## [Pol. p target] Modeling Microwave Unit Signal

a period is 23ms. with in this period, the modulation signal voltage is

$V_{ms}(b,s) = b + ( t - 12.5) s [V]$

$Max(V_{ms}) = 29.2 [V]$   $Min(V_{ms} = 0 [V]$

on the Gunn Oscillator, there is a mechanical switch, which can adjust the base frequency but changing the length.

$f_{base} (l) = 0.61 + 6.433 [GHz]$

this data is provided by 3 data point in the manual. the output frequency of the microwave is

$f_{out} = f_{base} + F_m ( V_{ms} )$

where $F_m$ is the modulation function, that we have to find out. linear?quadratic? at least get a good approximation for it.

the resonance frequency and its FWHM should depend only on the microwave cavity. an a absorption signal can be formulated by a Lorentzian distribution. and this signal will be converted to voltage by a linear conversion factor. ( the green words is an assumption )

$L( f_{res} , f_{out} , FWHM_{res} ) = 1/ ( 1 + (\frac { f_{res} - f_{out} } {FWHM_{res}} )^2 )$

From the relation between the length and voltage at peak. we can find out the modulation function. since the output frequency is equal to the peak frequency. thus, the output frequency is fixed

$f_{out} = f_{res} = 0.6 l + 6.433 + F_m (V_{ms})$

if we measure l and V_{ms} we can find out F.

by further measurement,  the modulation is non-linear. That’s also explained the FWHM on the CRO change with frequency. since the FWHM of the microwave cavity should be same and the change of the FWHM in CRO reflected that the gradient of the frequency output. for a linear frequency output, the FWHM should be the same. but if the gradient change with due to the modulation signal, the FWHM will change.

## Mircowave Unit

the Gunn Oscillator and the modulation signal were studied.

the problem is the IV converter. it should be a high-pass.

but there are 2 problems

1. the reflected microwave signal is negative voltage.
2. there are 2 things to determine the microwave frequency. – the modulation signal and the knob is Gunn Oscillator.

## [Pol. p target] Finished Circuit Connection and Test on MW system

The Above diagram is the Setup. The upper one is laser unit, the 2 devices between Sample Chamber and CRO is field Sweep Unit. and the lower part is the Microwave unit. and of course the NMR unit and the Power and Cooling unit for the Static B-field.

(some incorrect in here, the modulator is Gunn Oscillator, and the Gunn Oscillator is the power supply and Modulation signal. )

## Laser Unit

The Laser we use is a Class 4 Ar ion Laser ( Coherent TSM25 ), wavelength is 454.5 nm to 528.7 nm. Maximum power is 25W.

the laser beam was reflected by a mirror to fit the space of the lab. and it pass through a lens with 100mm focal length so that the beam gets converged on the position of the beam chopper. after the chopper, the beam diverged and it passes another 100mm focal length lens to be come parallel.

before it goes to the sample, a 1:99 beam splitter splits the beam such that 1% of it go to a power meter. the signal of the power meter is used to control the microwave and field sweep.

this part is the optical pumping for polarizing the electron.

although the chopper is moving at high frequency, when the chopper cut the laser, the power meter signal will be decreased. and this event will trigger the microwave and field sweep to transfer polarization to protons. the triggering is by the Controller.

## Field Sweep Unit

The field sweep unit is all-in-one. the field will be monitored by the CRO and controlled by the Controller.

## Microwave Unit

This part contains most devices and trouble me. since i just follow the menu and not fully understand the function of each devices. i try to explain.

Power Supply of the Gunn Oscillator and Modulation signal

this is the starting point. the voltage of the power supply can be adjusted by a knob. the Modulation signal can be adjusted by a “Bias ADJ” and “Output Cont”.

The “Bias ADJ” change the level. and “Output Cont” change the slope.

the frequency of the Modulation Signal is 23ms.

and the signal will chop out negative value.

the signal also monitored by a cable from the back to the CRO. the monitored signal is a fixed signal with fixed “Bias ADJ” and “Output Cont”.

the maximum power output is 150W to the Gunn Oscillator.

Gunn Oscillator

Gunn Oscillator is used for general microwave according to the modulation signal. when the voltage of the modulation signal is low, the frequency of the microwave is low.

Attenuator

This is for reduce the microwave power. the reason for using this, is that the RF amplifier has maximum power input 100W for pulse and 20W for CW signal. or to say, the working range is that.

RF amplifier

This is for amplifier the MW signal. and the RF amplifer can be controlled by a remote device, so that the amplify ratio can be change to on or off.

this is important, since after the laser polarized the electron, the chopper will cut the laser, then microwave and field sweep come in to transfer the polarization to the proton. therefore a remote controllable device is needed.

i don’t know the amplify ratio and maximum output.

Circulator

the RF signal will go to the circulator. there are 3 ports on the circulator. the function for the circulator is circulate the signal. the signal from port 1 will only go to port 2, port 2 will only go to port 3, and port 3 will only go the port 1.

we have to detect the reflected microwave to find out the resonance frequency of the microwave cavity in side the sample chamber. and we don’t want to mixed up the signals.

Directional Coupler

there are 4 ports in Directional Coupler, 1, 2, 3, 4. most of the signal from port 1 will go to part 2 and little bit of it will got to port 3. but most of the signal of form port 2 will go to port 4 and only less to the port 1.

$1\rightarrow 2 : 1\rightarrow 3 >>1$

$2\rightarrow 1 : 2\rightarrow 4 << 1$

i don’t understand this part.

Microwave cavity inside the Sample Chamber

the microwave then enter the cavity and get reflected when the input frequency is not the natural frequency of the cavity. the reflection signal will go to the port 2 of the directional coupler and then the port 2 of the circulator. the signal will be diverted to port 3 and enter an other attenuator, for decrease the power.

Output w/ adjust

This should be corrected to “Crystal Converter”. it convert the microwave into current signal.

the maximum input is 20W. therefore, it need an attenuator before the microwave come in.

I-V converter

it simple convert a current signal into a voltage signal, so that we can wee in CRO.

## NMR Unit

an easy part is the NMR system. since we have 1 single machine for generate NMR pulse and analyzing the NMR signal.

the only thing we have to do is adjust the tuner. the tuner is a variable capacitor, so that it can matching the impedance of the NMR frequency and the NMR coil ( which inside the chamber) to give Maximum power delivery.

## Power supply & Cooling Unit

this is for the static B-field.

____________________________________

when we run the microwave system, the absorption of the reflected wave is too small and not symmetric. we tried every possible setting and check the cables. not thing wrong.

may be the microwave coil inside the chamber has problem. that is what we are going to do.

# Motivation

In order to convert the NMR single to the absolute magnetic field strength of the polarization. the thermal polarization ( polarization at thermal equilibrium ) should be measure and used to calibrate the NMR signal.

the thermal polarization is given by the Boltzmann statistic. The excited and the ground state population is:

$\frac{ N_{\uparrow}} { N_{\downarrow} } = Exp \left( - 2 \frac { \mu_p B } {k_B T } \right)$

the thermal polarization is the ratio of the different of spin-up and spin-down to the total spin.

$P_{thermal} (B , T ) = tanh \left( \frac{ \mu_p B }{ k_B T } \right)$

where $\mu=p$ is the proton magnetic moment.

$\mu_p = g_p \mu_N = g_p \frac{e \hbar }{2 m_p} = 1.410606662 \times 10^{-26} J T^{-1}$

$k_B$ is the Boltzmann constant.

$k_B = 1.3806504 \times 10^{-23} J K^{-1}$

The proton magnetic moment is small, the thermal polarization can be approximated as a linear function:

$P_{thermal} ( B, T) = \frac{\mu_p B}{ k_B T}$

since our polarization is on $T = -5 ^oC$ and $B = 0.05 T$, thus, the thermal polarization is:

$P_{thermal} (0.05, 268.15) = 1.90509 \times 10^{-7}$

which is very small to be detected, or to say, the signal is smaller then the noise level.

the small system has a better sensitivity, down to $10^{-7}$.

# TO-do

• Connect the Static field power and water cooling system
• connect the Controler Unit
• connect the magnetic field sweeping
• Test Run

## First experiment of 6He with a polarized proton target

this paper reported a first spin polarized proton solid target under low magnetic field ( 0.08 T ) and hight temperature ( 100K )

the introduction overview the motivation of a solid target.

• a polarized gas target is ready on many nuclear experiment.
• on the radioactive beam ( IR beam ), the flux of a typical IR beam is small, since it is produced by 2nd scattering.
• a solid target has highest density of solid.
• most solid target can only be polarized on low temperature ( to avoid environmental interaction to reduced the polarization )
• increase the experimental difficult, since a low temperature should be applied by a cold buffer gas.
• high field ( the low gyromagnetic  ratio ).
• high magnetic field make low energy scattered proton cannot get out from the magnetic field and not able to detect.
• a solid target can be polarized at high temperature and low magnetic field is very useful

the material on use is a crystal of naphthalene doped with pentacene.

the procedure of polarizing the proton is :

1. use optical pumping the polarize the electron of pentacene
• the population of the energy states are independent of temperature and magnetic field.
2. by Dynamic Nuclear Polarization (DNP) method  to transfer  the polarization of the electron to the proton.
• if the polarization transfer is 100% and the relaxation time is very long. the expected polarization of proton will be 72.8%

The DNP method is archived under a constant microwave frequency with a sweeping magnetic field. when the magnetic field and  microwave frequency is coupled. the polarization transfer will take place.

the next paragraph talks about the apparatus’s size and dimension, in order to fit the scattering experiment requirements.

the polarization measurement is on a scattering experiment with 6He at 71 MeV per nucleons. By measuring the polarization asymmetry $\epsilon$, which is related to the yield. and it also equal to the polarization of the target $P_t$  times the analyzing power $A_y$.

$\epsilon = P_t \times A_y$

with a reasonable guess of the target polarization. the analyzing power of  6He was found.

the reason why the polarization-asymmetry is not equal to the analyzing power is that, the target is not 100% polarized, where the analyzing power is defined. when the polarization of the target is 100%, both are the same.

in the analysis part. it used optical model and Wood-Saxon central potential to simulate the result. And compare the result from 6He to 6Li at same energy. the root mean square of 6Li is larger then 6He. it suggest the d-α core of 6Li may responsible for that.

they cannot go further discussion due to the uncertainly on the polarization of the target.