Muon g-2: The inflector

As I mentioned previously, muons that are injected into our favorite ring need to enter it in a region with no magnetic field. In particular, every magnetic field has some sort of fringe region, and especially in this high-precision experiment, passing through this region (not to mention the possibility of entering the storage field too early) has the potential to deflect the mouns, which is no good for the ring's acceptance (how many of the 'injected' muons get stored). In a run-of-the-mill accelerator experiment, this issue is avoided by simply injecting particles in gaps between the magnets. In Muon g-2 (remember, that's pronounced gee-minus-two), we need an incredibly precise, fantastically uniform magnetic field in the muon storage region, which means we need a single continuous magnet all the way around the ring. That's the thing that just got transported, and the result is that the typical injection design just doesn't cut it.

The solution, at least for us, is what's called an inflector, which serves the dual purpose of injection and deflection (thus the name). It's responsible for allowing the muons to enter the ring tangent to the eventual orbit, and it does so by producing a region with essentially no magnetic field. As a result, the muons can simply drift into the ring without having to deal with the deflection from the magnetic field. But like so many things in the experiment, the inflector design had some serious constraints. They boil down to the critical issue of the constant magnetic field around the muon orbit - the inflector can't contain any ferromagnetic material or time-varying fields, as those would affect the magnetic field in the storage region. For the same reason, it cannot leak the magnetic field that it contains into the area the muons inhabit. Apart from that, the hope is to accept as many muons as possible, which means having a large opening for them to pass through.

That's a tall order, but all the requirements are satisfied by a superconducting inflector. It's roughly a cylinder that needs to cancel the ring's storage field, and it does so by generating a field of its own in the opposite direction. To get the muons to circulate, the storage field is vertical, so to cancel that, the (superconducting) coils in the inflector have to circulate length-wise, rather than just spiraling around the central axis of the cylinder (think right-hand rule). Much geometry and engineering later, we end up with a funky thing called a "truncated double cosine theta magnet," and it produces a highly uniform, roughly 1.5 T field in the region the muons occupy, along with a roughly 1.5 T field next door as return flux. When this is put into the magnetic field of the ring, the result is a net zero magnetic field in the muon's region, and an almost 3.5 T field for the return flux.

Even with a magnet design chosen to reduce the magnetic field flux that leaked into the storage region of the ring, this inflector still produced a high-gradient fringe field (meaning that it changes very quickly - so quickly, in fact, that the probes designed to map the field wouldn't be able to detect its change accurately). The solution the previous experiment arrived at was the use of a superconducting shield. Superconductors have this really cool property called the Meissner effect in which they expel external magnetic fields. As a result, getting the magnets cooled and running in the right order (first the storage field, then the superconducting shield, then the inflector) allows the shield to trap the main storage field while preventing any change in the flux from the inflector's field. This very effectively prevents any flux leakage, which allows the storage field to be very nearly uniform, and my understanding is that we'll be using the same sort of design in the new g-2 experiment at Fermilab.

There were a few issues with the previous experiment's inflector, though. The most crucial one was that in order to better trap its own magnetic field, the inflector had closed ends. That is, the superconducting wires actually cover both the entrance and exit of the inflector. This wreaked havoc with the muons being injected - it unsurprisingly turns out that running them into the wires decreases the number that make it into the ring. Luckily, the new experiment has invested a good deal of engineering in the design of an improved inflector, and I believe we're planning to open the ends of the inflector to allow muons to pass through unimpeded.

If you're interested in more information about the Muon g-2 experiment, you should check out its website. More g-2-related posts can be found here.

Muon g-2: The anatomy of the ring

While the large ring that was transported contained mostly the superconducting coils and their cryostat, there's a lot more to the final ring than that. We have to add quite a bit of material: vacuum chambers, yokes and poles, and so on. And in the end, of course, we also need to put our detectors into place. To complicate matters, the electrostatic quadrupoles take up their own fair share of space, and the inflector and kicker are necessary to allow muons into the ring in the first place. All this gets rather complicated fairly quickly, so before I get any further into the details of the experiment, I wanted to present a simplified picture of what's involved in the ring.

 

This is a somewhat simplified and very much not-to-scale sketch of where various components go in the ring. It's a view from above, and from here, we'll see the muons whiz around clockwise. Once any muon decays, some of its momentum is carried off by neutrinos, and the resulting positron ends up with lower total momentum. Since it's in the same magnetic field as before, this causes it to curl inwards, where the experiment detects it using calorimeters (energy-measurers) and trackers (which, as their name suggests, help to track particles and figure out their trajectories). In the case of the detectors (possibly including the not-yet-shown fiber harp) and inflector, I will hopefully write a bit about each component at another point in time, but here's a brief overview:

• Inflector: The issue with having an enormous ring with a strong magnetic field is that it's hard to get muons (or any particle, for that matter) into it in the first place. They are affected by the field too early, and end up on all sorts of funky trajectories. That's where the inflector comes in. It's another magnet, and it generates a magnetic field opposite to that in the ring, so that the muons can really just drift inside, blissfully unaware of the extreme bending forces within.
• Kicker: Well, now we have another issue: the inflector injects particles at a bit of an angle compared to the ideal trajectory. This can be viewed as the particles moving along a circular trajectory (since they're in a uniform magnetic field) with its center offset somewhat from the actual center of the ring. What the kicker does is produce a time-dependent burst of magnetic field that jolts the muons into the orbit we want them in. Of course, time dependent fields bring in their own sorts of problems, so the kick is an interesting area of study.
• Quads: I've previously mentioned the importance of quadrupole magnets (also known as strong-focusing magnets) for vertical focusing of a beam. Since a magnetic quadrupole would disrupt our beautiful, uniform-to-within-a-few-parts-per-million magnetic field, Muon g-2 actually uses electrostatic quadrupoles, which operate on the same principle but do so using electric fields. These extend for long sections of the ring, and (fun fact alert!) one of the quad plates on the first quadrupole (the one right after the inflector) is actually in the way of muons being injected! 
• Calorimeters: In any particle physics experiment, calorimeters, which measure the energy of incident particles, play a central role in identifying and describing particles. This is especially true in Muon g-2, since the critical measurement is the energy of decay positrons over time, which gives us a clue to the wiggle (precession) of the muons that produce them. We have 24 calorimeter stations, positioned in order to catch as many of the decay positrons as possible. They're outside the vacuum chamber (shown in thin black lines above), but only barely.
• Trackers! New in this iteration of the measurement, the Muon g-2 experiment has two tracker stations in front of calorimeters. These are useful in identifying pileup events, when two low-energy positrons hit the calorimeter at nearly the same time, and thus masquerade as a single higher-energy one. They also allow us to trace the trajectory back to the decayed muon, and that gives us a pretty good look at how the beam is behaving, a valuable asset in an experiment in which beam dynamics crucially affect the measurement.

Well, that's the whirlwind summary of the structures in the ring. I haven't mentioned things like the fiber harps, which monitor the beam, and collimators, which filter out muons that get too far away from the ideal parameters, and all of the magnetic field measurements. They're essential to the experiment, but I'm not even nearly an expert on them, so I'll leave their explanation to people more experienced than I.