Conventional NMR is based on the individual and linear response of nuclear magnetic moments to the applied static and rf fields (I=1/2 species, usually). The magnetisation remains small in the medium, even at high number density, since the nuclear polarisation obtained at thermal equilibrium is weak (3 ppm for protons in water samples at 1T, for instance). Therefore, only magnetic interactions between close neighbours may induce significant perturbations. This is actually the case in most solids. In liquids and gases, the contributions of all short-distance interactions are averaged out by the fast and free motion in the fluid (except intra-molecular ones, responsible for small chemical shifts).
Today, various hyperpolarisation techniques are used to obtain highly magnetised liquid samples. In such systems, the residual long-distance interactions are strongly enhanced and yield the so-called distant dipolar field, DDF. The non-linear, non-local contribution of DDF to the time evolution of the magnetisation gives rise to spectacular changes in the macroscopic response of the system to usual RF excitations.
See, e.g., for a review:
H. Desvaux, “Non-linear liquid-state NMR”, Prog. Nucl. Magn. Reson. Spectroscopy 70 (2013) 50–71.
Our group has made pioneering observations of such effects for free induction decay signals, in low-field NMR experiments with laser-polarised ³He fluids: spectral clustering (for near-longitudinal magnetisation) and precession instabilities (for nearly transverse magnetisation). Time reversal of DDF-induced instabilities has been achieved and, in particular, the onset of unstable precession has been carefully studied.
Then, we have investigated the generation of multiple echoes by basic conventional (single-echo) pulse sequence (see our “Research” topics section).
These phenomena are solely due to DDF, i.e., they result from the enhancement of intrinsic magnetic couplings. At high magnetisation, enhanced signal amplitudes may also cause strong radiation damping, RD, a well-known effect due to the extrinsic non-linear and global contribution of the resonant field generated by the rf current which is induced in the NMR coils during Larmor precession. This additional transverse field tends to flip the magnetisation back to its equilibrium state and, hence, to enhance transverse decay in a positive spin-temperature sample (or to sustain maser emission, in a negative-spin-temperature sample). Indeed, both kinds of non-linear couplings can jointly affect NMR dynamics and lead, for instance, to the development of spin turbulence and chaotic behaviour.
We have undertaken a systematic (experimental and numerical) investigation of the spatio-temporal behaviour of the nuclear magnetisation in presence of arbitrarily strong DDF and/or RD, using innovative computations on realistic 3D lattice models.
- Extensive low field NMR work with laser-polarised ³He solutions is performed at LKB.
- Some high field work with solutions of laser-polarised 129Xe has been performed in collaboration with experts of NMR spectroscopy at CEA Saclay (ANR-funded projects: DIPOL, 2007-2011, and IMAGINE, 2013-2016) and may be continued (thanks to the DIM Analytics-Ile de France project WIDENMR, 2016-2019).
For our work at low magnetic field, we can rely on an efficient and flexible method for the production of highly magnetised liquid samples (laser optical pumping of ³He followed by dissolution in superfluid 4He), which allows experiments with adjustable nuclear polarisation, ³He concentration, and temperature, in the isotopic mixture.
The dedicated experimental setup implemented at LKB includes an active feedback system to control the current flowing in the detection tank circuit, which allows studies of DDF effects with suppressed or enhanced RD.
A commercial, computed-controlled, MR console is used for the design and application of sophisticated sequences of rf and gradient pulses.
Computer simulations are performed on PC computers with compiled C-programs, which provide discrete 3D maps of the distribution of magnetisation in the sample at selected times during free or rf-driven evolution. Our models include DDF and RD and currently take into account many key experimental parameters (sample size and shape, ³He diffusion coefficient, rf and static field maps, etc).
Implementation and test of GPU-based algorithms are under way. A big gain in efficiency is expected, which will allow us to perform 3D lattice simulations of the time evolution of magnetisation with a much higher spatial resolution, especially in the most complex cases.
Non-linear NMR dynamics: experimental versus numerical data
The precession instabilities correspond to a catastrophic evolution, from a weak initial deviation towards a strong spatial disorder with vanishing average transverse magnetisation.
We wish to precisely analyse the onset of the instability and the development of the inhomogeneous spatial patterns that appear in our samples, either spontaneously or from a well-defined initial seed of inhomogeneity in the distribution of magnetisation.
A large body of experimental data of DDF-induced precession instabilities has been recently recorded, and some surprising observations are not yet fully understood.
The student will perform a detailed analysis of the available results, re-examine the pulse sequences designed for the latest experiments, and perform new simulations to elucidate puzzling signal features.
He/She may benefit from, or contribute to, the planned development of an improved version of the computer program (written in C language).
Presently, the topic is not open for PhD.