JJ Walding 07/09/2004
MICE Tracker: Dehydration of the Scintillating Fibres in a vacuum and the force exerted on the Carbon Fibre Station
Joseph Walding
Blackett Laboratory, ImperialCollegeLondon
7th September 2004
ABSTRACT
The MICE tracker consists of five stations on which scintillating fibres are laid. Under vacuum these fibres contract due to water loss thus applying a force to the station.
The aim of the experiment was to find the magnitude of this force and determine whether it would be detrimental to the stability of the station. Young’s modulus for the scintillating fibre was found to be (3.7±0.4) x109Nm-2. The force per fibre due to contraction was found to be 0.043±0.006N, which leads to a total force on each station of 195±30N. This is anon-negligible force. Because of this the recommendation is to dry the fibres and store them in suitable cases. The assembly of the fibre tracker should also take place in dry conditions so as to minimise the fibres rehydration.
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JJ Walding 07/09/2004
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JJ Walding 07/09/2004
INTRODUCTION
The MICE Tracker consists of five carbon fibre stationsonto which 4473scintillatingfibres are laid in three layers each rotated by 120 degrees from the other. The fibres are polystyrene doped with a 4450ppm fluorescent material. Polystyrene fibres naturally hold a level of water within them, when the fibres are exposed to a low pressure environment a water gradient is naturally induced, drawing the water out of the fibres. This water loss leads to the contraction of the fibres and hence a force on the carbon fibre station is produced. The objective of this experiment was to find the magnitude of the force and the time period over which the contraction occurs.
METHOD
To calculate the force exerted by the fibre on the frame requires the application of Hooke’s law and from this Young’s modulus is calculated. This allows calculation of the force due to the fibre contraction. The experiment was divided into two stages, and was carried out on both a fibre optic and the scintillatingfibre. The fibre optic was used so that an idea of the magnitudes of the forces and time periods could be established. Due to the expense and limited amount of scintillating fibre available for experimentation it was paramount that all experiments on the fibre would produce results.
The experiment is broken into two stages; firstly Young’s modulus is measured, and secondly the contraction due to the vacuum is observed and from this the force can be found.
Calculating Young’s modulus
figure 1 The experimental setup: a) The frame supporting the fibres b)The Vacuum pump attached to the second fibre chamber c) The Vernier Telescope d) The clamp used to hold the fibres under tension e) The viewing cylinders.
Figure 1 shows the equipment used for suspending the fibre. The top of the fibre was clamped in place whilst a clamp was attached to the bottom to hold the fibre under tension (figure 1e). To this bottom clamp weight was added and the extension was recorded using a Vernier Telescope (figure 1c).
By plotting extension versus the force applied to the fibre the spring constant can be found (see equation [1]).
[1]
where k is the spring constant, F is the force and x the extension from the equilibrium position of the fibre.
Maintaining the fibre under tension requires the use of the bottom clamp. The Vernier Telescope records the position of the fibre, taking the position of this hanging mass as zero, and all subsequent measurements are made relative to this (the mass to hold this fibre under tension was also set to zero). This will not affect the value for the spring constant, the intercept for an F vs. x plot would change but not the gradient which is the quantity of interest.
The Young’s modulus of a fibre is a superior method of comparing the mechanical properties between materials as it takes into account the magnitude of the material’s spatial dimensions (see equation [2])
[2]
where E is Young’s modulus, A is the cross-sectional area, x is the extension, L is the rest length and F is the force applied to the fibre.
It would be expected that as the scintillating and optic fibres are made of the same material bar a small level of a dopant that the Young’s modulus’ would be comparable even if the spring constants are not.
Calculating the force exerted on the carbon fibre station
Two fibres are supported by the frame, one as a control at atmospheric pressure, the second under evacuated conditions at a pressure of 5Pa. Both are held under tension using the clamps (figure 1e) and the relative contraction was recorded.
figure 2 Pictorial representation of the forces acting on the control fibre (1)and the evacuated fibre (2). Note: m’=2.35grams, m=2.38grams for this experiment.
Applying Hooke’s law to the above setup gives the equation
[3]
where k is the spring constant
Making the substitution
[4]
F’ is the force that the fibre exerts on the carbon fibre station due to the contraction. When calculating the total force on the station it is assumed that the fibres apply the force uniformly across the station, i.e. we assume circular symmetry. The time period of the contraction is also of interest and will be discussed later.
Unlike for the optical fibre which could be run in normal light, the scintillating fibre was held under orange light as the fibres are sensitive to the blue/UV end of the spectrum. It was only necessary to test the optical fibres such that an idea of the magnitude of the data could be found and also to hone experimental technique. For this reason the experiment was not carried out in a room specifically for the experiment as one was not available. This is not the case for the scintillating fibres which were tested in a room setup for them specifically and was such that elements such as the optical benchwere best suited to give accurate results and not blur any small extensions/contractions observed throughout the experiments (this can not be said for the optical fibre setup.)
RESULTS
Optical fibre: Young’s modulus
It was established that the time for extension of the fibre, after the addition of a mass, was under one minute thus all results were recorded after three minutes allowing extra time such that any fibre motion would have halted and the full extension would have taken place.
figure 3 Tensile Stress vs. Tensile Strain. Young’s modulus is (2.0±0.2)x1010Nm-2, this is equivalent to a spring constant of 560±50Nm-1. The fibre diameter is 220±5μm with the rest length, L, being 1500±5mm.
Figure 3 shows the plot of Tensile Stress versus Tensile Strain. It was found that for the optical fibre the point of breakage was in the region of 100grams. The maximum mass suspended from the fibre was 70grams. As figure 3 shows this is below the elastic limit for the fibre. These parameters were used for the scintillating fibre so as to avoid any fibre wastage due to snapping or the passing of the elastic limit.
Optical fibre: Fibre contraction force
figure 4 The contraction of the optical fibre. The contraction tends to 150±20μm for a suspended mass of 2.38 grams.
The optical fibre was investigated in a different room to the scintillating fibre. Due to the nature of the table supporting the Vernier Telescope the above result carries with it a large error as can be seen in figure 4. Therefore the time constant could not easily be determined as the contractions are comparable with the error. This was not the case with the scintillating fibre as can be seen later.
The results from figure 3 and figure 4 give a force per fibre acting on the carbon fibre station of 0.084±0.014N giving a total force for all 4473 fibres of 380±60N.
The results of the optical fibre give a non-negligible force, which if also the case for the scintillating fibre will require a compensating method to lay the fibres. These results have large errors associated with them,though they give an indication of the magnitude of the force expected when the scintillating fibre is tested, they suggest a long time period for the contraction however this is inconclusive.
Scintillating fibre: Young’s modulus
figure 5 Tensile Stress vs. Tensile Strain. Young’s modulus is 3.7±0.4x109Nm-2, this is equivalent to a spring constant of 215±25Nm-1. The fibre diameter is 330±5μm with the rest length, L, being 1500±5mm
This is approximately five times smaller than the Young’s modulus for the optical fibre. This was somewhat unexpected as the fibres only differ by a level of dopant and by their cross-sectional areas. However this is not so surprising as they clearly differed in properties such as malleability as the optical fibre would snap at the cutting point whilst the scintillating fibre would compress under the blade leaving a slightly tapered end once cut.
Scintillating fibre: Fibre contraction force
Due to the fact that the Vernier Telescope was fastened to an optical bench the results displayed in figure 5 and figure 6 are a much more accurate portrayal of the contraction compared with the optical fibre. For this reason it can be seen that the contraction occurs over a period of fifteen minutes rather than the period of hours suggested by the optical fibre results.
Taking the results from figure 5 and figure 6 gives a force per fibre of 0.043±0.006N. This corresponds to a total force acting on the station of 195±30N. Though this is smaller than the force due to the optical fibre it is still significant and so can not be neglected.To be noted, Young’s modulus was approximately five times smaller for thescintillatingfibre than for the optical fibre.
figure 6 The contraction of the scintillating fibre over time. The contraction tends to 205±15μmfor a suspended mass of 2.38grams with more than 99% of this contraction occurring in the first 15 minutes of evacuation.
The contraction that occurs however is comparable suggesting that the fibres still contain a similar level of water within them, in fact the scintillating fibre would seem to have the larger level of water as it contracted more which may help explain the different Young’s modulus’ found between the two types of fibre.
This slightly larger contraction leads to a difference between the forces by approximately a factor of two.
A run was also carried out to see how quickly the fibres rehydrate once exposed to atmospheric conditions. The results were somewhat inconclusive but seemed to suggest that after a period of hours the fibre had only extended by approximately 100μm held under tension by a 2.35gram mass, with more time this could be investigated further.
DISCUSSION
The experiment was carried out to investigate whether the fibre contraction would have any bearing on the construction of the station, be it the laying of the fibres or the thickness of the carbon fibre station itself. Though the forcecalculated is not large enough to damagethestation it is still of some significance and can not be neglected.
Also of concern is that with the contraction occurring so quickly that any fibres laid and glued could become unstuck once vacuum is achieved. This is a general problem as the glue must dry before the station is evacuated so that the fibres don’t slip because of some contraction, however the force involved could be large enough to release the fibres from the glue even after it has dried. This would require further investigation.
A solution to this problem is quite simple and is one that I would recommend. The fibres should be stored in evacuated cases before use, i.e. they should be dried beforehand so as to avoid any problems suggested above as well as any unforeseen problems. Producing cases into which the fibres could be held, and then constructing the Tracker under dry or evacuated conditions is the simplest of solutions.
The rehydration observed was not the same as the dehydration for the time that the experiment was run, with only 100μm being the extension seen after fifteen minutes and then no further extension noted. Though the rehydration would need to be investigated further the results suggest that if this rehydrated fibre were to then be dehydrated again this dehydration would correspond to a force of approximately 100N. For this reason it is best that any construction take place in dry/evacuated conditions to best insure a functioning Tracker.
Acknowledgements
With thanks to Dr Kenneth Long for supervising, and supporting all work undertaken. Thank you also to the HEP group of Imperial College London.
A special thanks to the Nuffield Bursary Scheme for financially supporting the author’s UROP placement for its duration; 28th June – 3rd September 2004.
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