The higher the alternating field the shorter the pulse must be, which eventually becomes a problem of its own. About 0.5T will lead to a 10us pulse, which is good enough, and even smaller fields are possible with the only downside of a loss of some sensitivity in the final spectrum. So no, I don't need a very high AC field. Thanks for the detailed explanation though, perhaps I can adapt some of that into my design.
Since your Larmor frequency is just ~500kHz, I'm wondering in fact whether a 10us pulse isn't much too short, as this leads to a pretty wide bandwidth of the pulse (-> about 20%, while 10us at say 100MHz rather leads to 0.1% bandwidth only). On the one hand this increases the chance that the spectrum of the pulse does include the Larmor frequency even in case of a bad match of the carrier frequency, but on the other hand it reduces the pulse's energy density per Hz of bandwidth.
I'm a complete NRM layman - just did read some basic stuff yesterday, and there is one thing I did not understand so far: In the literature, B1 is obviously trated as a constant value (although the excitation signal is actually AC and therefore a function of time). For a pure sine wave at the Larmor frequency, it makes sense that the value of B1 is simply the amplitude of the sinve wave. But how is the value of B1 defined for a spread-spectrum signal whose magnetic flow per Hz of bandwdith is a function of frequency? Which frequency band of the signal contributes to the value of B1? Do the protons have a particular (let me call it) "resolution bandwidth" inside which they react to the excitation, while any frequencies otside this spectral band are just wasted excitation, having has no effect?
To summarize: As far as I understand, the maximum pulse duration is eventually limited by the required bandwith (which depends in turn on the maximum chemical shift that needs to be captured). Reducing the pulse bandwith to 0.1% (which I guess is still sufficient?) whould lead to a 2ms pulse (instead of 10us) and would reduce 0.5T to only 250uT, right? And depending on the answer to my above question regarding the definition of B1, the smaller bandwidth may additionally help due to the lager magneric flow per Hz of bandwidth.
Yes, the field should match the Larmor frequency quite well, which itself would change if the static field was not stable. I doubt I can afford a good frequency synthesizer for this project though, as it is a rough proof of concept. If a minimal (and cheap) configuration starts looking promising, more investment could be made. But the goal right now is to get a detectable signal in the detector coils (which may be the alternating field coils or another orthogonal set). If that is not possible with basic, affordable electronics, low-field NMR becomes much less lucrative.
Every single-digit-$ radio tuner includes a reasonable frequency synthesizer today. I think that a $$ OXCO can be stabe enough for the use case (at least short term). For 500kHz, likely a DDS generator like AD9830 or similar (using an OXCO as reference for the clock) may well suffice, at least for generating the carrier for the excitation pulse.
The receiver side may be more challenging than the transmitter. Here I'm not sure yet reagarding the carrier phase noise requirements for your use case. And the major issue is likely that the signal is very weak. How big is actually the amplitude of the (~500kHz AC) magnitic flow which needs to be detected? Somewhere in the uT range, or even less? What's the area of the coil, btw?
EDIT: Btw, how many T is your B0?
From my understanding, a pulse with a nonzero bandwidth (e.g. a sinc pulse ideally) is used for MRI for the excitation of particular slices of space. However, for simply detecting an NMR signal a pure Larmor frequency sine wave is used. In that case, a rotating reference frame is created within which the magnetic moment of the sample is pushed down from the z-axis into the xy-plane at a constant speed, i.e. as neatly a possible. At that point, the width of the pulse (which is independent of bandwidth) will determine whether the sample gets to start relaxing before it's fully in the xy-plane. If it does start relaxing (i.e. long pulse) the overall signal will be lower.
My AC field only needs to be about 0.5mT (millitesla), not 0.5T. You're right that the pulse width will be inversely proportional to field strength, so the longer the pulse the lower the field I get to use. At the expense of sensitivity though, which may already be limited with a weak field.
Will definitely look into these signal generators. You're right that the receiver will be a challenge: I was planning to start another topic a little later to figure out how to go about detecting the microamperes or even nanoamperes of signal I will get. I have an aged digital oscilloscope, but will need some sort of amplifier to be able to detect the low currents in the receiver coils. I have heard of Dave's ucurrent gold, which helps do this, but it's apparently out of stock.
If you're asking for the area of the transmitter coil, it will probably be a few square centimeters. As far as the receiver goes, likely even smaller: maybe a square centimeter, maybe less.
Yes, the static field (B0) will indeed be about that low. Creating a much higher field in air requires prohibitively high currents for an air-cooled setup.
Thank you for taking the time to do this much research into the topic!
The AC excitation field should be relatively small compared to the DC field. This is at least the general assumption for the theory. Anyway 0.5 T would be really high for an AC field in air - remember a system made to get 0.1 T AC over a slightly larger volume: it was quite a beast with a few kW of RF power to a high Q resonator with water cooled coil. Kind of like induction heater, just higher frequency.
I have once used a system that seem to be made for low field NMR. It had an RF amplifier for some 2 kW for pulses up to 1 ms or so. This gives odd effects when one starts to see/hear arcing at BNC connectors. The NMR coil may not be well matched to the amplifier / cable impedance. One may have to consider this with the amplifier, not all power amps like a poorly matched load.
I don't think one would really need a pure sine wave, so square wave drive with a H bridge may be acceptable.
A point could be dampening the LC resonance at the end of the pulse.
Unit error. It's 0.5mT. You're totally right, the field would be insane at 0.5T.
That's a very interesting point. From what I understand, a square way may theoretically work (not 100% sure). It's usually done via sinusoid as that creates a rotating reference frame within which the magnetic moment goes from the z-axis to the xy-plane at constant speed. I believe at the very least, it would exhibit jerky movement in a square wave field. In a perfect world, I would use a sine wave so everything is as neat as possible, but if the square wave is many times easier to implement I could definitely consider it. I'm therefore officially welcoming suggestions for how to create an efficient square wave alternating field in the transmitter coils, it may be worth a try.