Reports: DNI5 48873-DNI5: Nuclear Spin Relaxation and Restricted Diffusion in Microtesla Magnetic Fields

Robert McDermott, University of Wisconsin (Madison)

We have developed a low-field nuclear magnetic resonance (NMR) scanner based on a Superconducting QUantum Interference Device (SQUID) detector. The SQUID is operated with a tuned input circuit with a center frequency at 4.8 kHz, corresponding to a proton Larmor frequency around 110 microtesla. The experimental protocol involves polarization of the protons in a relatively high field of order 100 mT; adiabatic removal of the polarizing field, which causes the spins in the sample to reorient toward the weak measurement field; application of audiofrequency excitation pulses to induce spin precession and form spin echos; and detection of the precessing magnetization from the sample using the SQUID, which is operated in a flux-locked loop as a null detector of magnetic flux.

To develop this low-field scanner, we have had to overcome a number of challenges to enable the detection of extremely weak NMR signals in the presence of significant noise and environmental interference in the detection band. First, we have fabricated a custom liquid helium cryostat to house the SQUID sensor. The cryostat contains a minimal amount of normal metal, to minimize magnetic noise from Nyquist currents in metallic components. Instead of using copper mesh for the thermal shield of the cryostat, we have implemented a thermal shield made from thin alumina rods epoxied to a thin-walled G10 fiberglass frame; the electrically insulating alumina allows for efficient heat transport, while introducing no magnetic noise. In addition, we have used a minimal amount of aluminized mylar in the tail section of the cryostat; moreover, the aluminized mylar was repeatedly crushed prior to assembly of the cryostat in order to disrupt electrical continuity of the aluminum thin film and prevent the flow of noise currents in large-area circuits. All of the shells, flanges, and end caps of the cryostat vessels were fabricated from nonconducting G10 fiberglass. These unique design features have enabled us to reduce the magnetic field noise from the cryostat to 3 fT/sqrt(Hz) in the measurement band, while maintaining an acceptable liquid helium boiloff rate of 5 liters per day.

In addition, we have had to suppress the environmental magnetic field noise at our 4.8 kHz detection frequency. To do this, we have employed a gradiometric configuration for the SQUID input circuit, consisting of two counterwound superconducting coils separated by 10 cm. The lower coil rests on the bottom of the cryostat inner vessel, and is tightly coupled to the sample, which is placed just under the end cap of the outer vessel. The gradiometric design allows strong magnetic coupling to the nearby sample, while providing good rejection of distant sources of magnetic interference. In addition, we have surrounded our experiment with a homemade eddy current shield made from 1/8”-thick plates of 5052 aluminum. The skin depth in this alloy is around 1 mm at 5 kHz; the shield thus suppresses the environmental contribution to the magnetic noise within our detection band by more than an order of magnitude.

To eliminate the noise contribution from our input circuit, we have employed superconducting NbTi wire for the pickup coils, and we have used a low-loss, polyester capacitor to tune the input circuit to our 4.8 kHz detection frequency. The contribution to the system noise from the sensor scales inversely with the quality factor (Q) of the input circuit. Our low-loss input circuit has a Q around 800, yielding a contribution to the overall system noise that is negligible. However, the bandwidth of the undamped input circuit is of order a few Hz, which is unacceptably small for the NMR investigations that we have undertaken. For this reason, we have implemented a feedback damping scheme, in which an appropriately attenuated and phase-shifted signal from the output of the flux-locked loop is fed back to the input circuit as a magnetic flux. With this scheme it has been possible for us to increase the bandwidth of our SQUID detector well beyond 100 Hz, with negligible degradation of the noise performance of our scanner.

In order to improve the signal-to-noise ratio of our scanner, we have employed a prepolarization scheme to enhance the sample magnetization far above the thermal magnetization in our weak detection field. We have designed custom electronics to realize the necessary pulsed magnetic fields. Currents of order 100 A are used to prepolarize the spins in fields of order 100 mT. Switching of the field is accomplished by embedding the polarization coil in an LC resonant circuit, where the capacitance is provided by a bank of electrolytic capacitors. Upon opening an IGBT switch, the magnetic energy of the polarization coil is transferred in a quarter period of the LC circuit to the capacitor bank, which is heavily damped by power resistors that dissipate the stored energy prior to the next polarization cycle.

With this system we are performing NMR spectroscopy to validate detector performance and to fine-tune the detector and optimize signal-to-noise. Currently we are integrating pulsed magnetic field gradient capabilities into this system. Carr-Purcell-Meiboom-Gill (CPMG) sequences will be used to probe the distribution of transverse relaxation times in porous rock. This data will be used to determine the content of different fluid species, and to extract the distribution of pore sizes in the rock. In addition, we will investigate longitudinal relaxation time contrast of different fluid species in microtesla fields. Finally, we will use pulsed-gradient spin echo (PGSE) experiments to probe restricted diffusion. In the absence of spurious internal-field gradients, the application of controlled gradient pulses will enable determination of pore surface-area-to-volume ratio and tortuosity. When combined with relaxation data, this information will be used to extract key flow parameters such as permeability.

 
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