In the design of an electron or ion gun, the radial distribution of current density along the axis, jz(r,z), is often a critical issue. Trak includes several independent methods to calculate the quantity. Because information on implementing the methods is spread throughout the extensive Trak manual, I thought it would be useful to summarize the options in one place. To begin, we must recognize that jz is a statistical quantity. The quality of the data from any of the methods depends on factors such as the number of model particles and the introduction of angular divergence at the source. Note that you can use several of the methods simultaneously to get comparative data
1. Deposition of current density on a mesh.
To implement this method, use the RelBeam mode even if the particles are non-relativistic. Trak sets up mechanisms to deposit current density as well as charge density on the electrostatic mesh. The program adds current when a model particle crosses an element facet on the mesh, and then sums current starting from the axis to find B?(r,z). One advantage is that you can create contour and element plots of the magnetic field in the Trak plot menu if the information from a run is saved with the BBDump command. In the RelBeam mode, you can use the command
CDENS ZPos Rmax NR
to calculate current density and to make a record in the listing file. The parameters are the axial position for the calculation (ZPos), the maximum radius (RMax) and the number of radial bins NR. The smoothness and accuracy of the calculation improves with the number of model particles per radial bin.
2. Analysis of PRT files with GenDist
The PRT file records the complete properties of the model particles. You can load the file in GenDist for extensive analyses of beam distribution properties. To plot the relative current density, use the 1D bin style, choose f(r) as the plot quantity and make sure that current weighting is turned on.
By default, Trak records the parameters of model particles at their stopping points in response to the PARTFILE command. Sometimes, the particle do not stop in the same plane. For instance, some of the particles make strike an electrode. In this case, you can filter the distribution by axial position in GenDist.
There are two commands that control how PRT files are recorded:
DIAG (Up, X) = 4.54
RECORD [UP,DOWN] [X,Y,Z,R] RP1 RP2 ... RPN
In response to the DIAG command, the PRT file that results from PARTFILE is recorded at a specified axial plane rather than the model particle stop positions. The RECORD command creates a set of PRT files at up to 10 axial positions.
3. The distribution menu
The distribution menu is a relatively new feature of Trak where you can walk along the beam line creating plots of the beam phase-space distribution or current density jz(z,r). The program uses information recorded in the plot file (TOU). The method is more interactive than the others, but may not be as accurate. Again, the quality of the results depends on the number of model particles.
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