Photoionization measurement study

An analysis was conducted of a gas window photoionization device for studying cosmic X-rays in the region 20 eV to 1 keV. The detecting element is an argon proportional counter whose window is a two-dimensional supersonic gas jet. Spectroscopic features of the incoming radiation can be determined by the choice of gas forming the jet (as well by the fluid dynamic parameters of the flow). The choice of gas can be made from pure substances and/or compounds with Z between 1 and 10. The counter walls can be prepared for selective analysis of the extreme ultraviolet radiation

Statistical Mechanics of Charged Particles in the Pressure of Magnetic Irregularities

Statistical mechanics of charged particles in presence of magnetic irregularitie

Study of cosmic rays in the solar environment Final report, 12 Jan. 1968 - 11 Jan. 1971

Convection-diffusion equation for closed formulation of cosmic ray transport theory in solar environmen

Research in the theory of magnetohydrodynamic turbulence Final report

Analytical models for magnetohydrodynamic turbulence and unstable plasma behavio

The quantum anharmonic oscillator in the Heisenberg picture and multiple scale techniques

Multiple scale techniques are well-known in classical mechanics to give perturbation series free from resonant terms. When applied to the quantum anharmonic oscillator, these techniques lead to interesting features concerning the solution of the Heisenberg equations of motion and the Hamiltonian spectrum.Comment: 18 page

Mirroring within the Fokker-Planck formulation of cosmic ray pitch angle scattering in homogeneous magnetic turbulence

The Fokker-Planck coefficient for pitch angle scattering, appropriate for cosmic rays in homogeneous, stationary, magnetic turbulence, is computed from first principles. No assumptions are made concerning any special statistical symmetries the random field may have. This result can be used to compute the parallel diffusion coefficient for high energy cosmic rays moving in strong turbulence, or low energy cosmic rays moving in weak turbulence. Becuase of the generality of the magnetic turbulence which is allowed in this calculation, special interplanetary magnetic field features such as discontinuities, or particular wave modes, can be included rigorously. The reduction of this results to previously available expressions for the pitch angle scattering coefficient in random field models with special symmetries is discussed. The general existance of a Dirac delta function in the pitch angle scattering coefficient is demonstrated. It is proved that this delta function is the Fokker-Planck prediction for pitch angle scattering due to mirroring in the magnetic field

Aberration of the Cosmic Microwave Background

The motion of the solar system barycenter with respect to the cosmic microwave background (CMB) induces a very large apparent dipole component into the CMB brightness map at the 3 mK level. In this Letter we discuss another kinematic effect of our motion through the CMB: the small shift in apparent angular positions due to the aberration of light. The aberration angles are only of order beta ~0.001, but this leads to a potentially measurable compression (expansion) of the spatial scale in the hemisphere toward (away from) our motion through the CMB. In turn, this will shift the peaks in the acoustic power spectrum of the CMB by a factor of order 1 +/- beta. For current CMB missions, and even those in the foreseeable future, this effect is small, but should be taken into account. In principle, if the acoustic peak locations were not limited by sampling noise (i.e., the cosmic variance), this effect could be used to determine the cosmic contribution to the dipole term.Comment: 3 pages, 1 figure, comments welcome. Submitted to ApJ Letter

Test particle propagation in magnetostatic turbulence. 1. Failure of the diffusion approximation

The equation which governs the quasi-linear approximation to the ensemble and gyro-phase averaged one-body probability distribution function is constructed from first principles. This derived equation is subjected to a thorough investigation in order to calculate the possible limitations of the quasi-linear approximation. It is shown that the reduction of this equation to a standard diffusion equation in the Markovian limit can be accomplished through the application of the adiabatic approximation. A numerical solution of the standard diffusion equation in the Markovian limit is obtained for the narrow parallel beam injection. Comparison of the diabatic and adiabatic results explicitly demonstrates the failure of the Markovian description of the probability distribution function. Through the use of a linear time-scale extension the failure of the adiabatic approximation, which leads to the Markovian limit, is shown to be due to mixing of the relaxation and interaction time scales in the presence of the strong mean field

Test particle propagation in magnetostatic turbulence. 3: The approach to equilibrium

The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above

Test particle propagation in magnetostatic turbulence. 2: The local approximation method

An approximation method for statistical mechanics is presented and applied to a class of problems which contains a test particle propagation problem. All of the available basic equations used in statistical mechanics are cast in the form of a single equation which is integrodifferential in time and which is then used as the starting point for the construction of the local approximation method. Simplification of the integrodifferential equation is achieved through approximation to the Laplace transform of its kernel. The approximation is valid near the origin in the Laplace space and is based on the assumption of small Laplace variable. No other small parameter is necessary for the construction of this approximation method. The n'th level of approximation is constructed formally, and the first five levels of approximation are calculated explicitly. It is shown that each level of approximation is governed by an inhomogeneous partial differential equation in time with time independent operator coefficients. The order in time of these partial differential equations is found to increase as n does. At n = 0 the most local first order partial differential equation which governs the Markovian limit is regained