Abstract.A fusion reactor concept on the basis of a linear trap is developing in BINP. These studies incorporate multiple-mirror sections which should reduce significantly longitudinal plasma losses from a confinement zone. In the paper, physics on the multiple-mirror confinement relevant to plasma behavior at reactor conditions will be discussed. Basic results were received in the GOL-3 multiple-mirror trap in which plasma of 10 21 m -3 density was heated by a highpower electron beam up to 2 -4 keV temperature. The key milestones were: the demonstration of effective plasma heating by the electron beam due to collective effects, the achievement of theoretically predicted level of energy confinement time under optimal conditions, and finally, the discovery of a bounce instability that improves longitudinal confinement. Direct demonstration of a confinement improvement by multi-mirror sections in the magnetic configuration relevant to the reactor one will be done in the GOL-NB facility that will be created in BINP. In addition, a new plasma device SMOLA with a helical multiple-mirror magnetic field for an active confinement control is discussed.