**Monitoring the consequences of ground motion on accelerators:**

**The *"ATL"* Law**

**Prepared by: Andre Prescod**

College of Science, Mathematics & Engineering Technology

South Carolina State University, Orangeburg

> [Fermi National Laboratory\
> Batavia Illinois\
> 60510-0500\
> ]{.underline}![](media/image1.png){width="0.8534722222222222in"
> height="0.8534722222222222in"}
>
> August 7^th^, 2008
>
> A Report submitted in partial fulfillment of the requirements of the
> SIST program.

**Supervised by: James T Volk**

Applications Physicist II

Accelerator Division

**Acknowledgements**

In the completion of this summer experience, I can only look back with
feelings of appreciation and respect for those who have helped and
guided me along the way. I would like to firstly thank God for enabling
me the opportunity to work in such a meaningful, pro-active and
eye-opening environment.

To the EOO administration; Ms. Dianne Engram, Ms. Linda Diepholz, and
Ms. Sandra Charles, a hearty thank you for all of your guidance and
patience with not just me but all of us interns. Your wisdom and
kindness in the handling of all of our needs; from living arrangements
to car rentals, even to our paychecks, served as an example of your
faith that we too would carry out our duties as interns. For this I can
only be grateful that I was allowed to work under your nurturing care.

I am thankful to God that I was able to work under my supervisor James
Volk. I feel fortunate, in that I worked under a man that saw this not
as an opportunity to just get some work done, but to genuinely expose a
student to the "life and times" of a particle physicists. I don't think
any other student could say they went into the mines in Aurora and mixed
cement in the name of science. I don't think any other could say they
learnt about epoxy adhesives, vacuum chambers, water levels, visual
basic programming, vibration isolation tables, x-ray producing tubes,
soldering and constructing a power source, again, all in the name of
science. To say it differently; a very special thanks to James Volk for
allowing me the chance to learn so much and see so much in twelve weeks.

Lastly I would like to thank Dr. Davenport as well as my mentor (Cosmore
ghjjku), for their guidance, in ensuring that a knowledgeable report
could be written from this experience; not just a figurative memory. For
your help and continued direction thank you very much.

**Abstract**

**Table of Contents**

**Table of Figures**

**Introduction**

**Presenting: Fermilab**

Initially known as the National Accelerator Laboratory, *Fermilab* was
renamed in 1974 in honor of 1938 Nobel Prize winner Enrico Fermi. The
"defined" mission of the lab is to advance the understanding of the
fundamental nature of matter and energy. More practically, the lab
attempts to explain/explore certain loopholes in the standard model by
observing matter in high energy collisions, and developing new theories
for a new dawn of physics. Founded in 1967, Robert Rathburn Wilson was
named as its first director. Fermilab has seen its share of acclaimed
and in some cases decorated physicists as its director, from then until
now. Among them 1988 Nobel Prize in Physics laureate, Leon Lederman, who
served as director until that prize-winning year. The current director
is 2005 Panofsky Prize winner Piermaria Oddone.

Particle acceleration is at the helm of Fermilab's very existence. A
particle accelerator basically uses electric fields to control electric
particles. Using the electric fields created by electromagnets, "beams"
of electrically-charged particles are steered and controlled, and over
time, accelerated within the particle accelerators at Fermilab. There
are a series of accelerators at Fermilab used in a step by step process,
of which the Tevatron is the largest and final accelerator. At four
miles in circumference it is substantially more powerful than any other
in the world; second only to the newly constructed Large Hadron Collider
(LHC) in Switzerland, and uses superconducting electromagnets as its
source of electric field. These accelerators are being used to create
collisions of proton and antiproton particles, and to record the results
of these high energy collisions. These experiments are in an attempt, to
discover the missing link, in the conditions of matter in the early
universe.

However central to all of this, is the ability of physicists to control
the beams, such that the collisions are best. Even further, being able
to control the beam suggests ideal electric fields, which in turn
suggests proper magnet alignment. Of course there would also be the
appropriate computer programs, and alignment algorithms to control these
alignments from a remote location. This paper however, focuses on the
impact of the earth's motion on this magnetic alignment. More directly,
this paper analyzes ground motion of water pools that were set up for
modeling the slow degeneration in the alignment of magnets. It explores
theories that have been found to express a relation between distance and
time and the existence of a *constant*, in the determination of an
alignment 'factor' at some point, based on these ground motion
variations. This paper also presents and evaluates data on this theory
to better determine a model for magnet alignment and how often it needs
to be done.

**Theory**

**Accelerators:**

*The Effect of Ground Motion*

The resultant motion of the proton/antiproton beam, due to the movement
of the quadrupole (magnet) itself, is quite substantial. For this reason
ground motion is of particular interest to accelerator builders. For
collider designs, the requirement to achieve a high luminosity at the
interaction point places the most stringent restrictions on ground
motion.

Ground motion and vibration can be a limiting factor in the performance
of colliders, in particular linear colliders and large hadron colliders.
Studies of ground motion have been carried out around the world for many
years and it has been found that ground motion and vibration have two
significant effects on a collider. They can cause the beams to miss each
other at the interaction point (IP), and they can cause beam emittance
growth, which reduces the luminosity.

Emittance refers to the extent occupied by the particles of the beam in
space and momentum phase space as it travels. A low emittance particle
beam is a beam where the particles are confined to a small distance and
have practically the same momentum. A beam transport system will only
allow particles that are close to its design momentum, and of course
they have to fit through the beam pipe and magnets that make up the
system. In a colliding beam accelerator, keeping the emittance small
increases the likelihood of particle interactions, resulting in higher
luminosity.

Luminosity is the number of particles per unit area, per unit time
multiplied by the opacity of the target, usually expressed in either the
cgs units, or cm^-2^ s^-1^ or b^-1^ s^-1^. Opacity describes the
absorption and scattering of radiation in a medium. A colliding beam
should have high luminosity and low emittance, to yield maximum
interactions. In an ideal accelerator with well-aligned magnetic
elements, the closed orbit passes through the centers of bending magnets
and quadrupoles to provide optimal conditions for the operation of the
machine.

It is not difficult to see then, why determining ground motion trends,
and curbing them somewhat, is important for current and future work in
particle acceleration. However in the collection of this data there are
a number of interpretations and/or data analysis techniques of ground
motion and they are: (Please refer to Appendix for these techniques with
the exception of the ATL law)

-   Power Spectral Density

-   Wave Propagation

    -   *P-waves*

    -   *S-waves*

    -   Surface waves

    -   *Love waves*

    -   *Rayleigh waves*

-   Apodisation

-   Velocity or Displacement Power Spectral Density

-   Coherence and Correlation

-   Ground Motion Spectra

    -   Tidal Motion

    -   Micro-seismic Peak

    -   Crustal Resonance

    -   Technical Noise and Cultural Noise

    -   Ground Motion due to Airplanes

-   The "ATL" Law

As mentioned before though, the scope of this paper is the ATL law and
its application to Fermilab.

*The ATL Law*

An alternative method for analyzing some components of low frequency
ground motion over long time intervals makes use of the so called \"ATL
law\". It is used to describe the diffusive or Brownian motion that
unconnected points on the ground (or structures attached to the ground)
undergo. It also acts as a low intensity baseline to the regular (in
time and space) motion due to propagating waves in the upper Earth\'s
crust. According to the ATL law, the relative motion of two point scales
is proportional to the product of the spatial and temporal interval
between measurements. This empirical rule gives the rms relative
displacement ![](media/image2.png){width="0.2604166666666667in"
height="0.19791666666666666in"} of two points separated by a distance
![](media/image3.png){width="0.15625in"
height="0.17708333333333334in"} and time
![](media/image4.png){width="0.15625in"
height="0.17708333333333334in"} as:-

![](media/image5.png){width="0.9270833333333334in"
height="0.3020833333333333in"}

Where the constant ![](media/image6.png){width="0.16666666666666666in"
height="0.17708333333333334in"} is of the order
of![](media/image7.png){width="1.1145833333333333in" height="0.25in"},
depending on conditions at the site, this corresponds to a power
spectral density of:-

![](media/image8.png){width="1.2083333333333333in"
height="0.4583333333333333in"}, for
![](media/image9.png){width="0.4166666666666667in" height="0.21875in"}
(where ƒ refers to frequency in Hz)

This law is particularly useful for modeling the slow degeneration in
the alignment of magnets in the accelerator which leads to the periodic
need for realignment. At Fermilab, the ATL law is applied via the use of
a water level system known as the Hydro Static water Level System for
collecting the data, which is then analyzed in Microsoft Excels VBA to
better determine the "A" value for this region.

**Experimental Details**

To facilitate the ground motion analysis 'HLS' are used to measure the
change in floor level, and the water level variations. Fermilab and
Budker institute have been collaborating on Hydro Static water Level
Systems to measure ground motion for many years. Tests are conducted
underground at a preferred depth of 100 or more meters below the surface
in the Galena Platteville dolomite. Two of the current systems are in
the near MINOS hall on the Fermilab site and the Lafarge (formerly Conco
Western) mine in North Aurora Illinois. Both systems are in the Galena
Platteville dolomite. Both systems use Budker institute designed and
produced HLS systems to measure the change in floor level (refer to
**Figure 3** for the basic setup of the HLS with the Budker sensor).

Hydro static water levels are based on the principle that water seeks
its own level. Distilled water is used since it is safe and the physical
properties are well known so that measured data can be corrected for
errors. There are two types of sensors being used in these HLS systems
at Fermilab: the Budker sensor and the considerably less expensive
Balluff proximity sensor (refer to **Figure 4**). For this study though
the focus was on the Budker sensor since the data collected was from the
Lafarge mine as well as on site at MINOS. In all cases a two pipe system
is used at Fermilab. One pipe is full of water and connects each vessel
or pool. This pipe is always below the desired level of water in each
pool. The second pipe is elevated above the pools and is full of air
(see **Diagram 1**).

![](media/image10.png){width="5.751388888888889in"
height="4.071527777777778in"}

Diagram 1: Simple diagram of the setup of the HLS system

The advantage of a two pipe system over a single half filled pipe is the
ability to manoeuvre over or around obstacles between each pool. A half
filled pipe system must be level throughout the installation. The
sensors are spaced 30 meters apart, and consist of a stainless steel
pool connected with 12.7 mm ID polyethylene tubing to adjoining pools
(water filled tubes). Figure 1 shows the actual setup of the HLS system
at MINOS.

**Figure 1: HLS setup at MINOS (BUDKER sensor)**

![](media/image11.png){width="4.959027777777778in"
height="3.7180555555555554in"}

In the body of the pool there is a temperature sensor that records the
water temperature and allows for corrections to be made for expansion
due to temperature changes. Each pool sits on a plate with adjustable
legs to allow for leveling of each sensor relative to the others. Since
the pools are connected by tubes, to ensure a level starting point the
legs are adjusted relative to one another. In some instances in LaFrage
mines precisely measured cement "foundations" had to be setup as to
allow for better leveling between adjacent pools (see **Figure 2**).

**Figure 2: LaFrage mine HLS setup with cement pillar.**

![](media/image12.jpeg){width="5.427083333333333in"
height="4.103472222222222in"}

On top of the pool is the sensor and electronics. The sensor measures
the capacitance of the gap between the sensor face and the top of the
water. These capacitive sensors are used to determine the distance
between the top of the water and the "cap" (or sensor face). The sensor
is heated to prevent condensation; this would interfere with the
precision of the measurements. Each sensor has been calibrated before
installation. The gap measurement is accurate to 1 micro meter over a
range of 10 mm. A power and data cable daisy chains between each sensor.
The data is read out through a National Instruments card into a PC.
Software reads out the data at 1 minute intervals and stores the data
for later analysis. Systems are checked every business day to ensure the
sensors and computers are functioning. At the end of every month data
taking is automatically stopped and restarted. A reset pulse is sent out
to each sensor in case a software hang occurred.

**Figure 3: Budker sensor**

![](media/image13.png){width="5.955555555555556in"
height="4.220138888888889in"}

![](media/image14.png){width="5.342361111111111in"
height="3.8340277777777776in"}

**Figure 4: Balluff sensor not used in this analysis but is used on site
at the MP8 tunnel for similar ground motion analysis**

![](media/image15.png){width="6.502083333333333in"
height="4.596527777777778in"}

The data that is read out through the National Instruments card into a
PC is then archived as comma separated files online at
<http://dbweb1.fnal.gov:8100/ilc/ILCGroundApp.py/index> . The data is
timed stamped in one minute intervals using Central time. All levels are
in micro meters, temperatures are in degrees C and pressure is in kilo
Pascal. In order to make this data 'useful' Visual Basic for
Applications was used.

**Visual Basic for Applications:**

*VBA for Microsoft Excel*

-   What was the intended outcome of using VBA in Excel?

> In order to make the comma separated data files of over 40,000 data
> points per month more useful, a suitable data analysis program was
> necessary. Microsoft Office Excel easily compiles the data into rows
> and columns. By copying the data from the online database into a
> notepad (.txt) file, then by renaming this file into a compatible file
> extension (.csv **C**omma **S**eparated **V**alue), the data becomes
> manageable. Once this is done, by writing a suitable macro data from
> [any]{.underline} month can be used to determine the 'A' value.
> Depending on the computer being used this file may actually be
> downloadable as a '*.csv'* file.

-   What is a Macro?

> A macro is a rule or pattern that specifies how a certain input
> sequence should be mapped to an output sequence according to a defined
> procedure. It basically is the group of instructions that the user
> wants executed within a given application (in this case Excel).

-   What does *this* macro do?

> The process is to first calculate the second differences for the
> system. In the case of the MINOS data for example, there are four
> sensors L0 through L3 two second differences can be calculated these
> are (in general a double difference is (D0-D1) -- (D1-D2)) ;
>
> SD012 = L0-2L1-L2
>
> SD123 = L1-2L2-L3

Where L0, L1, L2 and L3 are the levels recorded for each sensor in
micrometers.

This double difference is then squared for time slices from one minute
to the range selected by the user. The average of the selected time
slice is then found and divided by 30 to give the average dispersion per
meter (since the sensors are separated by 30 meters). This average
dispersion is plotted against time is second and the slope of this plot
represents the *A* value in the 'ATL' analysis.

However before any of these calculations could have been done, their
first needed to be some editing to the raw data. The macro needed to be
user friendly so that any user regardless of familiarity, would be able
to enter data of their choice and an *A* value would be returned. Simply
put, the macro is the most logical way of processing this data since it
would be rather time consuming to manually input these formulas on every
occasion, again calling to mind the amount of data points there are (at
least40,000 points per month for three years). Following are a series of
example images showing the comma separated data, the raw .csv data, the
final data, a plot of the dispersion and '*A'* value, and of course a
sample of the macro.

**Figure 5: Step by step sequence of calculating '*A'***

**Samples of the online comma separated data, and '.csv' file extension
data in Microsoft Office Excel.** ![](media/image16.png){width="6.05in"
height="3.959722222222222in"}

![](media/image17.png){width="6.293055555555555in"
height="3.3361111111111112in"}

**Data that has been processed and formulas entered**

![](media/image18.png){width="5.852777777777778in"
height="3.5208333333333335in"}

**Plot of the Dispersion per meter versus time in seconds, the slope of
which is '*A'***![](media/image19.png){width="5.933333333333334in"
height="3.8895833333333334in"}

![](media/image20.png){width="6.6930555555555555in"
height="4.045138888888889in"}

**Sample of the VBA macro**

**Results and Setbacks**

Data has been collected every minute for over 24 months in HLS systems
installed in the Lafarge mines and at MINOS. The value of the constant A
in the ATL law has been determined to be in the range of 2 to 6 x10^-6^
μm^2^/s-m (i.e. from 2x10^-6^ to 6x10^-6^ μm^2^/s-m) for the Fermilab
area. This would suggest then, that the root mean square relative
displacement of two magnets in this region, is equal to the product of
the distance between them, the time, and this constant. In the
determining of this constant however, there were a number of
modifications that had to be made.

*The macro:*

-   At first the method of applying the data to all selected cells, was
    a command called a '*for loop'.* In a '*for* *loop*' basically, the
    user directs the program to execute a command ***for*** the selected
    number of rows. Below is an example:

*Range(\"C6:C6\").Select*

*Selection.Copy*

*For r=6 To cRows*

*Cells(r,3).Select*

*ActiveSheet.Paste*

*Next*

This code selects a certain cell and then instructs the program to copy
its contents from row six to the selected row number. The problem with
this format was the amount of time it took Excel 2007 to execute. A
faster and easier format needed to be used.

-   The first macro also didn't allow for customizable month or day
    selection, in that only data input of a certain amount could be
    worked. The upgraded version took several weeks to tweak to its
    finished product. Any programmer can give testimony to the
    difficulties in just getting the program to do what is wanted
    without it disagreeing. It used the more basic *copy and paste*
    command. Following is an example of the improved macro:

*Set SourceRange = Worksheets(\"May Disp\").Range(\"H7\")*

*Set rrange = Application.InputBox(prompt:=\"Size of range(must iclude
cells to copy)?\", Type:=8)*

*SourceRange.AutoFill Destination:=rrange*

Although the actual code is longer, the execution time is considerably
shorter, and uses less memory. This method also allows for and input
dialogue box where the user can then choose the range to execute.

*Microsoft Office Excel 2007*

-   Unfortunately, as much as Excel was most suitable for the job, it
    also proved to be troublesome. Excel does not allow for plotting of
    any data as long as there are more than thirty two thousand data
    points. In fact, even though the data to be plotted was only ever
    going to be eleven, the mere fact that the data was derived from
    more than thirty two thousand data entries, caused excel to deny the
    macro. Because of this in designing the dialogue box that prompts
    the user to enter how many rows, there is also the warning that a
    value of fewer than thirty two thousand must be entered. If not, the
    macro would not work and instead a notification of an 'overload'
    would come up and subsequently end the macro.

**Evaluation**

In the process of this research a lot can be taken into deeper
consideration. There were no recognizable trends in the data from month
to month; therefore this surveying is something that will continue
indefinitely. Unless the earth stops spinning for some reason ground
motion will always be an issue facing accelerator builders, regardless
of how gradual this motion is. This leads to thinking of a possible
solution. For instance, the age-old anecdote that prevention is better
than cure. How realistic is it to suggest that this ongoing analysis and
subsequent re-alignment may not even be necessary? What preventative
measures exist and have they being utilized?

Below is a list of preventative measures that should be considered for
future accelerator construction:-

-   Design machines with parameters and lattices that are less sensitive
    to position errors

-   Choose a site where natural and man-made disturbances are minimised
    (Try to choose a site on scientific and technical grounds and not
    political ones)

-   Undertake careful design of building structure and foundations

-   Undertake careful design and modelling of all magnet support
    structures. Use FEA to predict resonant frequencies of all magnet
    structures and modify as appropriate

-   Do not spoil a good site by carelessly introducing sources of
    vibration from reciprocating pumps, cooling water etc., as well as
    maintaining constant temperatures with small gradients around
    sensitive components

Subsequently if the "vaccines" failed or were not administered, the
following cures may be used:

1\. **Periodic surveying and alignment of lattice magnets:** It is
possible to calculate the amount of diffusive **motion** of the lattice
magnets that can be expected (after their initial settlement). Given a
judgement of an acceptable period between realignment campaigns it is
then possible to calculate the likely steering corrector strengths
required. Note that this will tell you the levels of correction
necessary to get the beam back through the centre of the quadrupoles; it
does not mean that the beam is following the initial trajectory.

2.      **Vibration isolation:** This is possible for driving
frequencies some way above the resonant frequency of the structure, but
requires structures with very soft spring constants in the region of the
resonance.

3.      **Vibration damping:** This technique relies on coupling the
resonating structure to an object (say, for example, the floor) that is
not resonating at that frequency via a material with very specific
anisotropy in its properties. Unfortunately the properties of these
damping materials are usually highly dependent on temperature and
stress.

4.      **Dynamic alignment:** This is requires a source of misalignment
information (possibly from 5. below) plus a motorised realignment
mechanism to position the most crucial magnets back to a better aligned
position. The frequency range over which this would be expected to work
would need careful consideration.

5.      ** Beam-based feedback:** If all else fails, then some form of
beam-based feedback can be used to overcome a certain amount of
positional instability of the magnets, over frequency ranges that need
to be defined.

Surely though this research did not unearth some new need for ideal
treatment. It begs the question then, what measures were and/or are
already being undertaken at Fermilab.

**Conclusion**

**Future Works**

**References**