A linear dipole antenna has an impedance matrix of Toeplitz form. The problem of an acoustically long cylindrical antenna in a warm plasma thus becomes numerically tractable. Both the electromagnetic and acoustic wavelengths are evident in the current distribution for acoustically long antennas. Relative accuracies of 10−11 were obtained for inversion of a 5000×5000 complex impedance matrix, including both electromagnetic and acoustic contributions. Antennas up to 500 acoustic wavelengths long are considered in numerical examples.