In this Data form, the user can enter the gas mixture, pressure (pr, in torr) and temperature (Tg, in K), the dimensions of the simulation domain (Xmax, and Ymax, in cm), and the secondary emission coefficients g1, g2, g3, corresponding to the different ions of the mixture.
Checking
the box Initialization sets all arrays to their initial values.
If Initialization is not checked, numerical calculations begin using
values for arrays in the file res2d.out.
In the Control form, the user defines the frequency of writing the results on the screen (Run Bar, see below). The second parameter is the frequency of writing the res2d.out file (default is every 200 time step). The third parameter defines the frequency of writing in intermediate files Resxx.res which can be post-processed later (e.g. using the SIPDP-AC PlayBack feature). This frequency can be defined in terms of number of time steps or in time intervals. The file naming scheme is Res01.res, Res02.res,... where is xx to 0 when the initialization corresponding box is checked. Go to the Play Back page for more details on the Play Back mode
The CFL parameter can be used to adjust the time step. The time step during the current pulse, when the plasma is present, is automatically adjusted. In the prebreakdown phase or after the current pulse, the time step is controled by the CFL parameter . The default value is 500 and is a reasonable value. The default value in the previous version (v5.0) was 2000. The 500 value is slighlty more accurate, but larger values can be used if one is not concerned by the accuracy during the prebreakdown phase (the delay to breakdown becomes less accurate when this parameter is larger)
The acceleration parameter can also be modified by the user. This parameter sets up the value of the integration time step. The largest values correspond to larger integration time step. However for better accuracy, the recommended parameter is 3 default value). The first value ("0") corresponds to no acceleration i.e. to explicit integration of the continuity equations.
The last choice of the acceleration parameter ("ramp") allows very large time steps and should be used only for quasi-steady state situation like for example in the set-up period of the driving scheme of a PDP, where the voltage is slowly increased or decreased (slope on the order of V/ms), and the discharge stays in a Townsend regime.
The type of boundary conditions ("Symmetry" of "Periodic") and the initial plasma density are defined on this form.
When the Initialization box is checked, the programs starts with a uniform density of electrons and ions defined in this form. The default value (see the menu above) of the initial density is 107 cm-3.
The user can also run the simulation using a uniform production of electrons and ions ("source") in the volume of the cell. This is a supplementary source term of the electron and ion continuity equations and may represent, for example, the generationof electrons and ions due to other processes than electron impact ionization of atoms in the ground state (for example, generation of electrons and ions due to neighbouring cells, photoemission, etc...). Adding this source term may be necessary when studying the ramp voltages used for priming before addressing.
The applied voltage waveform is defined in this menu. Multipulse AC corresponds to a sequence of AC pulses (with a zero or finite rise time). Multipulse AC/RF corresponds to a combination of AC and RF pulses. Breakdown can be used to automatically calculate breakdown voltages and Paschen curves.
The Multipulse AC, AC/RF and the breadown options are chosen by clicking on the corresponding rectangular push buttons. The user must then fill in the proposed form. The different forms are described below:
Each line of this table corresponds to a given time interval (given in microseconds). The voltages (in Volts) applied to each electrode during the time intervals are defined in the columns. The numbering of the electrode voltages (V1, V2, V3 ...) is counter clockwise from the bottom left of the domain (see Electrode Numbering).
If there are three lines in the table, the entry in the box between End after and pulses should be 3.
A sequence of pulses can be repeated several times (see the Repeat sequence line) in a straightforward way.
When the option Step is chosen, the rise time of the voltage pulse is practically zero (equal to one time step). The time column (T (mms)) contains the duration of each voltage pulse (in microseconds). An example of the Step option is given in the table below.
When the option Linear is chosen, it is possible to define a non zero rise time. In that case, for a time interval given in line k , the voltage is supposed to increase linearly between the voltage value given at line k and the voltage value given at line k+1, for each voltage column (i.e. each electrode). The time interval given on the last line is therefore not used. An example of the Linear option is given below. This example is similar to the one above, but with rise times and decay times of 300 ns between pulses.
- Floating Electrodes
It is possible to include electrodes with floating voltage. The voltage on a floating electrode must be floating for the whole duration of the voltage pulse sequence.
In order to define a floating electrode, an integer greater or equal than 10001 must be written in the column corresponding to this electrode in the MultiPulse AC form. If only one floating electrode is included 10001 must be used. If two floating electrodes are included, 10001 must be written in the column corresponding to the first floating electrode, and 10002 in the column corresponding to the second floating electrode if they are floating separately. If the two electrodes are floating together (i.e. same floating voltage), the same value (10001) must be written in both columns (same for several floating electrodes). See exemple below (électrodes 3 and 4 are floating separately)
When the MultiPulse AC/RF option is chosen, two forms are successively presented to the user. The first one is identical to the one of the MultiPulse AC option described above and corresponds to the AC part of the applied voltage. When the MultiPulse AC form is filled in, a second form containing information about the RF part of the applied voltage is presented to the user. This form is shown below. The number of lines is identical to the one of the MultiPulse AC form and cannot be changed. The frequency of the sinusoidal voltage must be indicated in MHz. Each column contains the amplitude of the RF voltage applied to each electrode during a given time interval.
This option can be chosen to automatically calculate the breakdown curve for a given geometry. The dimensions are fixed and the pressure is incremented by the code, from the minimum value to the maximum value indicated at the bottom of the dialog box. The number of points in pressure is given on the top right of the dialog box. The breakdown curve is calculated for a given electrode (the electrode number is given on the top left of the dialog box), the other electrodes being kept at a fixed voltage indicated in the table. The code looks for the breakdown voltage by successive trials. The user must provide the first trial value and the increment.
To obtain the breakdown voltage, the code solves the electron and ion transport equations coupled with Poisson's equation (as in the simulation of voltage pulses). Whether or not breakdown occurs, for a given voltage value, will depend on the plasma density growth during a given time interval. If the charged particle density decays, the applied voltage is below breakdown and another trial value of the voltage, larger than the previous one is used. This process is repeated until the breakdown criterion is satisfied.
The breakdown criterion can be adjusted by the user as follows. Breakdown is said to occur when the maximum total ion density reaches a given value within a given time interval, both provided by the user. The result will obviously depend on the initial electron and ion density (supposed to be uniform in the gap). In the example below the initial density is 104 cm-3 and the maximum total ion density at breakdown is 1011 cm-3. A "good" choice would probably be to use an initial ion density as low as possible (even if not realistic) and a maximum ion density low enough that the space charge electric field is small with respect to the geometric field at the time of breakdown.
