Three-dimensional Tomography of the Galactic and Extragalactic
  Magnetoionic Medium with the SKA
  The magneto-ionic structures of the interstellar medium of the Milky Way and
the intergalactic medium are still poorly understood, especially at distances
larger than a few kiloparsecs from the Sun. The three-dimensional (3D)
structure of the Galactic magnetic field and electron density distribution may
be probed through observations of radio pulsars, primarily owing to their
compact nature, high velocities, and highly-polarized short-duration radio
pulses. Phase 1 of the SKA, i.e. SKA1, will increase the known pulsar
population by an order of magnitude, and the full SKA, i.e. SKA2, will discover
pulsars in the most distant regions of our Galaxy. SKA1-VLBI will produce
model-independent distances to a large number of pulsars, and wide-band
polarization observations by SKA1-LOW and SKA1-MID will yield high precision
dispersion measure, scattering measure, and rotation measure estimates along
thousands of lines of sight. When combined, these observations will enable
detailed tomography of the large-scale magneto-ionic structure of both the
Galactic disk and the Galactic halo. Turbulence in the interstellar medium can
be studied through the variations of these observables and the dynamic spectra
of pulsar flux densities. SKA1-LOW and SKA1-MID will monitor interstellar
weather and produce sensitive dynamic and secondary spectra of pulsar
scintillation, which can be used to make speckle images of the ISM, study
turbulence on scales between ~10^8 and ~10^13 m, and probe pulsar emission
regions on scales down to $\sim$10 km. In addition, extragalactic pulsars or
fast radio bursts to be discovered by SKA1 and SKA2 can be used to probe the
electron density distribution and magnetic fields in the intergalactic medium
beyond the Milky Way.
