Parametric instabilities in relativistic plasma

Parameteric instabilities in the relativistic plasma are considered. It is shown that in the electron relativistic plasma (T _em _0e c ²) the electron mass oscillation in the external electrical field leads to the instability of Langmuir and low frequency aperiodic oscillations as well. In the case of the hot electron ion plasma with relativistic electron temperature the low frequency aperiodic and periodic oscillations are studied. The wave increments for all considered cases are obtained.     

Neutrinooszillationen in Neutronensternmaterie

According to the suggestion of T. J. Mazurek (1979) neutrino oscillations occuring during the dynamic stellar collapse (M ≥ 10M) could be result in a transfer of leptonic zero-point energy to baryons. Then the adiabatic index increases above γ ≥ 4/3, and such an increase is necessary to reverse the collapse. From the theory of neutrino oscillations of B. Pontekorvo (1967) we derive the oszillation length L of neutrinos in vacuum and the characteristic oscillation lengh L^* of neutrinos taking into consideration the refraction index n_e of neutron star matter. The comparison of both oscillation lenghts shows that for electron densities, characteristically of neutron star matter, the oscillation lenght L is considerable larger than the oscillation lenght L^*. Therefore neutrino oscillations cannot influence the scenario for neutrino emission of the neutron star.     

Periodic orbits around an oblate spheroid

The general properties of certain differential systems are used to prove the existence of periodic orbits for a particle around an oblate spheroid.In a fixed frame, there are periodic orbits only fori=0 andi near /2. Furthermore, the generating orbits are circles.In a rotating frame, there are three families of orbits: first a family of periodic orbits in the vicinity of the critical inclination; secondly a family of periodic orbits in the equatorial plane with 0<e<1; thirdly a family of periodic orbits for any value of the inclination ife=0.     

Oscillations of a polytrope with a toroidal magnetic field

The radial and the non-radial (l=2) modes of oscillation of a gaseous polytrope with a toroidal magnetic field are examined using a variational principle. It is found that the frequencies of oscillation of the radial mode and the Kelvin mode (l=2) decrease due to the presence of the magnetic field. The shift in the frequency of the Kelvin mode may be split up into two parts, viz. the shift in frequency due to the magnetic field on the unperturbed sphere [(1²)m, say] and the shift in frequency due to the distortion of the structure by the magnetic field [(1²)s, say]. In the first order calculations using one parameter trial function, it is found that (1²)m is indeed positive but is overweighed by a negative (1²)s. In the second order calculations using a trial function with two variational parameters, we find that the general behaviour of (1²)m and (1²)s is unchanged but that (1²)m becomes negative for polytropic indicesn1.5.In Appendix I we study the effect of a small rotation and toroidal magnetic field on the structure of a polytrope. It is found that the resulting configuration is a prolate spheroid, a sphere or an oblate spheroid according as respectively. Here denotes the magnetic energy andT the kinetic energy due to rotation andq is a constant which depends on the polytropic indexn. The values ofq are given in Table I.     

The structure of the turbulent shock wave propagating in the solar atmosphere across the magnetic field

A consistent account of plasma turbulence in magnetohydrodynamics equations describing transport processes across the magnetic field is presented. The structure of the perpendicular shock wave generated in the solar atmosphere, as a result of either local disturbance of the magnetic field or dense plasma cloud motion with a frozen-in magnetic field, has been investigated. The region of parameters in the solar atmosphere at which the electron-ion relative drift velocity u exceeds the electron thermal velocity V _eand generation of radio emission becomes possible, has been determined. The plasma turbulence inside the front has been shown, under conditions of solar corona, not to cause the oscillation structure of shock front to break down. Under chromospheric conditions, the shock profile is aperiodical. Then, the condition u > V_ecan be satisfied and shock waves having an Alfvén Mach number M which exceeds the critical value M _c 3.3 for aperiodical shock waves can exist (Eselevich et al., 1971a). Arguments are given in favour of the fact that perpendicular shock waves are generated in the Sun's atmosphere when dense plasma clouds, with a frozen-in magnetic field, are expanded.     

Generation of a d.c. field by nonlinear electromagnetic waves in relativistic plasmas

A finite amplitude linearly polarized electromagnetic wave propagating in a relativistic plasma, is found to generate the longitudinal d.c. as well as the oscillating electric field at the second harmonic. In a plasma consisting of only electrons and positrons, these fields cannot be generated.The evolution of the electromagnetic waves is governed by the non-linear Schrödinger equation which shows that the electromagnetic solitons are always possible in ultra-relativistic plasmas (electron-ion or electron-positron) but in a plasma with relativistic electrons and nonrelativistic ions, these solitons exist only if 1(KT _e/m_eC²)<(2m _i/15m_e);m _e andm _i being the electron and ion mass andT _e the electron temperature. Both the d.c. electric field and the solitons provide a nonlinear mechanism for anomalous acceleration of the particles. This model has direct relevance to some plasma processes occurring in pulsars.     

Parameter distribution of small periodic librations about the equilateral points of the elliptic restricted problem

As previously shown (Rabe, 1970), two classes of small periodic librations exist, in the plane, elliptic restricted problem, for an infinite sequence of easily specified oscillation frequenciesZ _j . The present paper considers the dependence ofZ on the eccentricitye of the primary motion, in addition to its dependence on the mass parameter , and determines the resulting relations between ande, for any given periodic frequencyZ _j . These relationships are obtained from the conditionD (Z _j ,, e)=0, where the basic determinantD has been expanded up to terms of orderZ ²⁰, ⁵, ande ⁴.Presented at the Conference on Celestial Mechanics, Oberwolfach, Germany, August 27–September 2, 1972.     

The energy flux number and three types of planetary dynamo

It is proposed that the existence and nature of a planetary dynamo can be characterized by a dimensionless number Φ ≡ F_eR/ϱλ²ω, called the energy flux number, where F_e is the energy flux available for dynamo generation, R is the core radius (or thickness of the dynamo generating region), ϱ is the fluid density, λ is the magnetic diffusivity and ω is the angular velocity. For Φ ≲ 1, there is no dynamo. For 1 ≲ Φ ≲ 10^2.5 there is an “energy-limited dynamo”, in which F_e is insufficient to enable the dynamo to reach the dynamically desirable state A ≡ B²/8πϱλω ∼ 1, where B is a typical field amplitude (in Gauss). For 10^2.5 ≲ Φ ≲ 10⁵, there is a dynamically determined dynamo (Λ ∼ 1) in which the magnetic Reynolds number of turbulent eddies is small. For Φ ≳ 10⁵, there is a turbulent dynamo. Probable planetary examples of these three dynamo states are Mercury (Φ ∼ 10²-10³), Earth (Φ ∼ 10⁴) and Jupiter (Φ ∼ 10¹¹), respectively.     

The Process of Photon-Splitting and its Effect on Pulsar Emission:The Analytic Approach

Magnetic photon splitting γ → γγ, a quantum electrodynamic process that becomes important when magnetic field approaching the quantum critical value, B _c = 4.413 × 10¹³ G, may have important effects on pulsar radio emission. According to the standard model, the pulsar radio emission is produced by coherent curvature radiation of a large amounts of e ^± pairs, which are thought to be generated by the pair creation process γ + B → e ^±. However, if the magnetic field is strong enough, the photon splitting may dominate the pair creation process, then the amounts of e ^± pairs and the radio luminosity will be strongly suppressed and may be undetectable. Here we use the fitted analytical formula of the photon splitting attenuation coefficient to study the above process, and find that the photon splitting will strongly decrease the radio emission when B > 10¹³ G. We also note that the photon splitting can strongly but not totally suppress the creation of pairs due to the diminishing dependence of B in the attenuation coefficient. We find that the ratio of the probability of a photon being absorbed by photon splitting to that by pair creation is no more than about six. This revised version was published online in July 2006 with corrections to the Cover Date.     

Lower limit on pulsar birthrate set by cosmic ray positron measurements

A recent measurement of thee ⁺/(e ⁺+e ^–) ratio in cosmic rays between 5 and 50 GeV (HEAT experiment), is consistent with positron production theories via primary cosmic radiation interactions in the interstellar medium. This paper will show that atmospheric corrections result in a 50% level of uncertainty in thee ⁺/(e ⁺+e ^–) ratio measurements carried out with balloon-borne experiments. In light of the current theories on electron-positron production in neutron stars and by using different calculations for atmospheric corrections, a lower limit on Milky Way pulsar birthrate of 30–60 years can be set on the basis of recent observations of the positron fraction in cosmic rays.     

Expansions of (r/a)m cos jv and (r/a)m sin jv to high eccentricities

Expansions of the functions (r/a)^cos jv and (r/a)m ^sin jv of the elliptic motion are extended to highly eccentric orbits, 0.6627 ... <e<1. The new expansions are developed in powers of (e–e*), wheree* is a fixed value of the eccentricity. The coefficients of these expansions are expressed in terms of the derivatives of Hansen's coefficients with respect to the eccentricity. The new expansions are convergent for values of the eccentricity such that |e–e*|<(e*), where the radius of convergence (e*) is the same of the extended solution of Kepler's equation. The new expansions are intrinsically related to Lagrange's series.     

Decay of positronium in strong magnetic fields

We investigate the decay of bound electron-positron pairs (positronium) in strong magnetic fields (of order 10¹² Gauss, which are assumed for neutron stars) on the basis of a correct treatment of the two-body problem, thus improving previous work by Carr and Sutherland (1978). We find that, even in the presence of a strong magnetic field, the decay of the ground state of positronium must be momentum conserving, whereby the possibility of the one-photon decay is ruled out. We calculate the transition rate for the two-photon annihilation process which turns out to be larger than the field free transition rate by a factor (1/)² B/B _cr (where is the electromagnetic coupling constant, andB _cr=m _e ² c ²/(e)=4.41×10¹³ Gauss).     

Analytic properties of Hansen coefficients

Hansen’s coefficients in the theory of elliptic motion with eccentricity e are studied as functions of the parameter η = (1 − e ²)^1/2. Their analytic behavior in the complex η plane is described and some symmetry relations are derived. In particular, for every Hansen coefficient, multiplication by suitable powers of e and η results in an entire analytic function of η. Consequently, Hansen’s coefficients can be in principle computed by means of rapidly convergent series in powers of η. A representation of Hansen’s coefficients in terms of two entire functions of e ² follows.      

A model cosmology based on gravity-electromagnetism unification

In this article the GEM (Brandenburg, 1992; Brandenburg, 1988) theory is applied to the problem of the cosmos in which most of the matter is hydrogen, spacetime is flat, and a Cosmic Background Radiation CBR field exists. Using the two postulates of the GEM theory: 1. That gravity fields are equivalent to an array ofE ×B drifts or a spacially varying Poynting field, such that spacetime is determined by EM fields so that the stress tensor of ultrastrong fields is self-canceling; 2. That EM and gravity fields and protons and electrons are unified at the Planck scale of lengths and energies and split apart to form distinct fields and separate particles at the Mesoscale of normal particle rest energies and classical radii. A new derivation is made of the formula forG found previously:G =e ²/(m _p m _e ) exp(-2R ^1/2) = 6.668 × 10^–8 dynes cm² g^–2wherem _p andm _e are the proton and electron masses respectively,R =m _p /m _e and is the fine structure constant, shows that quantum processes may occur which make the vacuum unstable to appearance of hydrogen thus allowing matter creation and a steady state universe to occur. The value for the Hubble Time calculated from this model isT _o = (3/((2)(R ^1/2)⁴))^1/3(r _e /c)(e ²/Gm _p m _e )= 19 Gyr wherer _e =e ² / (m _e c ²)and follows the form first hypothesized by Dirac(1937). The CBR is traced to this process of matter creation and its temperature is calculated as beingT _CBR = ((3/4)Gm _e ² c/( ² _o ))^1/4 = 2.66K where is the Thomson cross section of the electron and _o is the Stefan-Boltzman constant.     

Molecular systems in a strong magnetic field

Brief overview of one-two electron molecular systems made out of protons and/or α-particles in a strong magnetic field B≤4.414×10¹³ G is presented. A particular emphasis is given to the one-electron exotic ions H₃⁺⁺(pppe), He₂³⁺(α α e) and to two-electron ionsH₃⁺(pppee), He₂⁺⁺(α α ee). Quantitative studies in a strong magnetic field are very complicated technically. Novel approach to the few-electron Coulomb systems in magnetic field, which provides accurate results, based on variational calculus with physically relevant trial functions is briefly described.      

Theoretical Ne v emission line ratios compared to solar observations

The recent level population calculations for Ne v by Aggarwal are used to determine the theoretical emission line ratios R ₁ = I(2s2p ^{3 1}D^o - 2s²2p^{2 1}D^e)/I(2s2p^{3 3}D ₂ ⁰ - 2s²2p^{2 3}P ₁ ^e ) and R ₂ = I(2s2p ^{3 1}D^o-2s²2p^{2 1}D^e)/I(2s2p ^{3 3}D ₃ ⁰ -2s²2p^{2 3}P ₂ ^e ). A comparison of these with observational data for a solar flare and erupting prominence obtained with the NRL XUV spectrograph on board Skylab reveals that R ₁ and R ₂ are in their predicted high density limits. Although the ratios cannot be used as density diagnostics for values of n _e typical of the solar transition region, it is shown that they are temperature sensitive and hence may be employed to determine the electron temperatures of Ne v line emitting regions.     

Equilibrium and stability of rotating masses with a toroidal magnetic field

We investigate the equilibrium, oscillations, and stability of uniformly rotating masses with a toroidal magnetic field, proportional with the distance to te axis of rotation. The equilibrium is an oblate or prolate spheroid according as the rotational energy is greater or smaller than the magnetic energy. The sequence of equilibrium figures exhibits a maximum value for the angular velocity in the oblate case and a maximum for the angular momentum in the prolate case. The dispersion relation is derived using Bryan's modified spheroidal coordinates. One obtains 2(n–m)+4 solutions for the oscillation frequency ifm0 and 1/2n or 1/2(n+1) solutions for ² according asn is even or odd ifm=0. The point where the Jacobi ellipsoids bifurcate from the MacLaurin sequence is unaffected by the magnetic field. However, the points of the onset of dynamical instability corresponding to the second and third harmonics and the point where a pear-shaped sequence bifurcate, depend upon the magnetic field. They are shifted to higher values for the eccentricity and can be suppressed by a sufficiently large magnetic field.     

Perturbation of the radial and non-radial oscillations of a star by a magnetic field

A generalization of the perturbation method is applied to the problem of the radial and the non-radial oscillations of a gaseous star which is distorted by a magnetic field. An expression is derived for the perturbation of the oscillation frequencies due to the presence of a weak magnetic field when the equilibrium configuration is a spheroid. The particular application to the homogeneous model with a purely poloidal field inside, due to a current distribution proportional to the distance from the axis of symmetry, and a dipole type field outside is considered in detail. The main result is that the magnetic field has a large and almost stabilizing effect on unstableg-modes, particularly on higher order modes. With the considered magnetic field the surface layers appear to have a large weight.     

Programme of the Galactic meridian: Star counts and galactic models. 1. Distributions of stellar magnitudes and colours

A comparison of observed stellar distributions with a three-component model of the Galaxy is presented. The analysis is based on photometric and photoelectric data obtained along the main Galactic meridian and in two fields near the North Galactic pole (programme MEGA). The assumed model considers the Galaxy as composed of the disk (main sequence and disk red giants), the thick disk and spheroid populations. To model the observed colour distribution, we distinguish main sequence stars and disk red giants as the disk subsystem; white dwarfs, subdwarfs and intermediate giants as the thick disk subsystem; extreme subdwarfs, spheroid giants and horizontal branch stars as the spheroid subsystem. A statistical relation between the apparent and absolute magnitudes of stars which make the maximum contribution to the star counts for a given disk subsystem is derived. In order to achieve the best agreement between the model and observations, we fit the values of the ‘dip’ (aw) of the disk luminosity function, the correction to the absolute magnitude of disk red giants (ΔM_V^RG) and the expression for interstellar extinction. As the main result, we obtained aw = 0.6 (logarithmic scale) and ΔM_V^RG = 0.5 mag; the interstellar extinction has to be taken into account by the modified Sandage law.     

The effects of intense magnetic fields on Landau levels in a neutron star

In this paper, an approximate method of calculating the Fermi energy of electrons (E _F (e)) in a high-intensity magnetic field, based on the analysis of the distribution of a neutron star magnetic field, has been proposed. In the interior of a neutron star, different forms of intense magnetic field could exist simultaneously and a high electron Fermi energy could be generated by the release of magnetic field energy. The calculation results show that: E _F (e) is related to density ρ, the mean electron number per baryon Y _e and magnetic field strength B.