Optimization of the Combined Multiple-Pulse Spin-Locking Sequence to Detect RDX and TNT by NQR Over all the Operating Temperature Ranges

Аннотация

Joint optimization of the parameters of the combined multiple-pulse spin-locking sequence has been performed with the aim to maximize the ratio of the ¹⁴N nuclear quadrupole resonance (NQR) signal to noise for the best detection of trinitrotoluene (TNT) and hexogen (RDX) over all the operating ranges of temperatures from 30 to −30 °C. It is based on the knowledge of spin–lattice T₁ and effective transversal T_2e relaxation times of ¹⁴N nuclei over all these temperature ranges. The problem is solved rigorously, without simplifying assumptions. It is established that the NQR signal-to-noise ratio at any given sequence duration T_s has a maximum not only in depending on the number pulses N in its subsequences, but also on the number m of their repetitions. On this basis, the system from two inter-related mutually compatible equations has been derived, each of which contains three unknowns, of which two ones are classified as optimum values of N_opt and m_opt, whereas the third one t_p only corresponds to them, being the correct value t_pc (t_p is the relaxation pause between the subsequences). This system is most conveniently solved for N_opt and t_pc if the parameter m is initially preset as an integer and optimum number. The selection of the suitable m_opt is dictated by that the calculated correct sequence duration T_sc at these N_opt, t_pc, and m_opt is to be equal or near to a scheduled time of explosive detection. In spite of the fact that the T₁ and T_2e times in these explosives essentially differ and strongly change with the temperature, the solution of these equations does not cause any difficulties over all the temperature ranges. Results of the calculations are presented in the graphical form and represent the temperature and m_opt dependence of values of N_opt, t_pc, and T_sc, and of the maximum factor of increasing the NQR signal-to-noise ratio determined by these parameters. They are compared with the results obtained previously for RDX in the high-temperature side of the range. It is discussed the influences of errors in the measured T₁ and T_2e times, as well as of rounding off decimal numbers in intermediate calculations on the accuracy of the calculated values of N_opt and t_pc.