Exploring the Construction of RICH Detectors

[ChrisVer]

I have some question about RICH detectors (in particular HERA-B RICH) and why are they constructed in such a way...I think all the RICH detectors though use the same construction that "confuses" me.
In their case the particle of some unknown velocity $\beta$ enters the gas of known refractive index $n$ and generates Cherenkov radiation at an angle given by $\cos \theta_c= \frac{1}{\beta n}$ . Knowing the angle and the $n$ we can determine the velocity $\beta$.

However I don't understand how the spherical and planar mirrors help in determining the $\theta_c$. (I wouldn't use spherical mirrors). One could say that they are used for focusing the light, but I don't understand why I should focus the light instead of measuring it directly and finding its ring radius instead of the "focused" one.

 

[dukwon]

How else would you measure the angle of light?

There are only really 3 types of Cherenkov detector:

1. Threshold detectors, which just tell you whether or not there's Cherenkov light at all

2. Differential detectors, which use collimation to only accept light at a certain angle.

3. RICH detectors, which can measure a range of angles.

This ray diagram may help explain why the spherical mirror is necessary for a RICH. Consider the yellow horizontal line to be the trajectory of your particle. The beige rays are the Cherenkov light being emitted at constant angle. The circular mirror focuses the rays to 2 points. The vertical displacement of these points (i.e. the radius of the ring) depends on the angle of the light. The horizontal distance is fixed and depends on the mirror's curvature (this is where you put your photodetector plane).

Now generalise this to 3D and you see how a spherical mirror will turn a cone of light into a ring. Planar mirrors are used to allow the photodetector plane to be placed somewhere sensible, i.e. not in the path of the charged particles

 

[ChrisVer]

wouldn't you measure the angle just by putting your detector at the spherical mirror's position? I mean you would get a ring signal at the same time, the light of which comes from the same point where it was emitted (see the figure, instead of reflecting the rays, detecting them)

 

[dukwon]

I'm not sure I understand what you're suggesting. Something like Super-K will get rings without any optics because the particle slows down rather quickly in a relatively highly absorbing medium. The cone of Cherenkov light is only emitted for a short distance.

This is undesirable with a detector at a collider or fixed-target experiment because you usually want the particles to make it to a calorimeter after passing relatively 'unscathed' through the RICH. As such, the photons from each track will fall within a solid circle. You typically get maybe ~20 photons per track, and multiple tracks, so it's not like you can reconstruct these solid circles.

 

[mfb]

The detectors are not sensitive to the direction of incoming light, and their time-resolution is not good enough to calculate it either.
Without spherical mirrors and with a large medium for Cherenkov light, you would get a solid disk (well, several isolated photons within a solid disk). And finding the radius of the solid disk (the outer photons correspond to the earlierst emissions) is much much harder as you ruin your statistics.

 

[ChrisVer]

So it's more like you need them for particles that are allowed to travel in the medium for very short times?
I didn't know... I thought that inserting mirrors is like enhancing your systematic errors.

 

[mfb]

So it's more like you need them for particles that are allowed to travel in the medium for very short times?

I don't understand that question.

With a spherical mirror every photon hits the ring, which allows a proper angle measurement (every photon contributes to it). Without a spherical mirror and with a large detector you get a mess without a clear angle measurement.

 

[Vanadium 50]

I thought that inserting mirrors is like enhancing your systematic errors.

Maybe it does, but it also puts the light where it is easier to detect. If you don't have a good signal, you tend not to worry about systematics.