We studied angular distributions of x rays emitted in resonant recombination of highly charged iron and krypton ions, resolving dielectronic, trielectronic, and quadruelectronic channels. A tunable electron beam drove these processes, inducing x rays registered by two detectors mounted along and perpendicular to the beam axis. The measured emission asymmetries comprehensively benchmarked full-order atomic calculations. We conclude that accurate polarization diagnostics of hot plasmas can only be obtained under the premise of inclusion of higher-order processes that were neglected in earlier work. 32.30.Rj, 31.30.jc, 34.80.Lx The observation of x-ray polarization in emissions from the Crab Nebula [1,2], with synchrotron radiation as its origin, fueled a strong interest in the astrophysics community for launching an x-ray polarimetry (XRP) mission [3][4][5][6][7]. X-ray Imaging Polarimetry Explorer (XIPE) has recently been selected as one of three candidates for the next medium-size satellite mission by the European Space Agency ESA. Its aim is studying the anisotropies of astrophysical plasmas which are found in the most extreme yet poorly understood sites in the Universe [8,9]. Up to now anisotropic plasmas were found in active galactic nuclei [10][11][12], pulsars [13], gamma-ray bursts [14][15][16], neutron stars [17,18], and solar flares [19][20][21]. They appear prominently also in the laboratory: in experiments with strong lasers [22,23], magnetic cusps [24], z -pinches [25], and fusion devices [25][26][27] such as tokamaks [28][29][30] and stellarators. The directionality of the electron-ion collisions leaves an imprint in the polarization of the plasma x rays [31][32][33][34][35][36]. Polarization measurements may therefore reveal the presence and orientation of particle beams, magnetic fields and, hence, provide information on the plasma heating and confinement mechanisms [25][26][27] in instances where spatial resolution is insufficient. In astrophysics, indeed, XRP is often the only technique for deriving information on the geometry of angularly unresolved sources [8,37].Ideally, the XRP data should be analyzed with detailed knowledge of the atomic polarization mechanisms. Until now, however, no or little experimental information is available for most atomic processes. Only very few studies of x-ray polarization and angular distributions have been performed for astrophysically relevant ions using electron beam ion traps (EBITs) [38][39][40][41][42][43][44][45][46]. Other studies with EBITs [47][48][49][50], electron accelerators [32, 51, 52] and storage ring [34,53] have focused on heavy ionic systems. Moreover, the photoelectric gas polarimeter [4,54] of the XIPE mission will not resolve individual x-ray transitions. This limitation is rather general, even if high resolution detectors were used, since Doppler shifts will most likely blur the signal. Thus, the polarization signal will contain contributions from many transitions and continuum radiation due to bremsstrahlung and recombination of plas...