Straight Magnetic Field Research Articles

Self consistent radio-frequency wave propagation and peripheral direct current plasma biasing: Simplified three dimensional non-linear treatment in the “wide sheath” asymptotic regime

A minimal two-field fluid approach is followed to describe the radio-frequency (RF) wave propagation in the bounded scrape-off layer plasma of magnetic fusion devices self-consistently with direct current (DC) biasing of this plasma. The RF and DC parts are coupled by non-linear RF and DC sheath boundary conditions at both ends of open magnetic field lines. The physical model is studied within a simplified framework featuring slow wave (SW) only and lateral walls normal to the straight confinement magnetic field. The possibility is however kept to excite the system by any realistic 2D RF field map imposed at the outer boundary of the simulation domain. The self-consistent RF + DC system is solved explicitly in the asymptotic limit when the width of the sheaths gets very large, for several configurations of the RF excitation and of the target plasma. In the case of 3D parallelepipedic geometry, semi-analytical results are proposed in terms of asymptotic waveguide eigenmodes that can easily be implemented numerically. The validity of the asymptotic treatment is discussed and is illustrated by numerical tests against a quantitative criterion expressed from the simulation parameters. Iterative improvement of the solution from the asymptotic result is also outlined. Throughout the resolution, key physical properties of the solution are presented. The radial penetration of the RF sheath voltages along lateral walls at both ends of the open magnetic field lines can be far deeper than the skin depth characteristic of the SW evanescence. This is interpreted in terms of sheath-plasma wave excitation. Therefore, the proper choice of the inner boundary location is discussed as well as the appropriate boundary conditions to apply there. The asymptotic scaling of various quantities with the amplitude of the input RF excitation is established.

Intensity variations associated with fast sausage modes

We determine the dependence of the observed properties of fast magnetoacoustic axisymmetric oscillations (the sausage mode) of a thick and dense flaring coronal loop, modelled by a magnetic cylinder, on the parameters of the equilibrium plasma configuration. The plasma inside and outside the cylinder is of low-beta, and penetrated by a straight magnetic field. The plasma density has a smooth profile across the magnetic field. Methods: We use three-dimensional ideal magnetohydrodynamic equations to model numerically the development of the perturbations of the cylindrical equilibrium, considering both leaky and trapped regimes. Results: Short-period sausage oscillations, trapped by the cylinder, are qualitatively consistent with the analytical results obtained in the models of a plasma slab or a cylinder with a step-function transverse profile. The period of trapped sausage oscillations is determined by the ratio of the phase speed, with the value between the internal and external Alfven speeds, to the wavelength. Longer-period sausage oscillations are leaky, and their decay times are longer for higher density contrasts between the internal and external media. Leaky sausage oscillations have longer periods than trapped sausage oscillations of the same cylinder. In the coronal conditions, sausage oscillations are essentially compressible and transverse, hence produce modulation of the thermal optically thin emission intensity and periodic Doppler broadening of emission lines. However, if the oscillating plasma non-uniformity is poorly spatially resolved, the variation in the emission intensity is weak and proportional to the actual amplitude of the oscillation squared. The latter variation property is connected with the transverse nature of the oscillation, causing the conservation of mass in the transverse cross-section of the oscillating plasma structure.

Slow magnetacoustic waves in magnetic arcades

Aims. We investigate two-dimensional effects on the evolution of impulsively-generated slow magnetoacoustic waves in magnetic arcades of the solar corona. Methods. We used a two-dimensional box model of a coronal arcade, neglecting the effects of gravity and magnetic curvature. Ideal finite-β magnetohydrodynamic equations were employed. The plasma was taken to be uniform, penetrated by a straight and uniform magnetic field. We applied line-tying boundary conditions at the magnetic footpoints. Results. Running and standing slow magnetoacoustic waves develop across the magnetic field due to the reflection from the footpoints in the arcade. The perpendicular group speed is lower than both sound and Alfven speeds. The speed grows with the increase in plasma-β, which is consistent with analytical theory. Slow magnetoacoustic pulse perturbs the magnetic field and current density; this effect is stronger for higher amplitudes. Standing waves spread across the field, forming a characteristic phase-mixing pattern of antiparallel flows. The two-dimensional effects are more pronounced for higher β. Our results confirm the plausibility of the interpretation of the observed evolution of two-ribbon flares in terms of slow magnetoacoustic waves in magnetic arcades.

Classical Transport in a Plasma

An ideal plasma of electrons and a single species of ions in the low collisionality limit subject to an almost straight magnetic field is considered. In such conditions, the linear theory of transport determines the 3 × 1 matrix of dissipative fluxes [J with circumflex above]r namely, the electric current, the electronic heat flux and the ionic heat flux, in terms of a 3 × 1 matrix of thermodynamic forces [X with circumflex above] combining the electric field with the gradients of the densities and of the temperatures. The classical transport coefficients are the components of the 3 × 3 matrix of tensors [L with circumflex above]rs of the linear flux-force relations [J with circumflex above]r = [summation from s=1 to 9][L with circumflex above]rs[X with circumflex above]. The theory is developed in the framework of the statistical mechanics of charged particles starting from the Landau kinetic equation.

Global modes of flute instability of a rotating cylindrical plasma

The influence of rotation on the flute instability of a cylindrical gravitating plasma in a straight inhomogeneous magnetic field is studied in the framework of one-fluid magnetohydrodynamics. The dispersion relation and integral expression for the instability growth rate of eigenmodes are derived. It is shown that, in the framework of the given problem, rotation is a destabilizing factor, and the corresponding theorem is proved for the general case. For a linear radial profile of the rotation frequency, the structure of eigenmodes is calculated. The growth rate of these modes is shown to increase with increasing rotation velocity and azimuthal mode number. It is found that plasma rotation in the eigenmode localization region leads to the displacement of perturbation from the rotation region, which results in a decrease in the instability growth rate. The absence of eigenmodes (i.e., exponential instability of the system) for certain profiles of the density and rotation frequency is demonstrated.

Classical Transport in a Plasma

An ideal plasma of electrons and a single species of ions in the low collisionality limit subject to an almost straight magnetic field is considered. In such conditions, the linear theory of transport determines the 3 × 1 matrix of dissipative fluxes [hat]Jr namely, the electric current, the electronic heat flux and the ionic heat flux, in terms of a 3 × 1 matrix of thermodynamic forces [hat]X combining the electric field with the gradients of the densities and of the temperatures. The classical transport coefficients are the components of the 3 × 3 matrix of tensors [hat]Lrs of the linear flux-force relations [hat]Jr = [summation]s=19 [hat]Lrs[hat]X. The theory is developed in the framework of the statistical mechanics of charged particles starting from the Landau kinetic equation.

On the Excitation of Leaky Modes in Cylindrical Loops

The role of leaky waves in the coronal loop oscillations observed by TRACE is not yet clearly understood. In this work, the excitation of fast waves in solar coronal loops modelled as dense plasma cylindrical tubes in a uniform straight magnetic field is investigated. We study the trapped and especially leaky modes (whose energy escapes from the tube) that result from an initial disturbance by solving the time-dependent problem numerically. We find that the stationary state of the tube motion is given by the trapped normal modes. By contrast, the transient behaviour between the initial and the stationary phase is dominated by wave leakage. The so-called trig leaky modes are clearly identified since the transient behaviour shows periods and damping times that are in agreement with the values calculated from the normal-mode analysis. Consequently, these radiating modes have physical significance. However, we have not found any evidence for the excitation of other types of modes, such as the principal leaky kink mode.

Sausage and kink oscillations in incompressible annular magnetic cylinders

Aims. The propagation of MHD waves in a structured magnetic flux tube embedded within a straight magnetic environment is studied analytically. The motivation for this analysis comes from the observations of damped loop oscillations indicating the possibility that only part of the loop is homogeneous in the radial direction and from the observation of two simultaneous waves with different speeds in the same magnetic loop in the solar atmosphere. Methods. The general dispersion relation of longitudinal wave propagation is derived for a flux tube configuration consisting of a core, annulus and external region each with straight distinct magnetic field. Modes of oscillation are examined from the general dispersion relation that is suitable for obtaining information not just on oscillations but also on some instability properties of this complex tube structure. Specific attention is given to the modification of the phase speeds and oscillation periods caused by the annulus structure, compared to a single monolithic tube. Results. It is shown that two purely surface modes arise. The relative change in periods due to the additional annulus layer is shown to be rather significant (up to 20% in some cases). In particular we found that in photospheric type annular tubes, periods are less than their counterparts in a monolithic loop while for a dense flux tube in the majority of cases the period was greater than the period of the counterpart monolithic flux tube. Both short and long wavelength approximations are considered for both the symmetrical (sausage) and kink modes. Conclusions. Annular structuring of a magnetic flux tube will reduce or increase periods of the allowed oscillations depending on the type of flux tube considered (either as a magnetic or as a density enhancement). The results are relevant to further our knowledge of solar magneto-seismology. In particular, the obtained results for the kink oscillations may be applicable from photosphere to corona, while the case for the sausage mode is more relevant in the lower part of the solar atmosphere.

Wave propagation in incompressible MHD wave guides: the twisted magnetic Annulus

The propagation of MHD waves in a structured magnetic flux tube embedded within a straight vertical magnetic environment is studied analytically. The motivation of this analysis comes from the observations of damped loop oscillations showing that possibly only part of the loop is homogeneous in the radial direction. The general dispersion relation of longitudinal wave propagation is derived for a fully magnetically twisted configuration consisting of a core, annulus and external region each with magnetic field of uniform, yet distinct, twist. Next, a simplified case representing coronal loops is analysed in detail considering magnetic twist just in the annulus, the internal and external regions having straight magnetic field. Modes of oscillations are examined from the general dispersion relation that is suitable for obtaining information on not just oscillations but also on some instability properties of this complex tube structure. It is shown that there are purely surface (i.e. evanescent) and hybrid (spatially oscillatory in the twisted annulus, otherwise evanescent) modes. Except for small wavenumbers, the surface waves show little dispersion; a property making them more suitable for observations. The hybrid modes show a more complex character. Though the frequency range seems to be rather limited, there is a continuum band of frequencies for a given wavenumber. Both short and long wavelength approximations are considered for the symmetrical (sausage) mode and with small twist in particular.

The reversed effect of the electromagnetic wave spatial multimodality on Alfven wave heating in a helical magnetic field

Spatial distribution of electromagnetic wave fields within the local Alfven resonance (AR) region is studied under the conditions when this distribution is governed just by a helical inhomogeneity of the confining magnetic field rather than electron inertia or finite ion Larmor radius. It is shown that accounting for the helical inhomogeneity of the steady magnetic field can remove the infinite discontinuity of the wave fields that takes place in the case of straight magnetic field rather than other weak effects. Radio frequency (RF) power absorption within the local AR region is compared with the case when AR structure is governed by other weak phenomena.

Dispersion equations for field-aligned cyclotron waves in axisymmetric magnetospheric plasmas

Abstract. In this paper, we derive the dispersion equations for field-aligned cyclotron waves in two-dimensional (2-D) magnetospheric plasmas with anisotropic temperature. Two magnetic field configurations are considered with dipole and circular magnetic field lines. The main contribution of the trapped particles to the transverse dielectric permittivity is estimated by solving the linearized Vlasov equation for their perturbed distribution functions, accounting for the cyclotron and bounce resonances, neglecting the drift effects, and assuming the weak connection of the left-hand and right-hand polarized waves. Both the bi-Maxwellian and bi-Lorentzian distribution functions are considered to model the ring current ions and electrons in the dipole magnetosphere. A numerical code has been developed to analyze the dispersion characteristics of electromagnetic ion-cyclotron waves in an electron-proton magnetospheric plasma with circular magnetic field lines, assuming that the steady-state distribution function of the energetic protons is bi-Maxwellian. As in the uniform magnetic field case, the growth rate of the proton-cyclotron instability (PCI) in the 2-D magnetospheric plasmas is defined by the contribution of the energetic ions/protons to the imaginary part of the transverse permittivity elements. We demonstrate that the PCI growth rate in the 2-D axisymmetric plasmasphere can be significantly smaller than that for the straight magnetic field case with the same macroscopic bulk parameters.

B34 Measurement of an athlete's back angle using magnetic north, accelerometer and a mechanical gyroscope

We desire to know the true three-dimensional absolute angle of an athlete's upper back while in vigorous motion. Much of the angle information can be obtained from a high-quality geomagnetic compass, provided the athlete is moving in an area with a straight magnetic field. Unfortunately the angle of rotation around the geomagnetic North direction cannot be detected by magnetic field sensors, and accelerometers cannot distinguish gravitation from acceleration, so at least one additional piece of angular displacement information is needed. In this paper we present a combined measuring method for the angle of a backpack worn by an athlete. With the athlete standing still, a triad of accelerometers measures the gravitational field and thus the true downward direction in the backpack reference frame. This is used to set the zero angle on two axes of a mechanical "vertical" gyroscope. During subsequent motion, rotation of the gyroscope axes is used to develop an incomplete quaternion, that is, one that does not account for rotation about the gyroscope rotor axis. A geomagnetic compass is used to develop another incomplete quaternion but this time with unknown rotation about the local Earth North vector. The unknown rotation axes could in principle align, but in practice this is easily avoided, so the two incomplete rotations can be resolved into a single quaternion representing the true absolute angle of the backpack. To illustrate the method, the design of the geomagnetic and gyroscope systems will be presented, along with details of the mathematics and an example of the measurement of a ski motion on a real ski slope.

Alfven wave reflection in a curvilinear magnetic field and formation of Alfvenic resonators on open field lines

Though shear Alfven waves have no reflection points, these waves can be partially reflected from sharp field‐aligned variations in Alfven velocity. Such a reflection can lead to the formation of quasi‐resonators, such as the ionospheric Alfven resonator, in which wave energy can be accumulated. We show that a similar partial reflection of Alfven waves can occur in regions with steep variations of geomagnetic field line geometry. For that, the propagation of Alfven waves in a plasma immersed in a two‐dimensional (2‐D) curvilinear magnetic field has been investigated. The Alfven waves comprise two modes with different polarization, toroidal and poloidal, which are described by 1‐D equations. These equations formally coincide with the equation for the case of a quasi‐uniform straight magnetic field with a modified Alfven velocity that takes into account the field‐aligned dependence of the Lamé coefficients. The toroidal and poloidal modes depend differently on the magnetic field geometry. The poloidal mode is efficiently reflected from regions where the magnetic field lines sharply converge or diverge, when its wavelength becomes comparable to the typical scale of magnetic field convergence. This effect can result in the formation of Alfven quasi‐resonators on open field lines. This mechanism can be used to interpret the occurrence of specific polar cap quasi‐periodic Pi3 pulsations with periods ∼15–20 min observed by the AGO magnetometer array in Antarctica. Also, such a reflection can limit the influx of Alfvenic wave energy along reconnected field lines from the solar wind into the magnetosphere at certain wavelengths. This effect has been observed as the occurrence of a low‐pass cutoff period ∼10–15 min in the spectral transfer function between conjugate IMF variations and ground magnetic disturbances.

On the possibility of reflection of Alfvén waves in a curvilinear magnetic field

The propagation of Alfven waves in a plasma immersed in a curvilinear magnetic field is investigated by using a 2D model. The waves are described by a 1D equation that formally coincides with the equation for the case of a quasi-uniform straight magnetic field with a modified Alfven velocity that takes into account the longitudinal dependence of the Lame coefficients. It is shown that toroidal and poloidal Alfven modes depend differently on the magnetic-field geometry. In the case of a 2D plane-parallel configuration of the magnetic field, poloidal modes are efficiently reflected from regions where the magnetic field lines sharply converge or diverge. This effect can result in the formation of open-field-line Alfven quasi-resonators.

Helicity resonant influence on the local Alfvén resonance structure in straight stellarators

Distribution of antenna-driven electromagnetic wave fields within the local Alfvén resonance is studied under resonant conditions such that the axial period of the fundamental harmonic of the magnetohydrodynamic oscillations in the axial direction is twice as large as the pitch length, and the poloidal number of the fundamental harmonic is twice as small as the polarity of the helical coils. It is shown that taking account of the helical inhomogeneity of the steady magnetic field can remove the infinite discontinuity of the wave fields that takes place in a straight magnetic field rather than with electron inertia or a finite ion Larmor radius.

Superfast expansion acceleration mechanism in the spontaneous fast magnetic reconnection

Thermodynamic supersonic (superfast) plasma expansion acceleration generated in the spontaneous fast magnetic reconnection process is studied in 2-dimensional magnetohydrodynamic (MHD) simulations. In contrast to the Petschek reconnection model, the reconnection outflow jet is found to exceed steadily the Alfven velocity measured in the upstream magnetic field region. In our MHD simulation for the symmetric anti-parallel magnetic field model, the final velocity of the plasma jet is observed to reach 1.4 times of the Alfven velocity, which is maintained until the jet encounters a fast shock generated in front of the magnetic loop (plasmoid). Also in asymmetric magnetic field models, in which the current sheet is put between two straight magnetic field regions with different intensities, the supersonic plasma acceleration mechanism is detected. Especially, in the asymmetric model in which uniform plasma density is initially assumed, the supersonic acceleration region tends to shift to the side of the higher intensity magnetic field region. In addition, the plasma jet region consists of two jet layers which have different Mach numbers and almost the same jet velocity. It means that the reconnection jet almost have reached a steady state. Hence, the generation of the superfast jet can be predicted by the Rankine Hugoniot relation for the slow shock. Once the superfast jet and magnetic loop are generated, the thermodynamic supersonic expansion acceleration can occur due to the change of the pressure balance around the magnetic loop.

Nonlinear magneto-acoustic waves in the solar atmosphere

Abstract The weakly nonlinear evolution of quasi-isentropic magnetoacoustic waves in the solar atmosphere is analyzed. The plasma is assumed to be initially homogeneous, in thermal equilibrium and with a straight and homogeneous magnetic field frozen in. Additionally, the plasma is assumed to be cooled by the standard cooling function in the range of 10 4 K 7 K and heated by a mechanism which is proportional to the density and temperature. The range of temperature where the plasma is isentropically unstable, the e-folding time for thermal instability and the corresponding time and length-scale for wave breaking are found.

Thermo-dynamic plasma expansion acceleration in asymmetric spontaneous fast magnetic reconnection

Asymmetric spontaneous fast magnetic reconnection model, in which the current sheet is initially put between two antiparallel straight magnetic field regions with different magnetic intensities, is studied by two-dimensional magnetohydrodynamic (MHD) simulations. Especially, the supersonic expansion acceleration process which has been already observed in the symmetric case is focused on. In this paper, we find that if the initial asymmetry features are weak and one side of the magnetic field regions consists of sufficiently low beta plasma, the supersonic expansion acceleration process is generated in the reconnection jet region, like the symmetric case. Hence, in such an asymmetric case, a fast shock is formed at the top of the magnetic loop.

Resonant Influence of Bumpy Steady Magnetic Field Ripples on the Structure of the Local Alfven Resonance

Distribution of electromagnetic wave fields within the local Alfven resonance is studied under the resonant condition such that a period of the fundamental harmonic of radio - frequency wave in the axial direction is twice as large as the period of the steady bumpy magnetic field. Account for the ripples of the steady magnetic field is shown to remove infinite discontinuity of the wave fields, that takes place in straight magnetic field. Arising of the gap in the Alfven continua caused by the ripples is discussed.

Resonant Influence of Bumpy Steady Magnetic Field Ripples on the Structure of the Local Alfven Resonance

Distribution of electromagnetic wave fields within the local Alfven resonance is studied under the resonant condition such that a period of the fundamental harmonic of radio - frequency wave in the axial direction is twice as large as the period of the steady bumpy magnetic field. Account for the ripples of the steady magnetic field is shown to remove infinite discontinuity of the wave fields, that takes place in straight magnetic field. Arising of the gap in the Alfven continua caused by the ripples is discussed.