  Compact DC high-voltage photo-electron guns are able to meet the
sophisticated demands of high-current applications such as energy recovery
linacs. A main design parameter for such sources is the electric field
strength, which depends on the electrode geometry and is limited by the field
emission threshold of the electrode material. In order to minimize the maximum
field strength for optimal gun operation, isogeometric analysis (IGA) can be
used to exploit the axisymmetric geometry and describe its cross section by
non-uniform rational B-splines, the control points of which are the parameters
to be optimized. This computationally efficient method is capable of describing
CAD-generated geometries using open source software (GeoPDEs, NLopt, Octave)
and it can simplify the step from design to simulation. We will present the
mathematical formulation, the software workflow, and the results of an
IGA-based shape optimization for a planned high-voltage upgrade of the DC
photogun teststand Photo-CATCH at TU Darmstadt. The software builds on a
general framework for isogeometric analysis and allows for easy adaptations to
other geometries or quantities of interest. Simulations assuming a bias voltage
of -300 kV yielded maximum field gradients of 9.06 MV/m on the surface of an
inverted insulator electrode and below 3 MV/m on the surface of the
photocathode.
