Appendix-1: A gedanken PBL-cycle

The 8 ESRs convene on the Monday, for a first session on a new PBL-task. The four women and four men have quite different personalities and have also some difference in English proficiency. Claus, Giuseppi and Mary are quite extrovert, Balazs is rather shy, Maria is very social but have some difficulties in expressing herself in English, Gunhild and Ana are rather similar with a good undergraduate knowledge and soft spoken. Antonio tends to want to dominate the meetings.

The supervisor distributes the text and figure describing the situation to address, and asks Ana to read it out load. Ana reads:

A team has made a set-up to measure the performance of a silicon detector. The set-up is shown in the attached figure.

 

The detector is exposed to a 10 GeV/c beam of p-s from an accelerator. The scintillator detectors, S1 and S2, before and after the silicon detector is used to trigger in an experiment to measure the collected charge from the silicon detector. The coaxial cable between S1 and the coincidence unit is 10 metres while the corresponding cable for S2 is 14 metres.

 

The output from the amplifier is first connected to an oscilloscope but no signals are observed. Both cables from S1 and S2 are connected to the oscilloscope and a decision is taken concerning the cable-lengths. The system is reconnected and a signal from the silicon-detector is now observed on the oscilloscope.

 

The output from the amplifier from the silicon detector is now connected to an ADC, gated by the S1-S2 coincidence, and read by a computer when triggered by the S1-S2 coincidence to do so.  Three parameters are varied for these measurements: The beam momentum, the high voltage over the silicon detector, the number of beam-particles to accumulate for each histogram.

 

  1. The momentum is kept at 10 GeV/c, 20 000 p- are accumulated for each histogram and the voltage over the silicon detector is varied. The polarity is first set to the opposite of what is shown in the figure; the current is just growing large and a high voltage cannot be applied. The polarity is changed back and the result is plotted in a diagram, and after some discussion they decide to keep the voltage at a specified tension in the future.
  2. The histogram over the collected charge for the p-s is lively discussed since they find it difficult to understand its tail. The average and variance of the distribution are determined and they consider if an accumulation of 20 000 is really necessary. One member says that future determination of higher moments may require this. However, some states that such moments are not needed to be determined.
  3. The histograms are collected for 10, 5, 2, 1, 0.5, 0.2 and 0.1 GeV/c beam momentum. A problem occurs at 0.1 GeV/c, when no signal at all is observed. The problem is ignored and the measurement at 0.1 GeV/c discarded. The averages as a function of momentum is then tabled and plotted in a diagram. During a discussion it is agreed that a description of the underlying physics is needed to define a mathematical expression that can be fitted to the data points. The group is not sure of what to optimize in the fitting procedure.
  4. The beam momentum is set to 1 GeV, but the particle type is changed to first electrons and then to protons. The histograms differ from each other and from that of the ps.
  5. One team member suggests that this can be used to identify different particles, but it would then be better to have a thicker detector. Another member contests this and says that it would be better to have several detectors.
  6. Another says that one could also use this to search if there are particles that are neither of the three.

The group spends five minutes in thinking about text, and the supervisor then asks if there is something unclear about the text or some words that have to be explained. Mary asks about ADC and gated, and the supervisor explains that it stands for Analogue to Digital Converter, an electronic unit that transforms an analogue electrical signal to a digitized number that can be read by a computer. With gated is meant that the ADC measures the signal only when a level is set by the S1-S2 coincidence to do so. The supervisor asks who is in line to chair the meetings, and Ana volunteers. She asks Claus to be secretary, and he draws a table on the black-board. The columns are: The facts, Problems, “Brainstorm output”, Attempts to explain, Learning Objectives. He also projects the figure of the set-up on the screen. The supervisor moves back a bit from the table, but will continue to follow closely the discussion and through small signs demonstrate that he does so.

Jump-1

Ana starts by stating that they should now write up the facts from the described scenario, and asks who would like to start.

Antonio jumps in immediately. He starts to explain the set-up using the figure as basis, and demonstrated clearly how well he understands how it is working. He lines up the facts: Signals from S1 and S2 must arrive simultaneously at the coincidence unit and the cable lengths matter, the silicon works differently at different tensions, all particles from the beam are of the same type and momentum, … .

Ana interrupts after a while to let other people put forward their observations.

Maria points out that the set-up that worked at 10 GeV/c stops working at 0.1 GeV/c.

Antonio comes in and says that is irrelevant, he knows that now and then equipment stops working because of bad contact etc. It is obvious that this is an irrelevant fact that should be ignored. He then moves on and start lining up another set of facts and moves over to how he interprets the situation.

The supervisor asks the chairperson for the word.

 - It seems as if you need to discuss a bit what this group is for. What is the purpose of our work here and in this form?

 Ana picks up on that, and after some discussion they recollect that the purpose is to understand the described situation, learn to collaborate and profit from each others ideas and thoughts.

 - Is that all that has happened during the last minutes? says the supervisor.

 - I understand, I have tried to dominate the situation too much and this may have hindered the group to work as such. I will restrain myself a bit. says Antonio.

The meeting can now continue and by the guidance of Ana all members contribute to build up the column of facts. It becomes quite large. Ana asks if the group thinks that all facts have been stated, she glance at the supervisor who discretely nods the head. She then suggests that they move over to jump-2.

Jump-2

 - We should now state the problems. I remind you that what we mean with problems are things we need to get explained or if there are unsatisfactory things in the situation that we need to do something about. says Ana.

She observes that Balazs has been very silent and looks at him.

- You want me to say something? I will try. I think there is a problem in that the silicon works with one polarity and not with another. It also works different with different tensions at the good polarity. What is happening in the silicon and how does that affect what happens after a p has traversed it? What does the diagram they draw look like and how does it help them to decide which tension to apply?

Giuseppi raises his hand and says:

- A central thing we need to understand is how these histograms look like. Clearly the ps ionizes the silicon and it is this ionization that is measured. The histogram shows how this ionization fluctuate particle-by-particle. They think this distribution look peculiar, so this we have to explain. There is also some basic statistics here, the uncertainty in average and variance. I’m also not sure of what they mean with higher moments, and in which way that is relevant.

- I want to come back to that it stops working at 0.1 GeV/c. I think this should be listed as a problem. says Maria.

The group continues until all unsatisfactory issues, things that have to be explained, and things that require actions have been listed in column 2. Ana suggest a short break before they move over to jump-3.

Jump-3

The group reconvenes and it is now time to discuss the problems and try, in a brainstorm manner, to suggest different relations and hypotheses.

- Who wants to start? says Ana, who is chairing the meeting.

Antonio raises his hand.
- The silicon must be a diode, which must be why it cannot operate as a detector with one polarity.

- The charges that have been liberated by the ionization, produced by the p, are what is measured. says Maria.

- The measurement is done when there is a simultaneous signal in S1 and S2, i.e. one measure that a particle has gone through them. says Balazs.

- Yes, but the velocity is different for the different momenta. Why don’t they have to change the cable lengths for each beam momentum? asks Gunhild.

- The particles are relativistic of course; they are all at the edge of light-speed. explains Claus.

- Also at 0.1 GeV/c? asks Maria.

- Maybe that's why it did not work! Or, maybe they decayed. says Claus.

- They measured the signals in the silicon and studied two things: The signal-distribution for a given momentum and the averages of these distributions for different momenta. I remember having read about this in the undergraduate course in nuclear physics. I think it was about the average value as a function of velocity, not momentum. remembers Giuseppi.

The group continues to try to express relations and remember from what they already know from different undergraduate courses. In the end they have noted a series of hypotheses in the third column on the blackboard.

Ana sense that it is time to move on:
- Friends, let us now move to jump-4 and try to group and systematize the relations that we have come up with.

Jump-4

Gunhild take the word and says:

- I think we need to classify the relations, since there are several different sub-issues in the scenario. We have the coincidence S1-S2 with its cable lengths, then there is the physics inside the silicon and what happens at different voltages, … .

- Yes, and then there is how the p ionizes in the silicon, and how that depends on the momentum. interrupts Antonio.

- Velocity, not momentum. corrects Giuseppi.

The group continues along this line until they arrived at a fourth column with the content:

  1. The signals from S1 and S2 arrive simultaneously at the coincidence unit. The timing is tuned with the cables but assumes that the p-velocity is constant despite different momenta. This may not be true at 0.1 GeV/c, and/or maybe all ps decay.
  2. The silicon may be like a diode. Reversed tension is applied of a value that allows all ionization to be measured. The signal may be amplified in the silicon?
  3. Ionization fluctuates with a wide distribution that is generated by the underlying physics. The distribution must be measured with large statistics to determine the average.
  4. The average of the ionization depends on the p velocity, or momentum. This relation must be known physics behaviour. This expression, ionization as a function of velocity, must have parameters that can be determined by fitting it to the measured averages at the different momenta.
  5. The distribution looks different for electrons, protons and ps for 1 GeV/c. Their charges and momenta are the same, but they have different masses. The difference is probably the velocity. This talks for that the ionization depends on velocity and not momentum.
  6. To use the measured ionization to identify if it was an electron, proton or a p requires a sufficient precision on the determined average.

 

The group looks at the blackboard and seems satisfied. Ana suggests that they move on to jump-5.

- Can I say something? asks the supervisor.

- Yes, please go ahead. says Ana.

- Well, there is the last point in the scenario. They talk about electrons, pions and protons in the beam. Could there be something else that could ionize in the silicon? asks the supervisor.

This prompts the Claus to write a 7th item in the column: There may be other particles in the beam.

Jump-5

- Ok, what do we need to learn until the next meeting? asks Ana.

- Relativity, says Gunhild. How varies the velocity at different momenta. Does the ps decay, and how often? Does that vary with velocity; I remember something about time dilation?

- We need to learn about the speed of the signals in the cables.

- How does a silicon detector function? What is the physics at the different voltages, and how does that effect the measured ionization?

The group continues until the study plan in the fifth column is filled. It spans issues of relativity, electrodynamics, condensed matter physics, statistics, mathematical methods for fitting procedures and particle physics.

Before adjourning the meeting to enter a several days of studies, the group evaluates its performance as a group during this session. They agree of the importance to be part of the group, and not communicate as an outsider, Ana get some feedback on how she has functioned as chairperson, etc. In general they are quite satisfied with how they have functioned.

The supervisor notes in his log-book how the individual participants have contributed to the group. He is happy to note that none have been just a passive observer.

Jump-6

The participants spend now some days on studies and calculations; some of them individually while a few others work together. They use the supplied literature lists but also searches on the web and picks up their old undergraduate literature. They discover that the scenario has opened up large areas that they are not familiar with, and also have to prioritize what they should focus on.

Jump-7

The group reconvene on the Thursday. Ana asks if the ordering, or grouping, of the issues in the fifth column needs to be revised. This is not the case. The presentation of the weeks findings are now gone through. They go through all problems they previously identified and verify that they can now address and understand them. The group has learned: 

They agree on the table of content of their report and distribute the writing-work among them. Claus should collect the contributions, merge them and send to Ana. She submits the report on the Friday afternoon to the supervisor.

Finally the group evaluates again how they have functioned with feedback to each other and on the group dynamics.

After the group has adjourned the supervisor continues to log his observations.

An independent examiner will after two months individually discuss with each member on the basis of the reports they produced from the PBL-cycles.