Rotation of Weakly Collisional Plasmas in Tokamaks, Operated with Alfvén Waves

In this paper we consider rotation induced by kinetic Alfvén waves in weakly collisional plasma of slightly rippled tokamaks in plateau and banana regimes. Rippled magnetic field of tokamaks retards the plasma rotation in toroidal direction. Here, we are going to find the quasistationary poloidal and toroidal plasma velocities and the radial electric field taking into account the complete form of ponderomotive forces.     

Rotation of Tokamak Plasmas by Alfvén Waves

Externally excited Alfvén waves can generate the poloidal and toroidal rotation in the collisional (edge) and core (weakly collisional) tokamak plasma. The necessary value of these velocities to achieve the L-H transition, can be obtained by manipulating the value of an absorbed power. This rotation linearly depends on dissipated power, decreases in banana regimes and did not depend on toroidal magnetic field. In the plasma layer where the RF power is absorbed, the radial electric field also appears. There is the very satisfactory agreement between our theory and experimental results obtained on Phaedrus-T tokamak. The methods developed in this paper can be applied to other tokamaks with another kind of waves, which can be used to operate the plasma dynamics taking into account the appropriate dispersion relation for that type of waves.     

Cooling of neutron stars with strong toroidal magnetic fields

We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the surface in a large part of the crust. As a result, the neutron star surface presents two warm regions surrounded by extended cold regions and has a thermal luminosity much lower than in the case the magnetic field is purely poloidal. We apply these models to calculate the thermal evolution of such neutron stars and show that the lowered photon luminosity naturally extends their life-time as detectable thermal X-ray sources. Work partially supported by UNAM-DGAPA grant #IN119306.     

Equilibrium of self gravitating polytropic cylinders with a magnetic field

The equations of hydromagnetics for a self-gravitating fluid of infinite conductivity are examined in the axisymmetric case in terms of toroidal and poloidal scalars. The stationary state with non-zero poloidal velocity scalar admits and analytical solution for polytropic cylinder of infinite length with a prevalent toroidal magnetic field. The case when the poloidal velocity scalar is zero is also considered.     

A radiation-driven disc wind model for massive young stellar objects

The generation of magnetic fields by a battery, operating in an ion–electron plasma around a Kerr black hole, is studied in the 3+1 split of the Kerr metric. It is found that the gravitomagnetic contributions to the electron partial pressure are able to drive currents. The strength of the equilibrium magnetic field should be higher than for the classical Biermann battery, which is found to operate in this relativistic context as well, since the gravitomagnetic driving terms can less easily be quenched than the classical ones. In axisymmetry the battery can induce only toroidal magnetic fields. Once a toroidal magnetic field is present, however, the coupling of gravitomagnetic and electromagnetic fields generates a poloidal magnetic field even in axisymmetry. A rotating black hole, embedded in plasma, will therefore always generate toroidal and poloidal magnetic fields.     

The periods of stellar models with linked poloidal-toroidal magnetic fields

First-order perturbation theory results for the changes in pulsation frequencies of a Cowling model star containing a magnetic field with both poloidal and toroidal components are presented. A toroidal field large enough to stabilize the poloidal field may reverse the sign of the frequency change caused by a purely poloidal field for some modes, including the fundamental radial mode.     

On poloidal mode coupling in the continuous spectrum of 2D equilibria

The continuous spectrum of linear ideal MHD is determined analytically in 2D magnetostatic models for coronal loops and arcades by means of a perturbation expansion. Poloidal mode coupling, induced by non-circularity of the cross-sections of the magnetic surfaces and/or variation of the plasma density along the magnetic field lines, is shown to occur in first order. The coupling is most pronounced on and near rational surfaces for particular poloidal and toroidal mode numbers and produces gaps in the continuous spectrum of ideal MHD.     

Axisymmetric magnetic fields in stars: relative strengths of poloidal and toroidal components

In this third paper in a series on stable magnetic equilibria in stars, I look at the stability of axisymmetric field configurations and, in particular, the relative strengths of the toroidal and poloidal components. Both toroidal and poloidal fields are unstable on their own, and stability is achieved by adding the two together in some ratio. I use Tayler's stability conditions for toroidal fields and other analytic tools to predict the range of stable ratios and then check these predictions by running numerical simulations. If the energy in the poloidal component as a fraction of the total magnetic energy is written as E_p / E , it is found that the stability condition is a ( E / U ) < E_p / E ≲ 0.8 where E /U is the ratio of magnetic to gravitational energy in the star and a is some dimensionless factor whose value is of order 10 in a main-sequence star and of order 10³ in a neutron star. In other words, whilst the poloidal component cannot be significantly stronger than the toroidal, the toroidal field can be very much stronger than the poloidal–given that in realistic stars we expect E / U < 10⁻⁶. The implications of this result are discussed in various contexts such as the emission of gravitational waves by neutron stars, free precession and a 'hidden' energy source for magnetars.     

The effect of asymmetry on toroidal hydromagnetic waves in a dipole field

The meridional and azimuthal electric wave fields are considered as the characteristic toroidal and poloidal components. Neglecting the exchange of energy between these fields leads to a toroidal mode wave equation which retains the principal longitudinal or asymmetric contribution. The asymmetric spectrum appears as a logical extension of the results for the symmetric field line oscillations. The model for this study consists of a dipole field magnetized plasma, whose density is commensurate with conditions in the plasmapause. Eigenperiods are calculated for a broad range of asymmetric modes. Because of the similarity in the latitudinal variation between the symmetric and asymmetric periods, it is imperative to revise current idealized magnetospheric models and incorporate such similarity in future models.     

Behandlung eines einfachen hydromagnetischen Dynamos mittels Linearisierung

The non-linear equations of the spherical α = const-dynamo are solved by a linearisation with respect to the deviation of α from the critical value. The magnitude of the induced magnetic field is derived. Representations of the toroidal and the poloidal component of the magnetic field are given.     

Axisymmetric stars with both poloidal and toroidal magnetic fields

Chandrasekhar and Prendergast have established a result which has been assumed to imply that axisymmetric stars with an internal toroidal magnetic field should have zero external poloidal field. By considering mildly singular functions, the range of solutions is increased, and models can then be constructed which have toroidal and poloidal fields in the interior and a non-zero, external, poloidal field. Both the magnetic field and its associated current are continuous everywhere.     

Energy conversions and storage caused by an unsteady poloidal flow in active solar regions

In this paper we discuss coupling processes between a magnetic field and an unsteady plasma motion, and analyze the features of energy storage and conversions in active region.It is pointed out that the static force-free field is insufficient for a discussion of storage processes, and also the pure unsteady plasma rotation is not a perfect approach. In order to analyze the energy storage, we must consider the addition of poloidal plasma motion. The paper shows that because the unsteady poloidal flow is added and coupling occurs between the magnetic field and both the toroidal and the poloidal plasma flows, an unsteady process is maintained which changes the force-free factor with time. Hence, the energy in the lower levels can be transferred to the upper levels, and a considerable energy can be stored in the active region. Finally, another storage process is given which is due to the pure poloidal flow. The article shows that even if there is no twisted magnetic line of force, the energy in the lower levels may still be transferred to the upper levels and stored there.     

A class of semi-analytical solutions for a rotating toroidal plasma

In this paper, the problem of stationary MHD flow for a rotating toroidal plasma is investigated by assuming that the entropy is a surface quantity. Then, the system of ideal MHD equations is reduced to a single second-order elliptic partial differential equation known as the modified Grad-Shafranov (or Maschke-Perrin) equation. Under the assumption that both the function,P _s andf ² are quadratic polynomials of the flux function, a class of semi-analytical solutions is obtained for a plasma contained in a perfectly conducting toroidal boundary with a rectangular cross section. The flux function, poloidal current and the generalized pressure are obtained and discussed for relevant values of the parameters.     

Ballooning modes in the inner magnetosphere of the Earth

In this paper the low-frequency ideal MHD (magnetohydrodynamical) perturbations in the inner magnetosphere of the Earth are studied. The set of partial differential equations obtained from the MHD equations in the ballooning approximation and the dipole model of the geomagnetic field is used for this purpose. These equations describe both small-scale and large-scale perturbations in the magnetospheric plasmas. In the “cold” plasma approximation the obtained equations describe poloidal and toroidal standing Alfvén modes. The account of plasma pressure leads to the appearance of an additional type of oscillations—the slow magnetosonic modes. The stability of the magnetospheric plasma with respect to the ballooning perturbations was analyzed. We describe the ballooning perturbations taking into account a coupling between the poloidal Alfvén modes and the slow magnetosonic modes.     

Quarter-wave ULF pulsations

Recent theoretical work has predicted the possible existence of “quarter-wave” ULF pulsation resonances, in which the wave electric field has a near-node in one ionosphere and an antinode in the conjugate ionosphere. Eigenvalues are derived for quarter-wave toroidal and guided poloidal resonances for a range of L-values and plasma density distributions. From these eigenvalues, resonant periods can be obtained.Three pulsation events with anomalously long periods (when interpreted as half-waves) are examined in the light of these results. It is decided that only one event is a good candidate for quarter-wave status; this event seems likely to be a driven resonance effectively in the quarter-wave guided poloidal mode.     

Observations of magnetic flux compression in jet impact experiments

The astrophysical jet experiment at Caltech generates a T=2–5 eV, n=10²¹–10²² m⁻³ plasma jet using coplanar disk electrodes linked by a poloidal magnetic field. A 100 kA current generates a toroidal magnetic field; the toroidal field pressure inflates the poloidal flux surface, magnetically driving the jet. The jet travels at up to 50 km/s for ∼20–25 cm before colliding with a cloud of initially neutral gas. We study the interaction of the jet and the cloud in analogy to an astrophysical jet impacting a molecular cloud. Diagnostics include magnetic probe arrays, a 12-channel spectroscopic system and a fast camera with optical filters. When a hydrogen plasma jet collides with an argon target cloud, magnetic measurements show the magnetic flux compressing as the plasma jet deforms. As the plasma jet front slows and the plasma piles up, the density of the frozen-in magnetic flux increases.     

P – ω Dynamo in Spherical Geometry

Based on the fundamental P – ω dynamo equation, using spherical polar coordinates, we carry out a study of turbulent plasma wave dynamo effect. For various rotation laws, different analytical solutions are derived. In the cases of no rotation and rigid rotation, the dynamo generates poloidal field only, while with differential rotation, regardless the differential rotation is radial or latitudinal, poloidal and toroidal fields are all generated. We may think that the solutions are the analytical forms of the magnetic field in a turbulent source region of celestial bodies. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Origin of Jets from Young Stars: Steady State Disk Wind Models Confronted to Observations

We discuss in this contribution constraints on the origin of mass-loss from young stars brought by recent observations at high angular resolution (0.1″ = 14 AU) of the inner regions of winds from T Tauri stars. Jet widths and collimation scales, the large extent of the velocity profile as well as the detection of rotation signatures agree with predictions from extended (R _e ≥ 1 AU) magneto-centrifugal disk wind ejection models. Detected poloidal and toroidal velocities imply large ejection efficiencies (ξ ? 0.05, λ ? 10), suggesting that thermal gradients (originating in an accretion heated disk corona for example) play an important role in accelerating the flow.     

Hydrodynamic model of spatial and temporal variations of poloidal and Toroidal components of three-dimensional solar flows

Numerical simulation results of the global solar flows are presented. The conclusion on the common hydrodynamic nature of the torsional oscillations and spatial-temporal variations of the poloidal flow was made. Both processes were shown to be toroidal and poloidal components of a single hydrodynamic oscillatory flow that is asymmetric about the solar equator. The basis for these processes is the physical mechanism of the loss of stability of the solar differential rotation.     

On axisymmetric hydromagnetic equilibria

The physical characteristics of possible axisymmetric equilibria are examined on the basis of the integrals of hydromagnetic equations. It is shown for nearly spherical configurations that a surface differential rotation is possible only in the absence of a meridional circulation with either purely toroidal or purely poloidal magnetic field. In the presence of a meridional circulation, it is shown that no surface rotation or constant rotation is possible if the magnetic field is purely toroidal, and that no rotation is possible if the magnetic field is purely poloidal. A brief discussion is given on the possible solutions including the case of stellar winds with force-free magnetic fields.The National Center for Atmospheric Research is sponsored by the National Science Foundation.