Engineering topics

Lu, Edward T.

Publications and source records attributed to Lu, Edward T..

10 records

NASA NTRS2005

Dynamic optical filtration

A dynamic optical filtration system and method effectively blocks bright light sources without impairing view of the remainder of the scene. A sensor measures light intensity and position so that selected cells of a shading matrix may interrupt the view of the bright light source by a receptor. A beamsplitter may be used so that the sensor may be located away from the receptor. The shading matrix may also be replaced by a digital micromirror device, which selectively sends image data to the receptor.

Chretien, Jean-Loup↗

NASA NTRS1993

Solar flares and avalanches in driven dissipative systems

The contention of Lu and Hamilton (1991) that the energy release process in solar flares can be understood as avalanches of many small reconnection events is further developed. The dynamics of the complex magnetized plasma of solar active regions is modeled with a simple driven dissipative system, consisting of a vector field with local instabilities that cause rapid diffusion of the field. It is argued that the avalanches in this model are analogous to solar flares. The distributions of avalanches in this model are compared with the solar flare frequency distributions obtained from ISEE 3/ICE satellite observations. Quantitative agreement is found with the energy, peak luminosity, and duration distributions over four orders of magnitude in flare energy, from the largest flares down to the completeness limit of the observations. It is predicted that the power-law solar flare frequency distributions will be found to continue downward with the same logarithmic slopes to an energy of about 3 x 10 exp 25 ergs and duration of about 0.3 s, with deviations from power-law behavior below these values.

Lu, Edward T.↗

NASA NTRS1991

Avalanches and the distribution of solar flares

The solar coronal magnetic field is proposed to be in a self-organized critical state, thus explaining the observed power-law dependence of solar-flare-occurrence rate on flare size which extends over more than five orders of magnitude in peak flux. The physical picture that arises is that solar flares are avalanches of many small reconnection events, analogous to avalanches of sand in the models published by Bak and colleagues in 1987 and 1988. Flares of all sizes are manifestations of the same physical processes, where the size of a given flare is determined by the number of elementary reconnection events. The relation between small-scale processes and the statistics of global-flare properties which follows from the self-organized magnetic-field configuration provides a way to learn about the physics of the unobservable small-scale reconnection processes. A simple lattice-reconnection model is presented which is consistent with the observed flare statistics. The implications for coronal heating are discussed and some observational tests of this picture are given.

Lu, Edward T.↗

NASA NTRS1990

Numerical solution of the time-dependent kinetic equation for electrons in magnetized plasma

A numerical solution is developed for the time-dependent kinetic equation describing the evolution of arbitrary distributions of electrons injected into a magnetized plasma. Included in the equation are pitch-angle scattering and energy loss because of Coulomb collisions and magnetic mirroring. The numerical code can be easily modified to include other scattering or radiation terms. The numerical results are shown to agree well with known analytic solutions for various simplified configurations such as homogeneous injection in a homogeneous plasma, electron beams moving with small pitch angle with respect to the magnetic field, and injection into a magnetic trap.

Hamilton, Russell J.↗

NASA NTRS1990

The relative timing of microwaves and X-rays from solar flares

The delay of microwaves relative to hard X-rays from solar flares is investigated. For short-time scale delays, it was found that for reasonable thick-target model parameters and for injected electron distributions which are separable in time, energy, pitch angle, and position, the observed delay cannot be explained by magnetic trapping of electrons in the corona. It can be accounted for if higher energy microwave producing electrons are accelerated later than lower energy hard X-ray producing electrons. For larger time-scale delays, it is found that the flux during the rising phase of the flares can be explained well in terms of the thick-target model, but during the decay phase this model predicts too little microwave flux. A number of possibilities for this excess microwave flux are explored including spectral hardening, magnetic trapping, and thermal synchrotron and free-free emission.

Lu, Edward T.↗

NASA NTRS1989

The ratio of microwaves to X-rays in solar flares - The case for the thick-target model

The expected ratio of synchrotron microwave radiation to bremsstrahlung X-rays for thick target, thin target, and multithermal solar flare models is calculated. The calculations take into account the variation of the microwave to X-ray ratio with X-ray spectral index. The theoretical results are compared with observed ratios of a sample of 51 solar flares with well known spectral index. From this it is concluded that the nonthermal thick target model with a loop length of and order of 10 to the 9th power cm and a magnetic field of 500 + or - 200 G provides the best fit to the data. The thin target and multithermal models require unreasonably large density or pressure and/or low magnetic field to match the data.

Lu, Edward T.↗

NASA NTRS1989

Development of a numerical solution to the time dependent kinetic equation

A numerical solution was developed for the time dependent Fokker-Planck equation for arbitrary distributions of electrons injected into a magnetized plasma. The code which includes energy loss and pitch angle scattering due to Coulomb collisions and changes in pitch angle due to inhomogeneous magnetic fields was calibrated and tested. The numerical method is versatile so that other scattering or radiation terms can be easily included. Using this code many processes associated with the impulsive phase of solar flares will be investigated.

Hamilton, Russell J.↗

NASA NTRS1988

The ratio of microwaves to X-rays in solar flares: The case for the thick target model

Lu, Edward T.↗

NASA NTRS1988

Rapid temporal evolution of radiation from nonthermal electrons in solar flares

Solutions of the time dependent Fokker-Planck equation was found for accelerated electrons undergoing Coulomb collisions in a magnetized, fully ionized plasma. An exact solution was found for arbitrary pitch angle and energy distribution in a uniform background plasma. Then, for an inhomogeneous plasma, a solution was found for particles with small pitch angles. These solutions were used to calculate the temporal evolution of bremsstrahlung X-rays from short bursts of nonthermal electron beams, and these spectra were compared with observed high time resolution spectra of short timescale solar hard X-ray bursts. It is shown that the observed softening in time of the spectra rules out a homogeneous background and therefore the possibility of electrons being confined to the corona either because of converging magnetic field or high densities. The inhomogeneous solution was also applied to a model with constant coronal density and exponentially rising chromospheric density. The spectra are shown to be consistent with that produced by a collimated beam of electrons accelerated in the corona with certain given conditions. These conditions could be violated if large pitch angle electrons are present.

Lu, Edward T.↗

NASA NTRS1987

Rapid temporal evolution of radiation from non-thermal electrons in solar flares

Solutions of the time dependent Fokker-Planck equation was found for accelerated electrons undergoing Coulomb collisions in a magnetized, fully ionized plasma. An exact solution was found for arbitrary pitch angle and energy distribution in a uniform background plasma. Then, for an inhomogeneous plasma, a solution was found for particles with small pitch angles. These solutions were used to calculate the temporal evolution of bremsstrahlung x-rays from short bursts of nonthermal electron beams, and these spectra were compared with observed high time resolution spectra of short timescale solar hard x-ray bursts. It is shown that the observed softening in time of the spectra rules out a homogeneous background and therefore the possibility of electrons being confined to the corona either because of converging magnetic field or high densities. The inhomogeneous solution was also applied to a model with constant coronal density and exponentially rising chromospheric density. The spectra are shown to be consistent with that produced by a collimated beam of electrons accelerated in the corona with certain given conditions. These conditions could be violated if large pitch angle electrons are present.

Lu, Edward T.↗