The onset condition of a thermoelectric instability in divertor tokamaks ha
s been studied analytically anti numerically by using a five point model ba
sed on SOL and divertor plasmas. The SOL current due to the thermoelectric
effect causes the thermoelectric instability and destabilizes the symmetric
equilibrium of the SOL and divertor plasmas below a critical divertor plas
ma temperature. The critical temperature of the thermoelectric instability
is equal to or higher than that of the thermal instability due to the diver
tor radiation, and depends on the midplane SOL plasma temperature and the d
ivertor radiation loss. Below the critical temperature, stable asymmetric e
quilibria are obtained. As the degree of the asymmetry in the divertor plas
ma temperature increases, the SOL current has no effect on the instability,
or even stabilizes the equilibrium. The SOL current generates spontaneousl
y the divertor asymmetry through the thermoelectric instability.