  We present X-ray spectral analysis of the accreting young star TW Hydrae from
a 489 ks observation using the Chandra High Energy Transmission Grating. The
spectrum provides a rich set of diagnostics for electron temperature T_e,
electron density N_e, hydrogen column density N_H, relative elemental
abundances and velocities and reveals its source in 3 distinct regions of the
stellar atmosphere: the stellar corona, the accretion shock, and a very large
extended volume of warm postshock plasma. The presence of Mg XII, Si XIII, and
Si XIV emission lines in the spectrum requires coronal structures at ~10 MK.
Lower temperature lines (e.g., from O VIII, Ne IX, and Mg XI) formed at 2.5 MK
appear more consistent with emission from an accretion shock. He-like Ne IX
line ratio diagnostics indicate that T_e = 2.50 +/- 0.25 MK and N_e = 3.0 +/-
0.2 x 10^(12) cm^(-3) in the shock. These values agree well with standard
magnetic accretion models. However, the Chandra observations significantly
diverge from current model predictions for the postshock plasma. This gas is
expected to cool radiatively, producing O VII as it flows into an increasingly
dense stellar atmosphere. Surprisingly, O VII indicates N_e = 5.7
^(+4.4}_(-1.2) x 10^(11) cm^(-3), five times lower than N_e in the accretion
shock itself, and ~7 times lower than the model prediction. We estimate that
the postshock region producing O VII has roughly 300 times larger volume, and
30 times more emitting mass than the shock itself. Apparently, the shocked
plasma heats the surrounding stellar atmosphere to soft X-ray emitting
temperatures and supplies this material to nearby large magnetic structures --
which may be closed magnetic loops or open magnetic field leading to mass
outflow. (Abridged)
