Theory, Design and Tests on a Prototype Module of a Compact ...

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72 5. RADIOFREQUENCY MEASUREMENT result to be the same for all the cells. Each cell has a ∆fi with respect to the calculated mean value. After the measurement of the single frequencies, all the cells are staked together <strong>and</strong> the resulting fπ/2 <strong>and</strong> the stop-b<strong>and</strong> value are measured. This value is very reliable since it comes from a measurement over 30 cells 4 <strong>and</strong> the systematic error due to the pressure on the first <strong>and</strong> the last cells does not play a recognizable role. The modification to be done on the ring of the single accelerating half cavity is calculated to correct the following frequency error ∆f AC i + (fπ/2meas − fπ/2goal), where the fπ/2goal is the design frequency which takes into account all the difference with respect to the effective operating conditions. In this sense, the steps of correction make the dispersion around mean value smaller <strong>and</strong> also make the mean value approaching the goal frequency. For the coupling cavities, the correction takes into account also the measured value of the stop-b<strong>and</strong> ∆f CC i + (fπ/2meas − fπ/2goal) + ∆fSB, where ∆fSB is considered with its sign. In figure 5.4 the results after each intervention are shown. The dispersion is reduced to a part over ten thous<strong>and</strong> for a frequency error which is largely in the margin of intervention of the movable tuners available after the brazing. 2.3. Quality factor measurement. From the electromagnetic theory it is known that the quality factor can be defined as Q = f0 ∆f where f0 is the resonant frequency <strong>and</strong> ∆f is the positive difference between the two frequency at which the transmission coefficient is 3 dB lower than the resonant peak. Often, the network analyzer has already this function inside. It is worth noting that for this measurement the probes must perturb the cavity as little as possible, in order to get the correct value for the quality factor. Otherwise the probes drain power <strong>and</strong> the measurement is not correct 5 . In this sense, the measurement of the quality factor for the half cavity rested on the conductor plane is not so significant, since incorrect values could arise from imperfect contacts at the joints. At least, the measurement could not be repeatable <strong>and</strong> reliable. In this case, the measurement of quality factor is necessary only to be sure that the 4 Note that 30 is greater then the requested number of tiles (25) for a tank. But, of course, more than the needed tiles are produced in order to discard the worst ones. 5In this case the quality factor is said loaded. This concepts is explained in the last paragraph.
2. RF MEASUREMENT ON A SINGLE CAVITY 73 Figure 5.4. The dispersion of frequencies before <strong>and</strong> after two steps of machining on the rings for the accelerating <strong>and</strong> coupling half cavities in the tank #1. For the accelerating cavities the dispersion around mean value is reduced to roughly 1.5 MHz (left), whereas for the coupling cavities is less than 1 MHz (right). quality factor is sufficiently high to give the requested precision on frequency measurement. 2.4. Shunt impedance measurement. Although several techniques can be conceived to permit the direct measurement of the shunt impedance, indirect methods are preferred. In fact, the ratio between shunt impedance <strong>and</strong> quality factor Rsh/Q do not depend on frequency <strong>and</strong> losses but only on geometrical factors. This fact implies that the measurement of Rsh/Q is more reliable than the direct measurement of the shunt impedance. In fact, the cavity under test can be built with two half parts or with an half part rested on a conductor plane because the losses in the joints do not affect appreciably the distribution of the fields <strong>and</strong> therefore, the measurement of Rsh/Q. Then, if the measurement of a single prototype with a low quality factor is performed, one can use an electromagnetic simulator to
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UNIVERSITÀ DEGLI STUDI DI NAPOLI F
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ii CONTENTS List of Figures 105 Ack
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iv INTRODUCTION In the state of art
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2 1. INTRODUCTION TO THE HADRONTHER
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8 2. LINAC AND SCL ACCELERATORS par
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10 2. LINAC AND SCL ACCELERATORS wh
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12 2. LINAC AND SCL ACCELERATORS at
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14 2. LINAC AND SCL ACCELERATORS 2.
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16 2. LINAC AND SCL ACCELERATORS f
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18 2. LINAC AND SCL ACCELERATORS Fi
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20 2. LINAC AND SCL ACCELERATORS re
Page 29 and 30: CHAPTER 3 Design T
Page 31 and 32: 1. GLOBAL PARAMETERS OF THE ACCELER
Page 33 and 34: 2. ANALYSIS OF COUPLED CAVITIES 27
Page 35 and 36: 3. SINGLE CAVITY DESIGN 29 Spice ha
Page 37 and 38: 20mA 15mA 10mA 5mA 3. SINGLE CAVITY
Page 39 and 40: 3. SINGLE CAVITY DESIGN 33 • HFSS
Page 41 and 42: 4. BRIDGE COUPLERS DESIGN 35 4. Bri
Page 43 and 44: 5. COUPLING BETWEEN WAVEGUIDE AND B
Page 49: 5. COUPLING BETWEEN WAVEGUIDE AND B
Page 52 and 53: 46 4. CIRCUIT MODEL where the matri
Page 54 and 55: 48 4. CIRCUIT MODEL For the latest
Page 56 and 57: 50 4. CIRCUIT MODEL left side of th
Page 58 and 59: 52 4. CIRCUIT MODEL and</st
Page 60 and 61: 54 4. CIRCUIT MODEL Under this hypo
Page 62 and 63: 56 4. CIRCUIT MODEL matrix of the w
Page 64 and 65: 58 4. CIRCUIT MODEL For the derivat
Page 66 and 67: 60 4. CIRCUIT MODEL Remembering the
Page 68 and 69: 62 4. CIRCUIT MODEL the bars is pro
Page 70 and 71: 64 4. CIRCUIT MODEL is unitary, one
Page 72 and 73: 66 4. CIRCUIT MODEL 120 100 80 60 4
Page 74 and 75: 68 5. RADIOFREQUENCY MEASUREMENT Ri
Page 76 and 77: 70 5. RADIOFREQUENCY MEASUREMENT Fi
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Page 82 and 83: 76 5. RADIOFREQUENCY MEASUREMENT In
Page 84 and 85: 78 5. RADIOFREQUENCY MEASUREMENT me
Page 86 and 87: 80 5. RADIOFREQUENCY MEASUREMENT pe
Page 88 and 89: 82 5. RADIOFREQUENCY MEASUREMENT Al
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Page 105 and 106: Conclusions and Ou
Page 107: CONCLUSIONS AND OUTLOOK 101 Finally
Page 110 and 111: 104 BIBLIOGRAPHY [23] U. Amaldi, B.
Page 112 and 113: 106 LIST OF FIGURES 2.12 Drawing of
Page 114 and 115: 108 LIST OF FIGURES methods, in add
Page 116: 110 ACKNOWLEDGEMENTS Naples, Italy
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