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The model under consideration is the classical two-dimensional one-componentplasma (jellium) of pointlike particles with charge $e$, interacting pairwiselyvia the logarithmic Coulomb potential and immersed in a uniform neutralizingbackground charge density. The system is in thermal equilibrium at the inversetemperature $\beta$, its thermodynamics depends only on the coupling constant$\Gamma=\beta e^2$. We put into an infinite (homogeneous and translationallyinvariant) plasma a guest particle of charge $Ze$ with $Z>-2/\Gamma$ in orderto prevent from the collapse of the jellium charges onto it. The guest particleinduces a screening cloud (the excess charge density) in the plasma. The zerothand second moments of this screening cloud were derived previously for anyfluid value of $\Gamma$. In this paper, we propose a formula for the fourthmoment of the screening cloud. The derivation is based on the assumption thatthe fourth moment is, similarly as the second moment, analytic in $Z$ around$Z=0$. An exact treatment of the limit $Z\to\infty$ shows that it is a finite(cube) polynomial in $Z$. The $\Gamma$-dependence of the polynomialcoefficients is determined uniquely by considering the limits $Z\to 0$ and$Z\to\infty$, and the compressibility sum rule for $Z=1$. The formula for thefourth moment of screening cloud is checked in the leading and first correctionorders of the Debye-H\"uckel limit $\Gamma\to 0$ and at the exactly solvablefree-fermion point $\Gamma=2$. Sufficient conditions for sign oscillations ofthe induced charge density which follow from the second-moment andfourth-moment sum rules are discussed.

Fourth Moment of the Charge Density Induced Around A Guest Charge in Two-Dimensional Jellium