION OVER THE PULSAR POLAR CAP

ABSTRACT Using an analytic, axisymmetric approach that includes general relativity, coupled to a condition for pair production deduced from simulations, we derive general results about the spatial distribution of pair-producing field lines over the pulsar polar cap. In particular, we show that pair production on magnetic field lines operates over only a fraction of the polar cap for an aligned rotator for general magnetic field configurations, assuming the magnetic field varies spatially on a scale that is larger than the size of the polar cap. We compare our result to force-free simulations of a pulsar with a dipole surface field and find excellent agreement. Our work has implications for first-principles simulations of pulsar magnetospheres and for explaining observations of pulsed radio and high-energy emission.

Fusion modeling approach for novel plasma sources

The physics involved in the coupling, propagation and absorption of RF helicon waves (electronic whistler) in low temperature Helicon plasma sources is investigated by solving the 3D Maxwell-Vlasov model equations using a WKB asymptotic expansion. The reduced set of equations is formally Hamiltonian and allows for the reconstruction of the wave front of the propagating wave, monitoring along the calculation that the WKB expansion remains satisfied. This method can be fruitfully employed in a new investigation of the power deposition mechanisms involved in common Helicon low temperature plasma sources when a general confinement magnetic field configuration is allowed, unveiling new physical insight in the wave propagation and absorption phenomena and stimulating further research for the design of innovative and more efficient low temperature plasma sources. A brief overview of this methodology and its capabilities has been presented in this paper.

Evolution of polarization of an electromagnetic wave propagating in magnetized plasma: Comparison between two alternative formalisms

Two alternative formalisms for the analysis of the evolution of electromagnetic wave polarization in a magnetized plasma are considered: the coupled wave formalism and the Stokes vector formalism. The first formalism is developed and extended to more general magnetic field configurations than considered hitherto, thus obtaining a new polarization evolution equation. The two formalisms are compared and their relative merits and limitations are described. In particular, it is shown that the equations for polarization evolution are valid for arbitrarily strong anisotropy induced by the magnetic field and that these equations treat implicitly the effect of coupling between the characteristic waves.

Role of the mean curvature in the geometry of magnetic confinement configurations

Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curvature are optimum for plasma confinement in multimirror open confinement systems and rippled tori.

Dynamics of Magnetic Loops in the Coronae of Accretion Disks

Axisymmetric magnetohydrodynamic (MHD) simulations are used to study the evolution of general magnetic field configurations where a magnetic field B threads different radii of a differentially rotating accretion disk. The differential rotation of the footpoints of B field loops at different radii on the disk surface causes a twisting of the coronal magnetic field, an increase in the coronal magnetic energy, and an opening of the loops in the region where the magnetic pressure is larger than the matter pressure (β 1). In the region where β 1, the loops may be only partially opened. Current layers form in the narrow regions that separate oppositely directed magnetic field lines. Reconnection occurs in these layers as a result of the small numerical magnetic diffusivity of the code. In contrast with the case of the solar coronal magnetic field, the combination of magnetic and centrifugal forces leads to significant matter outflow from the disk. The faster rotation of the inner part of the disk gives a stronger outflow from this part of the disk. The outflow accelerates with increasing distance from the disk up to velocities in excess of the escape speed. The outflows show some collimation within the computational region and have a large power output mainly in the form of a Poynting flux. Thus these outflows are pertinent to the origin of astrophysical jets. We present results of a survey of simulation runs for the behavior of magnetic loops and outflows for a wide range of field strengths B and mass outflow rates j. The model and processes observed are relevant to the coronae of accretion disks around stellar-mass objects, including pre-main-sequence stars, compact stars, and black holes, as well as the coronae of disks around massive black holes in active galactic nuclei. Opening of magnetic field loops may lead to transient and/or steady outflows, while reconnection events may be responsible for X-ray flares in such objects.

Ion Bernstein wave propagation and absorption in general magnetic field configuration

A linear analysis of ion Bernstein wave (IBW) propagation and absorption is considered in a general tokamak plasma magnetic equilibrium. The effects of elongation, triangularity, and Shafranov shift on radio-frequency (rf) absorption are discussed with respect to the simple case of circular and concentric magnetic surfaces. The ray-tracing equations are analytically and numerically solved in the flux surface coordinate system, and the power deposited in the plasma is calculated along the trajectory for the International Thermonuclear Experimental Reactor (ITER) [Nucl. Fusion 31, 1135 (1991)] plasma parameters.

Gyrokinetic energy conservation and Poisson-bracket formulation

An integral expression for the gyrokinetic total energy of a magnetized plasma, with general magnetic field configuration perturbed by fully electromagnetic fields, was recently derived through the use of a gyrocenter Lie transformation. It is shown that the gyrokinetic energy is conserved by the gyrokinetic Hamiltonian flow to all orders in perturbed fields. An explicit demonstration that a gyrokinetic Hamiltonian containing quadratic nonlinearities preserves the gyrokinetic energy up to third order is given. The Poisson-bracket formulation greatly facilitates this demonstration with the help of the Jacobi identity and other properties of the Poisson brackets.

DISPERSION RELATION OF GENERAL MAGNETICALLY CONFINED WEAK RELATIVISTIC PLASMAS

The dispersion relation for weak relativistic inhomogeneous plasma in general magnetic field configurations is derived from the relativistic gyrokinetic equations, which is valid for arbitrary frequencies. In the derivations the singular integrations with the quadratic denominator are represented by the drift plasma dispertion functions. This dispersion relation can be used to study the various micro instabilities driven by gradient and curvature of B, weak relativistic effects, and/or gyrofrequency shift. Extending the results to the nonequilibrium case such as loss-cone distribution is simple and straight forward. For demonstration, we apply it to investigate the lower hybrid drift instability. Using this dispersion relation we can recover the re-suits of Drake et al. in a straight forward and much more transparent way.

Linear relativistic gyrokinetic equation in general magnetically confined plasmas

The gyrokinetic formalism for linear electromagnetic waves of arbitrary frequency in general magnetic field configurations is extended to include full relativistic effects. The derivation employs the small adiabaticity parameter rho /L0 where rho is the Larmor radius and L0 the equilibrium scale length. The effects of the plasma and magnetic field inhomogeneities and finite Larmor radii effects are also contained.

Linear oscillations in general magnetically confined plasmas

A systematic formalism for investigating linear electromagnetic perturbations in general magnetic field configurations is developed. The formalism employs the small adiabaticity parameter rho /L0 and is valid for arbitrary frequencies. Here, rho and L0 are, respectively, the Larmor radius and equilibrium scale length. Effects associated with plasma and magnetic field inhomogeneities as well as finite Larmor radii are contained. The specific case of axisymmetric Tokamaks is then considered to illustrate the potential application.

Electrostatic waves in general magnetic field configurations

A scheme for investigating linear electrostatic waves in general magnetically confined plasmas is presented. The scheme is a generalization of the low-frequency (less than the cyclotron frequency) gyrokinetic formalism of Rutherford and Frieman as well as Taylor and Hastie to arbitrary frequencies. Governing integral wave equations for slab plasmas with magnetic shear as well as axisymmetric tokamaks are then derived to illustrate the applications.

Nonlinear gyrokinetic equations for low-frequency electromagnetic waves in general plasma equilibria

A nonlinear gyrokinetic formalism for low-frequency (less than the cyclotron frequency) microscopic electromagnetic perturbations in general magnetic field configurations is developed. The nonlinear equations thus derived are valid in the strong-turbulence regime and contain effects due to finite Larmor radius, plasma inhomogeneities, and magnetic field geometries. The specific case of axisymmetric tokamaks is then considered and a model nonlinear equation is derived for electrostatic drift waves. Also, applying the formalism to the shear Alfvén wave heating scheme, it is found that nonlinear ion Landau damping of kinetic shear-Alfvén waves is modified, both qualitatively and quantitatively, by the diamagnetic drift effects. In particular, wave energy is found to cascade in wavenumber instead of frequency.

On the particle number conservation inherent in the diffusion approach of the Fokker-Planck equation

Starting from the Fokker-Planck equation we show that, in a strict sense, the usual diffusive transport of charged particles in weak magnetic field fluctuations is not valid until the space-integrated number of particles per velocity interval has reached its final overall constant value and is conserved. Large anisotropies are thus not compatible with diffusion. Diffusion becomes exactly valid after an infinite time, but has reached a good approximation to the real transport before that. The particle-number conservation holds for quite general mean magnetic field configurations, and is not limited to the case of a constant mean field.

Saturation effects in magnetic resonances for a general magnetic field configuration

Various magnetic resonances appearing in optical pumping experiments have been analysed theoretically and experimentally. However, there is little work on the saturation effects caused by strong RF fields. Recently, The saturation effects of the multiple quantum resonances and of the Haroche resonances have been investigated by Stenholm (1972) and by Tsukada and Ogawa (1973). The saturation effects are treated for the more general case of a static magnetic field in an arbitrary direction with respect to the oscillating RF field. The experimental results are compared with the exact solutions computed by the numerical integration of the Bloch equation. It is shown experimentally and theoretically that the resonances similar to the Haroche resonance appear at omega /sub ///=n omega , where omega /sub ///= gamma H/sub ///, n is an integer, H/sub /// is the parallel component of the static magnetic field with respect to the oscillating RF field, and gamma is the gyromagnetic ratio.

Drift Wave Instability in General Magnetic Field Configurations

A method is presented for the investigation of the propagation and stability properties of drift waves driven by a density gradient and other low-frequency electrostatic waves in realistic magnetic field configurations confining a low-pressure plasma in static equilibrium. At the outset the method utilizes the guiding-center motion and associated invariants of the charged patricle in order to obtain the perturbation in the charge density in terms of the electrostatic potential associated with the wave. For linear stellarator-and levitron-type fields of infinite axial extent, unstable, nonseverely localized, normal modes are found in contrast to the severely localized modes of planar slab geometry with simulated shear. The imposition of boundary conditions on the linear stellarator-type field to simulate a closed toroidal field yields standing waves along the magnetic field line and high m numbers (short wavelength) for the azimuthal field transverse to the magnetic field line. The rapid helical winding, around the hard core, of the field lines of the linear levitron-type field of infinite axial extent constrains the maximum wavelength along the field line to a single helical turn, a constraint which leads to high m numbers for the azimuthal field. In both the case of the linear stellarator field with identified ends and the case of the linear levitron field of infinite axial extent, the stabilizing effect of shear is manifested by short transverse wavelengths for the drift wave leading to reduced anomalous diffusion.

Drift Instabilities in General Magnetic Field Configurations

A theory of low-frequency drift (universal) instabilities in a nonuniform collisionless plasma is developed for general magnetic field configurations including trapped particle effects, rather than the plane geometry which has previously received most attention. A type of energy principle shows that the special equilibrium distribution F(∈, μ), of interest in minimum-B mirror configurations, is absolutely stable to these modes provided ∂F/∂∈ < 0 together with a second condition on ∂F/∂μ. For equilibrium distributions not of this special form, in particular for a Maxwell distribution with a density gradient, the case of axisymmetric toroidal configurations with closed poloidal field lines is considered in detail. Three unstable drift modes are found, a flute-like mode, a drift-ballooning mode local to the region of unfavorable curvature, and a drift-universal mode. Stability criteria and growth rates for the modes are given. The equations also describe a recently discussed low-frequency trapped-particle instability.

Entropy and stability of plasma equilibrium configurations

The definition of the entropy functional introduced in preceding articles and the related variational techniques are extended and applied in the present paper to the characterization of the equilibrium and stability properties of many plasma configurations of practical interest. The entropy functional is minimum at equilibrium with respect to a large class of unstable modes, that is low frequency modes or high frequency nearly electrostatic modes which are initially zero at the boundaries of the plasma. Moreover, the minimum of the entropy can be connected with a negative variation of the electric and magnetic energy in a special class of interchanges. Known sufficient instability conditions prove to be the same as minimum conditions for the entropy. This is explicitly shown for the purely electrostatic micro-instabilities, the flutes, the shear instability, and the unstable mirror-type modes in plane or cylindrical geometry. Finally the conditions for a maximum entropy of a low β plasma equilibrium in a general adiabatic magnetic field configuration are discussed. A nonzero minimum- B configuration can satisfy these conditions, but for a plasma with a low but nonzero β other restrictions have to be imposed on the plasma pressure and on the magnetic field as functions of space.

Green's Function for Two-Dimensional Magnetohydrodynamic Waves. II

As an extension of an earlier paper the Green's function is evaluated for the Lundquist equation linearized about uniform magnetic field, constant matter density, and zero flow velocity. It is assumed that all quantities are functions of two space variables and time only. In the general magnetic field configuration considered here a pure Alfvén disturbance no longer exists; there is instead a wave with properties of both the Alfvén and fast-slow disturbance.