Ultra-long carbon nanotube (CNT) growth with Fe cluster sitting at tip end under AC magnetic field as a function of magnetic field, susceptibility of catalyst, number of cluster atoms, reaction time, reaction temperature, diameter of the carbon nanotube and damping factor of the system in chemical vapor deposition is investigated using a theoretical analysis on the phonon vibration of the system. Results show that CNT length in the presence of field increases. Also there is an optimum temperature which is reduced by increasing of magnetic field. Finally, it is shown that in the presence of magnetic field, Fe is a better catalyst than Ni because of its higher superparamagnetic susceptibility. Results of the theory are very useful for experimental works. (c) 2012 Elsevier B.V. All rights reserved.