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DIRECTED
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Journal of Directed Energy

Volume 5, Number 1 
Spring 2013 


The papers listed below constitute Volume 5, Number 1 of the Journal of Directed Energy. Print copies of issues of the Journal of Directed Energy are available through the online store.. DEPS members enjoy access the complete technical papers through links in the paper titles. Members should sign in to their online account and return to this page to access this additional content.  Join DEPS 
Elemental Theory of a Relativistic Magnetron Operation: Dispersion Diagram
Andrey D. Andreev, Kyle J. Hendricks, Shawn Soh, Mikhail Fuks, and Edl Schamiloglu; Raytheon Missile Systems and other affiliations
The cold dispersion diagram (resonant frequencies) of the Sband and Lband sixcavity
(A6) relativistic magnetrons are calculated assuming that (1) the A6 resonant
system has either a solid or transparent cylindrical cathode inside and no output irises,
and (2) the A6 resonant system with the solid cylindrical cathode is coupled (opened) via
either one (the classical MITA61 magnetron) or three (the AFRLA63 magnetron)
output capacitive iris(es), situated at the back of the anode resonant cavity(ies), with the
output waveguide(s). Results of the calculations show that when the solid cylindrical
cathode is replaced by the transparent cylindrical cathode, the dispersion diagram of the
closed (without output irises and waveguides) A6 resonant system is not significantly
changed and approximates that of the A6 resonant system without a cathode, when the
width of the interaction space (the distance between the cathode and the anode) is large
enough. Otherwise, when the width of the interaction space is small enough, the
dispersion diagram is significantly modified. Calculations of resonant frequencies of the
open (with output irises and waveguides) AFRLA63 resonant system with the solid
cylindrical cathode show that its dispersion diagram corresponds to that of a risingsun
magnetron, where the frequency of the p mode is significantly lower than the frequency of
the p mode of the closed symmetrical A6 resonant system.
KEYWORDS: Resonant cavity, Induced RF field, Mode pattern, Resonant frequencies, Dispersion diagram
PAGES 141

Progress in First Principles Modeling of HPM Effects
Larry D. Bacon, Jeffery T. Williams, Michael J. Walker, and Alan Mar; Sandia National Laboratories
The past few decades of research into radiofrequency directed energy (RFDE) have
witnessed the development of analytical and computational tools for modeling highpower
microwave (HPM) effects that are capable of nearly complete electrical and
mechanical characterizations of entire systems. These developments include advances in
numerical electromagnetics and semiconductor physics, multiphysics modeling, meshing
and gridding tools, and sheer computing power. We have progressed from analyzing
nearly canonical coupling problems to fully coupled, electromagneticelectrothermaldevice
physics models of small but realistic systems. At this juncture, we ask, How
deterministic can we make our assessment of RFDE effects? We must be able to
estimate, within acceptable bounds, the variability and repeatability of RFDE effects.
Even with precise knowledge of the physical geometry of the target, significant variability
and strong orientation dependence of RFDE effects remain due to the multiple ports of
entry feeding the terminal pairs of interest. This paper explores our progress in predicting
endtoend effects from first principles, defined as follows: modeling as much of the
physics as necessary to capture the significant effects in a specific problem. We focus on
the derivation, implementation, and validation of an active Thevenin equivalent network
approach (ATHENA) to solving the linear coupling and nonlinear circuit response selfconsistently
and efficiently.
KEYWORDS: HPM effects prediction, Multiport equivalent circuit, Modeling
PAGES 4250

Nonlinear Transmission Line Performance under Various Magnetic Bias Environments
J.W. Braxton Bragg, James C. Dickens, and Andreas A. Neuber; Texas Tech University,
Nonlinear transmission lines (NLTLs) loaded with ferrimagnetic materials act as solidstate
sources capable of generating subnanosecond risetime pulses and megawattlevel
microwave oscillations depending on the specific geometries, materials, and external
bias fields. NLTLs stand apart from other highpower microwave (HPM) sources such as
vacuum HPM tubes in the sense that they are able to operate at internally ambient or
higher pressures, are cost effective, and occupy relatively small volumes. Microwave
oscillations are formed through constructive interaction between an incident pulse and
an external magnetic bias field causing damped gyromagnetic precession of the ferrites
magnetic moments. The LandauLifshitzGilbert equation describes the magnetic moment
dynamics, and evaluation of this equation reveals that the bias field greatly affects
precessional magnitude and frequency. Pulse sharpening partly occurs due to the
nonlinear permeability sharply approaching unity (initially of order 1000) with the
application of a saturating pulse front. Further pulse sharpening is observed when an
external magnetic field is applied, which indicates that the magnetization dynamics and
flux reversal involved with precession also plays an important role. The shape and
magnitude of the external bias field highly affects the performance of NLTLs, and several
configurations are examined. The rise times and microwave generation are studied for a
single line having a length of 1 m with ferrites having dimensions 3 mm X 6 mm (ID X
OD) under varying bias magnitudes and lengths.
KEYWORDS: Damped gyromagnetic precession, Ferrimagnetic, Nonlinear transmission line
PAGES 5157

FarField Laser Intensity DropOuts Caused by Turbulent Boundary Layers
Stanislav Gordeyev, Jacob Cress, and Eric Jumper; University of Notre Dame
Usually aerooptical effects are quantified in a timeaveraged manner, such as timeaveraged
spatial rootmeansquare of optical path difference or timeaveraged Strehl
ratio (SR) on a target. However, for airborne freespace, laserbased communication
systems, instantaneous SR should be studied as well. An attached transonic boundary
layer, for example, provides a relatively high timeaverage SR; however, experimentally it
was discovered that it has many sharp intensity dropouts, which typically last for a
millisecond or so. Left untreated, these dropouts might lead to significant data loss,
potentially slowing down or even disrupting airborne laserbased communications. This
paper presents experimentally measured instantaneous nearfield wavefront statistics due
to laser transmission through subsonic boundary layers. The resulting farfield SR for
various flow conditions and aperture sizes are also presented. Using scaling laws for
boundary layers, a simple relation between flight conditions and the relative amount of
time when the SR drops below a prescribed threshold is developed. The model leads to
development of a method for predicting system performance for a freespace
communication system. The method is discussed along with possible approaches to using
it for designing and optimizing current and future laserbased communication systems. In
addition, statistics of the instantaneous dropouts and analysis of the relative intensity
variations caused by boundary layers are presented and discussed.
Erratum: Footnote 7 should read: Wang, M., Mani A., and Gordeyev, S., Annu. Rev. Fluid Mech. 44, 299 (2012).
KEYWORDS: Boundary layer, Communication, Laser
PAGES 5875

Simulation of AeroOptics over Conformal and Flat Window Turrets
Michael D. White, Philip E. Morgan and Miguel R. Visbal; Ohio Aerospace Institute and other affiliations
This work is focused on conformal and flat window turrets in a Mach number range of
0.35 to 0.4 and Reynolds number based on turret diameter of approximately 2 million. The
flow is solved using a hybrid Reynolds averaged NavierStokes/highfidelity implicit large
eddy simulation (hybrid RANS/LES) solution methodology. The optics are computedwith
both integration of the optical path difference and highorder integration of the parabolic
beam equations. Results of the simulation show that the conformal turret has much better
optical qualities over a far greater range of look angles than the flat window turret. At
backwardlook angles, the flat window turret may have advantages due to smaller and
more regular turbulent structures than the conformal turret. Qualitative agreement is
seen in the optics between the simulations and experiment, despite differences between
the actual tunnel environment and the simulation.
KEYWORDS: Aerooptics, Highorder compact differences, Hybrid turbulence methods, Turrets
PAGES 7692

Lasers Based on Highly Doped Lu2O3 Ceramics
Woohong Kim and others, Naval Research Laboratory and other affiliations
The performance of highly doped sesquioxidebased ceramics for highenergy, solidstate
lasers is first discussed. We also report on powder synthesis and the effect of the powder
quality and fabrication process on optical quality and lasing performance of lutetia
(Lu2O3 ) ceramic. Various powder synthesis methods such as coprecipitation and flame
spray pyrolysis, and postprocess techniques such as jet milling and ultrasonication are
also discussed to provide an efficient route to obtain finegrained ceramics that are
desirable for scaling to highpower lasers.
KEYWORDS: Ceramic lasers, Sesquioxides, Power scaling, Finegrain ceramics
PAGES 93104

Volume 5, Number 1, Journal of Directed Energy
