Hydrogen atom in intense magnetic field

The structure of a hydrogen atom situated in an intense magnetic field is investigated. Three approaches are employed. An elementary Bohr picture establishes a crucial magnetic field strength,H _a ?5×10⁹G. Fields in excess ofH _a are intense in that they are able to modify the characteristic atomic scales of length and binding energy. A second approach solves the Schrödinger equation by a combination of variational methods and perturbation theory. It yields analytic expressions for the wave functions and energy eigenvalues. A third approach determines the energy eigenvalues by reducing the Schrödinger equation to a one-dimensional wave equation, which is then solved numerically. Energy eigenvalues are tabulated for field strengths of 2×10¹⁰G and 2×10¹² G. It is found that at 2×10¹² G the lowest energy eigenvalue is changed from ?13.6 eV to about ?180 eV in agreement with previous variational computations.     

Neutrino luminosity by the ordinary URCA process in an intense magnetic field

The neutrino luminosity by the ordinary URCA process in a strongly magnetized electron gas is computed. General formulae are presented for the URCA energy loss rates for an arbitrary degree of degeneracy. Analytic expressions are derived for a completely degenerate, relativistic electron plasma in the special case of neutron-proton conversion. Numerical results are given for more general cases.The main results are as follows: the URCA energy loss rates are drastically reduced for the regime of great degeneracy by a factor up to 10^–3 for 1, andT ₉10, where =H/H _q ,H _q =m ² c ³/eh=4.414×10¹³ G. In the non-degenerate regime the neutrino luminosity is enhanced approximately linearly with for the temperature range 1T ₉10. Possible applications to white dwarfs and neutron stars are briefly discussed.We have been recently informed that in Gamow home-dialect (Odessa dialect) URCA means thief — (Private communication from Prof. G. Wataghin).     

Neutrino reactions in strong magnetic field

We present the energy losses due to several neutrinos processes: (1) synchrotron neutrinos, (2) pair annihilation neutrinos, (3) plasmon neutrinos, and (4) photoneutrinos in the presence of a superstrong magnetic field. Numerical results are tabulated and illustrated for several values of densities and temperatures. In the low density regime (10⁷ g cm^–3) the presence of a magnetic field decreases the luminosity, whereas the opposite is true at higher densities. This last effect is however almost entirely due to the existence of a new process the synchrotron neutrinos that disappear whenH0. Even though the overall effect can only be quantitatively ascertain after a complete cooling computation is performed, one should however expect a much lower temperature for neutron star surface than the one computed in theH=0 case.     

Vertical motions in an intense magnetic flux tube

In a recent discussion of intense photospheric magnetic fields we gave an expansion procedure that lead to a tractible system of differential equations governing vertical motions in a slender flux tube embedded in a quiescent environment. Transverse variations were taken into account in our discussion. In support of this expansion scheme we considered the special case of a straight flux tube in a uniform atmosphere. Wilson (1978, 1979b) has now criticised our treatment of this special case. We discuss his objections here, and show them to be without foundation.The cause of the disparity between our results and his lies not in a breakdown of the slender flux tube approximation but rather in the differing assumptions as to the nature of pressure variations in the tube's exterior. We generalize the slender flux tube approximation in a uniform tube, and obtain the governing dispersion relation. This dispersion relation contains, as special cases, both the results of Roberts and Webb (1978) and those of Wilson (1979a).     

Vertical motions in an intense magnetic flux tube

The recent discovery of localised intense magnetic fields in the solar photosphere is one of the major surprises of the past few years. Here we consider the theoretical nature of small amplitude motions in such an intense magnetic flux tube, within which the field strength may reach 2 kG. We give a systematic derivation of the governing expansion equations for a vertical, slender tube, taking into account the dependence upon height of the buoyancy, compressibility and magnetic forces. Several special cases (e.g., the isothermal atmosphere) are considered as well as a more realistic, non-isothermal, solar atmosphere. The expansion procedure is shown to give good results in the special case of a uniform basic-state (in which gravity is negligible) and for which a more exact treatment is possible.The form of both pressure and velocity perturbations within the tube is discussed. The nature of pressure perturbations depends upon a critical transition frequency, _p , which in turn is dependent upon depth, field strength, pressure and density in the basic (unperturbed) state of the tube. At a given depth in the tube pressure oscillations are possible only for frequencies greater than _p for frequencies below _p exponentially decaying (evanescent) pressure modes occur. In a similar fashion the nature of motions within the flux tube depends upon a transition frequency, _v . At a given depth within the tube vertically propagating waves are possible only for frequencies greater than _v ; for frequencies below _v exponentially decaying (evanscent) motions occur.The dependence of both _v and _p on depth is determined for each of the special cases, and for a realistic solar atmosphere. It is found that the use of an isothermal atmosphere, instead of a more realistic temperature profile, may well give misleading results.For the solar atmosphere it is found that _v is zero at about 12 km above optical depth ₅₀₀₀= 1, thereafter rising to a maximum of 0.04 s^–1 at some 600 km above ₅₀₀₀ = 1. Below ₅₀₀₀ = 1, in the convection zone, _v has a maximum of 0.013 s^–1. The transition frequency, _p , for the pressure perturbations, is peaked at 0.1 s^–1 just below ₅₀₀₀ = 1, falling to a minimum of 0.02 s^–1 at about one scale-height deeper in the tube     

Vertical motions in an intense magnetic flux tube

Solar Physics - The nature of convective instability in a slender magnetic flux tube is explored. A sufficient condition for stability is derived for the case of anarbitrary temperature profile in...     

Vertical motions in an intense magnetic flux tube

It is of interest to examine the effect of radiative relaxation on the propagation of waves in an intense magnetic flux tube embedded in a stratified atmosphere. The radiative energy loss (assuming Newton's law of cooling) leads to a decrease in the vertical phase-velocity of the waves, and to a damping of the amplitude for those waves with frequencies greater than the adiabatic value ( ) of the tube cut-off frequency. The cut-off frequency is generalized to include the effects of radiative relaxation, and allows the waves to be classified as mainly progressive or mainly damped. The phase-shift between velocity oscillations at two different levels and the phase-difference between temperature and velocity perturbations are compared with the available observations.Radiative dissipation of waves propagating along an intense flux tube may be the cause of the high temperature (and excess brightness) observed in the network.     

The spontaneous magnetic field direction in an anisotropic MHD dynamo

The phenomenon of magnetic field generation in an astrophysical plasma in the frame of developed magnetohydrodynamic (MHD) turbulence is considered. The functional quantum field renormalization group approach is applied to helical anisotropic MHD developed turbulence which is stabilized by the self-generated homogeneous magnetic field. The purpose of the study is to calculate the value as well as direction of the magnetic field in the stochastic dynamo model. The generated magnetic field is determined by ignoring divergent rotor part of Green function of the magnetic field. It is shown that the magnetic field direction is connected with unique existing vector n describing the anisotropic turbulence forcing.     

The flow field in a force-free magnetic field

We have obtained a complete set of the zeroth-order equations for a force-free field at large magnetic Reynolds numbers. One of the equations has often been overlooked in previous works. We discuss the question of uniqueness of solution of the Cauchy problem and outline a general method of solution in the plane and axisymmetric cases.     

The effect of a magnetic field on an adiabatic explosion

As a paradigm for various explosive processes in the interstellar medium we consider the problem of an adiabatic explosion into a uniform magnetic field which is frozen to the gas. A typical numerical run is described and reveals the following features. The outer shock becomes oblate with respect to the field lines whereas the inner hot gas prolate density and temperature contours. During the later stages the shock weakens and the explosion comes into equilibrium with the interstellar medium. The dominant feature at this stage is a concentration of accelerated material at each pole. We then try to interpret this analytically, considering the magnetic field as a small perturbation to a spherical explosion. This enables us to derive a formula for the eccentricity, which is proportional tot ^6/5. However, the linear perturbation is singular at the centre and needs to be matched to a self-similar flow there, for which we give an approximation. This similarity solution is eventually important outside the region occupied by the material initially responsible for the explosion. We give some discussion of the various asymptotic regimes involved.     

Motion and radiation of electrons in an inhomogeneous magnetic field

The motion and radiation of electrons in the neighbourhood of a neutral sheet are discussed. Formulae for the synchroton and cyclotron radiations in an inhomogeneous field are given. These results are compared with the radiations in a homogeneous field. It is predicted that the momentum of charged particles flying from the neutral sheet may take discrete eigenvalues.     

Radiative losses in a magnetostatic and intense electromagnetic field

The average energy radiation rate is calculated exactly for the case of a charged particle injected with arbitrary momentum into an intense electromagnetic field which is propagating along a uniform magnetostatic field. The treatment is relativistic.     

Material flows of an evolving magnetic field

The possibility of material flows to trace out the magnetic field configuration is examined through numerical simulations. In particular, the evolution of a magnetic arcade due to differential motions of its footpoints is considered. With the use of numerical scheme based on the method of projected characteristics and newly derived proper boundary conditions, it is shown that material flows develop to outline the configuration of evolving magnetic field. Physical implications of the results are discussed.     

Local solar magnetic and velocity field development and related photospheric and chromospheric activity

We have compiled the results of our long-term studies of the local magnetic field and its activity development, derived from investigating sunspot group evolution, photoelectrically measured longitudinal magnetic and velocity fields, and measurements of sunspot proper motions. We estimate certain regularities according to which the magnetic and velocity fields, and photospheric, as well as chromospheric activities develop. We speculate about the physical background of such processes.Dedicated to Cornelis de Jager     

Strong cosmic-ray scattering in an anisotropic random magnetic field

We calculate the kinetic coefficients and the transport mean free paths of high-energy particles parallel to the regular magnetic field in the approximation of a large-scale anisotropic random magnetic field by using a nonlinear collision integral, i.e., by taking into account the processes of strong random scattering. We consider the diffusion of solar and Galactic cosmic rays by two-dimensional turbulence. Strong random scattering by two-dimensional turbulence is shown to reduce the parallel transport mean free path several fold. The momentum dependence of the parallel mean free path does not change, Λ_∥ ∝ p^2?v. In the case of strong random scattering by turbulence formed by several modes, the parallel transport mean free path is Λ_∥ ∝ p. We show that two-dimensional turbulence can make a major contribution to the parallel transport mean free paths of cosmic rays in the heliosphere and the interstellar medium.     

The instability of a horizontal magnetic field in an atmosphere stable against convection

The theoretical problem posed by the buoyant escape of a magnetic field from the interior of a stably stratified body bears directly on the question of the present existence of primordial magnetic fields in stars. This paper treats the onset of the Rayleigh-Taylor instability of the upper boundary of a uniform horizontal magnetic field in a stably stratified atmosphere. The calculations are carried out in the Boussinesq approximation and show the rapid growth of the initial infinitesimal perturbation of the boundary. This result is in contrast to the extremely slow buoyant rise of a separate flux tube in the same atmosphere. Thus for instance, at a depth of 1/3R beneath the surface of the Sun, a field of 10² G develops ripples over a scale of 10³ km in a characteristic time of 50 years, whereas the characteristic rise time of the same field in separate flux tubes with the same dimensions is 10¹⁰ years. Thus, the development of irregularities proceeds quickly, soon slowing, however, to a very slow pace when the amplitude of the irregularities becomes significant. Altogether the calculations show the complexity of the question of the existence of remnant primordial magnetic fields in stellar interiors.This work was supported in part by the National Aeronautics and Space Administration under Grant NGL 14-001-001     

The large-scale solar magnetic field

The large-scale photospheric magnetic field, measured by the Mt. Wilson magnetograph, has been analyzed in terms of surface harmonics (P _n ^m )()cosm and P _n ^m ()sinm) for the years 1959 through 1972. Our results are as follows. The single harmonic which most often characterized the general solar magnetic field throughout the period of observation corresponds to a dipole lying in the plane of the equator (2 sectors, n = m = 1). This 2-sector harmonic was particularly dominant during the active years of solar cycles 19 and 20. The north-south dipole harmonic (n = 1, m = 0) was prominent only during quiet years and was relatively insignificant during the active years. (The derived north-south dipole includes magnetic fields from the entire solar surface and does not necessarily correlate with either the dipole-like appearance of the polar regions of the Sun or with the weak polar magnetic fields.) The 4-sector structure (n = m = 2) was prominent, and often dominant, at various times throughout the cycle. A 6-sector structure (n = m = 3) occasionally became dominant for very brief periods during the active years. Contributions to the general solar magnetic field from harmonics of principal index 4 n 9 were generally relatively small throughout this entire solar cycle with one outstanding exception. For a period of several months prior to the large August 1972 flares, the global photospheric field was dominated by an n = 5 harmonic; this harmonic returned to a low value shortly after the August 1972 flare events. Rapid changes in the global harmonics, in particular, relative and absolute changes in the contributions of harmonics of different principal index n to the global field, imply that the global solar field is not very deep or that very strong fluid flows connect the photosphere with deeper layers.The National Center for Atmospheric Research is sponsored by the National Science Foundation.