We report a study of the H30 alpha line emission at 1.3 mm from the region around Sgr A* made with the Submillimeter Array at a resolution of 2'' over a field of 60'' (2 parsec) and a velocity range of -360 to +345 km/sec . This field encompasses most of the Galactic center's ``minispiral.'' With an isothermal homogeneous HII model, we determined the physical conditions of the ionized gas at specific locations in the Northern and Eastern Arms from the H30 alpha line data along with Very Large Array data from the H92 alpha line at 3.6 cm and from the radio continuum emission at 1.3 cm. The typical electron density and kinetic temperature in the minispiral arms are 3-21*104 cm-3 and 5,000-13,000 K, respectively. The H30 alpha and H92 alpha line profiles are broadened due to the large velocity shear within and along the beam produced by dynamical motions in the strong gravitational field near Sgr A*. We constructed a 3D model of the minispiral using the orbital parameters derived under the assumptions that the gas flows are in Keplerian motion. The gas in the Eastern Arm appears to collide with the Northern Arm flow in the ``Bar" region, which is located 0.1-0.2 parsec south of and behind Sgr A*. Finally, a total Lyman continuum flux of 3*1050 photons s-1 is inferred from the assumption that the gas is photoionized and the ionizing photons for the high-density gas in the minispiral arms are from external sources, which is equivalent to 250 O9-type zero-age-main-sequence stars.