Field Precision title

Emission surfaces in Trak

A user recently sent a Trak setup where ions from an emission surface mysteriously moved backward, apparently in opposition to the electrical forces. The cause and resolution of the problem provide a good illustration of emission surface techniques.

To start, it is important to recognize 1) the concept of open and filled regions in the TriComp programs and 2) the method used to create emission surfaces in Trak. The conformal triangular meshes used in the TriComp programs fill a region in x-y or z-r space. The triangles are the elements. The vertices of the triangles are the nodes. Every element and node is associated with one of the regions of the solution. The physical properties of regions are assigned to the associated elements and nodes. In an electrostatic solution, the procedure is to calculate values of the electrostatic potential at nodes. The element quantity is typically the relative dielectric constant, while the most common node property is a fixed-potential condition (e.g., surface and interior of an electrode). An open region is one where the region number is assigned only to nodes. For example, an open line region could represent an infinitely-thin grounded foil. A filled region is one where the region number is assigned to all elements and nodes inside the region boundary. A filled region could represent a dielectric or an electrode with non-zero volume.

One of the outstanding features of Trak is the range of options for assigning surfaces for space-charge-limited emission. A simulation may include multiple surfaces of any shape or orientation with multiple particle species. Here's how the method works:

  • An emission surface is a open region of fixed-potential nodes on the surface of an electrode (filled region with the fixed-potential condition).
  • To model Child-law emission, Trak must construct a virtual emission surface a short distance from the physical emission surface in the direction of particle emission.
  • Given a facet on the physical emission surface, there are two possible locations for the virtual surface (right/left or up/down relative to the physical surface). Trak decides by projecting? a short vector normal to the facet in one direction. If the vector terminates in a fixed-potential element, the code projects the virtual surface in the opposite direction. If fixed-potential elements are detected in both directions, the code reports an error.

Figure 1 shows the setup created by the user. He defined the end plate with an open line region at zero potential at z = 24.0 cm. The nodes on the portion of the surface from r = 0.0 cm to r = 1.0 cm were associated with the emission region. Although he expected emitted protons to be pulled into the strong negative potential created by the electron beam on the left, the ions (red lines) moved to the right and exited at the boundary.


Figure 1. Incorrect solution, emission surface on an open region.

Based on the above discussion, we can understand what happened. There are no fixed-potential elements near the emission surface. Trak first tested the +z direction. Finding vacuum elements, the code decided that this was a valid location for the virtual surface and placed it on the right-hand side of the grounded surface. The protons were pulled to the right by the residual potential of the electron space charge in the dead space z > 24.0 cm.

Figure 2 illustrates the correct setup. The grounded end plate was defined by a filled, fixed-potential region of finite thickness. The presence of electrode elements signalled that Trak should locate the virtual emission surface to the left of the physical surface, giving the expected ion emission.


Figure 2. Correct solution, emission region on the surface of a filled electrode region.

In summary, a general rule applies to both Trak and OmniTrak: emission coatings must always be located on the surface of a filled electrode region (i.e., non-zero volume).

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