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**Maximizing the RF excitation of the sample **

. Planar Coil for Remote Detection of (14N) NQR J.Pirnat, J.Lužnik, and Z.Trontelj, Inst. of Mathematics, Physics and Mechanics, Ljubljana, Slovenia Aims: Sensitive detection of samples of different diameters with nuclear quadrupole (NQR) spectra at expected frequencies and being located at different distances from the sensor, using remote NQR pulse method. Additionally desirable: determination of the sample's distance, its size and the concentration of the quadrupole substance in the sample. INTRODUCTION In accordance with the circular loop shape, that is most frequently found in relevant NQR publications studying remote NQR detection1-3,etc., we investigate at present only circular kind of planar transmitter/receiver coils (t/r coils) in conjunction with pulse NQR spectrometer. Accommodations of the coil parameters like the radius, the number of turns, their distribution, the wire properties, combining the coils, etc., were studied in order to optimize the signal, following the history of the much more elaborated signal/noise studies of solenoidal coils4-6. c sample,s D coil radius Filling factor Solenoidal coil: Planar coil, remote sample ( D > 2∙c > 2∙s ; a – wire radius, s – ef. thickness of the sample’s most excited slice ): RESULTS & COMMENTS Maximizing the RF excitation of the sample Fixed turn number N; varying c causes simultaneous variation of inductance L in this particular case: c(Max) = D√2 (known result). However, if L is fixed, N 2c~const.: Optimization of the circular coil to receive the NQR signal The principle of reciprocity6: The circular coil of fixed inductance L, that causes maximum axial field along the symmetry axis at distance D from the coil plane is also the best to detect the field of an oscillating axially oriented magnetic dipole at the same distance D. Left: numerically calculated examples of the magnetic flux caused by the magnetic dipole at distance D, detected by different coils of the same L (different c , N adjusted to L). Here, the optimum c is slightly shifted because of the logarithmic factor in the expression for L. The maximum is broad and for samples with bigger s one would expect increase of the optimal coil radius just by the length of the sample radius: (~agreement with optim.excitation) Assume a coil L, c0, and a small sample disc s0 (c0 >>s0) at the distance D0 ≈ c0 (optimal), just above the detection limit. Suppose that a part of the sample is excited to the saturated regime (RF level B1), because the linearly excited signal alone (small flip angle) would be too weak to reach the distant receiving coil. So the quadrupole polarization is proportional to the disc area provided that RF excitation is sufficient. The next two tables show (in relative view) two ways to increase the detection distance: keeping the same coil and increasing only the sample radius and Brf and changing properly all, the coil radius, turns N, the sample radius and Brf. Better performance of the case (ii) is demonstrated. Coil radius [cm] Samp.rad. D3/2 [cm] Brf/B1 (from relat. B vs. D) Irf/I1 Brf Rel.signal at D0, B1 D3 Det.limit D(sig=1) [cm] 10 1 1.48 1.53 2.2 13 1.84 2 3.4 15 2.41 3 5.8 18 2.83 4 8 20 Coil radius [cm] Samp.rad. D3/4 [cm] Brf/B1 Irf/I1 ρc3/2 Rel.signal at D0, B1 ρs2 ∙ ρc3/2 Det.limit D(sig=1) [cm] 10 1 13 1.22 1.48 2.2 15 1.36 1.84 3.4 18 1.55 2.41 5.8 20 1.68 2.83 8 Differently shaped excitation fields from two different (fictitious) coils Example of combination of two adjacent planar coils exhibiting the mag.field distribution similar to the one shown in the left Fig.(b). Left: Fixed RF level pulses, adjustable pulse angular length : the most excited section of the sample (nearest to t/r coil) can be possibly in the saturated regime, (dark red, /2 pulse achievable, predominant contribution to the signal); the adjacent layers are in the linear regime (NQR signal Sig() , i.e. small flip angle, negligeable contribution to the signal). Increased (excessive) distance causes insufficient excitation (light orange) => even the nearest sample section, contributing mostly to the signal (?), is in the linear regime; very difficult detection. Problem: very inhomogeneous sample excitation, difficult distinction between saturated and linear regime (continuous increase of saturated sample portion; uncertain effective /2 or pulse setting). The coil b) can achieve at least locally a tidier magnetic field distribution (planar slices of ~uniform field, the RF gradient mostly in axial direction). This should enable more efficient multi-pulse sequences, similar to those performed in solenoid sample coils. Sample characetrizations Sample size estimation: measurement of the translational dependence of the signal. Sample distance: possible application of precalibrated dependence of the flip angle 0<(D)< on distance (e.g. “null” method using compensation of e.g. /2 pulses from two coils with differing dependences 1(D) and 2(D)). Sample concentration: comparison of sample size, signal amplitude and distance. CONCLUSIONS Some rules, valid for construction of optimal solenoidal coils have been adapted to one-sided transmitter/receiver circular coils and some specific features of the “new” coils are outlined. Further study is necessary considering small flip angles excitation and detection (linear regime, stochastic excitation). The electric shielding of the planar coil represents serious and interesting problem, which will deserve our attention in the following steps. References T. N. Rudakov, V. T. Mikhal’tsevich, V. V. Fedotov, and A. V. Belyakov, Pribory i Tekhnika Eksperimenta, No. 1, 101 (2001). B.H.Suits, A.N.Garroway, J.Appl.Phys., 94, 4170 (2003). G. V. Mozjoukhine, Z. Naturforsch. 57 a, 297–303 (2002). A.Abragam, The principles of Nuclear Magnetism, Clarendon Press, Oxford, 1961. H.D.W.Hill and R.E.Richards, J.Sci.Instr. (J.Phys.E), Ser.2 1, 977 (1968). D.I.Hoult and R.E.Richards, J.Mag.Res. 24, 71 (1976).

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1© Manhattan Press (H.K.) Ltd. 16.6 magnetic fields due to currents Long straight wire Circular coil Long solenoid.

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