Coaxial Cylinder (coaxT.pre)

Keywords:

coaxT, coaxial geometry, cylinder, current pulse, rlc circuit, step potential

Problem description

This example probes the electromagnetic properties of a semi-infinite coaxial cylinder. One end of the cylinder lies in the simulation space and its dimensions are large–well beyond the size of a coaxial cable. It’s outer radius is 8 cm, the inner radius is 2 cm, and the section considered is 20 cm long. The inner cylinder is shorter than the outer cylinder and there is an electron absorbing cap on the end of the outer cylinder. When the simulation initiates, a single EM pulse is launched into the open, continuous end of the geometry and propagates to the capped tip. Electrons are ejected from the tip of the inner cylinder when the pulse reaches it. The pulse has a period of ~0.7 ns and the simulation runs for 5 periods.

This computational model is equivalent to applying a step-potential at one end of the cylinder (location of the other, unseen end of the cylinder is arbitrary). The step-potential propagates at the speed of light (the medium is a vacuum) until it reaches the tip of the inner cylinder. There, an attenuating series of oscillations occurs. Gradually the tip potential stabilizes at the applied potential.

This simulation can be performed with a VSimMD license.

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Fig. 332 The electrons are emitted from the tip of the inner cylinder after the field reaches it.

Opening the Simulation

The coaxT example is accessed from within VSimComposer by the following actions:

  • Select the NewFrom Example… menu item in the File menu.
  • In the resulting Examples window expand the VSim for Microwave Devices option.
  • Expand the Introductory Examples (Text-based setup) option.
  • Press the arrow button to the left of Introductory.
  • Select Coaxial Cylinder and press the Choose button.
  • In the resulting dialog, create a New Folder if desired, and press the Save button to create a copy of this example.

The basic variables of this problem should now be alterable via the text boxes in the left pane of the Setup Window, as shown in Fig. 333.

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Fig. 333 Setup Window for the Coaxial Cylinder example.

Input File Features

Primary Parameters

EXTERNAL_RADIUS_EXTERIOR:
Radius of the coaxial cylinder’s outer wall
EXTERNAL_CYLINDER_LENGTH:
Length of the outer cylinder, determines simulation domain size
EXTERNAL_CYLINDER_WIDTH:
Thickness of the outer cylinder wall
NGRID:
Number of cells spanning the length of the simulation space (the axial direction)
MGRID:
Number of cells spanning the dimensions of the simulation space transverse to the cylinder axis
EMITTED_CURRENT:
The current emitted from the tip of the inner cylinder
VBAR:
The average velocity of electrons emitted from the inner cylinder

Secondary and Derived Variables

Can be found in the input file view.

INTERNAL_RADIUS_EXTERIOR:
Radius of the inner cylinder’s outer wall; equal to 0.25*EXTERNAL_RADIUS_EXTERIOR
INTERNAL_CYLINDER_LENGTH:
Length of the inner cylinder; equal to 0.7*EXTERNAL_CYLINDER_LENGTH or EXTERNAL_CYLINDER_LENGTH - EXTERNAL_RADIUS_EXTERIOR, whichever quantity is longer.
INTERNAL_CYLINDER_WIDTH:
Thickness of the inner cylinder wall
OMEGA:
Equivalent frequency of incoming EM pulse. Not an actual physical quantity since the pulse is non-periodic. but it does help determine the rise time of the pulse, called PERIOD below. The rise-time depends on the cylinder radius and is equal to \(2.405c\)/EXTERNAL_RADIUS_EXTERIOR \(= 9.01\times 10^9 \textrm{rad/sec}\) \(= 14.2 \textrm{GHz}\).
PERIOD:
The rise-time of the pulse. Equal to \(2\pi/\textrm{OMEGA}\). Not used for any physics, PERIOD determines the simulation run time.
TIMESTEPS:
Determines length of simulation. By default the simulation will run for 5*PERIOD.

Running the simulation

After performing the above actions, continue as follows:

  • Proceed to the Run Window by pressing the Run button in the left column of buttons.
  • To run the file, click on the Run button in the upper left corner. of the window. You will see the output of the run in the right pane. The run has completed when you see the output, “Engine completed successfully.” This is shown in Fig. 334.
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Fig. 334 The Run Window at the end of execution.

Visualizing the results

After performing the above actions, continue as follows:

  • Proceed to the Visualize Window by pressing the Visualize button in the left column of buttons.

To create the image seen in Fig. 335, proceed as follows:

  • Expand Scalar Data
  • Expand edgeE
  • Select edgeE_y
  • Select Clip All Plots
  • Click the Plane Controls button and set the normal to the Z-direction
  • Select Display Contours and set the # of contours to 10
  • Set the particle size to 6 and the symbol to Sphere
  • Expand Particle Data
  • Expand electrons
  • Select electrons_ux
  • Expand Geometries
  • Select poly (coaxTGeom)
  • Move the dump slider forward in time
  • Click and drag to rotate
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Fig. 335 Visualization of the coaxial cylinder as a color contour plot.

To obtain a clearer picture of what is happening at the cylinder tip, switch the Data View to History. One dimensional plots of the number of electrons (called numberOfMacroParticles), the electric potential, phi, and the current emitted and absorbed should come up automatically.

You can set Graph 2 to Location “Window 1” as in Fig. 336.

The potential is measured at the tip of the cylinder with the interior of the inner cylinder serving as a reference point. The potential plotted has a lot of noise on it resulting from the free electrons. It may be insightful to run the simulation once without electrons so you can see the ringing on the waveform of phi, which is not unlike the output of an oscilloscope hooked up to a coaxial cable. Electrons can be suppressed by setting the EMITTED_CURRENT parameter to 0 during setup.

The coaxial cylinder acts like an RLC circuit: the inner conductor serves as an inductor, the gap between the tip and the absorbing cap is a capacitor, and the spacing between the inner and outer cylinders constitutes a resistor. By default, the rise-time of the pulse is near the resonance period, and this makes it a good driver of the circuit.

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Fig. 336 The History visualization window with the electrons.

Further Experiments

Try experimenting with different geometry sizes. In particular, note the effects of radius on pulse rise-time and cylinder length on the phi History plot.