Switzerland day 41: Paul Scherrer Institut

Little by little, wean yourself. This is the gist of what I have to say. From an embryo whose nourishment comes in the blood, move to an infant drinking milk, to a child on solid food, to a searcher after wisdom, to a hunter of invisible game.

Rumi

September 29th: We drove 45 minutes down to the Paul Scherrer Institut in Villigen Switzerland. I picked up my previously-requested badge and dosimeter, and got a tour of where I might be performing my experiment next year.

The proton beam is accelerated to 560 MeV in a cyclotron under the surface in the foreground (which has a photo of what’s underneath it on top of it). It then goes out the right side of the picture, gets bent around through the upper right, and smashes into various targets in the rectangular gray enclosure in the upper left. Some of those targets produce pions, which decay into muons, which is what I need.

The mouth of the muon beam. I had originally thought that the beam was movable, but no, those magnets weigh like a ton each. The beam comes out at 1.5 m above the floor and I need to get my target there.

Aldo Antognini (my host) talking to students currently setting up an experiment in that bay.

Things were simpler in the 1950s, when Jeff Morrow could build a portable device to generate “mu mesons” to defeat The Giant Claw.

The particles were first called mesotrons (1936), then yukons after the particle predicted by Hideki Yukawa, then mu mesons after pi mesons were discovered, then muons after it was realized that they weren’t mesons at all but rather leptons, and that the real yukons were the pi mesons, which are mesons but still got shortened to pions. They were the first subatomic particles discovered that were not a component of atoms and thus seemed totally unnecessary, leading Isadore Rabi to quip “Who ordered that?”.

Anyway, I learned a lot about what I need to get done in the next couple of months before submitting the experimental proposal by January 10th. On the positive side, both Aldo (who gave me the tour) and Frank (who joined us for lunch) seemed positive about the experiment. Maybe they are getting a glimpse of how exciting it would be if this were correct.

On the negative side, there are lots of new issues to deal with, like getting insurance coverage, finding a second person to work with me, figuring out how to ship everything to Europe (and deal with customs etc.), running on Swiss 220V, dealing with beam impurities (including at least 10% electrons), and converting everything from wifi to hardwired ethernet (including optical ethernet links to get out of the sphere).

My biggest asset is that I am totally committed to making this happen. Whatever it takes, I will do.

Until one is committed, there is hesitancy, the chance to draw back, always ineffectiveness. Concerning all acts of initiative (and creation), there is one elementary truth, the ignorance of which kills countless ideas and splendid plans: that the moment one definitely commits oneself, then Providence moves too. All sorts of things occur to help one that would never otherwise have occurred. A whole stream of events issues from the decision, raising in one’s favour all manner of unforeseen incidents and meetings and material assistance, which no man could have dreamt would have come his way.

William H. Murray

But of course, we eventually had to leave for Bern. Our hostel was near the Thai embassy, so, after checking in, we had dinner at a Thai restaurant. Our theory was that the embassy wouldn’t allow it to be mediocre.

the Thai embassy in Bern

the Thai dinner, I think a Pad Kee Mao and a Pad Thai.

Hostel 77 was easily the most expensive lodging of our trip, but was quite basic (e.g. shared bathrooms). It did come with a decent free breakfast though. Still, Switzerland is far too pricey to be a good place to retire on a fixed income.

(Scintillator) Size Matters

I submitted version 5.1 of “The magnitude of electromagnetic time dilation” paper to General Relativity and Gravitation on Isaac Newton’s birthday. You can download it from ResearchGate here; I haven’t updated Vixra yet.

Since I can’t do much on the theory side until GeRG gets back to me, I’ve been thinking about the experiment more. In particular, the size of the plastic scintillator needed.

There are two main criteria. First, we need to be able to stop muons in the scintillator, and detect when they arrived. And second, we need to detect when they decay.

The thickness needed for stopping is pretty easy to simulate crudely using SRIM/TRIM software on Windows. For example, let’s assume we’re trying to use the $139 kit from iradinc on Ebay:

which has a 3″ (76 mm) diameter by 2.25″ (57 mm) thick chunk of BC-412. If we assume a 29 MeV beam in a vacuum, maybe in a non-conductive PVC pipe, it’ll first have to get out of the pipe and into the air that the rest of the experiment lives in. So we get a layer list that looks something like:

• 5.0 mm PVC (end cap of vacuum tube)
• 2.5 mm air (gap to VDGG sphere)
• 1.5 mm stainless steel (the sphere)
• 26 mm air (gap inside sphere to scintillator)
• 57 mm polystyrene (scintillator is actually polyvinyltoluene, but that’s not in the SRIM material list, so we substitute a different plastic with similar elemental composition and bond structure and density)

Simulating this in SRIM, using “H ions” (protons) with mass adjusted to 0.1135 amu to represent antimuons, and running 1,000 simulations, we get:

The average implantation depth is 64.0 +- 1.94 mm, which (since the plastic starts at 35 mm) means 29 mm into the 57 mm of scintillator, which is almost dead center (57/2 = 28.5 mm). So the beam energy is almost perfect. And a total scattered beam diameter of roughly (5.10 + 4.44)*2 = 19 mm means almost all of the muons will hit the 76 mm diameter scintillator. We’d probably lose about 1 in 1000 muons to a hard recoil that prevents it from reaching the scintillator (you can see one such recoil in the PVC above), and maybe 2 in 1000 to medium recoils that deflect it enough so that it passes in through the front edge of the scintillator but then out the side. Zero muons come anywhere close to exiting the back side of the scintillator; they just don’t have enough energy to penetrate all of it. So about 99.7% of the beam muons will stop in the scintillator, and they will dump most of their energy into producing photons.

So far so good. We can even reduce the radial scatter by cutting a hole in the sphere, so that the beam never hits the steel. (That would increase the implantation depth too.)

But a problem arises when considering the decay pulse. A muon (antimuon) decays into an electron (positron) and two neutrinos:

𝜇⁻ ⟹ e⁻ + 𝜈_𝜇 + 𝜈̅_e

𝜇⁺ ⟹ e⁺ + 𝜈̅_𝜇 + 𝜈_e

The neutrinos escape, taking all their energy with them. The electron/positron gets a random kinetic energy of up to about half the muon’s mass-energy of 105.7 Mev, following the Michel spectrum. So, maximum about 53 MeV and average about 40-45 MeV.

So at first glance, it seems like we should want a scintillator big enough to stop every electron and convert the maximum possible energy into photons. In the best possible case we can assume that the decay happens in the exact center. Thus the diameter needed would be twice the “depth” of a 53 MeV electron.

However, when I calculate that depth, the CSDA range for a 53 MeV electron is about r_CSDA = 22.008 g/cm², and the density of PVT is about d_PVT = 1.05 g/cm³, so we get an expected range of r = r_CSDA/d_PVT = 22.008 g/cm² / 1.05 g/cm³ = 20.96 cm. That means we would need a scintillator at least 42 cm diameter and 42 cm deep. That’s about (𝜋 × 21cm × 21cm × 42cm) / (𝜋 × 3.8cm × 3.8cm × 5.7cm) = 225 times as much plastic as in the iradinc kit. That would be expensive, costing perhaps $5-10K.

But something’s off here. The Teachspin student muon lifetime device is smaller than that, and I know it works because I’ve used it. The whole scintillator plus PMT plus HV supply fits in a cylinder that’s only 16.5 cm diameter x 36 cm tall:

so the scintillator inside that is probably only about 16 cm diameter x 18 cm tall. That’s only 1/16 the volume calculated above.

Let’s take a step back. We want to detect both the muon stopping pulse and the muon decay pulse. Since both hit the same PMT, and we will use a level discriminator to reject noise, it would be most convenient if both pulses were approximately the same height. Crudely, that means that both pulses deposit about the same amount of energy into the plastic.

So if the beam energy is 29 MeV, we don’t need to capture all (up to) 53 MeV of the decay pulse. We only need to capture the first 29 MeV of it. If the rest escapes, that’s fine.

So if the TOTAL range at 53 MeV is 21 cm, we need to find the range of a (53 – 29) = 24 MeV electron, and subtract that off. From the same tables as above (https://physics.nist.gov/cgi-bin/Star/e_table.pl) we get about 11.4 g/cm2 and thus a range of 11.4 g/cm2 / 1.05 g.cm3 = 10.9 cm. So that means we only need the first 21.0 – 10.9 = 10.1 cm, giving a roughly 20 cm diameter x 20 cm thick scintillator. This is a little larger than the Teachspin one, so we can be certain it’s adequate.

I guess that gives me some rough parameters. Maybe it’s time for g4beamline simulation.

Electron oscillators, 1905

Reading Einstein’s 1905 paper on the quantization of light for the first time, I was floored by the following passage in section 1:

Eine Anzahl Elektronen sei ferner an voneinander weit entfernte Punkte des Raumes gekettet durch nach diesen Punkten gerichtete, den Elongationen proportionale Kräfte. Auch diese Elektronen sollen mit den freien Molecülen und Elektronen in konservative Wechselwirkung treten, wenn ihnen letztere sehr nahe kommen. Wir nennen die an Raumpunkte geketteten Elektronen “Resonatoren”; sie senden elektromagnetische Wellen bestimmter Periode aus und absorbieren solche.

which is translated by Arons and Peppard as:

Furthermore, let there be a number of electrons which are bound to widely separated points by forces proportional to their distances from these points. The bound electrons are also to participate in conservative interactions with the free molecules and electrons when the latter come very close. We call the bound electrons “oscillators”; they emit and absorb electromagnetic waves of definite periods.

A linear force with distance (similar to a spring) gives a parabolic potential; Einstein is (crudely) describing the Quantum Harmonic Oscillator a couple of decades before anybody solved it or realized how important it was! In some ways, this even anticipates the Quantum Field Theory of the 1940s-1960s with its emphasis on modeling the electromagnetic field as a set of non-interacting (“widely separated”) QHOs!

RIP Akira Tonomura 外村 彰

RIP Akira Tonomura (1942-2012), inventor of electron holography and leader of the Hitachi team that produced the most elegant and convincing proof of the misnamed “Aharonov-Bohm” effect (first proposed by Ehrenberg and Siday a decade before Aharonov and Bohm). Most of my current physics effort has been deeply influenced by his work. Vector potentials are real. The universe is not EM-gauge invariant, damn it!

Water has no excited states

Scientific tidbit for the day: “Water has no excited states.” If you hit a water molecule with enough energy to kick an electron up into a higher orbital, it will either break apart into H⁺ and OH⁻, or into H⋅ and HO⋅ free radicals. (This applies only to liquid water, where the H⁺ can be instantly hydrated; steam and ice may behave differently.)