Transcript Accommodations of Planar Coil for Remote Detection of 14N NQR

Planar Coil for Remote Detection of
.
14
( N)
NQR
J.Pirnat, J.Lužnik, and Z.Trontelj, Inst. of Mathematics, Physics and Mechanics, Ljubljana, Slovenia
([email protected])
INTRODUCTION
Aims:

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.

coil radius
c
sample,s
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.
D
circ. loop ~ solenoid
46
:
signal
noise
Filling factor
Solenoidal coil:
F ( pream.noise)  Tc (t / r coil T )  f (r.bandw.)
 
Planar coil, remote sample ( D > 2∙c > 2∙s ;
a – wire radius, s – ef. thickness of the
sample’s most excited slice ):
1 sample vol.

2 coil vol.

 ( fill. f .)  M Q (q. polar.)  Q(coil.qu.)  Q ( fr.)
sample vol. 
Bs 2
2 0
coil ' s all space mag .energy
 
ln(

8c
a
2


 s  s   D
   2  1
c  c   c

)2
Vs Bs 2
2
0 Lc I
2
3
RESULTS & COMMENTS
Maximizing the RF excitation of the sample
Optimization of the circular coil to receive the NQR signal
 Fixed turn number N; varying c causes simultaneous variation of inductance L in this
particular case:
c(Max) = D√2 (known result).
5.5
5 turns
10
8
4
E
11
12
10
15
9.4
8
6
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:
21
K
3
0.12
0.10
0.08
F
0.06
0.05
0.10
0.15
 [m]
0.20
0.25
(D=0.2m, L~50H)
0.30
R (ohm)
R (ohm)
0.8
0.6
0.4
0.05
0.10
 [m]
0.15
(D=0.1m, L~50H)
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:
(i) keeping the same coil and increasing only the sample radius and Brf and
(ii) 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)
10
1
10
Irf/I1
 Brf
Rel.signal
at D0, B1
 D3
Det.limit
D(sig=1)
[cm]
1
1
1
10
1.48
1.53
1.53
2.2
13
10
1.84
2
2
3.4
15
10
2.41
3
3
5.8
18
10
2.83
4
4
8
20
Differently shaped excitation fields from two different (fictitious) coils 
D1
a)
sample
t/r coil
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.
sample
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.
Brf/B1
Irf/I1
 ρc3/2
Rel.signal
at D0, B1
 ρs2 ∙
ρc3/2
Det.limit
D(sig=1)
[cm]
1
1
1
1
10
13
1.22
1
1.48
2.2
13
15
1.36
1
1.84
3.4
15
18
1.55
1
2.41
5.8
18
20
1.68
1
2.83
8
20
Coil
radius
[cm]
Samp.rad.
 D3/4
[cm]
10
Example of combination of two adjacent planar coils exhibiting the
mag.field distribution similar to the one shown in the left Fig.(b).
A
B
A+B
25
Problem: very inhomogeneous sample excitation, difficult distinction between saturated and linear
regime (continuous increase of saturated sample portion; uncertain effective /2 or  pulse setting).
D2
c (Max)  D  sample
(~agreement with optim.excitation)
L
20
15
B [arb.u]
flux/max_1
5
 1

c 2
Max 
 2
, c   c ( Max)  D
2 32
 c ( D  c )

flux/max_1
 However, if L is fixed, N 2c~const.:
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.
10
5
Sample characetrizations
0
 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.
coil A
coil B
-5
-0.2
-0.1
0.0
0.1
0.2
x coordinate [m]
Two circ.loops c=10,7 cm, centers' separation dc=20 cm, D=10 cm
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
1. T. N. Rudakov, V. T. Mikhal’tsevich, V. V. Fedotov, and A. V. Belyakov, Pribory i Tekhnika
Eksperimenta, No. 1, 101 (2001).
2. B.H.Suits, A.N.Garroway, J.Appl.Phys., 94, 4170 (2003).
3. G. V. Mozjoukhine, Z. Naturforsch. 57 a, 297–303 (2002).
4. A.Abragam, The principles of Nuclear Magnetism, Clarendon Press, Oxford, 1961.
5. H.D.W.Hill and R.E.Richards, J.Sci.Instr. (J.Phys.E), Ser.2 1, 977 (1968).
6. D.I.Hoult and R.E.Richards, J.Mag.Res. 24, 71 (1976).