Submitted by kcecire
on Monday, October 8, 2012 - 10:48
Development and utilities for the QuarkNet LHC fellows.
Tiny URL for this page: http://tinyurl.com/s2n-totemp.
Here is one way to use data from the TOTEM Experiment in the LHC to study wave properties.
The goal and why:
Students measure an upper limit to the diameter of the proton using proton elastic scattering data from the TOTEM Experiment. Because protons are quantum objects, they "interfere" with each other rather than simply bounce off as if there were marbles. We can use the interference pattern to determine an effective width, which we can think of as the closest approach the protons can make with each other and still collide elastically. Students use the same wave interference they see in optics!
What you'll need:
Create a histogram space on the wall or the black/whiteboard marked in 10's from -240 to +240 microrad.
There are 80 events, 2 per page, in the data file. Divide these among the students and then divide them into small groups.
Each student should find the scattering angle of both protons (shown as red and green dots) in each "Angular Topology" display they are given.
To find the scattering angle, follow the blue double-circle up or down from the dot the shortest way to the x-axis of the plot. Read the scattering angle in microradians - these are very small angles! Each display should show a positive and a negative scattering angle, usually very close in magnitude to each other. Record both in the tally sheet, rounding to the nearest multiple of 10 and making a mark next to that value.
When students are done measuring, they should put sticky notes the histogram using the same number of stickies as marks on their tally sheet for each angle.
When all of the data is in the histogram, what you get should look like an interference pattern with the middle cut out. The reason is that, in the LHC, this is where the proton beam is and the TOTEM detector cannot reach there without interference with the operation of the accelerator. Student should use the spacing of the remaining maxima they do see estimate the order (n=0,1,2,...) of one of them. Using that angle, they can use a simple interference realtion to estimate the width of the proton interaction area: d = nλ/sinθ.
To get wavelength λ, you can either:
- Use E = hc/λ with E= 4 TeV = 4 x 1012 eV (1 eV = 1.609 x 10-19 J), c = 3 x 108 m/s, and h = 6.63 x 10-34 Js to solve for the deBroglie wavelength of the proton, or
- Give the students the wavelength of 3.1 x 10-13 μm to use.
Also, you should note that sinθ = θ to an extremely good approximation for the very small angles used here. Then if you have figured out n and θ, you can simply use d = nλ/θ.
Expect the result to be greater than the accepted proton diameter.
Tiny URL for this page: http://tinyurl.com/s2n-rwr.
Here one way for a teacher to get Rolling with Rutherford rolling with his or her students.
The goal and why:
Students seek to find the diameter of a marble by indirect measurement. If a physicist wants to find the diameter of an atom in a crystal, for example, there is no question of using a ruler or a caliper. The atom is too small. Then she, like Rutherford, might fire particles at an array of those atoms and use numbers of hits and misses to figure out the size of the atom.
What you need:
For each student group, print 3 copies of the template. Cut out the crossed holes on one of these. Align and tape the pages together; fold the edges to make a barrier on each side. Back the holes with tape so the sticky side faces out through the holes. Tape the whole assembly down on a flat surface. Place a marble on each hole. The result should look something like the image to the right.
The places where the papers join should be completely taped over so that the path of a marble rolled from the beginning (where the single marble is in the image) to the end (past the 5 marbles) has as little obstruction to its course as possible,
You should also make a 0-10 horizontal axis on the wall, in a window, or on a chalk/whiteboard. Label the axis as the number of hits out of 10. This will serve for the histogram you will make.
Each student gets 10 rolls of the marble. He or she must take care to roll toward the 5 target marbles but must not aim. Misses are as valid as hits. When a taget marble is hit, it should be noted and the target marble returned to its place. The sticky-side-up tape should help. The student will get a score: the number of hits out of 10. The student should then take a sticky note and put it above her or his score on the histogram. Even if you have multiple groups working, all students put their scores on the same histogram. Get others to try, e.g. an administrator who happens to be passing by. You want statistics. If you do this activity in multiple classes during the day, let the histogram build over the course of the day.
Here is an example of building a histogram with a relatively small group in a workshop setting:
Note that, in the last frame, the group found a peak value of the number of hits out of 10. You should do the same with your students. Note also that the simplest version of calculation of the diameter of the target is used in the last frame. This does not take into account the size of the rolled marble: in workshop from which the images come, the group used targets much larger than the marble which was rolled. Thus, perhaps the simple approximation was acceptable. In our case, the target and the projectile are the same size.
To analyze the data, you need:
The probability of a hit from the point of view of the experimental data is P = n/10.
The probability of a hit for marbles of diameter D in the simple approximation above is
P = ND/L,
based on the fraction of distance L that is blocked by target marbles. Life is not that simple, of course, so we modify that equation based on what we know about the marbles and their collisions.
Looking at the diagram to the right, note that the center of the rolled marble can approach a target marble within a cross-section of 2D to make a collision. There are N target marbles, so the total target cross-section is N(2D). For the cross-section of the rolling area, the center of the rolled marble can get no less than D/2 from a side barrier; our actual rolling cross section is L-D. Thus we modify our original simple equation:
P = [N(2D)] / (L-D).
Set the probabilities from experiment and from calculation equal to each other, so
(n/10) = (2ND) / (L-D).
After some algebra,
D = Ln / (20N+n).
Do we "check" our result against a measurement made with a ruler? The physicist measuring those atoms has no such luxury. The indirect measurement is the measurement. Maybe we do, maybe we don't.
This page helps guide creation of a data workshop.
Request a Data Workshop for your group or institution by e-mail.
Data Workshops are workshops for teacher with physicists participating. They take a recommended 8-12 hours and are designed to be facilitated by a QuarkNet staff member or fellow. Data Workshops have been done both in and outside the U.S. with some success. For masterclasses, the Data Workshop provides the most thorough orientation for both teachers and mentors. Outside of masterclasses, they give teachers insights into how to bring particle physics data to their students in a way that enables them to start to look at the data as physicists might.
Please note that this document is subject to revision based on evaluation data.
- Teaching and Learning
Both objectives apply to all Data Worshops.
Teachers will be able to:
- expose students to the introductory physics concepts used in high-energy physics
- lead students in investigations using data from particle physics experiments.
Choose one of these depending on the flavor of the workshop, though others may apply as unstated objectives.
Participating teachers are able to:
- interpret event displays from ATLAS/CMS and explain their meaning (ATLAS or CMS)
- prepare students for and assist mentors in facilitating a masterclass (ATLAS or CMS)
- use and design activities that incorporate scientific inquiry. (Teaching and Learning)
Notes on objectives
- The Data Portfolio is not mentioned in this version of objectives but is incorporated as a key resource and organizing principle.
- Flavor-specific objectives are not mutually exclusive. For example, "use and design activities that incorporate scientific inquiry" can be a stated or unstated objective of a CMS Data Workshop.
- Some activities may go beyond the stated objectives but support and enhance them. For example, an ATLAS Virtual Visit may not give teachers additional skills toward doing activities with students but serve as an important affective link to the actual experiment and the people who perform it.
Coffee and Registration
Level 1 activity
Level 1 activity
Level 1 activity
Advanced Level 1 activity
Reflections and discussion
Coffee/Recap of First Day/Restate Objectives
Virtual Visit (Fermilab, CERN, or other)
e-Lab activity (Cosmic, CMS, or LIGO)
Discuss classroom impementation
Notes on Agenda items
- There are 3 standard Level 1 activities listed in the First Day.
- An example of an Advanced Level 1 activity might be Mass Calc Z. Another, not in currently in the Data Portfolio, is CMS Data Express.
- The number of Level 1 actviities of any type may vary.
- Masterclass and e-Lab are specficied here as they are main types of Level 2 and 3 activities.
- In this case, "e-Lab activity" can refer to a specific activity using an e-Lab, e.g. cosmic activities developed for the ILC workshops in Japan in June 2014.
- Data Portfolio
- PPT or PDF in support of workshop (e.g. Introduction/Objectives for CMS)
Additional workshop components
- non-Portfolio or activities (e.g., for now, CMS Data Express)
- Documents in support of related content (e.g. CERN Guide to LHC)
Additional resources for classroom
These may also be used in the workshop as enhancements. Examples include:
Are you ready to build an ATLAS or CMS masterclass at your institution? Are you just thinking about it? Start here.
The Project Chart shows the steps you need to take. Each major task has a link to a page with more information and resources.
The red bars show the recommended windows for completion of each task relative to the day of your masterclass.
|Descriptions||Images||Videos and animations||Downloads||Links|
Form student group
Organize student group
ATLAS detector slide
CMS detector slice
Tiny URL for this page: http://tinyurl.com/atlasde0.
ATLAS Data Express is a short particle physics masterclass investigation that can be used as part of a workshop or as a short class project. Participants examine static displays of a limited number of events. The main goal is to separate Z candidate events other events by visual inspection and then create mass plot for the Z boson.
The Z boson is important in LHC discovery science and as a marker for calibration of LHC detectors: it is a well-known particle, so the location and width of the mass plot give physicists a good idea of how the detector is performing. The Z candidate events we will study are "dimuon" events; the Z can decay into a muon-antimuon pair. Z candidates are identified by 2 long muon tracks; each will appear as a combination of a short blue track in the inner detector (inner black ring) and a longer orange track in the outer muon chambers (blue rings). Participants will search for Z candidates in the data.
Individual or pair:
- Participate in analysis prep seminar (slides) (ATLAS animation)
- Open the event display file
- Go to set of events assigned
- Categorize and record each event as
- Z → μ+μ- candidate (2 distinct muon tracks),
- background (anything else).
- For each Z candidate, note and record
- the mass, rounded to nearest odd number (found at upper right of event)
- whether it is an electron or a muon event.
- When finished, count how many instances of each odd number you have recorded.
Use your own resources to
- Combine numbers of "odd masses" in all groups.
- Create a histogram for whole group to observe.
- Analyze other aspects of the data (optional).
Help: Use the Google spreadsheet.
The histogram created by the group is a mass plot. Since the mass of any one type of particle is uncertain by nature and due to experimental uncertainty, it will have a distribution the peak of which is the experimental determination of the mass. Creation of mass plots and other histograms are the central measurements made in the CMS e-Lab but with many more events than used in this exercise.
- ATLAS or CMS virtual visit with an engineer
- Making it 'round the bend
- Design problem - getting to high field
- Calorimeter actvity
- Design problem - stopping high energy particles
- Testing activity (with ODUs? fiber? CRMD blessing and perf?)
- Tie together; discussion
Step 1: Analysis
Step 2: Discussion
- ILC home
- ILC public site (日本語)
- From design to reality
- ILC ニュ-ス (日本語)
- ILC in 2 minutes (video)
- Tohoku Big Bang (video, 日本語)