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A Wave Chaos Approach to Understanding and

Mitigating Directed Energy Effects

Steven Anlage, Thomas Antonsen,Edward Ott

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The Maryland Wave Chaos Group

Tom Antonsen Steve AnlageEd Ott

Jen-Hao Yeh James HartNow at Lincoln Labs

Biniyam Taddese

Graduate StudentsMing-Jer LeeHarita TennetiTrystan Koch

Undergraduate StudentChristopher Bennett

Post-DocDr. Gabriele Gradoni2010 URSI Young Scientist Award

NRL Collaborators: Tim Andreadis, Lou Pecora, Hai Tran, Sun Hong, Zach Drikas, Jesus Gil Gil

Funding: AFOSR MURI 2001; AFOSR; ONR MURI 2007; ONR AppEl

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A Wave Chaos approach to understanding / quantifying DE Effects in electronics

The model works for ‘ray-chaotic’ enclosures

Two incident rays with slightly different initial directions have rapidly diverging trajectories

Embrace CHAOS as the central organizing principle!

Many electronic enclosures display ray chaos

Computer enclosuresAircraft cockpitsShip compartmentsOfficesetc.

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The Random Coupling Model

A quantitative model of statistical and systematic aspects of HPM effects in enclosures

Statistical aspects:

The underlying classical chaos means that the waveproperties are ‘universal’ and governed by Random Matrix Theory (RMT)

► The statistics of all wave properties (resonant freqs.,standing wave patterns, Z, Y, S, etc.) are UNIVERSALand governed by a single loss parameter:

spacing

dB

f

f

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|)(| 2VP

Experimental Data

Terrapin Terrapin AlgorithmAlgorithm

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Experimental Data

Terrapin Terrapin AlgorithmAlgorithm

The non-universal aspects are captured bythe radiation impedance Zrad of the coupling ‘ports’

Zrad of the ports can be determined by a numberof techniques, both experimental and theoretical

RCM Web Site: http://www.cnam.umd.edu/anlage/RCM/index.htm

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Effect of Direct Ray Paths

Original Random Coupling Model (RCM) - RF energy is randomized on entering cavity - Only radiation impedance of ports, cavity volume and average Q are important

In some geometries, or in narrow frequency bands specifics of internal geometry are important

Modified Random Coupling Model - J. Hart et al., PHYSICAL REVIEW E 80, 041109 (2009) - Allows for systematic improvement by inclusion of geometric details if known - Can be used in conjunction with measured data

Systematic aspects of HPM EffectsInclusion of ‘Short Orbits’ in the RCM

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Extensions of The Random Coupling Model

Systematic aspects of HPM EffectsInclusion of ‘Short Orbits’ in the RCM

James Hart, T. Antonsen, E. Ott, Phys. Rev. E 80, 041109 (2009)

2/12/1avgavgavg RiRXiZ�����

is a complex matrix withuniversal fluctuations governedby the loss parameter f3dB/f↔ ↔ ↔

↔

↔

↔ ↔ ↔↔

↔ ↔ ↔↔

↔

Survival probability in the ensemble Uniform attenuation

)/(Ak

Theory work funded by AFOSR

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Data and Theory smoothedwith the same 125-cm

(240 MHz window) low-pass filter

Nonuniversal Properties Captured by the Extended RCMEmpty Cavity Data

Theory includes all orbits to 200 cm length

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J.-H. Yeh, et al., Phys. Rev. E 81, 025201(R) (2010); J.-H. Yeh, et al., arXiv:1006.3040

Experimental work funded by AFOSR,

and now ONR/AppEl

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Extensions of The Random Coupling Model

Realistic systems consist of many coupled enclosuresCan the RCM be extended to handle these situations?

J. P. Parmentier (ONERA)

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Extending the RCM to the case of Coupled Cavities

The statistics of coupling are dominated by the statistics of transmission through the first cavity,scaled by the mean impedance of the next cavity

Generalize to an arbitrary cascade of enclosuresand treat junction topology

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VZc

Fluctuations in transmissionthrough cavity 1

Mean properties of cavity 2

Cavity 1 Cavity 2

Approximations:high loss, weaktransmission

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Extending the RCM to the case of Coupled Cavities

Future Work:

Consider networks of coupled cavitiesGraph topology

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The Statistics of Tunneling between Enclosures

In some cases, two enclosures will be coupled by structures beyond cutoff

Examples include metal ducts at frequencies below cutoff,intermediate rooms/compartments that are below resonance

Can we use what we know about chaotic eigenfunctions to solve this problem?Does it make a difference if the enclosures are regular or chaotic?

Enclosure 1 Enclosure 2

Bar

rier

Work in collaboration with Lou Pecora @ NRL

Enclosure 1 Enclosure 2

Barrier

Regular Enclosure caseRay Chaotic Enclosure case

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The Statistics of Tunneling between Enclosures: The 1D Case

Energy splitting k2 is proportional to the tunneling rate through the barrier

ck

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Splitting Fluctuations versus Energy

These splittings, and their fluctuations, are predictable in the chaotic case

Numerical simulationsby Lou Pecora (NRL)

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Results of Wave Chaos Theory

The theory uses the random plane wave hypothesis to calculate the tunneling rate

Sliding average of mean splitting Sliding average of splitting fluctuations

Black lines (Data) – simulations by Lou Pecora (NRL)

Surprisingly, all threeagree quite closely…

Wave chaos theory in agreement with simulations

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Ray-ChaoticEnclosure

Barrier

InfiniteWaveguide

The tunneling escape rate will vary from mode to mode, giving fluctuationsin the quality factor of the modes.

The mean and fluctuations of the 1/Q with k2 should follow the wave chaos theory predictions

An Experiment to Test the Wave Chaos Tunneling Theory

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New Research and Transfer of RCM Knowledge Base to Naval Research Lab

We are collaborating with the group of Tim Andreadis to test the RCM is more realisticscenarios, and to transfer our knowledge / know-how to DoD

Experimental tests of the RCM in 3D enclosuresHai Tran and Zach Drikas

Radiation Impedance Measurement New Antenna Configuration

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Anlage et al. Acta Physica Polonica A 112, 569 (2007)

The Electromagnetic Chaotic Time-Reversal Sensor

60ns pulse with 7GHz (λ~4cm) center frequency.

Transmitted Sona

Work funded by ONR MURI 2007

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ELECTROMAGNETIC Chaotic Time-Reversal Sensor:- Injection of time reversed Sona

Sensors based on time-reversed pulse reconstruction:B. T. Taddese, et al., Appl. Phys. Lett. 95, 114103 (2009) B. T. Taddese, et al., arXiv:1008.2409

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Short Monopole Inside

Electromagnetic Time-Reversal of Enclosure with ApertureSun Hong, Zach Drikas, Hai Tran, Jesus Gil Gil, Tim Andreadis, NRL

( )ix t

( )y t

( )rx t

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Port 2

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Conclusions

The Random Coupling Model is being extended and generalized in new waysShort OrbitsConnected EnclosuresElectrically Large Antennas

Theory and Experiment work in parallel, and stimulate each other

NRL Collaboration has resulted in:New experiments and new applications for the RCM and time-reversed EMExtension of the RCMTransfer of know-how to DoD

IC Post-Doc grant: Nonlinear time-reversed electromagneticsDURIP proposal: System for Investigation of Terahertz Wave Chaos

Future Work:Experimental test of tunneling fluctuationsTheory of multiple connected and networked enclosuresModeling and experiments of fading statistics