Particle beam system comprising the following: a multiple beam particle source which is configured to generate a multiplicity of charged individual particle beams; a multi-pole lens sequence with at least one first multi-pole lens array and with at least one second multi-pole lens array, wherein the first multi-pole lens array comprises a multiplicity of individually adjustable first multi-pole lenses for generating first quadrupole fields and is arranged in the beam path of the particles in such a way that the individual particle beams substantially pass through the first multi-pole lens array and wherein the second multi-pole lens array comprises a multiplicity of individually adjustable second multi-pole lenses for generating second quadrupole fields and is arranged in the beam path of the particles so that the individual particle beams which pass through the first multi-pole lens array substantially also pass through the second multi-pole lens array; wherein groups of multi-pole lenses are formed by sequences of multi-pole lenses belonging to different multi-pole lens arrays (601, 602) through which the same individual particle beams pass, respectively, and a controller, characterized in that the controller is configured to individually control the generation of a first quadrupole field in the first multi-pole lens array and to individually control the generation of a second quadrupole field in the second multi-pole lens array for each group in such a way that the sequence of multi-pole lenses of each group exerts a substantially stigmatic focussing effect on the respective individual particle beam passing therethrough. a multiple beam particle source which is configured to generate a multiplicity of charged individual particle beams; a multi-pole lens sequence with at least one first multi-pole lens array and with at least one second multi-pole lens array, wherein the first multi-pole lens array comprises a multiplicity of individually adjustable first multi-pole lenses for generating first quadrupole fields and is arranged in the beam path of the particles in such a way that the individual particle beams substantially pass through the first multi-pole lens array and wherein the second multi-pole lens array comprises a multiplicity of individually adjustable second multi-pole lenses for generating second quadrupole fields and is arranged in the beam path of the particles so that the individual particle beams which pass through the first multi-pole lens array substantially also pass through the second multi-pole lens array; wherein groups of multi-pole lenses are formed by sequences of multi-pole lenses belonging to different multi-pole lens arrays (601, 602) through which the same individual particle beams pass, respectively, and a controller, characterized in that the controller is configured to individually control the generation of a first quadrupole field in the first multi-pole lens array and to individually control the generation of a second quadrupole field in the second multi-pole lens array for each group in such a way that the sequence of multi-pole lenses of each group exerts a substantially stigmatic focussing effect on the respective individual particle beam passing therethrough.