  The increasing data set of precise observations of very energetic and
collimated jets, with black hole (BH) as putative central engine, at different
astrophysical scales and in various environments, should soon permit to
discriminate and classify current theoretical models able to describe the jets
formation. We construct a purely gravitational theoretical model of perfectly
collimated jets of high energy particles in the ideal case where the central
engine is a Kerr BH of mass $M$ and angular momentum by unit of mass $a$. We
study in Weyl coordinates ($\rho $, $z$) the unbound Kerr 2D-geodesics which
are asymptotes to straight lines parallel to the $z$ axis of equations \rho
=constant= \rho_{1}= [(a/M)^2+Q/(E^2-1)]^{1/2} of which existence was recently
demonstrated (Gariel et al.,A & A, 2010). On these geodesics, flow test
particles of energy $E$, with a Carter constant $Q$ and (necessarily) an
angular momentum $L_{z}=0$. Studying the characteristics of the geodesics
equations system, in the special case of a double root, we exhibit jets with a
radial structure, whose energy flux can be calculated. From the observed data
of the jet powers, we obtain the mean particles density, the particles flow,
the speed and the Lorentz factor of the jets, for any charged or neutral test
particle. Then, we numerically apply these results to electrons. We also
discuss the domains of initial conditions for geodesics starting inside the
ergosphere. All these results come from the Kerr spacetime structure, and
enhance the Penrose process as a plausible origin for the high energy jets.
