Measuring a *really* fast magnetic field change - Page 1
Forum section: electronics / projects

author: BeePound
author_rank: Contributor
timestamp: October 19, 2021, 12:10:07 am
content: Hi all,I have a rather basic question about Hall sensors. I need to measure a pulsed magnetic field (say at 1 Hz) that is approximately 1 femtosecond (!) in length. Is this even remotely possible? Obviously even triggering the Hall sensor is difficult, but assume that that Hall sensor is triggered "correctly", so that it could feasibly measure the signal if able. The Hall sensor has some finite time that it measures the voltage across the Hall element, and so I wasn't sure if with such a short pulse the Hall sensor would a) completely miss the signal, or b) measure some integrated or averaged version of the magnetic field.I don't think Hall sensors generally have such a high bandwidth, but I thought I'd ask people more knowledgeable than meIf you are curious, the application is in particle physics, where we want to measure the charge in an electron beam moving very close to the speed of light. The length of the bunch is only about 500 nm, which is around a femtosecond. Yes, there are other ways to measure the charge, but I think there are some good reasons to do it this way (if it is possible, that is).Thanks in advance!

author: jmelson
author_rank: Super Contributor
timestamp: October 19, 2021, 02:40:07 am
content: While the pulse is 1 fs long, the magnetic field will spread this out to a few fs, at least. But, I doubt a Hall sensor can respond to this, as the field has to penetrate the somewhat conductive bulk of the sensor. I think everybody uses magnetic coils to sense things like this. A quite small coil will do, but you often have to shield the coil to prevent pickup of ambient electrostatic fields. The shield needs to be broken at one point to avoid creating a shorted turn. Then add a fast amplifier to the coil, and you should be set. Watch out for capacitance of coax cables.Jon

author: ejeffrey
author_rank: Super Contributor
timestamp: October 19, 2021, 02:50:57 am
content: No. First of all, a femtosecond pulse is an optical frequency. So you should be thinking more like "measure light" than "hall sensor"Second, unless your sensor is within a few hundred nanometers of the charge, and the sensor itself is a few hundred nanometers in size the magnetic field pulse will be much longer, defined by the size/separation of the sensor rather than the charge packet.

author: Marco
author_rank: Super Contributor
timestamp: October 19, 2021, 11:44:23 am
content: Just curious, isn't the amplitude of the signal imposed on the beam position monitor you probably have any way directly proportional to the amount of electrons in the beam?

author: BeePound
author_rank: Contributor
timestamp: October 19, 2021, 08:31:40 pm
content: @ejeffrey, these are fair points. I haven't looked into "how long" the magnetic pulse would be, I just assumed it would be pretty short. The sensors wouldn't be hundreds of nanometers away, the idea was to put them perhaps a centimeter away. Regardless, it is certainly worth looking into further (and probably finding out the measurement is still not feasible, but oh well). Thanks.

author: BeePound
author_rank: Contributor
timestamp: October 19, 2021, 08:36:24 pm
content: @Marco, you are right and you caught methere are already good beam current monitors that can measure charge. The design I was considering could/would measure charge, but the real innovation would be to actually spatially map or "image" the beam at the same time in a non-destructive fashion.

author: jbb
author_rank: Super Contributor
timestamp: October 19, 2021, 08:56:03 pm
content: Hmm, this is a challenge. On first reading I thought “a 500m bunch should only need MHz bandwidth!” Then I noticed the nano…Stand by for some arm chair hand waving :-).Electronics are available up to around 100GHz bandwidth, i.e. 10ps region. There’s research going on into THz regime but it’s difficult and I really don’t know much. So a direct electronic probe probably won’t resolve your rise times.A heavily averaged reading might be possible by using a wideband current transformer around the beam line, ie you might get an output pulse with time constants in the ns range that could be integrated.To try to get a finer view of the situation, it might be better to try measuring a different quantity. Here’s a random thought which is probably deeply flawed:- place a wiggler magnet somewhere along the beam line (probably a weak one so you don’t get X and gamma rays)- as the bunch passes it will produce a pulse of synchrotron radiation. Total photon count should be proportional to number of particles in the bunch?- an optical detector (photomultiplier or photodiode) can produce a pulse proportional to the total photon count but that doesn’t tell you much about the bunch shape- I could be spewing bull****, but I wonder if the bunch shape (principally length) will modulate the synchrotron radiation spectrum?- if spectrum shaping is expected, could some suitable optics transform this into a spatial shape such that a multiple pixel detector can be used to infer things about the bunch shape (same idea as a diffraction grating and photodiode array for basic spectrometer)?(I now want to say something like ‘mix with an optical frequency comb using a nonlinear element’ but honestly that would be over the line into technobabble for me :-D)

author: m98
author_rank: Frequent Contributor
timestamp: October 19, 2021, 09:08:20 pm
content: Uh, maybe I'm not really thinking this through, but shouldn't the signal produced by such a pulse have a pretty large bandwidth? Dirac-imulse and all? So maybe a coil with an RF envelope detector?

author: ejeffrey
author_rank: Super Contributor
timestamp: October 19, 2021, 09:31:25 pm
content: If I remember correctly, beam profiles are normally measured by scanning a fine wire through the beam profile and measuring how much hits the wire? That is what you want to avoid?How big is the beam cross section? How much resolution do you want? This is definitely a challenging problem.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 20, 2021, 02:03:04 am
content: As I recall, traditional method is a split in the metallic beamline, across which a bunch of coax cables are connected.The electron beam in beamline has a coaxial geometry, the shield carrying the image current of the beam (plus various and sundry modes, since we're talking optical frequencies; only the low frequency TEM00 mode is meaningfully sensible this way). Simply put, by connecting impedance in series with the shield, that image current is sensed.As I recall, this is good for some 10s of ps, and obviously you must be careful about the geometry of the slot and cable connections (and still sealing it up, and also getting meaningful bandwidth).Typically, the beamline is effectively blown up to a larger diameter, the added space being filled with a ferrite core to increase impedance at middle frequencies, and the cables connecting along the interior edges of the former beamline. The core extends the bandwidth down from ~GHz to ~MHz; notice this is merely a rearrangement of a current transformer, with coaxial symmetry. And those 10s of ps can't travel very far even in good quality coax, so place your timing/measurement equipment very nearby.If you need still better, perhaps consider passing a very tiny, intense magnet to let off a blip of synchrotron radiation. Put a detector after that and do whatever with it (preferably using optical means only, thus better preserving the high frequency content??).These are, as far as I know, pretty standard solutions in graduate physics to experimental particle physics? I'm rather more curious how you've gotten to this point, and not covered these aspects of the apparatus, or no instructor/advisor/coworker has provided references to such?!Tim

author: Terry Bites
author_rank: Super Contributor
timestamp: October 20, 2021, 02:26:37 am
content: The Rogowski coil is just the job.https://aip.scitation.org/doi/10.1063/1.4916094||https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwixotCK99fzAhUYi1wKHQBsBY4QFnoECCgQAQ&url=https%3A%2F%2Fwww.mdpi.com%2F2076-3417%2F11%2F5%2F2290%2Fpdf&usg=AOvVaw3rAyZJYEsC_ZqzOTE6ZBepRead TIs note designing PCB Rogowski coilhttps://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&cad=rja&uact=8&ved=2ahUKEwixotCK99fzAhUYi1wKHQBsBY4QFnoECAQQAQ&url=https%3A%2F%2Fwww.ti.com%2Flit%2Fpdf%2Ftidubv4a&usg=AOvVaw2bISB_wLtgM35isuCGEgzF

author: Marco
author_rank: Super Contributor
timestamp: October 20, 2021, 02:45:54 am
content: If you used a heavily segmented beam position detector instead of measuring just horizontal/vertical displacement, couldn't you infer the beam shape from the signals from the segments?Just measuring displacement current due to the electric field of the electrons seems to me easier than messing with magnetic fields.

author: BeePound
author_rank: Contributor
timestamp: October 20, 2021, 03:37:58 am
content: Image currents, coils, wire beam finders, all relevant points. Wow, thank you for all of your comments!I was trying to avoid saying exactly what I want to do, to get "first dibs" on the idea and all, but I honestly didn't expect much engagement on this topic and now I feel bad that so many of you have put time into responding. So here is the full explanation.One question in beam physics, specifically free electron lasers, is "what is the beam profile"? It has big implications as to how well the machine actually works. There are a variety of ways to measure the beam profile. If the beam is large enough, some type of phosphor screen + CCD camera will do. Other times, wire scanners are used (as in, scanning the wire across the beam and measuring the interaction). In both cases the technique destroys the beam. Also the beam has to be relatively large.The machine of interest, specifically, is what I stated before, which is a forward-looking spec: 500 nm pulse length with highly relativistic electrons. The peak current is several thousand amps (say 4000 A). The beam diameter is only about 5 micron, which is too small for either screen+CCD or scanning wire methods. You could defocus the beam, sure, but let's try to find a way to profile the beam without doing that first. It's also too small for cost-effective microfabrication (obviously you could pay a big fab a lot of money to make something for you, but that assumes you have a lot of money to spend.The idea is this. Let us put a ring of magnetic field sensors around the beam. Let's assume that these magnetic field sensors can actually measure the magnetic field from a relativistic electron bunch (this is the heart of the question that I originally asked). Then, since there are so many "knowns", i.e. the magnetic field at a whole bunch of different positions, we can in principle solve for the beam profile that could produce magnetic fields like those that we measured in the ring around the beam. There are obviously a lot of unsolved issues, but if the magnetic field can't be measured, then the other issues don't matter muchAnyway, this should clear up some of the questions (and accusations! good points Tim), thanks for engaging with me on this.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 20, 2021, 05:59:30 am
content: Ah, so looking for a non-contact, microscopic-resolution method. I see...Quote from: BeePound on October 20, 2021, 03:37:58 amI mean, it works well. I can heavily defocus the beam on my CRO and see every microscopic imperfection of the cathode active area, or at least I recall that's what it relates to. The same should work here, just more electron optics, give or take if there's anything different about them at relativistic velocities.Is the same true of synchrotron radiation? You'd have to measure it at quite a distance to get any kind of beam spreading though (e.g. x-rays that you can't do much with optics). If there's much visible to UV spectrum, it should be doable with ordinary optical lenses.QuoteAlso anything microscopic is likely going to be blasted to bits by the radiation.Money at least shouldn't be a problem... you don't run a lab like that without at least a modest budget. (...Right?)Maybe I'm severely overestimating the budget it takes to get a FEL online. It's not YouTube lab accessible yet, right? Grad, undergrad?QuoteTrouble is, even without the bandwidth issues, magnetic fields are limited by the field equations (Lorentzian I think?). You don't get a projection of an image, you just get an ever-fuzzier blur at a distance. It is why metal detectors can have large coils giving good depth sensitivity and poor spacial resolution, or small coils with good spacial resolution and no depth. Or why wireless power transmission is almost always something of a scam, etc.What's the beam cross section going to look like, anyway? Rough and spotty? Gaussian? Ring (like uh, Mexican hat or other distributions)? Will there be much velocity modulation to go with the spacial distribution -- is there anything else that can be used to infer it?I think, given the focusing systems usually used for that sort of stuff, the dispersion should be small, bunches tight (very short as you say), and then whatever the spacial pattern is, it is what it is... Well, there should be something that trades off with that, some focusing magnets perhaps, could one be used to expand the beam for testing, then scrunching right back down? Or is part of the problem, that exactly those magnets (and others involved in general confinement, focusing and acceleration) aren't well described enough for the final application? (In which case, could they not be better characterized? -- something that can be done at DC, with Hall effect sensors in fact, or others.)Tim

author: Marco
author_rank: Super Contributor
timestamp: October 20, 2021, 12:30:32 pm
content: Quote from: BeePound on October 20, 2021, 03:37:58 amWhy do you assume the magnetic field would give you more information than the electric field? (Which the beam position monitor already uses, a known working concept.) Lets say that you put 2^n pickup plates around the beam instead of the usual 4 and measure the induced voltage on each, if the beam is perfectly centered all signal will be minimal, any excursion towards a plate will increase the signal. Then with some priors you should be able to make some guesses about the beam shape.Even if it could work, 2^n magnetic detectors around the beam would not be able to give you any different information AFAICS. Without invasive probing you can only make a rough guess due to the 1D (angle) measurement.

author: BeePound
author_rank: Contributor
timestamp: October 20, 2021, 10:16:42 pm
content: QuoteWell, that is true, but since there are ways to measure the beam (as already discussed), this functionality is probably more of a "nice to have" than a "need to have".QuoteNominally, it would be Gaussian-ish. Thing is, with this very high-current, short pulse, small-diameter beam there are all sorts of other intra-beam effects that can cause issues, which would show up if one could profile the beam as hoped. Also, a requirement for a FEL is very little velocity modulation. I mean, its already ultra-relativistic so all the electrons are going essentially the same speed. I should say, the beam energy that we are looking at is around 1 GeV (that is kinetic energy only).QuoteThe magnets and system in general are never in a perfectly known state, so there is always some calibration to do before taking measurements. This comes because of pretty much anything you can imagine (slight temperature deviations, vibrations, differences in vacuum, deviations in power supplies, the phase of the moon [really, I'm not making that up:https://www.aps.anl.gov/files/APS-sync/lsnotes/files/APS_1418251.pdf], etc ... ). Part of the motivation of my proposal was to do away with all of that space-consuming, expensive equipment that would be required (kicker magnet, new beamline with the expander magnets and imaging systems, etc ...). It would be really nice to profile the beam inside or between some short period undulators (say ~7-10mm), which have a gap between the jaws of ~3mm (yes, even smaller than my quoted 1cm distance).

author: BeePound
author_rank: Contributor
timestamp: October 20, 2021, 10:23:21 pm
content: Quote from: Marco on October 20, 2021, 12:30:32 pmIf I could measure two piece of information per position (magnetic field Bx and By, for instance) instead of just one (current or voltage), that would be twice as good, right? Other than that, no, I don't think magnetic fields would be any better. I just hadn't considered using the electric field.But yes, at the moment, it seems like a collection of conventional beam position monitors is much more practically feasible. I hadn't thought of this, so thank you.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: October 21, 2021, 05:16:30 am
content: Quote from: BeePound on October 20, 2021, 10:16:42 pmAh yeah, so this thing isn't exactly compact either; which...Quote...There you have it.QuoteYeah, fairly compact, and very precisely aligned, shooting an immensely thin beam down many meters of beamline (and other structures).And still, those structures (some ~mm tubes or pole pieces or etc.) are massive compared to the bunches, like 1000x bigger, give or take.Huh, do the undulators have an exacerbating effect, tending to break up / disperse the beam? Is that part of the motivation?Can they be made to undulate while still keeping the beam fairly well focused? (Maybe/probably not -- I think focus is a conservative thing, right? There's nowhere for positional energy to be sunk, except perhaps as synchrotron emission. It can work in the main beamline -- I think? -- by rotating the positional offset (transverse <--> axial), thus converting it to dispersion, which then exchanges energy with the accelerator fields, tightening the bunches (axially) without causing additional spreading; thus beam intensity goes up, rather than remaining constant or decreasing, whereas just magnets alone I think can only exchange it. Do I have that right?)Quote from: BeePound on October 20, 2021, 10:23:21 pmThe thing is, if the electrodes are, say, a circular array of wires a few mm in diameter, but the beam cross section is some µm across, how can you really tell that the field at any given electrode, is due to the field of any given differential of the beam? Assuming superposition holds, of course (which, it ought to, anyway.)Which is what I was talking about with fields, they're blurry at a distance, there's nothing to tell about something up close. You need electrodes on the scale of the beam itself, in which case you might not have a problem with dipping them into the beam directly (or it happens accidentally, anyway, because we're talking 10s of µm alignments).Put another way, suppose the beam is misshapen with some elliptical section. If the distance from electrodes to beam are reasonably equal (everything's concentric), we might expect a small (potentially detectable?) quadruple moment aligned to the axis of that ellipse. Suppose the distribution is bimodal, two separate beams, one at each focus: could we even tell the difference? Or an elliptical shell, or anything else inbetween. And what if it's rotationally symmetrical, but the mean radius is 1um? 10? 100? Does the signal change at all?We can potentially get information from EM fields, to the extent that it emits (again, at these frequencies) an optical image or whatever, and thus be diffraction limited instead. But, does it? As I recall, the thing with LINACs is, that's the whole point, if it's not accelerating it's not shedding radiation, it's propagating smoothly. I guess the implication is that, yes there's optical emission, but it's all virtual, and it can only be made real under certain conditions.Also, how does that work, causally? Say the bunch moves past a metallic slot, so a current is induced (and some work done on its resistance): how does the bunch "know" it's lost some energy to that, since it's moving essentially at the speed of light? Oh, this is one of those advanced-retarded wave problems, isn't it; or equivalently, electrodynamics. Well, I shouldn't try thinking too hard about that, I think, but I'm not sure exactly where the "trust in the classical math, it's merely a pulsed current" line ends, and QM (or QED for that matter) picks up, and it seems like there might be something here. (Check the literature, someone must've thought of this before?)So, I wonder if there could be something about -- imagine the bunch moving through space, emitting electric field lines like sonic shock cones. If they superimpose, and if we can assume the bunch length is much shorter than its width, then at a given, stationary, point detector, we have a time-domain representation, and can do something like 2D tomography to figure out the source's cross section. All we need is an ADC with sub-ps resolution!...Also, for optical detectors, if we have coherent detectors (perhaps not outright impossible in such a compact, controlled environment?), we don't necessarily need to be diffraction limited, but can potentially do better (how much better, I don't know?). But this is an extremely fast (wideband) transient-field problem, can optics even be made to handle that? Let alone sample and downconvert it to a useful signal (something corresponding to beam cross section).Oh right, that's what a coherent solution would be, using synchronous ADCs; and presumably it'd be fine to synchronize that in turn to the bunch rate, so that we can do something like equivalent time sampling of the beam profile.There are optical techniques to essentially sample images with very short time apertures, so I guess that would be of some interest. I'm not sure offhand how to go from "current transformer" to "optical detector", and how to reconcile that with "unaccelerated beam doesn't emit". I think I've got some things inconsistent there, and I've just not done nearly enough particle physics (and in long enough time..) to know which...Tim

author: Berni
author_rank: Super Contributor
timestamp: October 21, 2021, 06:14:06 am
content: This sounds like it is going into the double slit experiment territory.You do need some sort of interaction to actually measure your electrons, so any way of measurement is going to affect your beam in some way. Even if you are using a hall sensor, then the electrons moving past have to convince a massive number of electrons inside the hall sensor to move over and produce the hall voltage. The work to push those electrons over has to come from somewhere. So by the point you have the hall sensor close enough to actually produce the signal there will be interaction with the beam. Having it really close to the beam is required because your electron packet "electromagnet" is so tiny that the magnetic field lines can close down on themselves very quickly, so there will be very little field to measure at a few millimeters of distance.I think a better way might be to let the beam pass trough a very low pressure gas that has some interesting interaction with the beam, like for example produce light that can be detected in extremely small quantities by existing light detectors out there. This still affects the beam since the energy has to come from somewhere, but at least it should make for a uniform attenuation across the whole area of the beam.

author: Marco
author_rank: Super Contributor
timestamp: October 21, 2021, 01:37:29 pm
content: How about scanning a laser beam transversely and measuring the deflection of parts of the photons by scattering? Or would the effect be too small to measure?

author: BeePound
author_rank: Contributor
timestamp: October 21, 2021, 03:50:36 pm
content: Quote from: Berni on October 21, 2021, 06:14:06 amThis is already done in existing machines (at least, I know for a fact they do it at the LCLS), though for a different reason. The amount of light produced is proportional to the amount of ionization which is proportional to the energy and amount of charge in the beam, so since they already know the energy, they can deduce how much total charge is in the beam. Maybe it could be used for mapping the beam, but I wouldn't know how to go about it. I think it would actually be a pretty tough problem since it would involve atomic physics (ionization and recombination), plasma physics (since ionization is pretty high and pressure is low, required for nonlinear focusing effects), and good old equipment know-how.

author: BeePound
author_rank: Contributor
timestamp: October 21, 2021, 04:00:14 pm
content: Quote from: Marco on October 21, 2021, 01:37:29 pmThat's a good question, I don't know if that would produce a measurable signal. Focusing down to ~5um shouldn't be a problem if you have a good enough laser and optics, but I think you would run into depth of focus issues. For example, for a Nd-yag at 1064 nm, and desiring a waist of 1 um (I know, diffraction-limited, bear with me), the depth of focus is only about 3 um, which would require a) pretty awesome focusing precision, and b) a really stable beam that you know the location of very precisely. Jitter can easily be on the order of microns (I know it is at the LCLS, beam jitter ruined a fair amount of my experiments there! but hopefully jitter is less for newer machines that were actually designed for FEL operation).Of course, perhaps one could actually use the defocus to their advantage. Only focus the beam down to 5 um or so, then let the beam defocus to be larger for actual detection. It isn't a scan anymore, per se, but a one-shot measurement. You were probably thinking this anyway, now I am just thinking out loud (out type? out forum? whatever). In this case you could at least get the 2D longitudinal projection of the beam. I guess if you were dedicated enough and did it from a few different angles you could tomographically reconstruct the 3D beam shape ... of course, it usually takes hundreds or thousands of angles to do such reconstructions ... but is interesting to consider nonetheless!

author: BeePound
author_rank: Contributor
timestamp: October 21, 2021, 04:21:50 pm
content: QuoteUndulators actually have inherent focusing/defocusing properties, so it would be nice to know what is happening to the beam inside the undulator. We are thinking about implementing an additional tunable focusing system inside the undulator, so in-situ beam characterization would be nice for that.QuoteAs far as I can tell, yesQuoteYeah, I thought I had this worked out in my head, but now I am doubting myself. I am starting to think that it would not work for smooth beams. I know I can definitely discriminate individual "wires", so maybe I cannot actually map the beam in it entirety, but I could pick out the peaks of the beam since the peaks break the symmetry. But I can also see what you are saying about the actual magnetic field being small - my initial calculations were for infinite wires, which have big magnetic fields at 4000 A, but little tiny 500 nm wires will have small magnetic fields by comparison. How small, I have not actually calculated.QuoteI am not an expert, but usually what I have seen is that at the front of the bunch, the resistive wakefields (that is the technical term for what you describe) have little to no effect. But the front of the bunch creates these wakefields, which then affect the trailing particles in the bunch.QuoteIts all good, food for thought anyway

author: tszaboo
author_rank: Super Contributor
timestamp: October 21, 2021, 04:22:09 pm
content: If you wish, I can put you in contact with a guy, who specializes in custom high end hall sensor development. Has a company and fab connections to manufacture them.

author: Marco
author_rank: Super Contributor
timestamp: October 22, 2021, 06:04:32 pm
content: Quote from: BeePound on October 21, 2021, 04:00:14 pmA curtain of laser light might be good enough. So one laser beam spread wide with a rod lens, only using a small part of the curtain in the middle so it's mostly uniform thickness for the entire electron beam instead of getting an oval, diverging going down to increase the width of the laser curtain for the sensor.At the bottom block out the direct laser light and if necessary have another rod lens along the length of the laser curtain to focus photons scattered directionally to varying degrees on a linear photodiode array. The amount of scattering might be so small all the scattered photons for one section of the electron beam fall into the sensor regardless, or the probability of scattering might be so small only single scattering events are likely to occur in which case almost all the scattered photons follow the same angle. Either way no lens strictly necessary, though even with single scattering if the energy of the electrons is varied significantly the scattering angle might vary significantly and a lens might be a convenient way to deal with that.I'm not a physicist, so I have no feeling for the magnitude/probabilities of scattering and I certainly can't do the math. I'm also assuming the laser will not have enough energy to affect the electron beam to a relevant degree (the electrons scatter a bit too, but they are a lot heavier). I'm just thinking about it like rubber bowling balls and marbles.

author: BeePound
author_rank: Contributor
timestamp: October 22, 2021, 06:13:05 pm
content: Quote from: tszaboo on October 21, 2021, 04:22:09 pmI appreciate the offer! I will reach out if we decide to move forward with this. Thanks so much.