The **Aether **code (scheduled for release on September 30) culminates 12 years of my research on fast numerical methods for electrodynamics. The frequency-domain techniques were adapted from a program called **RedWall **that I developed for NIST. The time-domain strategies were tested in **EMP3**.

The application of **Aether **to pulsed-power devices is particularly interesting to me because I spend a couple decades designing high-voltage generators and doing research with them. One of the main simulation issues posed by my colleagues was how to model a static-charged device (like a Blumlein line) with a code where pulses are created by time-varying currents. The initial state has **H** equal zero everywhere and nonzero values of **E**.

In the past I found some partially-successful approaches:

- Treat the state of a charged transmission line as overlapping traveling waves with amplitude
*V0*/2 and generate the positive-going wave with a current source. - Set initial values of electric field from known formulas.

These methods worked only for special structures with simple electric field variations. The second method usually resulted in high-frequency transients because of the discontinuous initial fields.

Two new features in **Aether **completely resolve the static-charge issue.

- The code can import electrostatic solutions from
**HiPhi**to set the initial electric field distribution. There is an exact correspondence to the structure, making it possible to treat structures like capacitors where fields are not described by a simple formula. The continuous field variations eliminate the problem of spurious transients. - The user can specify time-dependent conductivities to represent switches. For a physically-valid solution, I found that it was essential that the electrostatic field correspond exactly to the initial state of the electromagnetic solution. The implication is that all switch elements must be open-circuits at
*t*= 0.0 (i.e., σ(0) = 0.0). An additional benefit of conductivity variation is that it is possible to model the response time of real switch elements.

The first figure below shows a benchmark test with vacuum parallel-plate transmission lines. The solution includes a charge line (25 cm in length) and terminated output line separated by a switch region. The left-hand figure shows equipotential lines of the **HiPhi** solution with a continuous field distribution across the switch region. The initial electric field in the line is *Ey* = 50 V/m. In the **Aether **solution, the conductivity of the switch region changes smoothly from 0.0 S/m to 25.0 S/m in 1.0 ns. In the final state, the switch impedance is 25 times smaller than the line impedance. The figure on the right shows |**E**| in the **Aether **solution at *t* = 1.0 ns. As expected, a voltage wave with *Ey* = 25 V/m moves into the output line and a wave with *Ey* = -25 V/m moves into the charge line.

The next figure shows a three-dimensional example that is a real test of the code. The goal is to determine the effect of strong voltage reversal on the lifetime of a dielectric sheet. The plate and inductor are charged to a high static voltage. A switch shorts the electrodes, generating a oscillating voltage across the sheet. The assembly is immersed in transformer oil inside a grounded tank. Three-dimensional numerical methods are essential for this calculation for three reasons:

- The initial electric field distribution is quite complex.
- The effect of the tank walls and electrodes makes it difficult to estimate lumped element parameters.
- Transit-time effects play a large role in determining the electric field in the test insulator.

In the electromagnetic solution, the switch has an initial conductivity of zero and rises to 25.0 S/m in 5 ns. The time-variation of electric field inside the dielectric is plotted in the third figure. The waveform is approximately a sinusoidal function, as expected for an LC circuit. In contrast to the lumped-element solution, the electric field is larger on the negative cycle. This result reflects transit-time effects with pulse interference. Plots of |**H**| at different times show that the magnetic field energy moves back and forth along the helical inductor. We could determine capacitance and inductance values of the assembly with the *RF* mode of **Aether**. For a rough estimate, note that the dielectric gap has spacing 0.01 m and approximate area 7.85E-4 m2. The dimensions correspond to a capacitance of about 40.0 pF. The oscillation period is 20 ns, implying an inductance of 0.25 μH.

Please use this link for more information on **Aether**: http://www.fieldp.com/aether.html.