OmniTrak can include contributions of cathode temperature to the emittance of extracted electron beams. The theory of how the thermal energy of electrons emitted a hot cathode appears as an angular beam divergence is discussed in Sect. 11.2 of the OmniTrak manual. This example reviews setup techniques. The upper figure shows the geometry. The cathode, focus electrode and emission surface are at -10.0 kV and the anode is at ground potential. The calculation is performed in the SCharge mode. The emission surface that covers the planar cathode has region number RegNo = 4. To minimize the run time, the solution volume includes only the first quadrant, with field symmetry and particle reflection boundaries at x = 0.0 cm and y = 0.0 cm. The MetaMesh input file (HotCathodeOmniTrak.MIN) demonstrates the construction of an accurate emission surface. The emission commands in the OmniTrak input file HotCathodeOmniTrak.OIN have the form:
EMIT(4): 0.0000E+00 -1.0000E+00 3.0000E-02 2
TSOURCE 0.2
The parameter 2 in the EMIT command signifies that 2^2 particles are emitted from each facet of the emission surface, for a total of 5024. The TSOURCE command (described in Sect. 11.2 of the OmniTrak manual) designates that the electrons have a Maxwellian distribution of transverse energy leaving the cathode with an average value of 0.2 eV.
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Results
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The calculation gives a space-charge-limited current of 0.364248 A/quadrant. The total current of 1.456 A is within 1.4% of a Trak prediction. The lower figure shows the resulting radial phase-space distribution. The top illustration is for a cold beam with the TSOURCE command commented out. The bottom illustration shows the warm beam results. The phase-space distribution r-rp has an an angular spread of about 0.005 radians. For comparison, the predicted angular spread is on the order of (kT/Te), where Te is the exit energy in eV. Taking kT = 0.2 and Te = 1.0E4, the value is about 0.0045 radians.
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Comments
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For comparison, the same calculation performed with the 2D Trak code: cathode_temp_trak.html.
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