Introduction

Polarized targets are essential tools in probing nucleon spin structure within high-energy and nuclear physics experiments. The SpinQuest polarized target system at Fermilab includes key components such as a cryogenic evaporation refrigerator for high-power cooling at 1 K, a roots pump stack with 17000 m³/hour of pumping capacity, a microwave generator, and NMR system. The polarization is achieved using the DNP (Dynamic Nuclear Polarization) technique with 5T magnetic field and an extended interaction oscillator (EIO) microwave tube capable of producing 140 GHz. An ammonia target is used for both proton (spin 1/2) and deuteron (spin 1) as well as neutron (spin 1/2) polarization. A Q-meter based nuclear magnetic resonances (NMR) system is utilized to measure the polarization over the course of the experiment. The SpinQuest polarized target system has achieved well over 90% polarization with solid NH₃ and has completed a set of target commissioning runs and taken some production data.

NMR Measurements (Parameters of Q-Meter and Microwave frequency)

• In field B apply RF field to material at Larmor frequency ω_0
• Coil of L_0 perpendicular to B_0 to induce spin flip
• LCR circuit (so that ω_0=1/√LC ) to observe change in impedance with frequency
• As frequency changes: circuit response to Q-curve and polarization signal
• Sweep frequency around ω_0 to integrate in ω.

Microwave setup

Dynamic Nuclear Polarization System

• DNP takes place at very low temperatures, around 1 Kelvin, using a combination of a homogeneous magnetic field and a microwave field.
• The interaction between electron spins creates a separate energy reservoir. This reservoir is only connected to the Zeeman and lattice energies through the properties of transverse relaxation and diffusion.
• The nuclear spins get polarized through their interaction with the paramagnetic spin systems.
• Microwaves alter the spin temperature, interacting with the proton Zeeman system; effective DNP requires nuclear spin relaxation to be much slower than that of paramagnetic centers.
• Tuning microwave frequency determines whether proton spins become polarized parallel or antiparallel to the magnetic field, achieving either positive or negative polarization.

_{Courtesy of C. Keith, JLAB}

Polarization Calculation

• NMR Calibration (Thermal Equilibrium): Used to establish a proportionality relation for determining enhanced polarization under varying thermal conditions.
• Q-Curve NMR Signal: The area of this signal at a constant magnetic field is key to finding the polarization.
• μ_e≈ 660 μ_p: Polarization of electrons are much higher than protons and the electron and protons spin flips when applying RF field.
• At equilibrium, populations follow Boltzmann distribution:

• Natural Polarization for Spin-1/2 Particles: Described by the TE measurement formula.

μ – Magnetic moment

B – External Magnetic field

T – Temperature

k – Boltzmann constant

Sources of error

• nλ/2 cable length: leads to steeper Q-curve, making smaller polarized signals much more difficult to analyze using traditional background subtraction and signal extraction methods.
• Q-meter configurations (calibration constant)
• Changes in Radio frequency (RF) environment
• Temperature Change
• Statistical errors dependent on DAQ

 + noises, and other factors …

Uncertainty calculation for δP_E/P_Ecan be expressed as:

δG : uncertainty of gains

δS_TE  : uncertainties acquired during the thermal equilibrium calibration measurements

δS_E  : uncertainty estimates due to the systematic effects over time

SpinQuest Polarized Target System

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Covariance Matrix

Parameters (Characteristics of Q-Meter) to be included in the Q-Curve Covariance Matrix:

V - Input voltage

C_knob - tuning capacitance

trim- cable length defined by nλ/2 (n/2 is the trim, and λ is the Larmor frequency of the material)

η - Filling factor of the coil

∅ - phase offset

C_stray, Stray capacitance – parasitic capacitance of the system

Phase cable length, QMeter temp, noises, and other factors

Hessian Fit with Covariant Matrix results performed using the Iminuit python library.

Target Polarization Systematics

• Signal covariance matrix (Per each channel): Depends on proton/deuteron signal line-shape
• Magnetic field inhomogeneity
• Microwave distribution inhomogeneity
• Polarization decay in x, y, z directions over time (with modifications to the calibration insert)
• Uncertainty from the Calibration Constant

Temperature: Based on the cernox sensors and (or) Helium vapor pressure
Area under the signal: associated systematic uncertainty 

Online Polarization Crosscheck:

Calibration constant was re-calculated by taking the average area and average He4 Temperature directly from the available NMR data - Online CC and the recalculated CC were almost the same as below:

NMR Polarization Display Panel

How Polarization was achieved during SpinQuest Commissioning runs:

Offline Polarization Measurements: Area under the NMR Signal

1. Plot the Baseline:

2. Plot the RawSignal

3. Get the difference of Baseline and the RawSignal and plot the difference

4. Select a suitable data range on left and right wings of the plot and make a polynomial fit (or apply a Voigt fit) for the selected data

5. Plot the residuals (Difference between Polynomial fit and the Baseline-RawSignal plot). Apply a cut for both sides of the wings and calculate the area under the curve.