EXCLUSIVE

Mariah Carey has privately made a demand to James Packer ... he needs to pay her $50 mil ... or else.

Sources connected to the now warring ex-couple tell TMZ ... Mariah believes James has cost her tens of millions of dollars, and here's why:

-- She claims he got her to move from New York to L.A., uprooting her entire life, so he could be near his kids.

-- She claims the incident on the yacht in Greece -- where she says he did something awful to her assistant -- has traumatized Mariah so much she had to cancel the South American leg of her tour.

-- He made various financial promises to her.