Field Precision software tips » HiPhi

HiPhi boundary input from EStat

shumphries — Sun, 23 Nov 2008 22:29:54 +0000

Many improvements to our programs follow from user suggestions. My consulting projects often provide motivations for new features. I am presently working on a simulation of a large cylindrical vacuum insulator for a pulsed-electron-beam injector. The issue is whether non-symmetrical flaws in the insulator surface will cause substantial field perturbations. I started by creating a 2D EStat solution for the ideal insulator for the following reasons:

I wanted to get a sense of the baseline electrical field magnitude in different regions and to check the sensitivity to changes in the dielectric properties of surrounding structures.
I could use the DXF import capability of the Mesh drawing editor to create a set of outlines for the complex turnings. After testing, I moved them directly to the MetaMesh script.
I wanted benchmark values to check that the 3D solution was set up correctly.

Because 2D solutions run quickly, I incorporated the entire injector assembly in the mesh. Extending this solution volume to three dimensions would have resulted in a huge mesh and many hours of run time. I feel that if a run takes more than one hour, there is probably a better way to solve the problem.

Since the flaws were relatively localized, it would be possible to get a good idea of their effect by limiting the axial extent of the solution to a space near the insulator. In this case, I could define a fixed-potential region on the solution volume boundaries in -z and +z and assign a spatial variation using data from the EStat solution. The existing version of HiPhi supported the definition of potential variations from mathematical functions using the command:

POTENTIAL NoReg > f(x,y,z)

Here, f(x,y,z) is any algebraic function of the Cartesian coordinates. In order to use the feature, it would have been necessary to take a radial scan of potential and then to fit the results with a power series in ?[x^2 + y^2]. This approach seemed like it would be a lot of work, and I didn’t feel like doing it.

Instead, I took advantage of my unique position as deity of the HiPhi source code and added a new program feature. It is ideally suited to using a 2D solution as the basis of a 3D microscopic solution. Here is the corresponding script command

POTENTIAL NoReg TABLE [x,y,z,r] TabName

The string TabName is the name of a text file defining the potential variation along the specified direction (the variable r is interpreted as ?[x^2+y^2]). It consists of a set of data lines:

r[n]    phi(r[n])

For the project I prepared tables for the downstream and upstream boundaries directly from EStat scans, using ConText to remove unwanted columns. The process took only a few minutes.

The figure below shows a test solution for the potential inside a grounded cylinder. The bottom boundary in z is grounded and the potential on the top follows a tabular variation in r (a partial cosine function). The top picture shows equipotential lines in the plane x = 0.0 and the bottom shows lines in a plane normal to z near the defined fixed-potential boundary.

I modified the HiPhi instruction manual, describing how to use the new command forms. While I was at it, I decided to ex[and the existing commands for relative dielectric constant, conductivity and space-charge density to handle table input.

For more information on HiPhi, please use this link: http://www.fieldp.com/hiphi.html.

Static fields in a dynamic code

shumphries — Tue, 22 Jul 2008 14:35:10 +0000

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., ?(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 ?H.

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

Simulating a pulsed-power system with Aether

shumphries — Mon, 14 Jul 2008 20:28:02 +0000

The development of Aether continues on schedule for release in September. Capabilities for time-domain simulations are complete are we are creating several examples for the tutorial manual. In this example, the full three-dimensional capabilities of the code are used to characterize a pulsed power system. The goal is to design a dummy load to test a low-impedance generator that drives a long parallel-plate transmission line. The design of the load resistor is a rather poor one to illustrate how the code can highlight problems. The example highlights two Aether techniques: 1) modeling a portion of a long periodic system using symmetry boundaries and 2) generation of a pulse with desired properties in a transmission line.

The first figure below shows the geometry. The transmission line has a long length along. The load consists of a series of identical resistors. The length along x of each cell is b = 8.0″. The spacing between the inner and outer conductors of the transmission line is a = 2.00″. The resistive solution inside the alumina housing has radius r = 0.875″ and length L = 4.0″. Most of the assembly volume is filled with purified water. A voltage pulse of magnitude V0 = 1.2 MV and risetime tr = 3.0 ns is incident from the right-hand side.

Although only a short length (D = 6.00″) of the transmission line is included in the model, we would like the line to behave as though it extended an infinite distance past the right-hand border. The technique is to include a termination layer on the boundary and to excite the pulse with an internal current source. Any reflected waves pass through the source and are absorbed by the layer. The second figure, a two-dimensional projection in the plane x = 0.0″, illustrates the computational mesh and the regions of the calculation. An element size of 0.10″ gives a good representation of the curved surfaces. The mesh contains about 600,000 elements. The outer wall, center conductor, metal cap and connecting rod are represented as metals in the calculation. The purified water and resistive solution have ?r = 81.0, while alumina has a relative dielectric constant ?r = 7.8. We need to determine two quantities: 1) the current density of the source layer to produce a 1.2 MV pulse and 2) the conductivity of the resistive solution for a matched termination.

The impedance of purified water is ? = 377.3/?81 = 41.922 ?. The characteristic impedance of a section of the dual-sided parallel-plate transmission line of length b is

Z0 = ? (a/2b) = 5.2403 ?.

For a 1.2 MV pulse, the source should supply a total current 2V0/Z0, where half the current travels down the line and half is lost to the absorbing layer. Inserting values, the peak total current is 458.0 kA. Therefore, the current in the top and bottom source regions should have peak magnitude I = 229.0 kA. The source has dimensions 0.1″‘ by 8.0″‘, so the cross-section area is 5.161E-4 m2. The peak current density magnitude is therefore jy = 4.437E8 A/m2. The cylindrical load has resistance

R = L/(??r^2).

Taking R = 5.2403 ? and inserting the dimensions, we find that the matched conductivity is ? = 12.49 S/m.

Here are links to the input files:

http://www.fieldp.com/myblog/examples/chargeline.min
http://www.fieldp.com/myblog/examples/chargeline.ain

Some entries in the Aether script are of interest:

The simulation time is 30.1 ns, long compared to the transit time of 4.57 ns along the 6.0″‘ length of transmission line.
The SMod command invokes the standard normalized Step function starting at ts = 0.0 ns with a risetime tr = 3.0 ns.
The upper and lower boundaries along x are set as symmetry planes. The assignment is valid because 1) pulse propagation is parallel to the planes and 2) the magnetic field is symmetric about the planes.
The two source regions have the dielectric constant of water and peak current densities jy = ±4.437E8 A/m2.
Snapshots of the field distribution are recorded at 5.0 ns intervals, and probes are located at the midpoints of the transmission line and resistor.

The Aether run takes about 5 minutes. The final figure shows the electric field distribution in the plane x = 0.0″‘ at early (5.0 ns) and late (20.0 ns) times. The view at the top shows the initial plane pulse moving down the line. The field magnitude agrees with the theoretical prediction, |Ey| = V0/a = 2.362E7 V/m. The bottom view shows the distribution at t = 20.0 ns. The reflected pulse in the transmission line indicates a poor impedance match. The source of the problem is the high inductance of the small-radius connecting rod and resistive solution. Another concern is the strong concentration of electric field on the resistor end cap and across the insulator housing.

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