  We present APEX LABOCA 870 micron observations of the field around the
high-redshift radio galaxy MRC1138-262 at z=2.16. We detect 16 submillimeter
galaxies in this ~140 square arcmin bolometer map with flux densities in the
range 3-11 mJy. The raw number counts indicate a density of submillimeter
galaxies (SMGs) that is up to four times that of blank field surveys. Based on
an exquisite multiwavelength database, including VLA 1.4 GHz radio and infrared
observations, we investigate whether these sources are members of the
protocluster structure at z=2.2. Using Herschel PACS+SPIRE and Spitzer MIPS
photometry, we derive reliable far-infrared photometric redshifts for all
sources. Follow-up VLT ISAAC and SINFONI near-infrared spectra confirm that
four of these SMGs have redshifts of z=2.2. We also present evidence that
another SMG in this field, detected earlier at 850 micron, has a counterpart
that exhibits Halpha and CO(1-0) emission at z=2.15. Including the radio galaxy
and two SMGs with far-IR photometric redshifts at z=2.2, we conclude that at
least eight submm sources are part of the protocluster at z=2.16 associated
with the radio galaxy MRC1138-262. We measure a star formation rate density
SFRD ~1500 Msun yr^-1 Mpc^-3, four magnitudes higher than the global SFRD of
blank fields at this redshift. Strikingly, these eight sources are concentrated
within a region of 2 Mpc (the typical size of clusters in the local universe)
and are distributed within the filaments traced by the Halpha emitters at
z=2.2. This concentration of massive, dusty starbursts is not centered on the
submillimeter-bright radio galaxy which could support the infalling of these
sources into the cluster center. Approximately half (6/11) of the SMGs that are
covered by the Halpha imaging data are associated with Halpha emitters,
demonstrating the potential of tracing SMG counterparts with this population
(abridged).
