  This is the second paper in a series where we build a self-consistent model
to simulate the mass-loss process of a close-orbit magnetized giant exoplanet,
so-called hot Jupiter (HJ). In this paper we generalize the hydrodynamic (HD)
model of an HJ expanding hydrogen atmosphere, proposed in the first paper, to
include the effects of intrinsic planetary magnetic field. The proposed
self-consistent axisymmetric 2D magnetohydrodynamics model incorporates
radiative heating and ionization of the atmospheric gas, basic hydrogen
chemistry for the appropriate account of major species composing HJ's upper
atmosphere and related radiative energy deposition, and H3+ and Ly{\alpha}
cooling processes. The model also takes into account a realistic solar-type
X-ray/EUV spectrum for calculation of intensity and column density distribution
of the radiative energy input, as well as gravitational and rotational forces
acting in a tidally locked planet-star system. An interaction between the
expanding atmospheric plasma and an intrinsic planetary magnetic dipole field
leads to the formation of a current-carrying magnetodisk that plays an
important role for topology and scaling of the planetary magnetosphere. A
cyclic character of the magnetodisk behavior, composed of consequent phases of
the disk formation followed by the magnetic reconnection with the ejection of a
ring-type plasmoid, has been discovered and investigated. We found that the
mass-loss rate of an HD 209458b analog planet is weakly affected by the
equatorial surface field <0.3 G, but is suppressed by an order of magnitude at
the field of 1 G.
