Distribution function of relativistic electrons in a strong magnetic field

The motion and radiation of relativistic particles with radiation reaction in a strong magnetic field has been considered. The kinetic equation determining the relaxation of the distribution function with radiation reaction has been investigated. The universal one-dimensional distribution function is found to which any isotropic ultrarelativistic distribution in a strong magnetic field is relaxed. It is of power type ^–3 for ultrarelativistic energies mc ². Estimations are made which indicate that under the pulsar conditions the one-dimensional electron distribution function is likely formed due to radiation losses while for ions the one-dimensionalization is associated with the conservation of the adiabatic invariant.     

Unsteady flow of a relativistic radiating gas in a gravitational field

The unsteady flow of a relativistic radiating neutrino gas is studied in a gravitational field. The curved body is assumed to be a vertical flat plate on which is imposed a time-dependent perturbation on a basic flow. For small perturbations, the ill-posed problem is reduced to a well-posed one and analytical solutions are developed.     

Gnetic wave instability in a plasma ith relativistic particles in a random magnetic field

A new mechanism, which accounts for the direct excitation of electromagnetic waves by relativistic particles moving in random magnetic fields, is considered. We are then able to study maser-type wave excitations by slightly anisotropic particle distribution functions as well as electromagnetic wave emissions in beam-plasma interactions     

Propagation of cylindrical relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of cylindrical relativistic shock waves in the presence of a constant azimuthal magnetic field or in its absence for the medium, where the nucleon number density is uniform. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Propagation of plane relativistic shock waves in the presence of a magnetic field

In this paper we obtain similarity solutions for the propagation of plane relativistic shock waves in the presence of a transverse magnetic field for the medium, where the nucleon number density obeys a power law of distance from the plane of explosion. The shock surface moves with constant velocity and the total energy of the disturbance is dependent on time. The solutions are applicable only to an isothermal medium or a cold gas.     

Effect of a magnetic field on the spectrum of relativistic electrons in a plasma turbulent reactor

Conclusions Our study shows the universality of the power-law spectrum with =3 in PTR in the presence of a magnetic field. This result is important to astrophysical applications because there is no doubt that magnetic fields are present in many different types of cosmic objects. This universality can be compared with the known statistical analysis of the spectra of various cosmic radio sources (Fig. 5); the most probable value is close to =3. The spread in the observed values of could be due to the escape of particles, nonuniformity, and so on, and requires further study.Moscow Institute of Engineering Physics. Translated from Astrofizika, Vol. 12, No. 1, pp. 107–120, January–March, 1976.     

Energy spectrum of HeII in a strong magnetic field and bound-bound transition probabilities

The ground state energy of the Heii (singly ionized helium) atom is determined in magnetic fields up to 10¹² G. The 13 lowest excited states and bound-bound transition probabilities are calculated in magnetic fields from 10⁷ to 10⁹ G.     

Partially degenerate nonrelativistic isothermal gas spheres in the presence of a magnetic field

The effect of a weak poloidal magnetic field on the equilibrium structure of a partially degenerate nonrelativistic isothermal gas sphere has been studied. Models have been computed for varying degrees of central degeneracy and the effect of the magnetic field on the various parameters, e.g., mass, central condensation, moment of inertia, and oblateness has been looked into. It is found that as the central degeneracy parameter is increased, the central condensation in general decreases and, hence, the eccentricity of the configuration decreases.     

An explosion in non-ideal gas with magnetic field,II

Similarity solutions for a point explosion in a non-ideal gas, are investigated in the presence of magnetic field. The shock ahead of the point explosion is assumed to be strong. The energy of the expanding wave has been assumed to be time-dependent obeying a power law. The equation of state in the suitable form for such gases is found to be fairly accurate at low density region.     

The motion of the cylindrical-symmetrical relativistic shock wave in the presence of an axial magnetic field

Some observed astrophysical phenomena, such as the blast of a supernova, suggest the necessity to study the motion of shock waves in a relativistic fluid flow in the presence of a magnetic field. This paper deals with the motion of a special relativistic shock wave which propagates from the center line outwardly after an explosion with the assumption that the magnetic field which has an axial component only. Similarity solutions which depend on the parameter =r/t are constructed. Two special cases are then studied in detail. In the first case, there is an ultrarelativistic fluid in front of the shock and in the second case, there is a cold fluid in front of the shock.     

Energy spectra of particles accelerated in a reconnecting current sheet with the guiding magnetic field

Electron and proton acceleration by a super-Dreicer electric field is investigated in the non-neutral reconnecting current sheet (RCS) with a non-zero longitudinal component of the magnetic field ('guiding field'). The guiding field is assumed parallel to the direction of electric field and constant within an RCS. The other two magnetic field components, transverse and tangential, are considered to vary with distances from the X null point of an RCS. The proton and electron energy spectra are calculated numerically from a motion equation using the test particle approach for model RCSs with constant and variable densities. In the presence of a strong or moderate guiding field, protons were found fully or partially separated from electrons at ejection from an RCS into the opposite, 'electron' and 'proton', semiplanes. In the case of a weak guiding field, both protons and electrons are ejected symmetrically in equal proportions as neutral beams. The particles ejected from an RCS with a very weak or very strong guiding field have power-law energy spectra with spectral indices of about 1.5 for protons and 2.0 for electrons. For a moderate guiding field, the energy spectra of electrons ejected into the opposite semiplanes are mixed, i.e. in the 'electron-dominated' semiplane power-law energy spectra for electrons and thermal-like for protons, while in the 'proton' semiplane they are symmetrically mirrored.     

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.     

Propagation of low frequency electromagnetic waves in a relativistic electron gas

In this paper the propagation of low frequency electro-magnetic waves with large amplitudes in a magnetized plasma is discussed. It is shown that penetration of the magnetic-dipole radiation in the medium of the Crag Nebula seems possible     

A computation of the equation of state for a Fermi gas

Calculation of equation of state in stellar interiors becomes difficult as contained gas deviates from perfect gas. We present a method for the calculation of electron pressure in terms of density and temperature in the presence of degeneracy. The method is applicable forT<10⁹ K, and requires complete ionization.     

Transient flow of a relativistic radiating gas past a horizontal plate

The problem of unsteady flow of a relativistic radiating neutrino gas is studied by imposing a time-dependent perturbation on a basic flow. When the perturbation is small, the problem, which is ill-posed, is reduced to a well-posed spatial value problem for the transverse velocity and the temperature. Subsequently the axial velocity and number density may be obtained by straightforward integration with respect to time and imposition of the initial condition. The solution for the initial value problem is tackled by the Laplace transform technique and the results are discussed quantitatively.     

Plane relativistic shock waves at the edge of a gas

Similarity solutions for propagation of plane relativistic shock waves through a medium of decreasing nucleon density and approaching the edge of the gas as well as for the subsequent motion of the gas after the shock front arrives at the vacuous boundary are studied in this paper. The medium in the pre-disturbed stage is assumed cold and in the disturbed stage its equation of state is taken as that of a photonic gas.     

Line formation in a magnetic field

The effect of noncoherent scattering is examined for an absorption line formed in a uniform magnetic field. It is shown that the Stokes parameters of the line radiation may be computed by using the line source function in the absence of a magnetic field as a first approximation for that in the presence of a magnetic field.