**Aim:** search and study of such configurations of the electromagnetic field, in which due to the strong localization of the energy of pulsed radiation in space and in time, intensities can be achieved that are sufficient to observe the nonlinear properties of the vacuum (for example, generation of electron-positron pairs) at the required energy the level of existing or planned to build laser systems in the near future. Generation of electron-positron pairs requires taking into account quantum-electrodynamic (QED) effects, and the process of generating pairs as a cascade (similarly to gas breakdown) can be started at field intensities that are noticeably lower than the Schwinger field. One of the most promising opportunities considered in modern studies is the use of sharp focusing of radiation in the form of an inverted dipole wave.

Tasks:

1. A detailed study of the linear stage of the development of QED cascade in the field of several beams focused in the form of E- and B-dipole waves.

2. Investigation by means of numerical simulation of the evolution of plasma structures both at the linear and nonlinear stages of the development of QED cascade in the field of several laser beams focused in the form of a dipole wave.

3. Investigation by means of numerical simulation of the stability of regimes of interaction of laser radiation with the plasma with respect to variations in the parameters of laser beams: amplitude, focusing and synchronization accuracy. Theoretical study of various variants of highly localized field configurations created by several coherently summed beams, optimal for observing vacuum nonlinearity.

Tasks:

1. A detailed study of the linear stage of the development of QED cascade in the field of several beams focused in the form of E- and B-dipole waves.

2. Investigation by means of numerical simulation of the evolution of plasma structures both at the linear and nonlinear stages of the development of QED cascade in the field of several laser beams focused in the form of a dipole wave.

3. Investigation by means of numerical simulation of the stability of regimes of interaction of laser radiation with the plasma with respect to variations in the parameters of laser beams: amplitude, focusing and synchronization accuracy. Theoretical study of various variants of highly localized field configurations created by several coherently summed beams, optimal for observing vacuum nonlinearity.