Various possibilities of improving of tandem mirror systems are considered. Methods of reducing significant disadvantage of open system - intensive emission interaction between plasma and chamber wall surface and possibility of decreasing of electrostatic barrier value are considered. Creating so-called double tandem mirror system is suggested to obtain mirror based confinement system without magnetic force lines, piercing chamber wall surface. Besides, principle of realising other suggested method of protecting of plasma - magnetic insulation is presented. It is shown, that magnetic insulation in mirror based fusion reactor can give significant protective effect.