Background

The concept of background media refers to volumes of the finite difference problem space to which material properties are assigned that are not explicitly meshed, but are implicitly meshed in EMA3D®. There can be multiple background specifications. Background regions can be defined to envelop the entire finite difference problem space or exist only within certain localized volumes. A background can be specified as linear or nonlinear. All linear backgrounds consist of frequency independent, isotropic material definitions. Nonlinear backgrounds employ a three-species air chemistry formalism for modeling air breakdown and ionization. A single linear background media, enveloping the entire problem space and possessing vacuum electromagnetic parameter values, is implicitly programmed in EMA3D. If this is the background desired, and it usually is, then no further action is necessary. However, if different background parameter values, or multiple localized backgrounds, are desired, then these must be specified.

There is only one keyword associated with specifying the background. This keyword is listed below.

• BACKGROUND

Background material parameters are characterized by user-supplied values of the conductivity (σ_e), the permittivity (ε), the permeability (μ), and the magnetic conductivity (σ_m). For most background materials, the permeability is equal to the vacuum value (1.257e-6 henries/meter) while the magnetic conductivity is zero. The allowable ranges for these parameter values in EMA3D are listed below.

Assigning values outside of this range will illicit an error message and EMA3D program termination. Nonlinear backgrounds are so termed because the three-species air chemistry formalism results in a conductivity that depends upon the strength of the applied electric field. The initial value of nonlinear backgrounds will be automatically set to vacuum electromagnetic parameter values. There are two additional user-defined parameters associated with the nonlinear background in EMA3D. These parameters are the relative air density (ρair) and the absolute percent humidity (pw). The relative air density is related to the air density at sea level (1.22 kilograms/meter). A value of 1.0 implies a sea level density. The absolute percent humidity should not be confused with the relative humidity often provided by meteorological forecasts. The relative humidity usually expands the range from 12% in arid desert climates to 100% during periods of precipitation. However, the absolute humidity rarely exceeds 6%, even in some of the densest thunderheads. The allowable ranges for these variables are given below:

Assigning values outside of this range will result in an error message and EMA3D program termination.

A word of caution concerning the relative air density is warranted. The algorithms used for the implementation of nonlinear backgrounds involve parameters that were derived from experiment. Setting the density to an extremely low value, perhaps less than 0.01, may be pushing this parameter into an untested realm.

The ability to specify multiple backgrounds over different regions of the problem space has many advantages. The primary advantage is the ability to incorporate large volumes of materials that do not have to be explicitly meshed. Such materials could constitute a lossy ground or a circuit board dielectric substrate upon which traces are built or embedded. To mesh such structures without the use of the multiple background feature would require many mesh cells, thereby substantially increasing the size of the EMA3D GUI database.

The terminology employed consists of global and local backgrounds. A global background expands over the entire finite difference problem space, while a local background usually occupies a smaller volumetric region of the problem space. Only one global background can be defined while many local backgrounds may be specified. The single vacuum background media enveloping the entire problem space, discussed above, is a global background. If a global background possessing different electromagnetic parameter values, or a nonlinear global background is desired, then these may be defined.

In cases involving multiple local backgrounds, some may overlap or be embedded within others. Only one global background may be defined while many local backgrounds are possible. For local linear backgrounds, there is an order dependency. This order depends on the order of specification. When local linear backgrounds overlap, the resultant electromagnetic parameter values within such overlapped regions will always assume the values of the latest specified background to envelope the region. This dependency is present to allow one region to overlap, or be embedded within another, without compromising the electromagnetic parameter values of the overlapped or embedded region. Thus, a lossy ground can be placed within air while still maintaining the electromagnetic parameter values of the lossy ground.

The order dependency described above applies only to linear backgrounds. A nonlinear background will always supersede a linear background. If two nonlinear backgrounds overlap, then the relative air density and the absolute percent humidity parameters are averaged in the overlapped region, possibly creating a third nonlinear background. There is thus, no order dependency for nonlinear backgrounds.

As discussed in Section 4.3, all other materials supersede the background designations. Materials placed within any background medium maintain the specified given material parameter values.