微放电-二次电子倍增仿真VORPAL

1、Multipacting in Coaxial WaveguideProblem DescriptionMultipacting, which is the resonant build up of secondary electrons, is often a concern inradio frequency structures. Anytime a there is an oscillating electromagnetic fieldacross a gap between two surfaces there exists the possibility that for the

2、 right fieldamplitude across the gap a resonance condition will exist allowing the exponential buildup of secondary electrons. A coaxial waveguide is such structure where these conditionscan exist.Input File FeaturesThe simulation setup consists of a coaxial waveguide where an electromagnetic wave i

3、s launched at one end and then propagates down the waveguide leaving the simulation at an open boundary. The Yee electromagnetic model, along with the Dey-Mittra cut-cell algorithm, are used to model the electromagnetics in the simulation. Typically the simulation is run once without particles to de

4、termine a normalization amplitude for the wave launcher. This allows following simulations to run where it is easy to specify a specific wave amplitude.After the wave has been established in the waveguide, a line of seed electrons is introduced at the outer radius of the coax every time step for a w

5、ave full period. This insures that all the phases of the wave are checked for multipacting trajectories. Variable weight, tagged particles are used. The particle weight corresponds to the electron growth along the particle trajectory and the tag allows for the use of particle tracking histories. Usi

6、ng the secondary electron routines in VORPAL, every time an electron impacts the waveguide walls with an energy in the correct range, they will produce at least one secondary electron. Instead of producing more macro particles in the simulation, the electron is re-emitted with its particle weight mu

7、ltiplied by the secondary electron yield.Several histories are used in this simulation. The electric field is sampled half way across the gap normal to the amplitude for the wave launcher. A Poynting flux history records the power being transmitted down the wave guide. The trajectory and internal pa

8、rticle variables are recorded for a subset of electrons in the simulations. The particle weight is the last component of the internal variables. Monotonic growth in the particle weight is what demonstrates multipacting. To find the subset of the particles tracked, the simulation is run without the p

9、article tracking histories.Theparticles with the largest growth in the particle weight are then identified and the simulation is re-run with those particles tracked by their tags.Running the SimulationThe VORPAL input file can be found .Once you have saved the input file, open it in VORPAL Studio. T

10、he file should be displayed in the right pane of the studio. Click on the green arrow in the menu bar at top to run the file. Save the file if necessary. The tab will switch to Output and you can see the real time output of the run.This file should be run in serial to reproduce the results below. If

11、 run in parallel, the histories will not necessarily track the same particles as the particle tag is different on serial and parallel. It is also important to note that some of the features in the input file are new and VORPAL Studio will not recognize them as valid. These warnings can be ignored an

12、d the file can be run as is.Viewing the OutputAfter the run has completed, view the data written by VORPAL to HDF5 files by clicking on the “Visualize Results With VorpalView” button at the bottom of the Output tab or by switching to the Work Space tab and double clicking on any of the files ending

13、with the '.h5' extension.To view the electric field, pull down the Field dropbox and choose YeeElecField. The components of the field can be chosen by pulling down on the Component dropbox. You can now step through the dumped data by using the slider at the bottom to observe the evolution of

14、 the field.To view the particle trajectories, the internal variables for the particles (which includes the particle weight) or other histories, navigate to the History tab. The histories are shown in alphabetical order and the initial three show the electric field, the internal particle variables an

15、d the Poynting flux. To change which history is displayed, pull down on the Data dropbox.ResultsBy selecting the last component of the internal variable history which corresponds to the weight, and the first (x) and second (y) components of the trajectory history we see that the first particle track

16、ed demonstrates multipacting. Figure 1 shows these three histories as a function of time.Each time the particle weight increases, indicates a collision with the waveguide walls has occurred andsecondary electrons have been produced. These increases in the particle weight correspond to points on the y posi