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At least 325 records · Page 18

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NASA NTRS1971

Extreme ultraviolet flashes of solar flares observed via sudden frequency deviations - Experimental results.

Properties of solar-flare EUV flashes are described as inferred from ionospheric events called sudden frequency deviation (SFD). SFD's are sensitive to bursts of radiation in the 1-1030 A wavelength range. He II 303.8 A, O V 629.7 A, H L-gamma 972.5 A and C III 977.0 A have essentially the same impulsive time dependence as the 1-1030 A flash responsible for SFD's. Soft X-rays (2-20 A) and certain EUV lines have a much slower time dependence than the 1-1030 A flash. Most SFD's have some fine structure, but marked quasi-periodicity in EUV flashes is quite rare. EUV flashes are closely associated with hard X-ray bursts, white-light emission, microwave radio bursts and small bright impulsive kernels in the H-alpha flare. The intensity of EUV flashes depends on the central meridian distance of the H-alpha flare location; the intensity decreases at the limb.

Donnelly, R. F.↗

NASA NTRS1972

Quantum-mechanical transport equation for atomic systems.

A quantum-mechanical transport equation (QMTE) is derived which should be applicable to a wide range of problems involving the interaction of radiation with atoms or molecules which are also subject to collisions with perturber atoms. The equation follows the time evolution of the macroscopic atomic density matrix elements of atoms located at classical position R and moving with classical velocity v. It is quantum mechanical in the sense that all collision kernels or rates which appear have been obtained from a quantum-mechanical theory and, as such, properly take into account the energy-level variations and velocity changes of the active (emitting or absorbing) atom produced in collisions with perturber atoms. The present formulation is better suited to problems involving high-intensity external fields, such as those encountered in laser physics.

Berman, P. R.↗

NASA NTRS1972

Variational solutions by the use of stepwise constant functions. I - Linear case.

Demonstration that accurate solutions to the integral equation or to the extremal function can be easily obtained by the variational method in many cases when a stepwise constant function is used for the trial function. The evaluation procedure is simple and straightforward; integrals of the kernel function can be evaluated analytically; the method provides, when the solution involves singularities, the best mean value across the singularity; the results are accurate in both the detailed physical quantities and their averages; the resultant solution can be further integrated analytically over the parameters associated with the problem; and the method can be readily applied to nonlinear integral equations.

Yoshikawa, K. K.↗

NASA NTRS1972

General theory of spherically symmetric boundary-value problems of the linear transport theory.

A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.

Kanal, M.↗

NASA NTRS1972

A sandwich plate with a part-through and a debonding crack.

The stress analysis of a metal base plate stiffened by a fiber-reinforced composite layer is considered. It is assumed that the two materials are bonded through an adhesive of constant thickness which is treated as a two-dimensional shear spring in the analysis. The metal plate is assumed to contain a through crack of finite length. The composite plate has no flaws. However, due to the high stress concentration around the crack and on the interface, a debonding crack is assumed to exist, encircling the crack in the base plate. The problem is reduced to a pair of integral equations of the second kind with Fredholm-type kernels. By solving these equations the stress intensity factor in the base plate, the boundary of the debonding crack, and the interface shear stresses acting on the adhesive are calculated.

Erdogan, F.↗

NASA NTRS1972

Limb radiance inversion: Iterative convergence for a nonlinear kernal

The features of the limb inversion problem that differentiate it from the nadir problem are described; the most important of these are the sharply peaked weighting functions and the nonlinear kernel that arises because the atmosphere is required to be in hydrostatic balance. The problem may be split into two parts: given the pressure at one level and the measured radiances, can the temperatures be retrieved? And how can the pressure be obtained at one level? The second problem is shown to depend on the first, which is solved iteratively. The convergence properties and final accuracies are presented. Inversion to obtain trace constituents is briefly discussed.

Gille, J. C.↗

NASA NTRS1973

Two bonded half planes with a crack going through the interface

The plane problem of two bonded elastic half planes containing a finite crack perpendicular to and going through the interface is considered. The problem is formulated as a system of singular integral equations with generalized Cauchy kernels. Even though the system has three irregular points, it is shown that the unknown functions are algebraically related at the irregular point on the interface and the integral equations can be solved by a method developed previously. The system of integral equations is shown to yield the same characteristic equation as that for two bonded quarter planes in the general case of the through crack, and the characteristic equation for a crack tip terminating at the interface in the special case. The numerical results given in the paper include the stress intensity factors at the crack tips, the normal and shear components of the stress intensity factors at the singular point on the interface, and the crack surface displacements.

Erdogan, F.↗

NASA NTRS1972

Common radiation analysis model for 75,000 pound thrust NERVA engine (1137400E)

The mathematical model and sources of radiation used for the radiation analysis and shielding activities in support of the design of the 1137400E version of the 75,000 lbs thrust NERVA engine are presented. The nuclear subsystem (NSS) and non-nuclear components are discussed. The geometrical model for the NSS is two dimensional as required for the DOT discrete ordinates computer code or for an azimuthally symetrical three dimensional Point Kernel or Monte Carlo code. The geometrical model for the non-nuclear components is three dimensional in the FASTER geometry format. This geometry routine is inherent in the ANSC versions of the QAD and GGG Point Kernal programs and the COHORT Monte Carlo program. Data are included pertaining to a pressure vessel surface radiation source data tape which has been used as the basis for starting ANSC analyses with the DASH code to bridge into the COHORT Monte Carlo code using the WANL supplied DOT angular flux leakage data. In addition to the model descriptions and sources of radiation, the methods of analyses are briefly described.

Warman, E. A.↗

NASA NTRS1973

Interaction between a circular inclusion and an arbitrarily oriented crack

The plane interaction problem for a circular elastic inclusion imbedded into an elastic matrix which contains an arbitrarily oriented crack is considered. Using the existing solutions for the edge dislocations as Green's functions, first the general problem of a through crack in the form of an arbitrary smooth arc located in the matrix in the vicinity of the inclusion is formulated. The integral equations for the line crack are then obtained as a system of singular integral equation with simple Cauchy kernels. The singular behavior of the stresses around the crack tips is examined and the expressions for the stress intensity factors representing the strength of the stress singularities are obtained in terms of the asymptotic values of the density functions of the integral equations. The problem is solved for various typical crack orientations and the corresponding stress intensity factors are given.

Erdogan, F.↗

NASA NTRS1972

X-radiation /E greater than 10 keV/, H-alpha and microwave emission during the impulsive phase of solar flares.

A study has been made of the variation in hard (E greater than 10 keV) X-radiation, H-alpha and microwave emission during the impulsive phase of solar flares. Analysis shows that the rise-time in the 20-30-keV X-ray spike depends on the electron hardness. The impulsive phase is also marked by an abrupt, very intense increase in H-alpha emission in one or more knots of the flare. Properties of these H-alpha kernels include: (1) a luminosity several times greater than the surrounding flare, (2) an intensity rise starting about 20-30 sec before, peaking about 20-25 sec after, and lasting about twice as long as the hard spike, (3) a location lower in the chromosphere than the remaining flare, (4) essentially no expansion prior to the hard spike, and (5) a position within 6000 km of the boundary separating polarities, usually forming on both sides of the neutral line near both feet of the same tube of force. Correspondingly, impulsive microwave events are characterized by: (1) great similarity in burst structure with 20-32 keV X-rays but only above 5000 MHz, (2) typical low frequency burst cutoff between 1400-3800 MHz, and (3) maximum emission above 7500 MHz.

Vorpahl, J. A.↗

NASA NTRS1973

One-dimensional line radiative transfer.

Integrations over solid angle and frequency are performed in the expressions for the radiant heat flux and local energy loss of a line in a region of strong variations of the source function in one direction. Approximations are given for coefficients and kernels in the resulting forms which involve integrals over the physical coordinate.

Harstad, K. G.↗

NASA NTRS1973

Geometry program for aerodynamic lifting surface theory

A computer program that provides the geometry and boundary conditions appropriate for an analysis of a lifting, thin wing with control surfaces in linearized, subsonic, steady flow is presented. The kernel function method lifting surface theory is applied. The data which is generated by the program is stored on disk files or tapes for later use by programs which calculate an influence matrix, plot the wing planform, and evaluate the loads on the wing. In addition to processing data for subsequent use in a lifting surface analysis, the program is useful for computing area and mean geometric chords of the wing and control surfaces.

Medan, R. T.↗

NASA NTRS1973

Plotting program for aerodynamic lifting surface theory

A description of and users manual for a USA FORTRAN IV computer program which plots the planform and control points of a wing are presented. The program also plots some of the configuration data such as the aspect ratio. The planform data is stored on a disc file which is created by a geometry program. This program, the geometry program, and several other programs are used together in the analysis of lifting, thin wings in steady, subsonic flow according to a kernel function lifting surface theory.

Medan, R. T.↗

NASA NTRS1973

Boundary condition program for aerodynamic lifting surface theory

Users manual for a U.S.A. FORTRAN 4 computer program which determines boundary conditions for a thin wing lifting surface program is described. This program, the geometry program, and several other programs are used together in the analysis of lifting, thin wings in steady, subsonic flow according to a kernel function lifting surface theory. The program calculates specific types of boundary conditions automatically such as those necessary to determine pitch and roll damping derivatives. The program also accepts descriptions of the camber or downwash and twist in the form of tables and/or coefficients of equations. The program performs interpolations so that tables and/or coefficients can apply at stations selected by the user and not at stations dictated by the control point locations.

Medan, R. T.↗

NASA NTRS1973

Influence matrix program for aerodynamic lifting surface theory

A users manual is described for a USA FORTRAN 4 computer program which computes an aerodynamic influence matrix and is one of several computer programs used to analyze lifting, thin wings in steady, subsonic flow according to a kernel function method lifting surface theory. The most significant features of the program are that it can treat unsymmetrical wings, control points can be placed on the leading and/or trailing edges, and a stable, efficient algorithm is used to compute the influence matrix.

Medan, R. T.↗

NASA NTRS1974

Normal loads program for aerodynamic lifting surface theory

A description of and users manual are presented for a U.S.A. FORTRAN 4 computer program which evaluates spanwise and chordwise loading distributions, lift coefficient, pitching moment coefficient, and other stability derivatives for thin wings in linearized, steady, subsonic flow. The program is based on a kernel function method lifting surface theory and is applicable to a large class of planforms including asymmetrical ones and ones with mixed straight and curved edges.

Medan, R. T.↗

NASA NTRS1973

Theory of microwave and X-ray emission

The behaviour of the nonthermal electrons created at the impulsive phase of flares has been deduced from the microwave impulsive bursts and hard X-ray burst by many researchers. There is almost no doubt of the emission mechanisms that radio emissions are due to gyrosynchrotron emission and hard X-rays are collisional bremsstrahlung. However, there remain three controversial problems. One is whether the emission sources of the microwave impulsive burst and hard X-ray burst are common or not. Another is whether the injection of the nonthermal electrons into the source is impulsive or continuous. The other is the relation among the nonthermal electrons, soft X-rays, EUV flash, H-alpha kernels, and white light flares. These three problems are not independent of each other.

Takakura, T.↗

NASA NTRS1973

Optical, hard X-ray, and microwave emission during the impulsive phase of flares

A study was made of the variation in hard (E greater than or equal to 10 keV) X-radiation, H-alpha, and microwave emission during the impulsive phase of solar flares. Most important, the observations showed that there is an optical impulsive component in addition to the well-known hard X-ray and microwave spikes. Properties of these H-alpha kernels are given. Further analysis shows that the rise time in the 20- to 32-keV X-ray spike depends on the slope in the electron spectrum. A picture of the impulsive phase is given that is consistent with observations of the three above emissions.

Vorpahl, J. A.↗