IPhO2001-THEO - IPhO2001 - theoretical competition...

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IPhO2001 - theoretical competition Theoretical Competition Monday, July 2 nd , 2001 Please read this first: 1. The time available is 5 hours for the theoretical competition. 2. Use only the pen provided. 3. Use only the front side of the paper. 4. Begin each part of the problem on a separate sheet. 5. For each question, in addition to the blank sheets where you may write, there is an a nswer form where you must summarize the results you have obtained. Numerical results should be written with as many digits as are appropriate to the given data. 6. Write on the blank sheets of paper whatever you consider is required for the solution of the question. Please use as little text as possible ; express yourself primarily in equations, numbers, figures, and plots. 7. Fill in the boxes at the top of each sheet of paper used by writing your Country No and Country Code, your student number ( Student No ), the number of the question (Question No) , the progressive number of each sheet (Page No), and the total number of blank sheets used for each question (Total No of pages). Write the question number and the section letter of the part you are answering at the top of each sheet. If you use some blank sheets of paper for notes that you do not wish to be marked, put a large X across the entire sheet and do not include it in your numbering. 8. At the end of the exam, arrange all sheets for each problem in the following order; answer form used sheets in order the sheets you do not wish to be marked unused sheets and the printed question Place the papers inside the envelope and leave everything on your desk. You are not allowed to take any sheets of paper out of the room.
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IPhO2001 - theoretical competition Question 1 1a) KLYSTRON Klystrons are devices used for amplifying very high-frequency signals. A klystron basically consists of two identical pairs of parallel plates (cavities) separated by a distance b , as shown in the figure. An electron beam with an initial speed v 0 traverses the entire system, passing through small holes in the plates. The high-frequency voltage to be amplified is applied to both pairs of plates with a certain phase difference (where period T corresponds to 2 π phase) between them, producing horizontal, alternating electric fields in the cavities. The electrons entering the input cavity when the electric field is to the right are retarded and vice versa, so that the emerging electrons form bunches at a certain distance. If the output cavity is placed at the bunching point, the electric field in this
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IPhO2001-THEO - IPhO2001 - theoretical competition...

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