Envelope method for calculation of transport channels

Envelopes of charged particle beams with a finite emittance in systems containing magnetic quadrupole lenses and uniform-field sector magnets have been analytically found and investigated. Using the obtained expressions the great number of dependences of the beam crossover position beyond the magnet on the system geometrical parameters have been calculated. Conclusions have been drawn that analytical expressions for envelopes of charged particle beams with a finite emittance considerably facilitate calculation of charged particle transoort channels