Why not tax all fossil carbon fuels with a universal refundable tax of $1/kg? That way you wallop the private jets at ~$1000/hr and more importantly you also discourage the real culprits, Americans driving around in pickup trucks, with a smaller but still effective incentive. Plus, being universally refundable, it also acts as a sort of UBI that puts money into the pockets of people who don't use fossil fuels.
The revenues of the tax are redistributed to everyone with a regular payment. For example a weekly or monthly check. Americans buy roughly 1 gallon of motor fuel per day per capita, so a $5/gallon (example) tax would result in a household of 4 people receiving a $600 check every month. For people who use less than the average amount of fuel, it's free money.