Abstract
High energy testing of the Tevatron has been continuing for many
years in an attempt to raise the energy of the Tevatron. A model
was developed to aid in the testing. This paper will explain
what improvements have been made to the model, how it has helped
with high energy testing, and how the model can help in the future.
Background information is also given to help in understanding
the discussed material.Introduction
In order to help the high energy testing of the Tevatron, a mathematical
model in an Excel database was developed to aid in the prediction
of quenching magnets. The author improved this model to make
it more reliable in identifying quenching magnets, to analyze
temperature profiles and training in magnet strings, to calculate
heat leak in magnet strings, and to develop a plan for the future.
Purpose
Previously, the Tevatron has run at 800 GeV for fixed target
operation and 900 GeV for collider operation. The goal is to
increase the energy of the Tevatron up to 1 TeV for collider Run
II. To do this, a 3% safety margin is required. This will entail
the energy of the Tevatron to successfully reach 1030 GeV. If
this cannot be achieved by the time for Run II, operation at 990
GeV will be adequate. This has already been proven possible because
this last session of high energy testing successfully raised the
energy of the Tevatron to 1015 GeV.
Tevatron Design
The Tevatron had many design restrictions placed on it because
it had to be built so that it could fit under the Main Ring.
The Tevatron consists of 774 dipoles, 216 quadrupoles, and about
100 various other pieces such as spools and bypasses. The magnets
of the Tevatron use superconducting wires to obtain higher energies
than achievable by the Main Ring. In order to make the magnets
superconducting, the wires must be cooled to a very low temperature,
only a few degrees above absolute zero. This is accomplished
by the cryogenic system of the Tevatron. The Tevatron is divided
into 6 sectors of 4 sections each. At each section, helium and
nitrogen are supplied to a house above the ring containing heat
exchangers, refrigerators, and various other devices, that then
feeds the fluids down to the magnets in the Tevatron. When the
fluids reach the Tevatron, they split. Half of each fluid flows
through an upstream magnet string while the other half travels
through a downstream magnet string. Upstream and downstream refer
to the direction of the protons in the ring. (Refer to Figure
1. Note: Only one magnet string shown)
Magnet Design
The magnets themselves required extra design consideration. They needed to have a small cross section to fit under the old Main Ring. This meant that the superconducting wires could not be cryostatically stabilized. Primitively, cryostatically stabilized wires have enough copper surrounding the superconductor that should a small pocket of heat form, the current will pass around the hot area by means of the copper. This dissipates heat more readily to the helium; the copper stabilizes the heat formation. The helium will carry away the heat so the current can start flowing through the superconductor again. The wires in the Tevatron do not have sufficient copper to stabilize the wires. A small hot area will continue to grow till the magnet quenches. Therefore the magnets had to be protected in the event of a quench. A quench occurs when the wires in the magnet stop being superconducting due to heat or a high enough magnetic field, and the magnet expels its stored energy. In addition the cables containing the wires had to be attached to the magnet in such a way so that slipping would not occur while ramping the accelerator. Such movement could cause heat to build up and induce a quench. This usually occurs after a magnet has been warmed to room temperature and cooled down again to near absolute zero, called a thermal cycle. This can occur many times with each successive cycle giving a higher quench current till it finally levels off, and the true quench current is reached. This event is called training. Thus the magnets needed enough cooling to reach temperatures as low as 3.5 K while being subjected to heat leaks, ramping magnetic fields, and coil movement.
The magnets were designed to act as heat exchangers. (See Figure
2) In the center of the magnet is the beam tube. Surrounding
this are the superconducting cables and the single phase liquid
helium that cools the coils to the very low temperatures. The
coils are held in place by stainless steel collars. The helium
flows along the length of the magnet in two regions. One is between
the beam tube and coils, and the other is between the collar assembly
and the outer single phase tube. These two will be referred to
as the single phase (1f) inner and
the single phase outer, respectively. Next is the two phase (2f)
helium that is composed of liquid and gaseous helium. This is
composed of 1f helium that has passed
through the magnet string, expanded and cooled in a JT valve,
and is now returning back through the magnets. Therefore the
2f helium flows opposite the 1f
helium and acts as a counterflow heat exchanger with the
1 outer.
Model
A model is used to aid in the high energy testing of the Tevatron. If a magnet is identified as quenching, it is removed from the ring and replaced with a magnet that can operate at the higher energy the previous magnet could not. It is tested at MTF to determine if it is a hopeless magnet or if it might be able to be recycled in a cooler spot in the ring. Recycling magnets is required because there are so few replacement magnets. It would be possible to isolate bad, but not hopeless, magnets to a few of the houses, and operate them at a temperature of 8 psia while the other houses with better magnets are operated at a higher temperature of about 11 psia. The model can easily rearrange data and develop a plan of removal and recycling.
The mathematical model simulates a heat exchanger. It was written
in an Excel worksheet as a Visual Basic program by Mike McAshan.
The data was collected from MTF data records on all the pieces
in the Tevatron. In order to solve the problem, many assumptions
have to be made.
This last statement is added because gaseous helium does not aid in cooling the 1 outer. It was previously assumed by the designers that the 2 liquid and gas would be well mixed, like carbonated water. In reality the liquid falls to the bottom while the gas rises to the top of the tube. Using these assumptions, the heat exchanger model reduces down to simply calculating the heat leak in watts, dividing by the flow rate, and setting that equal to the enthalpy.
The model starts with a function that calculates temperature given enthalpy, TempFnH, and a function that calculates enthalpy given temperature, HFnTemp. The next function reads a data series identifying the device in that location and assigns a slot length. The following four functions are the heart of the model. They calculate the enthalpy and temperature for the upstream and downstream strings. Given the initial 2 helium temperature at the feedcan, the model computes NextHU, TempU, NextHD, and TempD. The function “current” reads the MTF quench current data and adjusts it to find a corrected quench current. Magnets typically improve their quench current by 13% / K. The model then calculates the Tevatron Energy for the corrected quench current. The TFnPsat function calculates temperature as a function of saturated pressure because the data for temperature is measured as a corresponding 2 pressure. The next function uses Newton’s Method to calculate a differential temperature, DTFnPsat, that is again a function of pressure. Spool is a function that assigns heat leaks to the 11 different types of spool pieces in the Tevatron. Each heat leak is different because each spool has a different number of differing devices on it. The last function is used to compute the heat leak in each device in the Tevatron.
In order for the model to function properly, data needs to be taken on every device in the Tevatron. This includes dipoles, quadrupoles, spool pieces, bypasses, and others. The dipoles are the main focus of the model; they cause the quenches. There are two types of dipoles, TB and TC. The first magnets put into the ring are some of the poorest performing magnets. They had to be installed as quickly as possible, so they were hastily assembled and tested to see if they were capable for use in the Tevatron. These magnets were built so hurriedly that time could not be taken to improve the quality of the magnets. Afterwards magnet production improved. Towards the end of production, however, magnets were not as good as they were in mid-production. This was due to old cables being spliced with new cables. It is observed as one looks at magnet serial numbers, related to when the magnet was made, that low numbered magnets, 200 to 400, and some high numbered magnets, 1000 to 1100, have the lowest quench current.
Quadrupoles, or quads, do not quench like dipoles. The purpose of quads is to focus the beam whereas dipoles bend it. Unfortunately the Tevatron contains many more dipoles than there are quadrupoles.
Spools are another major part of the ring. There is about one spool for every eight dipoles. They are essentially tubes with transfer lines in them for the helium, nitrogen and beam. On the outside of a spool, however, are many instrumentation devices to record temperature, pressure, and such. This causes more heat leak in a spool than in a magnet. In addition there is no heat exchange in a spool as there is in the magnets, so as helium flows through a spool, heat is added to it. The hot helium flowing out of the spool causes the following dipole to run hot; this lowers the quench current of that magnet. This is considered a bad spot in the ring.
Bypasses are devices in the Tevatron that allow for good heat exchange and have minimal heat leak. Enthalpy is calculated through a heat exchange equation. The other devices in the ring consist of doglegs and feedcans. These are few in number and only account for a small amount of heat leak and heat exchange.
Improvements to the Model
The model can calculate quench current and energy of each magnet in the Tevatron. It also provides a temperature for the helium in each device in the ring. All this information makes it possible to identify problem magnets, bad locations in the Tevatron, and training magnets from the MTF data. The author improved the model in many ways. These improvements made the model more accurate, capable of new functions, and easier to use.
The first improvement made on the model was to create global variables for the functions in the model. There are a number of variables that each function use, so in order to vary the operating conditions, one needed to enter the new condition many times. The global variables made it possible to enter the new condition once, and the program would calculate the new scenario. This enables the user to work quicker and more efficiently.
Another improvement includes adding a function to the program that will calculate the heat leak in each magnet string. This was done simply by adding all the heat leak from each item in a string. Finding the heat leak is important because it will aid in understanding the operation of the refrigerators. It is known that dipoles have a heat load of 8 W. Quads have heat leaks slightly less than that. Different spools have different heat leaks, so the easiest way to compute heat leak is in the model. Experiments were done that suggest the heat leak in each section to be about 500 watts, but recent measurements point toward heat loads of 360-400 watts. The values that the model puts forth vary greatly for each section. Many values agree with the latter measurements. However, there are some sections where the heat leak was calculated to be as high as 460 watts. This is explained by the fact that some sections have more spools or spools with higher heat loads. The values of the model, however, are only raw guesses.
The model also improved upon the accuracy of the predictions. This was done by adjusting the functions in small ways. To begin with, the heat leak in the magnets was studied. It was known that, at the connections of a dipole, 3 W are added to both helium streams at the downstream end, and 1 W is added to both helium streams at the upstream end. As the helium flows through a magnet, it splits. The 1 inner consists of 50% of the total single phase flow. The other 50% travels as the 1 outer. Along the length of the dipole, 2 W are added as heat leak to the 1 outer and the 2 helium. However, half of the 1 outer, 25% of the total, is in heat exchange with the 2. It transfers all its heat to the 2f till the temperature difference between them is 50 mK, previously thought to be 10 mK. It was believed that there might be some heat added to the 1f inner due to ramping current, Qac, but this was found to be negligible.
On the other hand, a quad is shorter than a dipole and has a
slightly different configuration and connections. This makes
the heat leak on the quad different from the heat leak of a dipole.
In a quad more of the 1f helium flows
as the 1f inner, about 80%. This reduces
the amount that is recooled to only 10%, half of 20%. Since the
quad is shorter only half of the heat leak in a dipole is added
along the length. This means that the 1f
outer and the 2f receive 1 W each,
but the 1f outer is still cooled to
50 mK higher than the 2f temperature.
The upstream end of the quad is basically the same as a dipole,
so there is also a 1 W heat leak to the 1f
and 2f helium. The downstream end,
however, is simpler in a quad. The heat leak there is only 1
W compared to 3 W in the dipole. Making these adjustments in
the functions that calculate enthalpy greatly improve the ability
of the model to simulate the actual situation.
Testing
After the improvements to the model, it was implemented for the first time in conjunction with high energy testing. Previous testing has brought up many questions:
This model was developed to help answer those questions.
The first question is an important one. This arose from a December 1993 test in which 14 of the 15 quenches signified training. If one is trying to study high energy physics but 770 magnets quench 3 times before they start operating properly, and it takes 3 hours to retune the Tevatron after a quench, nothing would be accomplished. One can sometimes predict when a magnet is training. Magnets always quench in flattop. If a magnet quenches on the ramp up to flattop, that usually signifies training. Using the model one can identify training if the predicted quench current is much higher than what the measurements read, and the magnet is old. Three houses were thermal cycled and were studied to see to what extent training would occur. Training was observed in one of the houses that had cycled. A magnet in C42U quenched twice early in the testing. The first quench was at 977 GeV at 11 psia on the way up to flattop. The second quench occurred at 991 GeV at 11 psia, also on the way up to flattop. Later a magnet in C44L quenched at 1000 GeV and 14 psia leading to the assumption that the C42U magnet trained twice, and then left the limiting magnet in the house to quench at the higher temperature and energy. The model confirmed this because the three magnets in C42U were predicted with higher quench currents than what was seen. The fourth magnet did not have data, but it was made at the time when the best magnets were being made. One magnet was rated at 1009 GeV at 11 psia, but was ruled out because the model rarely overestimates quench energy. The power test quench log from 1993 was compared with the model, and most of the magnets were found to be trainers. It is concluded from the May-June 1996 testing that training might not be a problem. It appears that about one house per every three houses trains. This seems to agree with the December 1993 tests. If the whole ring goes warm, about 8 to 10 houses will experience training.
The next question was answered using temperature profiles of magnets in the model. As seen in a plot of A1 (Figure 3), the magnets attempt to reach a temperature where heat exchange will not take place. Dipoles are shown as squares, quads are open squares, spools are diamonds, bypasses are open diamonds, the feedcan is a triangle, and the dogleg is an open triangle. At the beginning of the string, the temperature rises to reach this average. Spools have no heat exchange, however, and just add heat to the system. This shoots the temperature so high that the magnets then act to slowly cool down the temperature. This temperature rise and cooling is seen clearly in the graph. This shows that one of the worst, or hottest, spots in a magnet string is next to a spool. Another analysis of A1 compared the temperature change of magnets in a string as pressure was changed (Table 1). This was done by recording the temperature of each magnet in a string as the pressure varied from 20 psia to 6 psia. As can be seen, magnets next to spools experience less of a temperature change than other magnets. The closer to the feedcan, the lower the temperature, but the farthest away from the 1 outlet of a spool, the better the temperature change for lower pressures.
The question of whether or not bad magnets can be predicted is
the most important question. The model accurately predicts the
performance of ring sections (See Table 2). The column Tev
refers to the performance rank of each house in the Tevatron.
This information is based on past problems of each house. The
model ranking is in the column MTF/Thermal rank. The three highest
ranked have the highest quench energy. The model then predicts
D1 and E2 to be ranked 5 and 6, but Tev ranked them as 15 and
12, respectively. They were tested and found to be in accordance
with the MTF rank rather than the Tev rank. This proves the ability
of the model to predict. But when it comes down to the actual
magnets, problems arise. Time can be taken and PDQ tests can
be done to identify quenching magnets, but that takes time. If
there is no time, the model can give an approximation of what
the magnets should be doing. From this an educated guess can
be made. (Refer to Table 3 and plots) All but the first three
magnets on the list quenched during the last period of testing.
The shaded areas signify one problem magnet, but one magnet cannot
be singled out from the list the model gave. Therefore all the
possible magnets are given. The model can sometimes be accurate.
This is seen in the magnets at B18-4, A48-3, E27-5, and C43-3.
The first two have been identified by PDQ. The others are guesses,
but they are near certainties. On the other hand, the model can
give funny results, as seen at B46-5 that quenched at 1015 GeV.
However, the model predicted the magnet would quench at 954 GeV,
a large difference. This simply shows the erratic predictions
of the model leading to the question of whether the problem magnet
is the worst magnet the model predicts or the magnet that closely
resembles what is actually happening. The answer to that question
is unknown. This is why one magnet cannot be picked from the
ones in the shaded area. However, if a choice had to be made,
it is recommended that the worst magnet be removed. This advice
is based on the fact that the model often underestimates the performance
level of a magnet and has only occasionally given extremely high
or extremely low values. If a situation occurs where two magnets
have nearly the same rating as with D19-4 and D19-5, it is recommended
that the older magnet be taken out of the ring.
Problems
The model is far from perfect as is the case in any real life
situation. The model is trying to recreate something that changes
constantly. There is just so little known that the model cannot
be made to give exact results. It relies on the information supplied
to it. If variables are left out, the accuracy lowers. An example
is each magnet has three splices in the cable that are not accounted
for in the model. Doing so would make the model more realistic,
but how does one calculate what a splice in the cable will do?
Some variables are important but not conceivably possible to
incorporate into the model. Averages also lower the preciseness
of the model. Assuming that every magnet improves their quench
current by 13% / K is false. It has been shown that some only
improve by 11%. After every possible variable is integrated into
the model, only then can it be considered complete.
Future
A major problem that demands repair is a 2 pressure block in
B1 and F3. This should be done as soon as possible because it
will soon limit the operation of the Tevatron. While waiting
for this to be finished, the easiest activity to do for the future
is improve the model in any way possible. Data can be studied
and manipulated to find the houses with the most bad magnets or
where the spools have a small heat load. Any magnets taken out
of the ring can be tested to see if they might operate in one
of the cold houses. They would then be exchanged with a better
magnet that can operate at a higher temperature. This magnet
removal process would take place in the event of something failing
and requiring warm up to sections of the Tevatron. The list of
weak Tevatron magnets would be used to decide the magnets to be
removed. As stated before, if there is more than one possible
magnet causing the quench, removal of the lowest rated magnet
is suggested, or more than one could be taken out if enough spares
are available. Of course, more testing is required for further
understanding.
Conclusion
High energy testing does not depend on the reliability of the
model. It has succeeded in obtaining 1015 GeV in June 1996 with
little or no aid from the model. But so much more can be achieved
with it. After it has been perfected a little more, it will become
an invaluable tool in understanding the Tevatron. The model can
be tuned a little more, but it will take time. Through diligent
work, 1 TeV can be reached by Run II.
Acknowledgments
First of all, I would like to thank Dianne Engram and Elliott McCrory for this great opportunity. I would also like to thank Bob Webber for the time he took in getting me this job. I learned a great deal and enjoyed the work. I want to thank those in the Cryogenics Department for their time and help especially Jay Theilacker, Bill Soyars, John Brubaker, and Jean Poore. I wish to thank Mike McAshan for all the hours he spent teaching and showing me how everything works and for offering me the job. This has been a memorable summer.
Bibliography
Edwards, H. T., 1985. Ann. Rev. Nucl. Part. Sci. 35:605-60
Appendices
Appendix A
Global Variable List
Unit Models
Appendix B
Figure 1
Figure 2
Figure 3
Table 1
Table 2
Table 3
Plots
Appendix A
Global Variable List Global variables used in the model
Unit Models Program written for the model
Appendix B
Figure 1 Diagram of flow from sattelite refrigerator house
to a magnet string
Figure 2 Cross-section of a dipole
Figure 3 A1 temperature profile
Table 1 Temperature change study in A1
Table 2 Tevatron higher energy quench performance
Table 3 Identified weak Tevatron magnets
Plots Magnet current for given pressure in houses E2 and D1