  Recent spectropolarimetric observations of otherwise ordinary G, K, and M
giants revealed localized magnetic strips in the HRD coincident with the
regions where the first dredge-up and core He-burning occur. We seek to
understand the origin of magnetic fields in such late-type giant stars. In
analogy with late-type dwarf stars, we focus primarily on parameters known to
influence the generation of magnetic fields in the outer convective envelope.
We compute the classical dynamo parameters along the evolutionary tracks of
low- and intermediate-mass stars at various metallicities using stellar models
that have been extensively tested by spectroscopic and asteroseismic
observations. These include convective turnover timescales and convective
Rossby numbers, computed from the PMS to the tip of the RGB or the early AGB.
To investigate the effects of the very extended outer convective envelope, we
compute these parameters both for the entire convective envelope and locally,
that is, at different depths within the envelope. We also compute the turnover
timescales and corresponding Rossby numbers for the convective cores of
intermediate-mass stars on the main sequence.
  Our models show that the Rossby number of the convective envelope becomes
lower than unity in the well-delimited locations of the Hertzsprung-Russell
diagram where magnetic fields have indeed been detected. We show that
alpha-omega dynamo processes might not be continuously operating, but that they
are favored in the stellar convective envelope at two specific moments along
the evolution tracks, that is, during the first dredge-up at the base of the
RGB and during central helium burning in the helium-burning phase and
early-AGB. This general behavior can explain the so-called magnetic strips
recently discovered by dedicated spectropolarimetric surveys of evolved stars.
