This section describes the methodology employed in modeling the physics of devices using object-oriented technology. Physical devices have a complicated relationship to the world outside the system under consideration, and exhibit complicated behavior internally as well. Modeling is an attempt to describe a physical device in mathematical terms. Simulation is the study of the behavior of a model to stimuli; note that this is different from studying the behavior of the physical device.
The object-oriented methodology is employed in going from the physical device to the mathematical model, and finally to the discrete model for simulation. The physical device, shown in Figure 1, includes the complete physical description of the a device in the physical world. This is the tool of the experimentalist, who must extract information from the device using a measurement and observation technique. Although the complete set of data is contained in the physical device, the act of observing the device can influence its behavior. Furthermore, any measurement involves compromises and limitations inherent in the diagnostic apparatus. Experimentation is often prohibitively expensive, and in many cases is not conducive to rapid variation of parameters or complete control of the external influences on the device.
For example, attempting to study the behavior of the disk-loaded microwave beam device shown in Figure 1 may involve constructing the device, applying a signal to the input waveguide, and measuring the signal at the output waveguide. Care must be taken in designing the device itself as well as the wave input generator, wave transmission system and output diagnostic. Each of these items can have a strong effect on the results of the experiment. If the experimentalist hypothesizes that the pitch or size of the slow wave structures controls the performance of the device, he must build a new device to test his theory. Thus, there exist many cases when experiment cannot provide sufficient detail on the behavior of a physical device, or characterize variations to the existing device without substantial time and expense.
The mathematical model describes the physical device in terms of the robust language of mathematics. An example of a mathematical model of a microwave beam device is shown in Figure 2. The model also includes a set of equations which are simplified from the full set of behaviors describing the physical device. This model can include such assumptions as azimuthal symmetry in cylindrical coordinates, for example. Even if virtually every aspect of a device is known and understood, it is seldom fruitful to describe the device fully. The mathematical model may also incorporate some effects with simplified descriptions, such as incorporating the quantum mechanical affects of the electrons bound to surface aluminum atoms via a secondary emission model which provides an electron return current and velocity distribution for a given incident current and distribution.
Figure 2. An example of a mathematical model of a microwave beam device.
The mathematical model may divide the device into various regimes with different physical properties which are best described with heterogeneous sets of equations. In Figure 2, the device is divided into three regions: the emitter (region 1), the beam circuit (region 2), and the collector (region 3). This division is useful since the emitter and collector regions are primarily governed by electrostatic processes, while the beam circuit region is governed by electromagnetic processes which vary on timescales several orders of magnitude faster than the electrostatic regions. The dashed lines in Figure 2 indicate the edges of each region, where boundary conditions are used to interface to other regions and the external world. Thus, each region in a mathematical model may be modeled with different sets of equations, each with its own simplifying assumptions, interacting through boundary conditions.
Figure 3. An example of the discretization of a mathematical model of a microwave beam device.
The mathematical model may be used to obtain an analytic solution, or may require a computational solution due to its complexity. With many physical devices, the smallest set of equations which sufficiently describe the device and can be solved analytically provide only a gross description of the device due to the simplifying assumptions made. A more complete description often requires a computational solution.
The discrete model, such as the discrete model of the beam-circuit region of the disk-loaded microwave beam device shown in Figure 3, provides an approximate description of the mathematical model. The discretization is necessary for simulation using a finite state, or digital, computer to solve the governing equations. The discrete model is independent of the implementation; both the structured and object-oriented approaches may share the same discrete model, and differ in the implementation. This model level describes the code representation of the physical device, and in the case of an object-oriented paradigm the discrete model provides a natural guide for the choice of objects.
In the example shown in Figure 3, the space is gridded so that the electric and magnetic fields and current can be defined at discrete points. Values of gridded quantities can be approximated at intermediate points by interpolation. Particles are discrete representations of some statistical group of physical particles. Boundaries provide the boundary conditions necessary to complete the equations describing the particles and fields.