Combining Equation 2.1 and Equation 2.5, one can see that γopt is proportional to the light power per unit area and inversely proportional to the absorption cross-section width Γ (i.e., the target cell's pressure). After a period ∼(γopt+ ΓSD)−1 ∼γopt−1 ∼ 10 microseconds, (compare Equation 2.11 and Equation 2.6), the electron spin polarization reaches its maximum steady value.
Spin-exchange Collisions
In Equation 2.30, R is the distance from the 3He nucleus to the center of the alkali metal atom, and φe(R) is the unperturbed electron wave function for the alkali metal without 3He present. The efficiency is determined by the ratio of the spin exchange rate of the alkali metal atom. Since each photon transfers an angular momentum of ½ h/2 to the electron of the alkali metal atom, this is the case by definition.
Spin annihilation is mainly due to the rotational interaction of the alkali metal and 3He atom pairs, which ignores the contribution of collisions between alkali metal atoms. The 3He nuclear polarization evolution has a similar form to the alkali metal atoms polarization evolution Equation 2.14.
Target Cells
Cell Design
- Geometry Considerations
- Material Considerations
To successfully polarize 3He, the geometry of the cell and the laser optics are both required to be optimized to improve the overall laser light transmission efficiency into the cell. The cell should also have a low permeability to 3He to reduce diffusion loss of 3He through the cell over long periods. The key factors are designing the cell geometry and choosing the correct glass materials to build cells.
Wall relaxation rates in Corning 1720 cells can be tens of hours−1 or less. It is also worth noting that, unlike Corning 1720 glass, Ge-180 glass is easy to use for glass blowers, is cheaper and available in the market.
Cell Fabrications
The results in our laboratory confirm that GE-180 glass is an ideal material for polarized 3He cells. Bare cells made of Ge-180 glass in our laboratory consistently have wall relaxation times of about 50 hours. These procedures were repeated until the pipe reached the desired diameter for a certain wall thickness.
In this case, a direct measurement of the wall thickness is necessary, since the wall thickness cannot be calculated by assuming that the wall thickness is inversely proportional to the diameter. The other end of the tube served as an entrance from the whole cell manifold to the vacuum system.
Cell Filling
Gas System
A residual gas analyzer (SRS model RGA 200) is connected to the vacuum manifold to identify and analyze gas contaminants remaining in the system. When the vacuum pressure was lower than 10−4 torr, the RGA was turned on to monitor the gas contaminants in the system. The RGA was placed under the lower part of the vacuum system near the pumps, while the hot ion meter was placed at the top of the cell array.
We use the values from the ion meter to characterize the cell pressure, since the meter is close to the cells. The removal of impurities from the alkali metal is believed to be critical to the final performance of the cell.
Cell Construction
Target Setup
Overview
Lasers and Optics
Magnetic Fields
Heating Oven and Temperature Measurements
Adiabatic Fast Passage
Spin Motion in Magnetic Fields
For a uniform field B = Bzeˆz, the magnetic moment precesses along ˆez at the Larmor frequency f =γBz. Under such conditions, it can be shown that the last counter-rotating term in equation 4.12 is negligible. According to equation 4.15, the magnetic moment precesses along the effective field Be with a Larmor frequency ω =γBe in the rotating frame.
By inserting the magnitude of Be from equation 4.14 into equation 4.17, with a first-order approximation for B1/Bz, the resonance frequency is solved and becomes. Compared to equation 4.16, the resonance frequency is shifted by a factor of (B1/2Bz)2, which is of the order of 10−6 for our experiments.
Adiabatic Fast Passage
The adiabatic theorem [3] states that if the swing rate ˙B is slow enough, the angle between the magnetization and the effective field will be constant. Given this initial condition and the fact that the amplitude of the magnetization is a constant, one can deduce from Equation 4.3 that the magnetization will follow the effective field during a sweep. The magnetic field Bz is swept by resonance at Bz = ωγ0 until the effective field Be is anti-parallel to the z-axis (Bz(t)− ωγ0 À B1).
The adiabatic condition is satisfied when the relative rate of change of the effective field Be in the radial direction is significantly slower than the Larmor precession frequency. Since the magnetization of the target is proportional to the 3He polarization, the B˙ sweep rate cannot be too slow in order to depolarize the 3He.
Measured AFP Signals
The integral over the area R ds of the pickup coil can be isolated as a geometric parameter A. The line shape of Equation 4.29 can be used to estimate the rf field strength as the FWHM (full width half maximum) of the signal S(t) in Equation 4.29 is The reference signal from the lock-in amplifier is locked to the drive source of the rf coils.
Electronics Setup
Magnetic Coils
The holding magnetic coils were designed to create a uniform magnetic field of up to 40 Gauss along the z-axis. The power supply was operated in constant current mode to reduce magnetic field fluctuations caused by fluctuations in the supply network. The magnetic field strength was measured with a magnetometer (Bell Inc, model 615) and calibrated to the power supply voltage readings as shown in Figure 4.4.
The relationship between the voltage across the coils and the strength of the magnetic field is given by. The rf frequency was set to 85.6 kHz, which corresponded to the AFP NMR resonance magnetic field for 3He at 27.2 Gauss.
Signal Detection
In Figure 4.3, the equivalent circuit of the pickup coils is shown in the dashed line block. Furthermore, setting the time constant of the lock-in amplifier will slightly modify the signal. The time constant parameter of the lock-in amplifier is the inverse of the bandwidth of the low-pass filter in the frequency domain.
However, if the width of the peak signal is comparable to the time constant, the signal itself is attenuated. For certain conditions, the coupling of the pickup coils with the 3He magnetization can be prominent.
Water Signal Calibration
The average of the up and down peak amplitudes is taken as the water polarization signal. In this chapter, measurements of 3He polarization and exchange rate coefficients of 3He and alkali metal atom pairs are discussed. The Swater water signal in Table 5.1 is the average of the upstream and downstream NMR-AFP peak water measurements.
Suppose that the volumes of the upper and lower chambers are Vu and Vb, respectively. To determine the number density of 3He in the lower chamber, it is necessary to know the internal volumes of the chambers and the chamber temperatures.
Spin-exchange Rate Coefficients
Overview
- Room Temperature Relaxation Rates
Without the laser light present, the 3He polarization relaxation depends only on the cell temperature, which can be easily stabilized to within ±1◦C. The 3He polarization wall relaxation rate in the cell, 1/ΓHe, can be found from a room temperature 3He polarization relaxation measurement as shown in Figure 5.4. For long-lived cells, since the 3He polarization relaxation rate is slow, it is necessary to correct for the NMR-AFP loss in the data before performing the fit.
The 3He polarization relaxation measurements are straightforward for a warm single chamber cell, similar to the room temperature measurements. By plotting the hot 3He polarization relaxation rates as a function of Rd[K], the spin exchange coefficient kSE can be found from the slope and wall relaxation.
Alkali Metal Vapor Density Determinations
- Vapor Pressure Formulae
- Direct Vapor Density Measurements by the Faraday
In our laboratory, we have also carried out direct measurements of the density of alkali metals using the Faraday rotation method to further test the applicability of the vapor pressure formulas [86]. The probe light passes through the target cell along the direction of the restraining magnetic field. Since the alkali metal vapor inside the cell is circularly birefringent, the linear polarization plane of the probe will be rotated by an angle proportional to the density of the alkali metal vapor.
The rotation angles were measured at different wavelengths of the probe light at the same temperature, after which an adjustment of the angles versus wavelengths yields the measured alkali vapor density. In this thesis, the vapor pressure method is still used to determine the vapor density of alkali metals because we found no evidence of vapor violation.
![Figure 5.6: Alkali vapor densities as functions of temperature. The rubidium and potassium formulae are from Reference [4] and the cesium formula is from Reference [11].](https://thumb-ap.123doks.com/thumbv2/123dok/10403002.0/116.918.264.716.96.463/densities-functions-temperature-rubidium-potassium-formulae-reference-reference.webp)
Calculations of Spin-exchange Rate Coefficients
The slope of the line in Figure 5.9 shows that the spin exchange rate coefficient is the same at a temperature of 197◦C. As discussed in Chapter 2, the spin exchange rate coefficient kSE has a temperature dependence in the form of 1/√. The hot3He polarization wall relaxation time constant from the intersection in Figure 5.11 is found to be 68 ± 13 hours.
The spin exchange rate coefficient for rubidium-3He pair has been previously measured by several groups. At the time this thesis was written, no cesium-3He spin exchange rate coefficient measurements had been measured.
Future Work
This potentially low-cost imaging technique offers the possibility of high-resolution imaging using both polarized noble gas and proton MRI of tissues in the same scanner. This potentially low-cost imaging technique offers the possibility of high-resolution imaging using both polarized noble gas and proton magnetic resonance imaging of tissues in the same scanner. 129Xe magnetization was excited using a 40° flip angle, which allowed multiple excitations before the cell had to be repolarized in the laser system.
From the NMR signals for xenon and water, the polarization of the xenon cell was found to be about 4%. The pulled seal where the cell was removed from the vacuum system caused a small extrusion of the spherical cell as you can see in the picture.
A double-chamber cell used in the experiments. The background is an
A string of cells on a manifold. The dimensions of the pumping chamber
The vacuum system used for cell filling
A typical RGA scan before baking the cell
A typical RGA scan before filling the gas into the cell
