Using of hyperpolarized ³He for accurate measurements of high magnetic fields
Motivation and theoretical background
Penning traps are nowadays the most suitable devices for high-precision mass measurements of nuclides . The mass is determined via the measurement of the free-space cyclotron frequency ν = qB/2𝜋m of an ion with charge-to-mass ratio q/m stored in a homogeneous magnetic field B. Frequencies, to be more precise: frequency ratios, can generally be measured with very high precision. Therefore, relating a mass measurement to a frequency measurement is advantageous. The B-field has to be constant in time. Therefore, only superconducting magnets with a high spatial homogeneity are used in high-precision Penning-trap mass spectrometry. Moreover, the real magnetic field shows a temporal drift and short-term fluctuations . Thus, a magnetic field stabilization and a fast measurement of the frequency ratio are essential to gain very high precision, in particular if 𝛥m/m < 10-11 is demanded. PENTATRAP  is an example, where in one setup a stack of five Penning traps for high-precision mass measurements are used, allowing measurement cycles at which the ion exchange takes a few hundred milliseconds, in combination with a continuous observation of the magnetic field fluctuations during the whole measurement process. Still, the challenge is to find an appropriate monitor of the magnetic field and its temporal fluctuations. Measurement of the precession frequency of gaseous, nuclear spin-polarized 3He in high magnetic fields (> 1 T) allows determining the magnetic field strength with high accuracy. The Larmor frequency f of the precessing sample magnetization is related to the magnetic flux density B through f = 𝛾B/2𝜋, where 𝛾 is the gyromagnetic ratio of 3He. For high magnetic fields (> 1 T) a precession frequency is of 100 of Megahertz. The frequency can be measured by recording the signal amplitude of the free induction decay (FID) of the precessing spins after a resonant RF-pulse excitation (𝜋/2-pulse). If the coherent spin precession time T2 (transverse relaxation time) is in the range of some seconds simply counting the zero-crossing of the oscillation signal results in a precision in the order of 10-9 for the determination of B. Taking the full statistic of the recorded FID signal, this result can be improved significantly reaching sensitivity of order 10-10-10-11. Long T2-times in high magnetic fields (> 1 T) can be obtained if the inhomogeneity of the magnetic field over the volume of the 3He sample cell (V ≈ 1 cm3) is of order 𝛥B/B ≈ 10-7, what is typical for Penning trap fields.
The 3He can be polarized in-situ using a non-standard variant of the Metastability Exchance Optical Pumping (MEOP) process, described in detail below. A portable polarizing setup has been developed and tested. The cylindrical glass cells of size 10 to 30 mm are filled with 3He gas at a pressure of 1 mbar (Fig.1). 3He gas could be polarized directly in the high magnetic field. First tests in a 1.5 T superconducting magnet of a clinical magnetic resonance imaging system show that T2-times of up to 3 seconds can be reached, which, to our knowledge, is the longest spin-coherent relaxation time of a gaseous, nuclear spin-polarized 3He sample measured so far in high magnetic fields.
Fig. 1: 3He cell (pressure 1 mbar) at 2 T magnet (Jagiellonian University, Krakόw, Poland)
High nuclear polarization 3He by MEOP at high magnetic field
A high nuclear polarization of 3He gas can be obtained by the MEOP. In the standard operating conditions a low magnetic field, of the order of few mT, played the role of the guiding field for the nuclear polarization, and a low 3He gas pressure, of the order of about 1 mbar was used. In most favorable conditions, the achieved nuclear polarization could exceed up to 90%  but it dropped dramatically at higher gas pressure, due to increased relaxation by collision processes.
The hyperfine interaction plays a crucial role in the MEOP, providing both the physical mechanism for the polarization transfer from electrons to nuclei, and causing the destructive depolarization of helium atoms during various collision processes. The effective strength of the hyperfine interaction can be to some extent controlled by the applied magnetic field, due to decoupling effect. Therefore, there should be optimum values of the 3He gas pressure and magnetic field, at which the two competing processes would maximize the efficiency of MEOP in terms of total magnetization. This was suggested and demonstrated in 0.1 T at 30 mbar , and in 0.115 T at 32 mbar . At the optimum values of laser power and density of metastable states, the polarization of the order of 10 % was achieved. A detailed microscopic model for the MEOP at arbitrary magnetic field was developed , and an optical method for measuring the nuclear polarization at arbitrary magnetic field was proposed. Following these ideas, the MEOP was successfully performed at 1.5 T , producing 24% of nuclear polarization at 67 mbar.
Motivated by the above promising results, more systematic studies of MEOP at five magnetic fields (0.45, 0.9, 1.5, 2 T and 4.7 T) and at pressures ranging from 1 to 267 mbar were undertaken . A dramatic improvement of the MEOP results for high pressure as compared to low magnetic field was found.
At low pressure, MEOP efficiency at high field is lower than at low-field. Nevertheless the process is still feasible with the possibility to achieve high nuclear polarization level .
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