  Shocks in jets and hot spots of Active Galactic Nuclei (AGN) are one
prominent class of possible sources of very high energy cosmic ray particles
(above 10^18eV). Extrapolating their spectrum to their plausible injection
energy from some shock, implies an enormous hidden energy for a spectrum of
index ~-2. Some analyzes suggest the particles' injection spectrum at source to
be as steep as -2.4 to -2.7, making the problem much worse, by a factor of
order 10^6. Nevertheless, it seems implausible that more than at the very best
1/3 of the jet energy, goes into the required flux of energetic particles thus,
one would need to allow for the possibility that there is an energy problem,
which we would like to address in this work. Sequences of consecutive oblique
shock features, or conical shocks, have been theorized and eventually observed
in many AGN jets. Based on that, we use by analogy the 'Comptonisation' effect
and we propose a scenario of a single injection of particles which are
accelerated consecutively by several oblique shocks along the axis of an AGN
jet. We use detailed test-particle approximation Monte Carlo simulations in
order to calculate particle spectra by acceleration at such a shock pattern
while monitoring the efficiency of acceleration, calculating differential
spectra. We find that the first shock of a sequence of oblique shocks,
establishes a low energy power-law spectrum with ~E^-2.7. The consecutive
shocks push the spectrum up in energy, rendering flatter distributions with
steep cut-offs and characteristic depletion at low energies, an effect which
could explain the puzzling apparent extra source power as well as the flat or
inverted spectra from distant flaring sources.
