Electron beam evaporation with hot filament and magnetic field—Computer control and parameter estimation

Control of hot-filament ionization gauge emission current: mathematical model and model-based controller

“…Neglecting conductive heat losses for working pressures below 10 −1 Pa [9], the equation for the steady state filament heating process takes the following form:…”

“…To obtain a more accurate approximation of the emission current-temperature relation, the actual temperature distribution along the length of the filament must be taken into account. Using the results obtained in [9], the temperature distribution T (x) is given by:…”

“…The mathematical model describing the dynamics of the thermoemission process can be derived from the temperature increase of the filament. Taking into account the filament heating-power balance obtained in [9], the growth of the temperature at any point of the wire is given by: where c is the specific heat capacity of the filament material and δ is its density. As seen in equation ( 4), in the steady state the value of d 2 T / dx 2 is proportional to (T 4 m −T 4 ).…”

“…As the characteristic varies smoothly with U f , it is possible to develop useful approximate linear models of this behaviour [9]. However, to predict the time constants associated with the filament heating process, one must use a more adequate relation between P f and I e , namely, a nonlinear one.…”

“…However, to predict the time constants associated with the filament heating process, one must use a more adequate relation between P f and I e , namely, a nonlinear one. Once the time constants are known, one can then determine the control type and the optimal control law parameters [9] in the desirable working range.…”