[en] A dust-impact mass analyzer (DIMA) designed for determination of the chemical composition of cosmic dust of the Halley comet, placed aboard the ''Vega'' and ''Jotto'' space probes is theoretically analysed. DIMA represents a combination of a dust accelerator and a time-of-flight mass spectrometer (TFMS) of the ''mass-reflectron'' type. The problem on motion ofthe collisionless, cold plasma cloud expanding by inertia in the external electric field is theoretically solved. The solution is carried out within the scope of the perturbation theory. Non-steady-state flow and concentration of impurity ions are small parameters in this problem. The solutions obtained are used to built the theory of TFMS analysis in case when the ion source is the plasma cloud formed during collision of an ultrahighspeed dust with an obstacle. TFMS resolution capability, angular distribution of ions behind the removing screen and TFMS carrying capacity are calculated for multicomponent plasma. A case of oblique impact, when dust flies at an angle to the anode surface, is considered. It is shown that in this case only certain lines of the mass spectrometer can be lost due to proper ions carrying by a ion collector