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

Profiling and variation of laser pulse parameters as a way to preserve  the stability of self-injected bunches during excitation of a wakefield in  plasma