  The role and mitigation of space charge effects are important aspects of the
beam physics research to be performed at the Integrable Optics Test Accelerator
(IOTA) at Fermilab. The impact of nonlinear integrability (partial and
complete) on space charge driven incoherent and coherent resonances will be a
new feature of this accelerator and has the potential to influence the design
of future low energy proton synchrotrons. In this report we model transverse
space charge effects using the PIC code pyORBIT. First we benchmark the single
particle tracking results against MADX with checks on symplecticity, tune
footprints, and dynamic aperture in a partially integrable lattice realized
with a special octupole string insert.
  Our space charge calculations begin with an examination of the 4D
symplecticity. Short term tracking is done first with the initial bare lattice
and then with a matching of the rms values with space charge. Next, we explore
slow initialization of charge as a technique to establish steady state and
reduce emittance growth and beam loss following injection into a mismatched
lattice. We establish values of space charge simulation parameters so as to
ensure numerical convergence. Finally, we compare the simulated space charge
induced tune shifts and footprints against theory.
