Electronic – Should I avoid placing a SMPS inductor close to a magnetometer

My guess is that the inductor is probably not a major contributing factor to the failures. I say this because it's a inductor, and as such produces a magnetic field. The quartz in the crystal is not particularly magnetic. Second, you note that the inductor is shielded, so the external leakage field should be small. Still, the crystal output is pretty high impedance and induction could be adding a small voltage in series with it. This should be small and not much issue if the crystal is being driven properly with the right load caps.

I would look closely at the crystal circuit. This sounds like maybe you are using too low of a drive level setting or the load caps aren't right. What does the datasheet say the load capacitance of the crystal needs to be? What size cap do you have on each side? The chip driving the crystal may have different drive level settings if it's intended to run with a wide range of crystals. At 24 MHz you almost certainly should be using the highest drive level choice.

Look at the crystal driver output pin (input to crystal) with a high impedance probe. That should be a good strong signal. It could be sortof square wave looking with a bit rounded corners or nearly a sine wave. It should be a few Volts p-p, usually half the supply voltage or more. Check the frequency carefully to make sure it's not running on a harmonic. If it is, it's a indication one or both load caps aren't connected or are too low. Then look at the crystal output. That should be a nice 24 MHz sine wave at least a Volt p-p, preferably a little more. Does the unit suddenly work right when you put the scope probe on a crystal lead? If so, it's again missing, bad, or incorrect load caps.

Power out = power in minus losses. Power out is 300 watts therefore power in will be about 330 watts. At 14 volts and 330 watts, current in will be 23.6 amps but this is average current. The peak current will depend on the duty cycle and looking at it simplistically, for a 50% duty cycle the peak current might be about 2 x 23.6 amps = 47 amps worst case (borderline discontinuous).

Ideally you need to pick an inductor that doesn't saturate and one with a gap is going to work better. A solid ferrite core will tend to start saturating at a flux density of about 0.4 teslas. It might have a relative permeability of (say) 1000. Using B = \$\mu H\$ allows this to be estimated: -

H = \$\dfrac{0.4}{4\pi \times 10^{-7} \times 1000}\$ = 318 A.t/m

You need to know the mean length of the magnetic field and that is found in the data sheet for the ferrite you are using. Let's say it is 100mm, this means your maximum ampere-turns is 31.8 and of course this would be unsuitable for your application because you can immediately see that it is likely your amperage and one turn is going to heavily saturate the core.

So, if you put a gap in it might reduce the effective permeability to (say) 200 and this allows more 5x H field (5x more current or 5x more turns) but inductance is related to turns squared so there is a net gain because although the \$A_L\$ value for the gapped core has gone down by a factor of 5 you only need \$\sqrt5\$ more turns to recover the inductance.