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The vacuum state of SU(3) gluodynamics at high temperature is investigated. Aconsistent approach including the calculation of either the spontaneouslygenerated constant chromomagnetic isotopic $H_{3}$ and hypercharge $H_{8}$fields or the polarization operator of charged gluons in this background isapplied. It is shown within the effective potential including the one-loop plusdaisy diagrams that the specific values of the fields deliver a global minimumto free energy. The spectrum of the transversal charged modes is stable at hightemperature due to a gluon magnetic mass accounting for the vacuum fields. Thisleads to stable chromomagnetic fields in the deconfinement phase of QCD. Acomparison with the results of other approaches is done.Comment: some misprints were correcte

On the generation of Abelian magnetic fieldsin SU(3) gluodynamics at high temperature