[en] Tandem mirror Gamma 10 employs a thermal barrier to insulate the electrons in the end plugs from those in the central cell. Generation of the thermal barrier in Gamma 10 requires the creation of a hot mirror trapped electron population, heated by electron cyclotron resonance heating. We calculate creation of the hot electron population when only second harmonic electron cyclotron resonance heating is included in the thermal barrier region. We then calculate the plug and thermal barrier potential formation when fundamental electron heating and neutral beam injection are added, using our bounce averaged Fokker-Planck code. To study the hot electron build up in the thermal barrier region theoretically and numerically, we include the quasilinear electron heating effects in the Fokker-Planck equation. (Mori, K.)