Fundamental limit of self-field MPD thruster efficiency

A fundamental upper limit, $$\hat{\eta}$$ , for the thrust efficiency of self-field magnetoplasmadynamic thrusters (MPDTs) is derived from the generalized Ohm’s law and the minimization of the volume integral of the square of the current density, which controls dissipation in the MPDT. It is found that $$\hat{\eta}\simeq1/(1+4/R_{m_{ci}}\xi^4)$$ , where $$\xi$$ is the MPDT scaling number (the total current normalized by the current at which an equipartition of power occurs between thrust and ionization), and $$R_{m_{ci}}$$ is the magnetic Reynolds number evaluated at $$\xi=1$$ .