  Variability is a general property of accretion discs and their associated
jets. We introduce a semi-analytic model for particle acceleration and radio
jet/lobe evolution and explore the effect of Myr timescale jet variability on
the particles accelerated by an AGN jet. Our work is motivated by the need for
local powerful ultrahigh energy cosmic ray (UHECR) sources and evidence for
variability in AGN and radio galaxies. Our main results are: i) UHECR and
nonthermal radiative luminosities track the jet power but with a response set
by the escape and cooling times, respectively; ii) jet variability produces
structure in the electron, synchrotron and UHECR spectra that deviates from
that produced for a constant jet power - in particular, spectral hardening
features may be signatures of variability; iii) the cutoff in the integrated CR
spectrum is stretched out due to the variation in jet power (and, consequently,
maximum CR energy). The resulting spectrum is the convolution of the jet power
distribution and the source term. We derive an approximate form for a
log-normal distribution of powers; iv) we introduce the idea of $\sim 10$ GeV
'proxy electrons' that are cooling at the same rate that UHECRs of rigidity 10
EV are escaping from the source, and determine the corresponding photon
frequencies that probe escaping UHECRs. Our results demonstrate the link
between the history of an astrophysical particle accelerator and its particle
contents, nonthermal emission and UHECR spectrum, with consequences for
observations of radio galaxies and UHECR source models.
