A novel realistic Hamiltonian model system is introduced, the "kicked Hall system". This is a charged particle in a uniform magnetic field (in the z-direction) and in a uniform electric field (in the y-direction), periodically δ-kicked in time by a cosine potential with strength K in the x-direction. The electric-field strength is measured by a dimensionless parameter β. In the absence of an electric field (β = 0) and under certain resonance conditions (i.e., precisely four kicks in one cyclotron period), it is well known that the system exhibits a global (unbounded) chaotic diffusion in the velocity plane for arbitrarily weak chaos (i.e., arbitrarily small K). This diffusion takes place on a stochastic web with square symmetry. The web structure and the diffusion rate strongly depend on the value of a conserved coordinate x_c of the cyclotron orbit center.

For β ≠ 0, x_c is not conserved but vary linearly in time (Hall effect). We derive, for generic rational values of β, an exact expression of the integrable effective Hamiltonian H_eff for the system up to (and including) second order in K; this Hamiltonian describes in an average sense the basic phase-space structure in the weak-chaos regime. We find that, except of very special cases, the first-order term of H_eff  always vanishes while the second-order term is always independent on the initial value x_c⁽⁰⁾ of x_c and corresponds to a simple universal stochastic web. All this implies a generic suppression of weak chaos and chaotic diffusion on the universal web for essentially all values of β and x_c⁽⁰⁾, in sharp contrast with the β = 0 case, where the first-order term vanishes only for one value of x_c.

The first-order term does not vanish only for two rational values of β and is dependent on x_c⁽⁰⁾ in these cases. This term implies that ballistic motion in velocity occurs for generic x_c⁽⁰⁾ while a stochastic web arises only for special "critical" values x_cc⁽⁰⁾ of x_c⁽⁰⁾. The ballistic-transport rate vanishes like |x_c⁽⁰⁾ - x_cc⁽⁰⁾| as x_c⁽⁰⁾ approaches x_cc⁽⁰⁾.