High Altitude Electromagnetic Pulse (HEMP) Simulation Example

Notional Missile Responses to an EMP Environment Using FDTD Simulation Techniques

By Cody Weber

Contents
Analysis Motivation
How CEM Modeling is Used in a Verification Program
Supported Test Programs
In-flight System EMP Response
Simulation Approach
Simulation Software
Software Features
EMP Handbook Values
1st Model Simulation Setup
1st Model Antenna Response
2nd Model Simulation Setup
2nd Model Exposed Cable Response
3rd Model More Realistic Geometry
3rd Model Complex Harnesses
HEMP Plane Wave Source
3rd Model Surface Current Densities
3rd Model Antenna Response
3rd Model Harness Response
Equipment Susceptibility
Conclusions
References

Analysis Motivation

Many vehicles have a High-Altitude Electromagnetic Pulse (HEMP) hardening requirement for military aircraft certification. It’s rarely possible to perform certification testing on the entire aircraft for all incident field orientations. Compliance to the EMP environment often must be verified by some combination of testing and analysis. A computational electromagnetic (CEM) model can provide a detailed view of the EMP coupling processes and transient levels throughout the aircraft. This simulation analysis may help reduce elements of an expensive test program.

In this document, EMA demonstrates first that EMA3D can reproduce the HEMP Handbook predictions. Next, EMA extends the geometry in the simulation so that it is comparable to modern systems.

How CEM Modeling is Used in a Verification Program

Rocket with HEMP incident, then results for box testing

Supported Test Program

In CEM simulations, complex model geometries and there associated material properties can be captured with high fidelity. This information alone can provide valuable insight to a vehicle’s coupling response to an EMP environment Apertures and structural seams or joints can be trickier to accurately represent in CEM models. Experimental measurement programs can be used to help determine properties of critical seams and joints. The joints and apertures within the model can be tuned to incorporate SE and Zt experimental data.

In-Flight System EMP Response

The AFWL EMP handbook3 breaks the response of an in-flight system into four major components:
  1. The response of a missile as an antennae
  2. The antenna response of apertures and cables
  3. Coupling of interfering signals to cables and electronics
  4. The response of the electronics to the interfering signals
The analysis presented here looks at the first 3 items and briefly discusses the fourth.

Simulation Approach

A set of 3 notional missile models were generated. Models 1 and 2 are very simple and are used to compare with established coupling responses presented in the EMP Handbook. The 3rd model contains more realistic geometry and complex cable harnesses to demonstrate the capabilities of a FDTD algorithm with an integrated multi-conductor transmission line solver. The 3rd model provides sample pin transient analysis that can be used to define test levels for certification requirements.
The three rockets that are simulated are shown

Simulation Software

EMA3D V4 is a 3D full wave finite-difference time-domain (FDTD) solver of Maxwell’s equations that was used for the simulations in this document. The solver is integrated with a multi-conductor, multi-shield, multi-branched cable harness transmission line solver (MHARNESS).
Describes the work flow of using EMA3D

Software Features

Some modeling capabilities available in the software that are particularly useful to EMP simulation include:
  • LRC structural seam algorithm
  • Composite materials algorithm
  • Thin gaps
  • Thin wires (smaller than a cell size)
  • Complex harnesses (integrated multi-conductor, multi-branch, transmission line solver)
  • Skin depth effects of cable shields

EMP Handbook Values

The EMP handbook analyzes the response of a cylindrical antenna with end caps as shown below. The response of the antenna is determined by the length and the fatness factor, Ω. Most missiles have a Ω of ~5-63. The Ω for this comparison was set to 6, with the antenna dimensions being: L = 2h = 10 m, d = 2a = 1m. The source was a unit-step plane wave electric field, E = 1 V/m.
A drawing of the cylinder coordinate system and the equation for fatness factor

The Cylinder from the HEMP Handbook and the Omega value for comparisons in this document.

1st Model: Simulation Setup

A simple antenna was created with the same dimensions as used in the EMP handbook (L = 10m, d = 1m, Ω = 6) for simulation. The antenna was comprised only of PEC surfaces. The source was also a unit-step plane wave electric field,    E = 1 V/m.
A cylinder is shown with the incident E-field polarization vector

1st Model: Antenna Response

First, we consider the current induced on the cylinder, as shown: Drawing of equation of bulk current and rocket   As shown in the following figures, the agreement is of the antenna response for the current on the cylinder is good.

The HEMP Handbook Result

HEMP Handbook Result 1

EMA3D results 1 plotted for current versus time

EMA3D Result 1

2nd Model: Simulation Setup

The exact same configuration was used for the second model except an exposed cable was added as shown below.
Rocket cylinder with external cable

The 2nd Model Has an Exposed Cable

The cable resistance, R1, was set equal to the transmission line characteristic impedance Zc.
Characteristic Impedance Equation

The cable resistance, R1, was set equal to the transmission line characteristic impedance Zc

The source was again a unit-step electric field transient,    E = 1 V/m.

The incident field and an external cable are shown

The model now has an external cable

2nd Model: Exposed Cable Response

As shown in the following figures, the agreement is of the exposed cable response for the current on the cable is quite good.

The plot of the handbook results versus time

HEMP Handbook Exposed Cable Response Results

Plot of the results

EMA3D Exposed Cable Response Results

 

3rd Model: More Realistic Geometry

The rocket is shown schematically

Geometry Description for the 3rd Model

3rd Model: Complex Harnesses

Each harness has an overbraid shield and multiple shielded cables.
The cable harnesses in this model are shown

HEMP Plane Wave Source

The HEMP waveform taken from MIL-STD-4641 was used for the 3rd simulation with an amplitude of 50 kV/m. The source wave is shown below.
The waveform versus time is plotted

EMP MIL-STD-464 Waveform

The fft versus frequency is plotted

The Frequency Domain of MIL-STD-464 HEMP Source

3rd Model: Surface Current Densities

The surface current density is shown as a function of color

Surface Current Density False-Color Plot for HEMP Illumination

3rd Model: Antenna Response

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. Antenna Response (current on body) is plotted below.
Plot of the current versus time and frequency

The Current on the 3rd Model (Antenna Response)

3rd Model: Harness 1 Response

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. The bulk harness 1 current (bundle Current) is plotted below.
The plot of the cable current versus time

The Bulk Current Flowing on the 1 Cable Harness in 3rd Model

3rd Model: Harness 2 Response

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. The bulk harness 2 current (bundle Current) is plotted below.
The current versus time for the 2 cable is plotted

The Bulk Current Flowing on the 2 Cable Harness in 3rd Model

3rd Model: Cable Shield Response

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. The shield current (Ish) for 22 AWG TSP cable is plotted below.
sdf

The Current Flowing on the 1 Cable Shields in 3rd Model

3rd Model: Pin Isc Response (Twisted Shielded Pair Pin)

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. The pin short circuit current (Isc) for 22 AWG TSP cable is plotted below.
te

The Current Flowing on the 1 Cable 22 AWG Pins in 3rd Model

3rd Model: Pin Isc Response (Twisted Shielded Triple Pin)

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. The pin short circuit current (Isc) for 24 AWG TST cable is plotted below.
go

The Current Flowing on the 1 Harness 24 AWG Shielded Twisted Triple Pin in 3rd Model

3rd Model: Pin Voc Response (Twisted Shielded Pair Pin)

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. The pin open circuit voltage (Voc) for 22 AWG TSP cable.
The Pin

The Current Flowing on the 1 Harness 22 AWG Shielded Twisted Pair Pin in 3rd Model

3rd Model: Pin Voc Response (Twisted Shielded Triple Pin)

Non-normalized Response: 50 kV/m MIL-STD 464 EMP Environment. The pin open circuit voltage (Voc) for 24 AWG TST cable.
go

The Current Flowing on the 1 Harness 24 AWG Shielded Twisted Triple Pin in 3rd Model

Equipment Susceptibility

The 4th component of an in-flight system response to EMP involves the response of the electronics to the interfering signals on the cable. Further analysis can be performed on specific circuit susceptibility using the pin transient data à PSpice. This analysis can help determine the need for transient suppression or terminal protection devices (TPDs).

Conclusions

A CEM model can provide detailed responses of an aircraft to an EMP environment. The simulation results of models 1 and 2 provide a basic understanding of missile coupling response and compare well with the documented results of the EMP handbook. Model 3 results demonstrate the capabilities of a FDTD software with integrated transmission line solver. These results include sample data for a detailed pin transient analysis. This type of analysis may help shorten the certification process and reduce costs associated with an expensive test program.

References

    1. MIL-STD-464C: Electromagnetic Environmental Effects Requirements for Systems. United States Department of Defense, December 2010.
    2. MIL-STD-461F: Requirements for the Control of Electromagnetic Interference Characteristics of Subsystems and Equipment. United States Department of Defense, December 2007.
    3. Sandia Laboratories, Electromagnetic Pulse Handbook For Missiles and Aircraft in Flight EMP Interaction 1-1, AFWL-TR-73-68, September 1972, Air Force Weapons Laboratory, Kirtland Air Force Base, New Mexico 87117

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