ARL-TR-8055 ● JULY 2017

US Army Research Laboratory

Magneto-Hydrodynamic Simulations of a 

Magnetic Flux Compression Generator Using 

ALE3D

by George B Vunni

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ARL-TR-8055● JULY 2017

US Army Research Laboratory

Magneto-Hydrodynamic Simulations of a 

Magnetic Flux Compression Generator Using 

ALE3D

by George B Vunni

Weapons and Materials Research Directorate, ARL

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4. TITLE AND SUBTITLE

Magneto-Hydrodynamic Simulations of a Magnetic Flux Compression 

Generator Using ALE3D

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6. AUTHOR(S)

George B Vunni

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US Army Research Laboratory

ATTN: RDRL-WMP-D

Aberdeen Proving Ground, MD 21005-5066

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ARL-TR-8055

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

Magnetic flux compression is a proven technique for the generation of ultrahigh magnetic fields, large currents, and large 

energy densities. The intent is to supply a few mega-amperes of seed-current for a fast high current when large capacitor 

banks are not available. A magnetic flux device consists of coils surrounding a cylindrical armature where an explosive drives 

the armature radially and causes a drop in the inductance. In this report, the results of ALE3D magneto-hydrodynamic 

simulation of a magnetic flux compression generator designed by the US Army Research Laboratory are presented. The 

simulation results are compared with the experimental data from 3 experiments with identical generators but different seedcurrents. The simulation results show good agreement.

15. SUBJECT TERMS

magnetic flux compression, ALE3D, magneto-hydrodynamics, MHD, simulation, seed-current

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George B Vunni

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Contents

List of Figures iv

Acknowledgments v

1. Introduction 1

2. Technical Purpose and Benefits 1

3. Background 2

4. Computational Model of ARL’s MFCG Device for MHD Simulation 4

5. Simulation Results: Computational Mesh Convergence 6

6. Comparison of ALE3D Simulation with Experiment 7

7. Analysis of Simulation: Flux Compression Principle 11

8. Conclusion 15

9. Recommendations for Future Work 15

10. References 17

List of Symbols, Abbreviations, and Acronyms 18

Distribution List 19
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iv

List of Figures

Fig. 1 A cross-sectional view of MFC showing the generator and the load ... 2

Fig. 2 Experiment current profiles for seed-currents of 70, 117, and 

220 kA................................................................................................... 3

Fig. 3 Half-plane view of the geometry used in ALE3D simulation showing 

the materials.......................................................................................... 5

Fig. 4 Impact of mesh resolution on the current amplification for 70-kA 

seed-current........................................................................................... 6

Fig. 5 Comparison of ALE3D-MHD simulation (black line) and 

experimental current trace (red line) for a) 117- and b) 220-kA seedcurrents. The simulation is shifted 62 μs to account for the delay in 

the experiment....................................................................................... 8

Fig. 6 Comparison of the simulated and measured inductance evolution....... 9

Fig. 7 Generator total magnetic strength for 70-, 117-, and 220-kA s

eed-currents......................................................................................... 10

Fig. 8 Snapshots of the generator magnetic flux magnitude at 65, 75, 80, 

and 90 μs............................................................................................. 11

Fig. 9 Snapshot of the expansion angle of the armature ............................... 12

Fig. 10 Radial displacement of a point close to the armature at the axial 

position of 122 mm............................................................................. 13

Fig. 11 Radial displacement of the armature at 25-μs postdetonation time.... 14

Fig. 12 Qualitative comparison of the expanding armature at 25 us (after 

detonation): a) ALE3D simulation and b) experiment. Coil and 

crowbar are shown in the simulation image. ...................................... 14
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v

Acknowledgments

The author would like to thank Dr Robert L Doney and John Runyeon for useful 

comments and suggestions. The author would also would like to thank Dr Casey 

Uhlig and Peter Bartkowski for peer reviews of this work. Special thanks to Peter 

Bartkowski for making this work successful and providing the experimental data 

accompanying this report. Thanks also to Dr Anthony Johnson of Lawrence 

Livermore National Laboratory for lending his computational expertise and always 

being willing to have a technical discussion on modeling magnetic flux 

compression generators.

This work was supported in part by a grant of computer time from the Department 

of Defense High Performance Computing Modernization Program at the US Army 

Research Laboratory Department of Defense Supercomputing Resource Center. 
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vi

INTENTIONALLY LEFT BLANK.
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1. Introduction

Many advances in design, understanding, and performance of magnetic flux 

compression generators (MFCGs) have occurred since the concept of using high 

explosives to push a metal and compress a trapped magnetic field was first 

introduced.

1 In recent years, the US Army Research Laboratory (ARL) has been 

actively engaged in an experimental program using explosively driven MFCGs as 

pulsed-power sources for onboard Army vehicle platforms.

2 ARL’s research on 

MFCGs was initially focused on experimental development. However, recently 

there has been a shift toward developing new experiments informed by 

computational models and simulations. Previous efforts in modeling MFC (2010–

2012) using the 3-D ALEGRA magneto-hydrodynamic (MHD) code demonstrated 

continuous kinematics, current amplification, and answered questions regarding 

armature velocity on system performance, inductance scaling in helicoils, and how 

magnetic energy is partitioned among air, conductor, and explosive during 

compression. However, modeling a full device was prohibitive at the time due to 

the computational cost triggered by the then available magnetic boundary 

conditions.

3 This report presents the first successful simulation of ARL’s MFCG 

using ALE3D-MHD code.

4

The main objective of this work is to understand and analyze the mechanisms of 

ARL’s MFCG. To accomplish this, simulations were conducted using the ALE3DMHD multiphysics code developed by Lawrence Livermore National Laboratory 

(LLNL).

4 ALE3D is a multiphysics numerical simulation software tool using 

arbitrary Lagrangian-Eulerian (ALE) techniques.

4 The 3-D simulations were 

directly compared with experiments conducted at the ARL experimental facilities. 

The simulation results showed lower initial inductance but accurately predicted the 

current trace. Despite challenges to the 3-D MHD modeling, the complexity of the 

problem, and insufficient material conductivity models, the simulation result shows 

that ALE3D-MHD can provide useful insights into the generator operation that are 

otherwise unattainable from the experiment. 

2. Technical Purpose and Benefits

Numerical 3-D MHD simulation is one of the tools used for detailed understanding 

of, and a quantitative description for, physical phenomena occurring in explosively 

driven MFCG. Simulation of ARL’s current MFCG device could lead to an 

improvement in future designs and optimization. Matching measurable data to 

models is important for accurate validation.
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3. Background

Explosively driven MFCGs are compact pulsed-power sources of current and 

voltage. The interest in such devices stems from their unique capability to achieve 

very high energy densities, magnetic field strengths, and high current pulses. In a 

typical MFCG, a flux is established in a system of conductors arranged such that 

the magnetic flux is trapped. The system is explosively deformed to a smaller 

volume, thus compressing the magnetic flux and delivering electromagnetic energy 

into the connected load.

1,5 Compression of the trapped magnetic flux amplifies the 

initial seed-current (established by a small capacitor bank) injected into the coil. 

During this process, the inductance of the device rapidly decreases. In most MFCG 

devices the energy density (i.e., the ratio of the electrical energy delivered to the 

load and the MFCG volume) is typically a few joules per cubic centimeter.

The combination of high energy density and an operation on the microsecond time 

scale make the MFCG an excellent choice as part of a pulsed-power system. The 

tradeoff for the superior energy density of MFCGs compared with conventional 

pulsed-power sources is the single use nature of MFCGs.

Figure 1 illustrates a 3-D cutaway diagram, which shows the generator and the load 

section of a typical ARL-designed MFCG.

2 The generator has a length of about 

432 mm and an outer diameter of 114.30 mm. The initial inductance was 

approximately 2955 nH, and the final inductance was approximately 160 nH. The 

stator consisted of a helical coil machined from a seamless 6063-T6 aluminum tube. 

The coil was designed to have nine turns over 203.2 mm of axial length.

Fig. 1 A cross-sectional view of MFC showing the generator and the load2

The armature, a hollow metal tube filled with high explosive, was machined from 

a 6061-T6511 aluminum tube with an outer diameter of 7.62 cm. This yields an 

armature expansion ratio (final radius: initial radius) of 1.42 and an initial and final 

wall thickness of 6.4 and 4.5 mm, respectively. The explosive charge consisted of 
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a paper reinforced phenolic cylinder filled with Comp-B explosive. The phenolic 

cylinder was 25.0 cm long with an outer diameter of 6.35 cm. The Comp-B 

explosive charge filled the interior volume of a 5.08-cm diameter. The initial seedcurrent was supplied through copper stripeline from a 533-μF capacitor bank. The 

total inductance was 2955 nH with the load accounting for 160 nH, resulting in a 

theoretical lossless gain of 18.5.

Measured current profiles for seed-currents of 70 kA, 117 kA, and 220 kA are 

shown in Fig. 2, with peak-amplified currents of 414 kA, 714 kA, and 1.044 MA, 

respectively.

2 This represents current gains of 5.91, 6.10, and 4.73, respectively.2

The MFCG did not perform as well as predicted with respect to overall theoretical 

gain. The average gain for the 3 tests was 5.56 compared to a theoretical gain of 

18.5. Observation of the current plots reveals compression lasting for 

approximately 20 μs.

Fig. 2 Experiment current profiles for seed-currents of 70, 117, and 220 kA
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4. Computational Model of ARL’s MFCG Device for MHD 

Simulation

Simulations were performed using ALE3D-MHD, a 3-D multiphysics numerical 

simulation software tool using ALE techniques developed by LLNL.

4 ALE3D’s 

MHD model is capable of capturing the dynamics of electrically conducting solids 

and fluids. The MHD module was developed for the modeling of coupled electrothermal-mechanical systems that are inherently 3-D in nature.

The ALE3D-MHD module solves the resistive magnetic induction equation given 

a collection of specified current and voltage sources. The equation is solved in the 

Lagrangian frame using a mixed finite element method employing ∇ × H and ∇·H 

finite element basis functions, which preserves the solenoidal nature of the 

magnetic field. Electromagnetic force and resistive joule heating terms are coupled 

to the equations of motion and thermal diffusion in an operator split manner.

4 For 

problems that require mesh relaxation (explosively driven MFCGs), magnetic 

advection is performed using the method of algebraic constrained transport that is 

valid for unstructured hexahedral grids with arbitrary mesh velocities. The 

advection method maintains the divergence-free nature of the magnetic field and is 

second-order accurate in regions where the solution is sufficiently smooth. For 

regions in which the magnetic field is discontinuous (e.g., MHD shocks), the 

advection step is limited using the method of algebraic flux correction, which is 

local extremum diminishing and divergence preserving. Details pertaining to the 

ALE3D-MHD can be found in Anderson et al.

4

Figure 3 shows the MFCG material configuration used in the simulation, which was 

simplified by eliminating several components not significant to the physics 

investigated in the simulation. For example, it was not necessary to include the 

front-end explosive tamper (which is to diminish the resistive flux loss). 

Additionally, the capacitor bank and associated cables were not modeled directly, 

instead a direct current source applied to input region was applied. Unlike in the 

experiment, the seed-current was ramped from zero to its nominal value in 1 μs, 

kept flat for 20 μs, and then ramped back to zero. To reduce computational time, 

the seed-current was adjusted so that crowbarring (armature touching the crowbar 

and isolating the seed-current) occurred at approximately 6.5 μs. A further 

simplification included the use of copper rather than brass as reported in 

Bartkowski and Berning2 for the crowbar (a metallic cylindrical conductor used to 

short out the seed-current and trap the magnetic flux in the shrinking volume 

between the coil and armature). The material geometry shown in Fig. 3 was 

generated in Cubit6 using Python scripts,

7 and each component was exported as a 

tetrahedral mesh that was used for shaping materials into ALE3D. Material 
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equation-of-state (EOS) electrical and thermal conductivity models were taken 

from the ALE3D material database.4 Tabular EOSs were made available through 

ALE3D’s interface to LLNL’s SESAME data.8

Fig. 3 Half-plane view of the geometry used in ALE3D simulation showing the materials

There are 2 broad approaches to modeling in ALE3D. A mesh that conforms to the 

structural elements in the system generally gives the most accurate simulation, but 

creating this type of mesh can be time-consuming. Since MFCGs have a cylindrical 

geometry, a high-resolution mesh is not required; one can use a conformal mesh 

and paint (shape) the actual geometries onto the mesh, allowing mesh elements to 

intersect the user-defined shape. The mesh was defined by a built-in function of 

ALE3D. Symmetry and magnetic boundary conditions were applied at z = 0. All 

other boundaries have outflow boundary conditions. The high explosive was 

initiated at t = 0 at point label “D” (x, y, z) = (0, 0, 9.53 cm) shown in Fig. 3. A 

direct current source was applied to the input region connecting the front end of the 

armature and the coil.

The compressed current diagnostics is critical for comparing the simulation results 

with the experiment. It is one of the most important quantities of the simulation to 

predict magnetic compression in the MFCG discharge. In the simulation, the 

current was measured by introducing a 360° ring of B-field tracers around the 

output as illustrated in Fig. 3. The orientation was such that B-field tracers follow 

the direction of the magnetic field along the vector line of the ring allowing it to 

measure accurately the compressed current. From the generated time histories of 

the magnetic field B, an element of the tracer length was integrated over the loop 

using Ampère’s law given by

∮BB�⃗ . dddd ���⃗ = μoo IIeeeeee , (1)

which was used to calculate the current enclosed by the line integral. A 

postprocessing Python script written by Anthony Johnson9 of LLNL and modified 
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by this author, converted the B-field data into a current inside the ring, effectively 

simulating a Rogowski coil placed around the load.

5. Simulation Results: Computational Mesh Convergence

One of the key aspects of numerical simulation is the effect of mesh resolution on 

a given parameter of interest. Simulations require adequate resolution to ensure 

convergence of the solution. If the mesh resolution is too coarse, numerical errors 

may become significant and physically important features may not be resolved. To 

check for numerical convergence of the current, 4 computational cases were run 

(using the 70-kA seed-current), varying the number of elements. For each case, the 

current-time history is plotted and compared with the experimental data. The results 

of this convergence study are shown in Fig. 4. The simulation is time shifted and 

overlaid on top of the experimental plot. In general, (for all mesh resolution) the 

current plots match well for the first 20 μs and then slightly overshoot the 

experimental current.

Fig. 4 Impact of mesh resolution on the current amplification for 70-kA seed-current
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The low resolution (element count of 13 million) resulted in a maximum current of 

420 kA that is 1.4% more than the experimental value. At higher resolutions 

(element count of 14.5–15 million), the calculated maximum current begins to 

converge at 7–11 % higher than the measured value. These convergence tests are 

on the same length scale as the real problem, and both the low and high resolution 

consumed approximately the same computational resource (i.e., time, number of 

cores).

The results of the convergence simulations indicate that the compressed current is 

sensitive to element size and evaluation of JJ��⃗ × BB���⃗ coupled to the equation of 

motion. The EOS and the nonlinear relationship between the electrical conductivity 

and the joule heating may also influence the magnetic flux at the end of the 

compression, thus increasing the compressed current (current was derived from the 

B-field using Ampère’s law). In addition, the change in electrical conductivity 

produced by the shock wave from explosive loading of the armature, arcing, and 

stray magnetic flux is not considered in this simulation, and it was neglected in 

calculating the compressed current. Further analysis will help with understanding 

the increase of the magnetic flux with mesh resolution at the end of the 

compression. For simulations using the 117- and 220-kA seed-current, mesh 

density of 14.5 million elements was used. 

6. Comparison of ALE3D Simulation with Experiment

Figure 5 shows the current profiles from ALE3D-MHD simulations and 

experiments for 117- and 220-kA seed-currents. Similar to Fig. 4, the agreement 

between simulation and experiment is reasonable up to a few microseconds before 

the peaking of the current. For the 220-kA seed-current, the simulation predicted a 

maximum current of 1213 kA, which differs from measured peak current of

1044 kA by 16%. For the 117-kA seed-current, the maximum current was 

overpredicted by 4%.
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Fig. 5 Comparison of ALE3D-MHD simulation (black line) and experimental current trace 

(red line) for a) 117- and b) 220-kA seed-currents. The simulation is shifted 62 μs to account 

for the delay in the experiment.
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The time-varying inductance of the device is a critical point of the simulation. 

Deviations from the actual inductance value will lead to a mismatch of theory and 

experiment in the temporal current waveform. Since most of the action (i.e., high 

current amplitude) occurs toward the end of generator operation, typically during 

the last 10 μs, the inductance calculation needs to be especially accurate for these 

last moments before generator burnout. Figure 6 shows a plot of calculated and 

measured inductance.

Fig. 6 Comparison of the simulated and measured inductance evolution

The time history of the simulated inductance compared with the measured 

inductance in Fig. 6 is somewhat puzzling during the early portion of the 

experiment. The measured static inductance (~2900 nH) differs significantly from 

the ALE3D simulation (~2300 nH). At late times (end of compression), the 

agreement with the experiment is quite good. The differences may be explained by 

the method used in deriving the inductances. In the simulation, the dynamic 

inductance was derived from the magnetic energy that is extracted from the time 

history of the scalar circuit current (the magnetic energy is only correct for materials 

with constant value of permeability). However, it is difficult to accurately measure 

the time variations of the inductances during the detonation. The experimental 

inductance was measured in the laboratory using a meter. The measurement was 
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performed with a conical sliding insert resembling the armature movement inside 

the stator.

2 The time history of the inductance was then calculated using the 

detonation velocity of the explosive. 

Figure 7 shows the total magnetic field strength of the generator, scaled by the 

initial field strength from the seed-current. The peak magnetic field strength of 

1.2 MegaGauss (MG) or 120 tesla (T), 0.4 MG (40 T), and 0.1 MG (10 T) were 

obtained for seed-currents of 220 kA, 117 kA, and 70 kA, respectively. These 

values should be compared with experimental values in the future.

Fig. 7 Generator total magnetic strength for 70-, 117-, and 220-kA seed-currents

Figure 8 shows typical snapshots of the magnetic flux during current compression,

indicating the increase in field strength. The unique feature of the generator is 

shown in the last snapshot, where the magnetic flux has been transferred from the 

coil on the right to the load on the left.
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Fig. 8 Snapshots of the generator magnetic flux magnitude at 65, 75, 80, and 90 μs

7. Analysis of Simulation: Flux Compression Principle

The current gain of a generator (GG) is defined by the ratio of initial to final 

inductance. Theoretically, the larger the initial inductance ( LLii) and the smaller the 

final (load) inductance ( LLff), the more gain is expected. Of course, our assumption 

of ideal flux conservation cannot hold true for a real system, as we will always have 

ohmic losses in the conductors and other intrinsic flux losses. However, by adding 

a figure of merit (ββ), we can write

GG = �

LLii

LLff

�

ββ

(2)
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for an ideal generator ββ = 1.0. For experiments reported in Bartkowski and 

Berning,

2 the average value of ββ = 0.62 compared to the average simulation value 

of 0.77.

Figure 9 showsthe armature expansion angle. The armature will expand in a conical 

shape with an angle determined by the ratio of the mass of the aluminum tube to 

the mass of high explosives. Figure 9 shows a snapshot of the expanding armature 

22 μs after initiation of the high explosive. The contact point between the armature 

and stator is at position A (z = 173 mm, r = 50 mm), and the tube begins to move 

at position B (z = 230 mm, r = 34.8 mm). The expansion angle is defined as the 

angle of the line between the 2 points A and B relative the generator axis. The angle 

α is calculated according to

αα = arctan� 50−34.8

230−173� = 14.9°

, (3)

which is close to the calculated (using Gurney equations) value of 15.2° reported 

in Bartkowski and Berning.

2

Fig. 9 Snapshot of the expansion angle of the armature

Deformation and Kinematics of Armature

The simplest way to look at an expanding armature is to think of it as having the 

consistency of butter, in which case the resting crowbar will cut through the 

armature just like a knife through butter. This is indeed the case, as the image in 

Fig. 9 reveals (crowbar is light blue, right-hand side of image). In Fig. 10, a plot of 

the radial displacement history of a point on the armature located at the axial 

position of 122 mm. The dip in the plot (the point marked with a letter A) is due to 

the crowbar cutting into the armature. 
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Fig. 10 Radial displacement of a point close to the armature at the axial position of 122 mm

The radial expansion history of the armature at 25 μs (after detonation) and images 

of the expanding armature are shown in Figs. 11 and 12. The measured armature 

expansion is also shown. Letter “A” marks the point of crowbar impact caused by 

the downward spike. The simulation result shows the end-effect (a bell-shaped 

contour of the armature at the detonation side).1 This behavior is attributed to the 

fact that in MFCGs the detonation end is normally open to outside air. When the 

explosive is detonated, some of the detonation pressure escapes through the open 

end, which in turn reduces the outward expansion of the armature at this location. 
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Fig. 11 Radial displacement of the armature at 25-μs postdetonation time

Fig. 12 Qualitative comparison of the expanding armature at 25 us (after detonation): a) 

ALE3D simulation and b) experiment. Coil and crowbar are shown in the simulation image.
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Away from the detonation point, the experimental measurements and ALE3D 

simulations of the armature expansion agree but differ at the detonation point. The 

difference is explained because the experimental data were calculated from 

expansion of the armature only (no crowbar and stator, allowing the armature to 

expand freely unlike in the simulation). The most important conclusion to be drawn 

from the comparisons is that the radial expansion is in excellent agreement away 

from the detonation point. 

8. Conclusion

In this work, the results of a 3-D numerical study of the ARL-designed MFCG 

using ALE3D-MHD code from LLNL are presented. Results of 3-D ALE3D 

simulations of the MFCG were compared with the experimental data and show 

good agreement at low-mesh resolution (a 1.4% difference). However, at highmesh resolution, the code overpredicted the compressed current by 7–14%. There 

is also good agreement of the inductance and armature expansion. In the simulation, 

arcing, stray magnetic flux, nonlinearity in the conductivity model, and magnetic 

pressure was neglected. The comparison of ALE3D results with the well-diagnosed 

experiments indicates that the code is capable of giving accurate results until the 

end of the compression.

9. Recommendations for Future Work

Some areas of the magnetic flux compression have not been studied; it would be 

considerably relevant in understanding potential experimental improvements. 

Future continued modelling will include the following areas, as they have not been 

studied:

• Perform deeper analysis of magnetic forces inside the generator.

• Calculate magnetic losses due to switching flux, electrical breakdown, 

resistive heating, and temperature of the materials during flux compression.

• Test the model with transition reduction elements in ALE3D code (a 

mechanism for putting a mesh where it is needed, and a method of creating 

elements with one number of faces on one side and a different number on 

the opposing side).

• Conduct simulations using lumped circuit model for the seed-current. This 

may increase the computational time, but it is of particular value for 

predictive modeling.

• Investigate breakdown that occurs in the compression phase. 
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• Investigate possible effects due to electromagnetic forces acting inside the 

generator. For example for high currents, the rotational effect of the 

armature produced by the electromagnetic forces.
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10. References

1. Neuber AA. Explosive driven pulsed power: helical magnetic flux 

compression generators. Berlin (Germany): Springer; 2005.

2. Bartkowski P, Berning P. Design and testing of the ARL squeeze 4 helical flux 

compression generator. Aberdeen Proving Ground (MD): Army Research 

Laboratory (US); 2013 June. Report No.: ARL-TR-6477.

3. Doney RL, Bartkowski P. Magnetic flux compression simulations using 

ALEGRA. Aberdeen Proving Ground (MD): Army Research Laboratory (US); 

2012 July. Report No.: ARL-RP-384.

4. Anderson A, Barton N, Biagas K. User manual for ALE3D, an arbitrary 

Lagrange Eulerian system. Version 4.24. Livermore (CA): Lawrence 

Livermore National Laboratory; 2014 Sep 5.

5. Shearer JW, Abraham FF, Aplin CM, Benham BP. Explosive-drive magnetic 

field compression generators. J Appl Phys. 1968;39:2102–2116.

6. Morris R. Cubit 13.2 user documentation. Albuquerque (NM): Sandia National 

Laboratories; 2017.

7. Reitz K. Python guide documentation. Release 0.01. Wilmington (DE): Python 

Software Foundation; 2017 May 1.

8. Lynon SP, Johnson JD. SESAME, The Los Alamos National Laboratory 

equation of state database. Los Alamos (NM): Los Alamos National 

Laboratory; 1992. Report No.: LA-UR-92-3407. 

9. Johnson AJ. Lawrence Livermore National Laboratory, Livermore, CA.

Personal communication, 2016 Oct.
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List of Symbols, Abbreviations, and Acronyms

3-D 3-dimensional

ALE arbitrary Lagrangian-Eulerian

ARL US Army Research Laboratory

EOS equation-of-state

LLNL Lawrence Livermore National Laboratory

MFCG magnetic flux compression generator

MHD magneto-hydrodynamic
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1 DEFENSE TECHNICAL

(PDF) INFORMATION CTR

DTIC OCA

2 DIRECTOR

(PDF) US ARMY RSRCH LAB

RDRL CIO L

IMAL HRA MAIL & RECORDS

MGMT

1 GOVT PRINTG OFC

(PDF) A MALHOTRA

1 SNL

(PDF) J NIEDERHAUS

18 DIR USARL

(PDF) RDRL WMP A

P BERNING

C UHLIG

M COPPINGER

J FLENIKEN

RDRL WMP D

G B VUNNI

R DONEY

S SCHRAML

D KLEPONIS

D KEELE

C RANDOW

J RUNYEON

F MURPHY

RDRL WMP E

P BARTKOWSKI

D HORNBAKER

M LOVE

P SWOBODA

J HOUSKAMP

C KRAUTHAUSER
Approved for public release; distribution is unlimited.

20

INTENTIONALLY LEFT BLANK.