I Single particle energy detection

[Malamala]

Hello! If I have a single ion traveling at a given energy (on the order of 10 keV), is there a way to read out its energy in real time with a single pass? Basically I was wondering if there is a device able to measure the current or magnetic field induced by the ion passing through it (while letting the ion pass through further on)? Thank you!

 

[Twigg]

It sounds like what you're asking is if there's a way to measure the energy of a passing ion in situ. Otherwise, time-of-flight (ToF) is the standard methods for measuring ion energies.

Sounds like what you have in mind is something like a wire chamber but without the ionizable target gas. However, I believe the signal will be simply too weak. I did some back-of-the-envelope estimates and saw that a wire at 500nm from the ion will only see a 100 microvolt induced EMF. That's pretty hard to detect in a single pass, and a 500nm mesh of wires is already pushing the limits of technology.

However, I have a much simpler suggestion for you: look at the Doppler shift of an atomic line. 10 keV is quite fast and won't leave you a lot of time for the ion to absorb enough photons for you to detect, so you'll need an intense probe beam. Perhaps focus a nanosecond pulsed dye laser onto the beam? (Dye laser so you have the wavelength tunability to tune into resonance)

 

[Astronuc]

However, I believe the signal will be simply too weak. I did some back-of-the-envelope estimates and saw that a wire at 500nm from the ion will only see a 100 microvolt induced EMF. That's pretty hard to detect in a single pass, and a 500nm mesh of wires is already pushing the limits of technology.

I was thinking that one would have a very low signal-to-noise ratio. One would need a really cold (very low thermal noise) detection system.

I was also thinking of a Penning trap.

Lo and behold, S. Djekic et al., "Temperature measurement of a single ion in a Penning trap",
Eur. Phys. J. D 31, 451-457 (2004)
https://doi.org/10.1140/epjd/e2004-00168-1

Maybe it's possible, but I haven't looked into the details.

Usually, one measures a population of particles/ions.

 

[Twigg]

I was also thinking of a Penning trap.

Lo and behold, S. Djekic et al., "Temperature measurement of a single ion in a Penning trap",
Eur. Phys. J. D 31, 451-457 (2004)
https://doi.org/10.1140/epjd/e2004-00168-1

Maybe it's possible, but I haven't looked into the details.

The PS200 experiment (measuring gravity of the antiproton) captured about 50,000 antiprotons with energies up to 30 keV in a Penning trap, so it's definitely possible (with a big enough budget). And that was in 1993, so I imagine high-voltage amplifier and high magnetic field tech has only improved. But I feel that it defeats the in situ aspect of the OP's question (if I understand that correctly!). By trapping the ions, you are grossly changing their trajectories (even reflecting them). I believe the OP wants a way to measure the ions' energy without changing their trajectory.

Another thought: I know parallel-plate avalanche counters (PPACs) are used to count the incidence of MeV charged particles, and you could (in principle) put two of them in series to generate a non-destructive ToF measurement. However, my gut feeling is that 10keV is too low and the ions will be deflected or decelerated significantly. Also, to do a ToF measurement you'd need the rise/fall-time of the PPACs to be significantly less than the ToF, which will put a lower bound on the length of your ion's beam path. Many parameters to juggle!

What variation in energy do you expect? 100's of eV variation? 10's of eV's? That will be a key parameter if you do a Doppler-type measurement.

P.S. I double checked my back-of-the-envelope estimate for induced EMF on a wire with mathematica and got similar results. 500nm spacing gives you around 100 microvolts of signal. If the detection region (length of the pickup wires) is something like 10cm long, then the characteristic timescale of the measurement is 10cm / v = 1.7 ns. That's not a lot of integration time to measure 100 microvolts, and the bandwidth is probably fairly large since your signal will be a pulse. The short version is that the wire chamber approach is looking less and less feasible the more I think about it.

You might do some research into the tricks used in heavy ion storage rings. I'm sure those folks have thought about your problem in depth.

 

[mfb]

Let's not run into xy questions. What's the context here - where do the ions come from, what happens with them afterwards, what do you do with the measurement result?

 

[Malamala]

@Twigg @Astronuc Thank you for your replies! Actually what I had in mind when I asked my question was something similar to the way they detect single particles in a Penning trap. Usually they care about the frequency of the oscillations, so they do a Fourier transform over multiple oscillation cycles. However, I read that in principle, if the amplitude of the ion (axial one, I will ignore the other motions) is significantly bigger than the thermal noise, one can measure the ion oscillation in real time (i.e. the signal would be a sinusoidal, with some noise on top due to thermal noise). Also I understand that with the proper cryogenic setup, one can even measure currents as low as $10^{-15}$ A. So now, using the formula for induced current in a penning trap:

$$i_{ind} = \frac{qv}{D_{eff}}$$

where q is the ion charge, v its velocity and $D_{eff}$ the effective electrode distance which is about 1mm to 1cm (assuming my calculations are not wrong), this would give a current of about $5\times 10^{-12}$A, which is 3 orders of magnitude bigger than the value mentioned above.

So basically just using a Penning trap setup (without the magnetic field), it looks like we can easily measure this current in real time (i.e. it will be huge compared to the noise of a cryogenic circuit). Also this is a non-destructive measurement, and we can easily send the particle in and out of the trap (this is what is done in a normal Penning trap). On top of this, in a real Penning trap there are further constraints due to the magnetic field (and the other 2 direction of motion), so I imagine that if one aims just to measure the current, they can get even better results (e.g. reducing the value of D)?

Does this make sense? Am I making some wrong assumptions along the way? I would really appreciate your input. Thank you!

 

[Twigg]

Sorry for the late reply, been on a trip.

Also I understand that with the proper cryogenic setup, one can even measure currents as low as 10−15 A

This is a bit misleading. When you say that you can measure $10^{-15}\mathrm{A}$, one must ask "over what integration time?" Is it $10^{-15}\mathrm{A}$ in a single shot of your experiment? Is it $10^{-15}\mathrm{A}$ over the lifetime of some group's Penning trap? That could be averaged over hours or even days of data. Current measurement noise in a cryogenic tank circuit will have a noise power spectral density (NPSD) with units of $\mathrm{A}^2/\mathrm{Hz}$ or $\mathrm{A}/\sqrt{\mathrm{Hz}}$. This number (or plot, for a reactive circuit) will tell you how to calculate the measurement noise for a given integration time.

I'm a little confused. What do you gain by turning off the magnetic field? It doesn't change the axial motion. Also, if you have anywhere over ~10eV of energy in the radial motion, that ion will be gone before you manage to switch off the magnetic field.

 

[Malamala]

Sorry for the late reply, been on a trip.This is a bit misleading. When you say that you can measure $10^{-15}\mathrm{A}$, one must ask "over what integration time?" Is it $10^{-15}\mathrm{A}$ in a single shot of your experiment? Is it $10^{-15}\mathrm{A}$ over the lifetime of some group's Penning trap? That could be averaged over hours or even days of data. Current measurement noise in a cryogenic tank circuit will have a noise power spectral density (NPSD) with units of $\mathrm{A}^2/\mathrm{Hz}$ or $\mathrm{A}/\sqrt{\mathrm{Hz}}$. This number (or plot, for a reactive circuit) will tell you how to calculate the measurement noise for a given integration time.

I'm a little confused. What do you gain by turning off the magnetic field? It doesn't change the axial motion. Also, if you have anywhere over ~10eV of energy in the radial motion, that ion will be gone before you manage to switch off the magnetic field.

Thank you for your reply! I am a bit confused about what you mean by integration time. My explanation/question was based on the idea of measuring a signal in real time (i.e. measure the sinusoidal signal due to the axial motion of the ion). I don't think there is any integration time in this case.

About the magnetic field what I meant is that if I just care about the induced current in the cryogenic circuit, and not about trapping the particle, I don't need a magnetic field at all (I didn't mean turning it on and off at different times). Basically what I meant to say is that the setup would be much simpler than an actual Penning trap, as we don't need a magnetic field at all. The ion would come from the left, pass through the cryogenic circuit and give a signal then exit the cryogenic circuit.

 

[Twigg]

Every measurement has an integration time somewhere. If you're reading out the superconducting circuit voltage on an oscilloscope, then the integration time is 1 over the scope's bandwidth. For your proposed setup, "real time" just means that the integration time must be short relative to the time of flight, $D/v$ where $D$ is the distance between electrodes. I bring this up because I don't think you should take the $10^{-15} \mathrm{A}$ number at face value, as discussed above.

Got it. I see what you mean now for the layout. I think the aspect ratio (electrode diameter / distance between electrodes) will be the most difficult parameter to get right for your application. You need the electrode diameter to be large enough and the distance between to be short enough that you see sufficient signal. In other words, as you said, $D_{eff}$ must be small.

 

[Twigg]

To put the integration time issue in perspective, consider the alphatrap experiment as an example. They have an rms voltage noise(when resonant with the tank circuit) of about $10 \mathrm{\mu V/\sqrt{Hz}}$ and an impedance on the order of 100 megaohms, and the tank circuit has a bandwidth of about 100Hz. The integration time is 1/100Hz = 0.01s, and the rms noise floor is $\sqrt{(10 \mathrm{\mu V/\sqrt{Hz}})^2 \times 100\mathrm{Hz}} = 100\mathrm{\mu V}$. Dividing by the impedance, that's an rms current noise floor of $10^{-12}A$ over the 10ms integration time.

In your case, a 10keV ion will travel 3 kilometers in that 10ms integration time, and even if you had a 3 km long Penning trap-like structure you'd still only see an SNR of 1.