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DIRECTED
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Journal of Directed Energy

Volume 3, Number 4 
Summer 2010 


The papers listed below constitute Volume 3, Number 4 of the Journal of Directed Energy.
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Exposure to Backscattered Laser Radiation
George Megaloudis and Edward Early, TASC and Paul Kennedy, Air Force Research Laboratory
A laser beam propagating in the atmosphere undergoes scattering and absorption by atmospheric molecules and
suspended particles. A portion of the scattered radiation is backscattered and propagates toward the
location of the laser source. There is concern that the backscattered radiation produced by a
highenergy laser may pose ocular or skin hazards to personnel in the vicinity of the laser source. To
assess these hazards, equations are derived for the backscattered irradiance from both continuouswave
and pulsed lasers. The derivations are based on the definition of the atmospheric backscatter
coefficient and the principles of beam propagation theory. The expression for the backscatter irradiance
of a pulsed laser is shown to reduce to the LIDAR (LIght Detection And Ranging) equation under
conditions that characterize typical remote sensing scenarios. The application of the derived equations
to backscatter hazard assessments using the applicable ANSI standards for safe use of lasers is
discussed.
KEYWORDS: Aerosols, Backscatter, Backscatter coefficient, Beam irradiance, Laser safety
PAGES 289303

Use of a Finite Element/Cohesive Zone Hybrid Method for Predicting the Failure of Structural Panels Irradiated by a Laser Source
Valmiki K.Sooklal, Michael C.Larson, and Jesse McClure, University of Colorado at Colorado Springs
A computational finite element/cohesive zone hybrid method is used to simulate the fracture failure of
structural panels that are irradiated by a laser source. Results from the computations are compared to
those of experiments of laser irradiation from a CO2 laser beam on pretensioned 2014 T6 aluminum
specimens. Modified middle tension dogbone geometry specimens are subjected to a displacementcontrolled
boundary condition during irradiation. An iterative technique is employed that allows the key parameters
used in the constitutive model for the cohesive elements to be related to the thermal field induce by
the laser. The resulting computational technique accurately predicted the crack initiation and
propagation in specimens subjected to a 200W continuous beam. Peak temperatures in the range of 258 degrees C
were realized prior to failure.
KEYWORDS: Laser irradiation, Temperaturedependent cohesive elements, 3D finite element analysis, 2014 T6 aluminum
PAGES 304319

BroadSpectrum Optical Turbulence Assessments from Climatological Temperature, Pressure, Humidity, and Wind
Edward Early and George Megaloudis, TASC and Paul Kennedy and Robert J.Thomas, Air Force Research Laboratory
Previous reflected laser beam hazard evaluations have been based primarily on simplifying and overly conservative
assumptions. In the case of highenergylaser (HEL) field tests, such assumptions typically produce
reflected nominal ocular hazard distance (RNOHD) results that cannot be contained within the boundaries
of existing test ranges. This severely limits the ability to test HEL systems under operational
conditions. A methodology was developed to address the need of the laser safety community for a more
rigorous and accurate procedure to determine RNOHDs to support HEL field tests. The methodology consists
of several physically based models and is applicable to scenarios in which a single laser illuminates a
target while both move along independent trajectories. The salient features of the methodology are
consideration of reflections only in the specular direction, the use of reflecting properties of actual
materials, and calculation of exposure times for specific engagement scenarios. The equations and
procedures of the methodology are demonstrated using an example engagement scenario.
KEYWORDS: Beam propagation, Exposure time, Highenergy laser, Irradiance, Laser safety, Reflected beam, Reflected nominal ocular hazard distance (RNOHD)
PAGES 320342

ElectroOptic and MagnetoOptic Sensors for HighPower Microwave Applications
Anthony Garzarella and Dong Ho Wu, Naval Research Laboratory
Tests are described using fiberattached, alldielectric sensors for the noninvasive detection of electric
and magnetic fields. The sensors utilize nonlinear optical materials (electrooptic and magnetooptic crystals)
nd are tested in a variety of radio frequency and highpower microwave sources.
KEYWORDS: Electrooptic, HPM, Magnetooptic, Probe, Sensor
PAGES 343348

Elemental Theory of a Relativistic Magnetron Operation: Anode Current
Andrey D.Andreev and Kyle J.Hendricks, Air Force Research Laboratory (RDHPS) and Mikhail I.Fuks and Edl Schamiloglu, University of New Mexico
The analytical expression allowing one to calculate the anode current of a relativistic magnetron is derived.
The anode current is described as a cathodetoanode drift of electron guiding centers in crossed
external dc and induced RF (radio frequency) electric and magnetic fields along equipotential lines
forming a magnetron spoke. The drift velocity of the electron guiding centers is calculated in the frame
of reference moving with the phase velocity of the traveling RF wave associated with the induced RF
electromagnetic field. Electron charge density near the cathode is considered as a parameter determining
the electron guiding center charge density within the magnetron spoke. Anode current is calculated as a
product of the electron guiding center cathodetoanode drift velocity, the electron guiding center
space charge density within the magnetron spoke, and the number of magnetron spokes. Results of the
analytical calculations of the anode current of the A6 relativistic magnetron are compared with computer
PIC simulations of the anode current of this magnetron.
KEYWORDS: Anode current, Drift in crossed E X H fields, Electronguiding centers, Relativistic magnetron
PAGES 349383

Development of a FeedForward Compensation Technique to Calculate Beam Position in the Mitigation of PlatformInduced Jitter
Matthew Roberts, Joe Watkins, and Oscar Barton, Jr., U.S.Naval Academy
Beam control is essential for the development and operation of a directed energy system, especially when
operating in the air or on the sea in a combat maritime environment. Directed energy beams are
susceptible to jitter due to platforminduced vibrations and atmospheric effects. To correct jitter
caused by mechanical vibrations without feedback from the target, the exact position and orientation of
the platform must be determined in real time. A unique laser jitter control test bed is used to develop
the necessary algorithms and sensor placements that are suitable, for calculating the platforminduced
error in the directed energy beam in real time. This error can then be used in a feedforward
compensation technique to calculate the beam position that mitigates platforminduced jitter. The paper
introduces the algorithm and initial results in predicting jitter for a complex pitch motion using a
leastmeansquares adaptive filter.
KEYWORDS: Directed energy, Feed forward, Jitter, LMS filter
PAGES 384397

Adaptive Facet Reflection Modeling
Albert Bailey and Edward Early, TASC and Paul Kennedy and Robert J.Thomas, Air Force Research Laboratory
Calculating the reflected irradiances produced by a specularly reflecting object at many observation points
is computationally intensive, the total computational load proportional to the product of the number of
facets times the number of observation points. To capture specular glints at all observation points, it
is necessary to finely discretize the surface of the object into a large number of facets. This can
result in a massive number of computations. The computational load can be reduced by approximating the
surface of the object by curved triangular facets modeled as either quadric surfaces or pointnormal
triangles. Starting with a coarse discretation of the surface, a finer representation can be produced by
subdividing the initial facets. For a single observation point, only a small fraction of the surface
contributes to the specular glint; therefore only a few facets need to be significantly subdivided for
accurate computations. By adaptively subdividing, the number of facets required per observation point is
greatly reduced, resulting in fewer computations and thus increased overall computational speed. The
speed increase is illustrated for a cylindrical object and different angular widths of the specular
peak. As the width decreases, adaptive faceting increases the computational savings.
KEYWORDS: Adaptive modeling, BRDF, PN triangle, Quadric surface, Reflection modeling
PAGES 398404

Volume 3, Number 4, Journal of Directed Energy
Last updated: 6 September 2017
