# Why are LIGO's beam tubes so wide?

Gravitational wave detectors and particle accelerators have at least one thing in common -- they require long vacuum tubes through which a narrow beam is fired (a laser in the gravitational wave case, a particle beam in the accelerator case). In both cases, the vacuum tube is many orders of magnitude wider than the beam itself. But interestingly, while the LHC's vacuum tubes are 6.3 cm in diameter, LIGO's are about 20 times wider at 1.2 m in diameter.

So my question is: why are LIGO's vacuum tubes so wide? This must have been a conscious design consideration, since it means that a much larger volume of vacuum must be maintained, and more material must be used to construct the tube. The main consideration for tube width that I can think of is that you have to be able to aim your beam within the width allotted, but surely on these grounds LIGO could have gotten away with a much narrower tube. (Actually, I have no idea -- is this even the deciding factor for the tube width at the LHC?)

• I suspect the difference between LIGO and LHC is that the beam is actively steered in the latter case. So one simply adjusts one's magnets until the beam makes the circuit it needs to. There's no way to steer light, aside from bumping it into mirrors. So some of the size difference will simply be to guarantee clear aperture notwithstanding construction errors and the like. But your question is a most excellent one. – WetSavannaAnimal May 26 '16 at 1:43

The LIGO beam is 200 W as generated at the input mode cleaner; the beam is then recycled multiple times in the arms, increasing the power density significantly. This requires large optics with near perfect coatings in order to avoid "hot spot/cold spot" damage from various types of possible defects.

But there is an additional reason for the large beam size, and I quote from Advanced LIGO, section 2.1: "In order to reduce test mass thermal noise, the beam size on the test masses is made as large as practical so that it averages over more of the mirror surface. The dominant noise mechanism here is mechanical loss in the dielectric mirror coatings, for which the displacement thermal noise scales inversely with beam size. This thermal noise reduction is balanced against increased aperture loss and decreased mode stability with larger beams."

Inspecting LIGO's optics for contaminants.

When I was a grad student in the early 1990s, we worked on extremely sensitive, non-destructive techniques based on non-linear optics which could find the coating defects: location and classification. Our detector scanned the surface, and recorded amplitude and phase changes based on the photothermal effect, so I always take a personal interest in the success of LIGO; after all, they helped pay my way!

LIGO Hanford.

• Wow, thanks! I guess it just never occurred to me (though it probably should have!) that a laser could actually be on the order of a meter wide! – tcamps May 26 '16 at 2:53
• Ah, so it's another case of "gravity is so weak that we have to eliminate noise to an absurdly low tolerance to have a chance of seeing a gravitational wave at this distance"? – Luaan May 26 '16 at 8:41
• @Peter Dieher I am new to this; DeLaunay unduloid tubes (which have minimum surface area for given volume geometrically) so are the worst choice,(once a volume is designed/determined ) right? But would it not put a cap on further mechanical mirror coating loss? – Narasimham May 26 '16 at 15:59
• @Narasimham: there are many considerations for vacuum systems, which only increase in complexity for ultrahigh vacuums. The first step is to measure the capacitance, and limit it: this is done by using wide open volumes, like a sphere or a cylinder. Increased capacitance limits pumping speed, even when larger pumps are used -- and since the surfaces will always outgas some hydrogen, one must always keep pumping. – Peter Diehr May 26 '16 at 16:05
• LIGO’s arms have a modification called Fabry Perot cavities which use additional mirrors near the beam splitter so that the light travels about 400 times the length of the arm, or 1600 km. I think those are separate from the "power recycling" mirrors that increase the power of the beam. I wouldn't be surprised if both of those features required a larger vacuum system size. – John Fistere May 31 '16 at 21:09

This must have been a conscious design consideration, since it means that a much larger volume of vacuum must be maintained

While I don't think that it's what motivated LIGO, the volume is not as much a consideration in high-vacuum as the surface area. Once the chamber has been pumped out, the ultimate vacuum level is set by the rate of desorption/outgassing from molecules that have adhered to the chamber walls.

But still, you say, the larger chamber has a larger surface area than a smaller one.

The rate at which residual gas molecules are pumped away is determined in part by the cross-sectional area - the larger the area, the more quickly molecules will diffuse around and 'fall into' the pump. The rate of flow is actually proportional to the diameter cubed [wikipedia].

The ratio of surface area to volume is smaller for the larger chambers, which means that for a given rate of outgassing per surface area, there's a lower density of gas molecules in the chamber.

In short, it can be easier to achieve better vacuum in larger chambers than smaller ones.

However, there are ultimately tradeoffs that limit how big you want to make the chamber - you still need larger pumps, for instance. At the LHC, they need to have cryogenics and magnet windings around the beam path, which aren't feasible to make much bigger.

• Great insight, even if it isn't the main reason for LIGO: hadn't thought about this before, so I've learnt something +1 – WetSavannaAnimal May 26 '16 at 10:08

• Peter's link (§2.1) confirms the beam's $1/e^2$ radius at ~5cm. – Emilio Pisanty May 31 '16 at 19:30