A supersonic lean fuel combustion plasma arc turbine comprising: a plasma arc torch comprising: a cylindrical vessel having a first end and a second end, a tangential inlet connected to or proximate to the first end, a tangential outlet connected to or proximate to the second end, an electrode housing connected to the first end of the cylindrical vessel such that a first electrode is (a) aligned with a longitudinal axis of the cylindrical vessel, (b) extends into the cylindrical vessel, and (c) can be moved along the longitudinal axis, a linear actuator connected to the first electrode to adjust a position of the first electrode within the cylindrical vessel along the longitudinal axis of the cylindrical vessel, a hollow electrode nozzle connected to the second end of the cylindrical vessel such that a center line of the hollow electrode nozzle is aligned with the longitudinal axis of the cylindrical vessel, and wherein, in use, the tangential inlet and the tangential outlet create a vortex within the cylindrical vessel, and the first electrode and the hollow electrode nozzle create a plasma that discharges through the hollow electrode nozzle; a cyclone combustor connected to the hollow electrode nozzle of the plasma arc torch, wherein the cyclone combustor has a tangential entry, a tangential exit, and an exhaust outlet; and a turbocharger having a turbine connected to a compressor via a shaft, wherein a turbine entry is connected to the tangential exit of the cyclone combustor, a compressor exit is connected to the tangential entry of the cyclone combustor. a plasma arc torch comprising: a cylindrical vessel having a first end and a second end, a tangential inlet connected to or proximate to the first end, a tangential outlet connected to or proximate to the second end, an electrode housing connected to the first end of the cylindrical vessel such that a first electrode is (a) aligned with a longitudinal axis of the cylindrical vessel, (b) extends into the cylindrical vessel, and (c) can be moved along the longitudinal axis, a linear actuator connected to the first electrode to adjust a position of the first electrode within the cylindrical vessel along the longitudinal axis of the cylindrical vessel, a hollow electrode nozzle connected to the second end of the cylindrical vessel such that a center line of the hollow electrode nozzle is aligned with the longitudinal axis of the cylindrical vessel, and wherein, in use, the tangential inlet and the tangential outlet create a vortex within the cylindrical vessel, and the first electrode and the hollow electrode nozzle create a plasma that discharges through the hollow electrode nozzle; a cylindrical vessel having a first end and a second end, a tangential inlet connected to or proximate to the first end, a tangential outlet connected to or proximate to the second end, an electrode housing connected to the first end of the cylindrical vessel such that a first electrode is (a) aligned with a longitudinal axis of the cylindrical vessel, (b) extends into the cylindrical vessel, and (c) can be moved along the longitudinal axis, a linear actuator connected to the first electrode to adjust a position of the first electrode within the cylindrical vessel along the longitudinal axis of the cylindrical vessel, a hollow electrode nozzle connected to the second end of the cylindrical vessel such that a center line of the hollow electrode nozzle is aligned with the longitudinal axis of the cylindrical vessel, and wherein, in use, the tangential inlet and the tangential outlet create a vortex within the cylindrical vessel, and the first electrode and the hollow electrode nozzle create a plasma that discharges through the hollow electrode nozzle; a cyclone combustor connected to the hollow electrode nozzle of the plasma arc torch, wherein the cyclone combustor has a tangential entry, a tangential exit, and an exhaust outlet; and a turbocharger having a turbine connected to a compressor via a shaft, wherein a turbine entry is connected to the tangential exit of the cyclone combustor, a compressor exit is connected to the tangential entry of the cyclone combustor.