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The paper considers the excitation of a wakefield in a metal-density plasma using a chain of x-ray laser pulses. The profiling parameters and the necessary parameters of laser pulses for obtaining stable high-quality bunches are found. An essential problem is the destruction of self-injected bunches in the course of their motion. The results of the study are one of the ways to solve the problem of transverse betatron oscillations, which lead to the destruction of bunches.

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