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Beam bunch length measurement for the ARIEL e-LINAC Vrielink, Alysson Jan 16, 2013

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Beam Bunch Length Measurement forthe ARIEL e-LINACAlysson VrielinkSponsor: Robert LaxdalENPH 479Engineering PhysicsThe University of British ColumbiaProject Number 1269January 16, 2013Executive SummaryThe following document presents measurements conducted to determine andmanipulate the beam bunch length in an electron linear accelerator at TRIUMF?snew ARIEL facility. This method uses a radiofrequency resonant cavity that oper-ates in a mode with transverse electromagnetic fields on axis. These fields deflectelectrons by a magnitude dependent on the phase of the radiofrequency fields atthe arrival time of the electron. Therefore, it is possible to convert the spread ofelectrons after the deflection to a profile of the beam in the time domain beforeit reached the deflecting cavity.This relationship between bunch length and vertical spread after the deflectingcavity requires that certain properties of the cavity be measured. In particular, theeffective shunt impedance must be known, a parameter that gives the relationshipbetween input power and effective cavity voltage. To obtain this measurement,we look at the effect of the deflecting cavity on the beam and compare this withresults obtained from simulations using a 3D beam dynamics program, GeneralParticle Tracer. Preliminary results suggest the effective shunt impedance of thedeflecting cavity is 0.81 M?, however this should be confirmed with further datacollection.In addition to beam bunch length measurements, this project characterized thebunching cavity, a radio-frequency resonant cavity designed to focus the beam inthe time domain. Using the bunching cavity in conjunction with the deflectorcavity, we were able to measure the nominal bunching power for optimal focusingat the deflecting cavity to be 48.5W. When compared with computer simulations,the shunt impedance of the buncher was calculated to be 0.326M?. Thiis shuntimpedance can be used to determine the input power required for optimal tem-poral focusing of the beam at any point along the beamline. This is important asa focused bunch is highly desirable for downstream users.As these results are only a first estimate, it would be useful to do furtherdata collection to confirm these values and obtain error bounds. In addition,the computer simulations could be improved by using more recent estimates ofthe input beam characteristics (standard deviation of the bunch in the x, y andz directions, beam energy, etc...). Having obtained the most accurate resultspossible for the shunt impedance of the deflecting cavity, a final recommendationwould be to develop a program that can rapidly analyze images of the beam afterthe deflector and output the beam bunch length.1Contents1 Background and Motivation 71.1 The ARIEL Project . . . . . . . . . . . . . . . . . . . . . . . . . . 71.1.1 The e-LINAC . . . . . . . . . . . . . . . . . . . . . . . . . 81.2 Beam Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.2.1 Bunch Length Measurement . . . . . . . . . . . . . . . . . 91.2.2 The Deflecting Cavity . . . . . . . . . . . . . . . . . . . . 91.2.3 Bunch Energy Spread Measurements . . . . . . . . . . . . 111.2.4 The Buncher Cavity . . . . . . . . . . . . . . . . . . . . . 121.3 Beam Dynamics Simulations . . . . . . . . . . . . . . . . . . . . . 131.4 Project Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . 141.5 Project Scope and Limitations . . . . . . . . . . . . . . . . . . . . 152 Discussion 172.1 Experimental Set-Up and Data Collection . . . . . . . . . . . . . 172.1.1 Beam Optics . . . . . . . . . . . . . . . . . . . . . . . . . 172.1.2 Experimental Procedure . . . . . . . . . . . . . . . . . . . 182.1.3 Data Analysis and Results . . . . . . . . . . . . . . . . . . 202.2 Beam Dynamics Simulations . . . . . . . . . . . . . . . . . . . . . 252.2.1 General Set-Up . . . . . . . . . . . . . . . . . . . . . . . . 252.2.2 Input Parameters . . . . . . . . . . . . . . . . . . . . . . . 272.2.3 RF Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . 272.2.4 Running the Code . . . . . . . . . . . . . . . . . . . . . . 292.2.5 Simulation Results . . . . . . . . . . . . . . . . . . . . . . 303 Conclusions 354 Project Deliverables 375 Recommendations 386 Acknowledgments 39A Buncher Cavity Power Calculations 41B Beam Optics Settings for Data Collection 45C Experimental Procedure 492D GPT Code 523List of Tables2.1 Input Parameters for the GPT Simulation . . . . . . . . . . . . . 282.2 Comparison of GPT output and experimental results at DB1 forthe deflecting phase . . . . . . . . . . . . . . . . . . . . . . . . . . 324List of Figures1.1 An overview of the E-LINAC project . . . . . . . . . . . . . . . . 71.2 A diagram of the injector line for the ARIEL e-LINAC . . . . . . 81.3 The deflector cavity installed in the injector line . . . . . . . . . . 101.4 Effect of the Dipole Magnet- Small Energy Spread . . . . . . . . . 111.5 Effect of the Dipole Magnet- Large Energy Spread . . . . . . . . . 121.6 Buncher Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1 The experimental set-up. . . . . . . . . . . . . . . . . . . . . . . . 182.2 The Collimating Slits . . . . . . . . . . . . . . . . . . . . . . . . . 192.3 Effect of the Deflector Cavity on the Beam at DB1 . . . . . . . . 202.4 The rotated y centroid position (in pixels) as the deflector phase isscanned. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.5 Effect of the Bunching Cavity on the Beam at DB1 . . . . . . . . 222.6 The rotated x centroid position (in pixels) as the buncher phase isscanned. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.7 Effect of bunching on the deflector induced vertical smear at DB1 242.8 The rotated y length (in pixels) as the buncher phase is scanned. . 252.9 The rotated x length (in pixels) as the buncher setpoint is increased. 262.10 The GPT User Interface . . . . . . . . . . . . . . . . . . . . . . . 272.11 The simulated trajectory of the beam before the dipole. Note thesignificant loss of particles due to the collimators in place. . . . . 292.12 The simulated trajectory of the beam starting at the dipole. Notethe effect of the dipole, bending the beam by 90?. . . . . . . . . . 302.13 GPT Simulation Results: Effect of the deflector on screen outputat DB1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.14 GPT Simulation Results- Effect of the buncher operating in thebunching phase on the screen output at DB1. . . . . . . . . . . . 335List of AbbreviationsTRIUMF TRI-University Meson FacilityARIEL Advanced Rare IsotopE LaboratoryVECC Variable Energy Cyclotron Center (Kolkata, India)e-LINAC Electron Linear AcceleratorGPT General Particle Tracer (3D Simulation Software)DB1 Diagnostic Box 1RF Radio-FrequencySRF Superconducting Radio-FrequencyNIM Non Intercepting MonitorFFC Fast Faraday CupERL Energy Recovery Linac (Cornell)GUI Graphical User InterfaceBPM Beam Profile MonitorFC Faraday CupHP Slit High Power Slit6Chapter 1Background and Motivation1.1 The ARIEL ProjectTRIUMF, Canada?s national laboratory for particle and nuclear physics, is en-tering an exciting new phase with the upcoming completion of the Advanced RareIsotopE Laboratory (ARIEL) project. This facility will triple TRIUMF?s currentcapability for producing rare isotope beams used by researchers in fields rangingfrom astrophysics to materials engineering to particle physics, as well as in cancertreatment and radiation therapy. This will be accomplished by the installation ofa 50MeV, 10mA continuous wave electron linear accelerator (e-LINAC) that willoperate using highly efficient superconducting radiofrequency technology1.Figure 1.1: An overview of the E-LINAC project1http://www.triumf.ca/ariel/e-linac71.1.1 The e-LINACThe first stages of the e-LINAC project are already well under way as TRIUMFworks with collaborators from the Variable Energy Cyclotron Center (VECC) inKolkata, India to commission the injection line. This injection line will be used toemit and accelerate the electrons up to relativistic speeds necessary for optimalacceleration in the superconducting resonant cavities. As pictured in figure 1.2,the injector consists of a thermionic electron gun (on the far left), followed byseveral devices to focus and steer the beam, as well as diagnostic devices to de-termine beam characteristics. The electrons are emitted from the electron gun inbunches with a length that depends on the cathode bias of the gun. Electronswill only be emitted from the gun when the sinusoidal RF gun voltage is higherthan the cathode bias. This phase window is called the conduction angle.From the gun, the beam proceeds downstream until it reaches the dipole mag-net, shown as a rotated green box in figure 1.2, where depending on the stateof the magnet, the beam will either be bent 90? into the analyzing leg of theinjection line, or will continue straight through to the end of the line. While thebeam currently stops at a beam dump on the far right, as other stages of theaccelerator are completed, the beam will continue through to the next stage (i.e.the accelerating cavities).Figure 1.2: A diagram of the injector line for the ARIEL e-LINAC81.2 Beam DiagnosticsApart from ensuring the beam is of a high enough energy, an important con-sideration for accelerator engineers is the quality of the beam reaching the down-stream users. Diagnostic devices are interspersed along the injection line thatallow us to measure characteristics of the beam such as the cross sectional distri-bution of the beam in the x?y plane and the average beam current. Characteris-tics that are not as easy to measure include the temporal distribution of the beamas well as its canonical conjugate, the energy distribution of the beam. Havinga beam that is focused in time and with small energy spread is as important asobtaining a small cross sectional area.1.2.1 Bunch Length MeasurementWith a bunch length on the order of 85 picoseconds long, it would require avery high resolution device to analyze the beam in the time domain. There aredevices installed in the beamline that are capable of very high sampling rates, suchas a fast faraday cup which outputs a current proportional to the rate of electronshitting the cup. This current is converted to a voltage and sampled by a high speeddigital oscilloscope. Another possible method of determining the bunch length isusing a non intercepting monitor (NIM) that picks up the harmonic content ofthe beam. From this signal, one can measure not only the bunch length, but alsothe phase of the electrons in the bunch relative to the gun RF phase. Both ofthese options have been tested in conjunction with an RF bunching cavity thatfocuses the beam in the longitudinal direction (i.e shortens the time spread of thebunch). Unfortunately, the fast faraday cup does not produce a reliable signalwithout very high beam current, while the NIM installed in the injector can notsample quickly enough to give anything other than the average phase content ofthe beam.1.2.2 The Deflecting CavityFortunately, there is a third device that has been designed specifically forthese measurements. Pictured in green and labeled RF Sweep in figure 1.2, thelow power, room temperature deflecting cavity is a resonant cavity that deflectselectrons depending on their arrival time. The transverse electromagnetic fieldsinside the resonant cavity have a time dependence, resulting in the electrons expe-riencing different forces depending on the RF phase of the cavity when the electronenters. Essentially, this device maps from the time domain to the space domain,where we already have several high resolution devices capable of measuring thebeam position and profile.The deflecting cavity for the ARIEL e-LINAC, pictured installed in the ana-lyzing leg of the injector line in figure 1.3, was commissioned over the summer.However, to utilize the cavity as a means of determining the bunch length mea-surement, we must know the relationship between the arrival time of an electron9Figure 1.3: The deflector cavity installed in the injector lineat the cavity, and its position in the x? y plane at the diagnostic box on the endof the analyzing leg (pictured in blue in figure 1.2). This relationship depends onseveral factors, including the RF characteristics of the deflecting cavity, the inputpower to the cavity, the energy and position of the beam when it reaches the cav-ity and the focusing elements in place after the cavity. Indeed, the relationship issignificantly complicated by a solenoid focusing element in between the deflectorand the measurement point (shaded in red); this solenoid is necessary to collimatethe beam before the diagnostic box but couples the x and y elements of the beamtrajectory. This results in a rotated x-y axis after the solenoid, evident on thescreen at DB1.The main characteristic of the deflecting cavity that needs to be determinedto obtain the relationship between vertical spread and bunch length is calledthe shunt impedance of the cavity. This gives us the relationship between inputpower to the cavity (known), and the effective voltage of the cavity (unkown). Ifwe know the effective deflecting voltage, we can determine the energy impartedto an electron in the y direction, and from this we can get a relationship betweenvertical spread and bunch length. Theoretically, this value can be calculated fromRF simulations using programs such as CST Microwave Studio, however due todifferences in the actual constructed cavity and the computer model, the shuntimpedance needs to be measured.10Pcavity =V 2Rsh(1.1)1.2.3 Bunch Energy Spread MeasurementsWe have discussed how to obtain the bunch length of the electron beam, but asmentioned, the energy spread of the beam is equally important. This is also ameasurement that is difficult to obtain using standard diagnostic devices, but aclever method of measuring energy spread has been built directly into the accel-erator design. The analyzing leg has specifically been placed at a 90 degree angle,with a dipole magnet used to direct the beam.The magnet will bend the trajectoryof the electron with a radius of curvature given by equation 1.2, where B is themagnetic field of the dipole magnet, m0 is the rest mass of an electron and q isthe charge of an electron.R = ?m0?cqB (1.2)Depending on the energy of the electron (represented by ? in equation 1.2),the radius of curvature of the electron will change and thus the trajectory afterthe dipole magnet will be related to the electron?s energy before the dipole. Inparticular, because the magnet is bending the beam in the x direction, an energyspread before the dipole magnet will map to a spread in the x direction afterthe dipole. Similarly to the deflector cavity mapping from the time domain tothe space domain (y direction), the dipole magnet is mapping from the energydomain to the space domain (x direction). Figures 1.4 and 1.5 demonstrate thisconcept, showing simulations of a beam going through the dipole magnet withand without a large energy spread.Figure 1.4: A beam bending through the dipole magnet with small energy spread.The y axis represents the x direction, and the x axis represents the z direction(direction of travel of the beam after the dipole).11Figure 1.5: A beam bending through the dipole magnet with energy spread 100times larger than in the previous figure. The spread in the x direction (y axis) ismuch larger after the dipole.Therefore, we can measure the spread in the x direction using the diagnosticbox at the end of the analyzing leg, represented by a brown rectangle in figure1.2, and use this measurement to determine the energy spread of the beam beforeit reached the dipole magnet.1.2.4 The Buncher CavityThere is one final element in the injector beamline that is very important whenconsidering both the time and energy spread of the beam. The buncher cavity,depicted in figure 1.2 by the first green rectangle on the left, is a radiofreqencyroom temperature resonant cavity that is designed to focus the beam bunchesin time. It does this by slowing down electrons at the front of the bunch andaccelerating electrons at the back of the bunch. This is accomplished using asinusoidal RF field, such that depending on the time of arrival of the electron, itwill experience a different phase of the RF as it passes through the resonant cavity.For the buncher to properly focus, it must be operated at the correct phase,as shown in figure 1.6, called the bunching phase. If operated ?90? away fromthe bunching phase, the bunch will experience a maximum net acceleration or de-celeration while if operated at 180? away from the bunching phase, fast electronswill be accelerated and slow electrons further decelerated causing an increase inthe time spread of the bunch (this is the debunching phase).It is important to note that in bunching the beam, the buncher reduces thespread in time but in doing so, imparts further energy spread in the beam. A moredetailed discussion of the buncher cavity RF and determination of the optimalbuncher power can be found in Appendix A.12Figure 1.6: A sinusoid depicting the fields in an RF bunching cavity. The middleof the bunch reaches the cavity at the zero crossing point while electrons arrivingat a later phase (lagging) undergo acceleration and electrons arriving at an earlierphase (leading) undergo deceleration.1.3 Beam Dynamics SimulationsIn the preceding sections, we have discussed the importance of knowing thetime and energy spread of our bunched beam as well as the tools required to con-vert these parameters into the space domain, where they can be measured. Thesetools consist of the deflecting cavity and a dipole, used to map from the time andenergy domains respectively. We also have access to a buncher cavity designed tofocus the bunch in the time domain at the expense of increasing the energy spread.As we can see from figure 1.2, the aforementioned devices are not the onlyelements acting on the beam. There are also focusing solenoids, magnetic steerersand collimators used to remove electrons that are too far from the center of thebeam in the radial (x-y) direction. All of these devices will affect the beam profileand must be taken into account when determining the time and energy spreadfrom the y and x spread of the beam.As the factors mentioned above depend on design parameters unique to thee-LINAC, there is clearly no off-the-shelf solution to this problem but rather amodel must be derived from first principles where possible, and the results ofcomputer simulations. Fortunately, while the exact beam optics set-up is unique,modeling beam dynamics is a common problem and there are numerous 2D and3D computer simulations to model beam dynamics [5, 2]. In addition, the use of13deflector cavities is fairly common in accelerator engineering and there are severalpapers discussing methods of measuring the longitudinal beam profile from thedeflection of the individual particles. The TRIUMF e-LINAC deflecting cavity isbased off a design used by Cornell which has considerable documentation ([1, 4, 3])regarding bunch length diagnostics and beam dynamics using the code, GeneralParticle Tracer (GPT) 2.While the codes already exist, it is not necessarily straightforward to solve forthe trajectory; all of the input parameters must be defined, and if more than onecode is necessary to simulate the multiple features in the beamline, it will be nec-essary to merge the simulation results. As the parameters also change dependingon the operating conditions (beam current, beam energy, etc...) this model mustbe versatile, with the option to easily adjust such parameters. For this project,the RF fields for the buncher and deflector cavities were simulated using CST Mi-crowave Studio, and then these fields were used in a GPT simulation that modeledthe entire injection line up to the diagnostic box at the end of the analyzing leg.This beam dynamics simulation in GPT can be used to compare with resultsobtained experimentally, and useful information regarding the RF cavities as wellas beam characteristics can be obtained.1.4 Project ObjectivesThe main purpose of this project is to provide accelerator engineers and down-stream users of the ARIEL project with a rapid and straightforward method ofdetermining the electron beam bunch length of the e-LINAC. This will be in theform of a MATLAB program that takes input parameters such as the RF charac-teristics and input power of the deflecting cavity, and the current of the solenoid.It will then uses the raw data obtained from the diagnostic box after the deflectorcavity to output the bunch length.There are varying degrees to which this program can be implemented, withthe final objective being a one-click solution where the program interfaces withthe existing framework to obtain all required input parameters and measurementdata. However, the scope of this project will be limited due to time constraintsand most likely will not reach that level of functionality.The following list shows what this project expects to accomplish by the middleof January, 2013:2http://www.pulsar.nl/gpt/14USER INPUTS? Deflector Cavity Shunt Impedance,Q factor and Input Power? Solenoid Current? RF Gun Voltage (Initial electronenergy)? Field of the bending dipole magnet? Conduction Angle? Beam position measurements afterthe deflectorPROGRAM OUTPUT? The length of the bunch ?5 ps? The energy spread of the bunch ?1keV? A profile of the beam in the timedomain, in the form of a graph ofbeam current vs. longitudinal po-sition (if possible)1.5 Project Scope and LimitationsThe preceding section outlined the intended project objectives, however as theproject progressed it became clear that this would be well beyond what could beaccomplished by one individual given the time constraints at hand. In addition,while the original objectives focused only on the deflector cavity, the final projectincludes analysis of the bunching cavity as well.Although the computer application described above ended up being outsidethe scope of this project, significant progress was made in characterizing the RFcavities of the injection line so that it would now be possible to continue withsuch a program. Several of the following accomplishments were required beforethe primary objective, given in section 1.4, could be addressed. There are alsoseveral that pertain to the bunching cavity which were not included in the originalproject scope.? Determined the optimal beam optics set-up for measuring the time andenergy spread of the beam bunches? Developed operating procedures for the buncher and deflector cavity? Worked on the experimental set-up (the injection line) so that data couldbe collected. This was more involved than was expected, and due to sev-eral projects underway in the VECC area, it was difficult to maintain theexperimental set-up in the configuration necessary for our data collection.? Provided quantitative and qualitative evidence that the buncher and deflec-tor cavity were working as expected? Determined the RF characteristics of the buncher and deflector cavity asinstalled in the injection line including power losses through the input cables15and the shunt impedance of the cavities, which is the most important qualityin determining the relationship between effective voltage and input power? Developed, in collaboration with members of the beam optics group andcollaborators from VECC, a model of the injection line in General ParticleTracer, a 3D computer simulation software.16Chapter 2Discussion2.1 Experimental Set-Up and Data CollectionTo fully characterize the RF devices (buncher and deflector), we needed tolook at their effect on the beam. This was done by running beam in the injectionline and comparing the output of the diagnostics at various RF power levels andphases. The buncher and deflector were tested separately, looking solely at theeffect of one while the other was turned off, and then finally the deflector was usedin combination with the buncher to determine the nominal bunching power. Fig-ure 2.1 shows the injection line, highlighting the RF devices that were adjusted,as well the diagnostic box where the data was collected; we chose this diagnosticbox, DB1, as it is the only one that placed after all of the devices in question,including the dipole magnet.2.1.1 Beam OpticsWhile eventually the intent is to use the buncher and deflector to adjust andprobe the beam, for this experiment we are essentially doing the opposite, usingthe beam to probe the RF devices. As such, the first aspect of setting up the ex-periment was to tune the beam optics (devices used to steer and focus the beam)so that the beam had a very small emittance (tightly focused) before the deflectorcavity. This is necessary for several reasons; in particular, if the beam isn?t tightlyfocused as it passes through the deflector, electrons far from the reference trajec-tory will see fields that are considerably different than the on axis fields. This willskew the results obtained at DB1. In addition, if we are trying to compare thebeam spread in the x and y directions after the deflector, we want these values tobe very small so that the effect of the deflector will be more noticeable.We obtained a tightly focused beam by adjusting the solenoid settings (solenoidsare shown in red in figure 2.1) and by placing two collimators in the beamline be-fore the dipole magnet. These collimators consist of a thin strip of metal with twoslits at 90 degree angles, and a small hole with a 1mm radius, as shown in figure2.2. The collimator is inserted into the beamline in such a way that it blocks thebeam, with a small portion of the beam passing through one of the slits or the17Figure 2.1: The experimental set-up.hole in the middle, depending on the position of the collimator. By placing thehole in the center of the beamline, we limited the beam size at the collimatingpoint to a radius of 1mm, blocking off any electrons that were further from thereference trajectory.The beam optics settings, i.e. the current drawn by the steering and focusingelements, were saved and are attached in Appendix B. Note that the dipolemagnet current setting is incorrect as it is no longer controlled by the VECC userinterface, but by an external power supply. The setting for the dipole magnetwas approximately 170mA, although this is not necessarily repeatable as workhas been done on the dipole magnet since the data was collected.2.1.2 Experimental ProcedureHaving completed the experimental set-up, data collection could begin. Datawas collected on several occasions, and this data was used to ensure the buncherand deflector were properly connected and the low level RF was functioning cor-rectly. The data collected earlier in the project was also used to develop a finalexperimental procedure, answering questions such as how the beam should beset-up and whether or not the focusing solenoid after the deflector was necessary.The project supervisor, Bob Laxdal, wrote the majority of the final experimentalprocedure, however I have attached it in Appendix C for completeness. I havealso revised this experimental procedure to accurately reflect the process usedduring the most recent round of data collection on November 26, 2012, which is18Figure 2.2: Depending on the depth of insertion (collimator enters on a 45 degree),the beam will pass through one of the slits or the hole, reducing the beam size tothe shape of the collimating slit or hole.the primary data set that will be discussed in this report.Summarizing the experimental procedure, the first goal is to set up the beamcorrectly, as discussed in the previous subsection. The deflector can then be setup with the buncher off; this includes finding an input power that provides a rea-sonable vertical smear on the screen at DB1, and determining the phase whichproduces no deflection, and max deflection (0 degree phase). Having set up thedeflector it should be turned off and the buncher can be configured, which includesdetermining the accelerating and decelerating phases, at 90 degrees to the bunch-ing and debunching phases. The bunching phase can be determined by turningon the deflector at the predetermined operating power and deflecting phase, andidentifying the buncher phase at which the vertical spread is minimized. Theoptimal bunching power, at which point the beam is maximally focused in timeat the deflector, can be determined by slowly increasing the buncher power anddetermining the point at which the vertical spread in the beam at DB1 is mini-mized. At some point the beam spread will start increasing because the buncheris overfocusing in which case the beam is optimally focused in time at a pointcloser to the buncher than the deflector. Using the analogy of the human eye,overbunching is equivalent to nearsightedness, with the eye focusing light beforethe retina.Data was collected with the deflecting cavity at a forward power of 17W. Con-sidering the 3dB loss in the input cable this actually corresponds to a cavity inputpower of 8.52W. This is less than the expected nominal power of around 20-50Wdepending on bunch length, which is probably due to the time spread being muchgreater than expected as the gun was not specifically set-up to output a beam withshort bunch length. Space charge would also increase the amount of deflectionobtained at a given input power and bunch length.The conduction angle (bunch length) could have been reduced by increasingthe cathode bias. In our case, we ran the cathode bias at 101V, while it has beenoperated at voltages exceeding 240V. For this test, however, a small time spreadwas not needed as we were solely interested in measuring it, which is possible19(a) Beam with no RF deviceson(b) The deflector at maximumdeflecting phase (0?)(c) The deflector at the peakamplitude phase (90?)Figure 2.3: Effect of the Deflector Cavity on the Beam at DB1as long as the bunch length is significantly less than one period of the deflectorRF. The buncher was then turned on, with the deflector off, to a forward powerof 15W. Accounting for the 1dB loss in the input cable, this corresponded to acavity power of 11.9W. The bunching phase was identified, and with the deflectoron at 8.5W forward power, the nominal power could be determined. The collecteddata was then analyzed, and the results are discussed in the following subsection.2.1.3 Data Analysis and ResultsThe Deflecting CavityAs discussed in the introduction, the purpose of the deflector cavity is to mapfrom the time domain to the space domain; we therefore expect that by turning thedeflector on, the vertical spread of the beam will increase significantly, reflectingthe fact that the bunch is spread out in time. This was very clearly demonstratedin the collected data with the deflector on at 8.5W. Figure 2.3 compares picturesof the beam at the screen at DB1 with and without the deflector on (in all casesthe bunching cavity is off).Note that in this figure, particularly 2.3(b), the spread is not perfectly in they direction but on an angle. As mentioned in section 1.2.2, the focusing solenoidafter the deflector cavity rotates the x-y axes. While the spread induced by thedeflector is really only in the y direction, it appears on an angle because of theeffects of the solenoid. Through image processing of the data collected for thedeflector and buncher in Matlab, it was determined that the coordinate system isrotated by approximately 36 degrees with the solenoid operating at 1.3A.Figure 2.3 also demonstrates the effect of the deflector operating phase on thebeam. As explained earlier, it is because the RF fields have a sinusoidal timedependence that the deflection is a function of time, and this is what providesthe spread in the y direction. However, this also means that average deflectionseen by the bunch will be a function of the RF phase at which the center of the20bunch reaches the deflecting cavity. In figure 2.3(b) the deflector is operating suchthat the middle of the bunch reaches the deflector at the 0 degree phase so thecenter electrons experience no net deflection. Comparatively, in figure 2.3(c) thedeflector is operating such that the middle of the bunch reaches the deflector atthe 90 degree phase. At this point, there isn?t much spread in the y directionbecause the top of a sinusoid is relatively flat (ie, electrons at the extremities ofthe bunch experience very similar fields to the center of the bunch). As a whole,the bunch experiences maximum deflection, which explains why we see a relativelyfocused beam with y centroid at a maximum distance from the y centroid withthe deflector off.The phase dependence is clearly illustrated in figure 2.4, where the rotated(solenoid coupling taken into account) y centroid of the beam is plotted as afunction of deflector phase offset. In this figure the phase is relative to the electrongun RF, so is somewhat arbitrary. Clearly from this plot we can identify thatthe maximum deflecting phase (0 degree) occurs at approximately -90? and 100?according to the low level RF phase relative to the electron gun. Note the lowlevel RF period isn?t exactly 360? as it should be, meaning that changing thephase by 1 degree on the user interface changes the actual RF phase by slightlyless than 1 degree.Figure 2.4: The rotated y centroid position (in pixels) as the deflector phase isscanned.21(a) Beam with no RF deviceson(b) The buncher at a nonaccelerating (bunching or de-bunching) phase(c) The buncher at an acceler-ating phaseFigure 2.5: Effect of the Bunching Cavity on the Beam at DB1The Bunching CavitySimilarly to identifying the deflecting phase of the deflector cavity, the firstobjective when running the buncher was to determine the bunching phase, as de-picted in figure 1.6. The effect of the buncher on the beam at the screen at DB1is shown in figure 2.5. Figure 2.5(b) is clearly one of the non accelerating phases(either the bunching or de-bunching phase), but we cannot determine which with-out operating the deflector as the image does not give us any information aboutthe time spread.We can identify the phase as being fairly close to the non-accelerating phasebecause the x centroid is in approximately the same position as the x centroidwith the buncher off, which is what we?d expect when the buncher is operatingat a zero crossing point. Because the slope of a sinusoid is maximum at the zerocrossing point, we would also expect to see a beam that is very wide in the xdirection as the spread in energy imparted by the buncher is greater at this phase.This larger energy spread manifests itself as a horizontal smear due to the effectof the dipole (section 1.2.3). Once again, due to the solenoid coupling, the axesare rotated, so the smear actually appears on an angle of around 36 degrees.Contrasting the non accelerating phase, figure 2.5(c) shows the beam when thebuncher is operating in one of the maximum accelerating phases. We can mostlikely identify this as the maximum deceleration phase because the center of massis on the left of the reference beam (figure 2.5(a)), suggesting the beam had asmaller radius of curvature than the reference trajectory. From equation 1.2, thisimplies the beam had a lower energy. Another trait of the maximum acceleratingphases is that the spread in energy imparted by the buncher will be significantlyless because the slope of a sinusoid is at a minimum when the amplitude is at amaximum. In comparing the beam in figure 2.5(c) with figure 2.5(b), we can seethat there is significantly less spread in the rotated x direction.22The sinusoidal dependence of the x centroid position on the buncher phasewhen the electrons arrive at the cavity can be seen quantitatively in figure 2.6. Wecan identify the non accelerating phases from the fitted curve with more accuracythan by looking solely at the images. These phases occur at the intersect of thered and blue lines, at approximately 180? and -10?. These are not 180 degreesapart, as we would expect, which is due to the fact that there is clearly a slightconstant offset, such that the average of the buncher x centroid position is notquite the same as the the centroid position of the reference beam. The actual nonaccelerating phases are therefore closer to 175? and -5?.Figure 2.6: The rotated x centroid position (in pixels) as the buncher phase isscanned.Having identified the non accelerating phases, the deflector needed to be turnedon to determine the bunching phase. When collecting the data we used -98 de-grees as our deflecting phase, which is very close to the -90 degree deflecting phaseidentified in figure 2.4. Therefore, in determining the bunching phase and nominalbuncher power, we turned the deflector on at a power of 17W forward (8.5W withlosses) and phase of -98? . We were then able to identify that the buncher phasewas approximately ?20?, close to the -5? expected from figure 2.6. The effect ofturning on the buncher at a forward power of 14.2W (cavity power of 11.3 W afterinput losses) is shown in figure 2.7.23(a) Beam with no RF deviceson(b) Deflector at 8.5W and -98? (c) Deflector at 8.5W and -98? and buncher at 11.3W and?20?Figure 2.7: Effect of bunching on the deflector induced vertical smear at DB1Keeping in mind that the solenoid is still rotating the axes, we can see thatthe buncher has significantly decreased the vertical smear evident when only thedeflector is on, in figure 2.7(b). However, in doing so, the x spread of the beamhas increased, as expected due to the increased energy spread imparted by thebuncher cavity. This reciprocity between reducing the time spread and increasingthe energy spread is due to what is known as Liouville?s theorem, which statesthat the phase space volume of a system of particles is constant in time. As timeis the canonical conjugate of energy, by decreasing the spread in time, Liouville?stheorem implies there must be an increase in the spread in energy.Having determined the bunching phase, the final step was to identify the nom-inal bunching power. This was done by keeping the deflector and buncher at thesame settings described above, but by slowly increasing the buncher power, takingscreenshots of the screen at DB1 throughout. The nominal bunching power willbe the point at which the spread in time of the bunch is at a minimum, implyingthe length of the beam in the y direction is also minimized. Using Matlab toconduct image processing on the data collected, figure 2.8 was produced, showinga minimum in the y spread at a setpoint of approximately 450, correspondingto a buncher power of 61.1W (48.5W including losses). Returning to Liouville?stheorem, figure 2.9 shows a maximum in the energy spread (x spread at DB1) atthe same setpoint.From this analysis, it is clear that the experimentally determined nominalbunching power is approximately 48.5W ? 5W. Compared to the theoreticallycalculated nominal power of 5W, determined in Appendix A, this is significantlyhigher. There are several factors that contribute to the increased actual buncherpower. Space charge makes it more difficult to focus the beam as the electrons arerepelling each other. In addition, the trajectory of the electrons depends on theenergy imparted by the buncher and the time of arrival at the deflector will varydepending on the path the electron takes (this is not considered in my theoreticalanalysis). Finally, the fact that there is already energy spread in the beam when it24Figure 2.8: The rotated y length (in pixels) as the buncher phase is scanned.reaches the buncher is not taken into account in the theoretical analysis, but couldplay a role in increasing the required bunching power. An electron that reachesthe buncher first will probably have a higher energy, so even in slowing down theelectron, it won?t be going as slow as an electron arriving early but with the sameenergy as the center electrons, which is what was assumed in my calculations.2.2 Beam Dynamics Simulations2.2.1 General Set-UpGeneral Particle Tracer (GPT) was used to simulated the beam, starting atthe beginning of the injection line and going all the way to the diagnostic boxat the end of the analyzing leg, DB1. It was necessary to simulate the entire25Figure 2.9: The rotated x length (in pixels) as the buncher setpoint is increased.beamline because the output on the screen at DB1 is not only a function of thebuncher, dipole magnet and deflector cavity, but also the various other elementsin the beamline. The effects of one element on the beam will propagate down theentire line and must be considered.GPT is a software package to study 3D charged beam dynamics in electromag-netic fields. The package consists of the GPT executable, which does all of thenumber crunching, as well as various pre- and post-processing tools to analyzeand display the data. In particular, the Windows version includes a graphicaluser interface to facilitate running the batch files and viewing the results whichare stored in a custom binary file.26Figure 2.10: The GPT User Interface2.2.2 Input ParametersTo determine the beam profile at the output we must first enter the beamcharacteristics as the electron bunch leaves the gun. This includes the averageand standard deviation in the x, y and z directions of the beam, which is assumedto be a Gaussian distribution of particles. Instead of writing the standard devi-ation in z, however, in the GPT simulation the distribution of the beam is givenin time instead (which is related to z by the speed of the electrons). The initialtime spread of the beam depends on the experimental settings, and was about 16degrees of 650MHz, or 68ps, in our experiment. We also need to know the averageand standard deviation in the momentum in the x, y and z direction, and finallythe normalized emittance in the x and y directions, Nx and Ny, a measure ofthe area of the beam in phase space.Unfortunately, a simulation of the electron gun output at 85keV and with themost recent modifications to the gun design has not been conducted, so insteadthe input parameters listed below are for a 100keV beam, with a slightly smallercathode than the gun currently has. Table 2.1 describes the input parametersused in the GPT model.2.2.3 RF FieldsIn the GPT simulation, there are pre-defined elements that can be used tomodel resonant cavities with time dependent, user defined fields. We used theseelements for the buncher and deflector cavities, obtaining the field profiles from27Table 2.1: Input Parameters for the GPT SimulationName Value UnitConduction Angle 16 ?x 0 mmy 0 mmt 0 ps?x 0 -?y 0 -?z 0.5147 -?x 0.621286 mm?y 0.619437 mm?t 68 psNx 1.32 mm-mradNy 1.30 mm-mrad?E 0.293365 keVRF simulations done using CST Microwave Studio. The fields obtained from CSTMicrowave Studio are normalized to a cavity energy of 1J. We want to multiplythese fields by a field multiplication factor based on the actual cavity energy. Thiscan be determined using equation 2.1.RshQ =V 2?U (2.1)The geometry factor for the deflecting cavity is Rsh/Q = 196?. Thereforethe cavity voltage for an energy of 1J is V1J=1.79MV. Similarly, for the bunchercavity the geometry factor is Rsh/Q = 167? and the cavity voltage for an energyof 1J is V1J=1.65MV.Our field multiplication factor, F, used in the GPT simulations is then givenin terms of the cavity power as:F =?Pcav ?RshV1J(2.2)282.2.4 Running the CodeHaving modeled all of the relevant injection line optics elements in the GPTsimulation, it was necessary to set up the simulation exactly as it was in the actualbeam loaded tests. This involved placing collimators at the appropriate points inthe simulated beamline, and setting the solenoid magnetic fields based on thesolenoid current settings used.Having done this, the code was run with the input parameters outlined in sec-tion 2.2.2 and unfortunately, on average only 0.7% of the simulated beam madeit past the first two collimators. This also occurred when doing the beam loadedtesting, however it caused a greater problem in the simulations, as to obtain astatistically meaningful result at the end, the number of initial particles requiredwas too great to simulate in a reasonable timeframe.This problem could be avoided by running the experiment in two stages. Thefirst stage goes from the start of the beamline to the start of the dipole. The out-puts from this stage, beam statistics at the start of the dipole magnet, are thentransferred via a MATLAB script to another batch script which uses the results asthe model for a much larger distribution of particles. This new distribution actsas the input of the second stage of the simulation which extends from the start ofthe dipole to the end of the analyzing leg. See Appendix D for the GPT code used.Figure 2.11: The simulated trajectory of the beam before the dipole. Note thesignificant loss of particles due to the collimators in place.29Figure 2.12: The simulated trajectory of the beam starting at the dipole. Notethe effect of the dipole, bending the beam by 90?.2.2.5 Simulation ResultsDeflector CavitySimulations were first done using solely the deflector cavity, some results ofwhich are shown in figure 2.13. Comparing with figure 2.3, we can see that quali-tatively, we have the same beam shape and orientation in our GPT screen outputas in the output from the real screen at DB1. This very promising result confirmsthat the model we are using for the experimental set-up in GPT matches fairlyclosely the actual set-up.One significant difference between reality and our simulation is that the de-flector cavity model in GPT uses the theoretical shunt impedance, and what wewant to determine is the effective shunt impedance of the cavity as installed inthe beamline. If we can obtain this, we will know the relationship between inputpower and the effective voltage of the cavity (equation 2.3).Veff =?Pin ?Reff (2.3)This, in turn, will provide the relationship between the beam bunch lengthbefore the deflector, and the measured vertical spread at DB1:?y = f(Veff ,?t) (2.4)To obtain this effective shunt impedance, we need to find the simulated de-flector cavity power that gives us the same magnitude of vertical spread at DB130(a) Beam with no RF devices on(b) Deflector at 8.5W, at the deflecting phase(c) Deflector at 8.5W, 90? from the deflectingphaseFigure 2.13: GPT Simulation Results: Effect of the deflector on screen output atDB131as was measured in the real injection line. By running simulations at several dif-ferent powers, it was determined that the simulated input power which producesthe closest results was 16.8 W. Table 2.2 compares the beam parameters at thevirtual (GPT) screen and the real screen.Table 2.2: Comparison of GPT output and experimental results at DB1 for thedeflecting phaseName GPT Experimental UnitInput Power X 8.5 W?y 4.3 4.3 mm?x 1.0 1.1 mmKnowing that an actual input power of 8.5W corresponds to a theoretical inputpower of Psim = 16.8W, and that the theoretical shunt impedance for a ? = 0.51electron of the deflector is Rsim=1.6M? (1P definition), we can determine theeffective shunt impedance of our actual cavity using the relationship in equation2.5. This gives an effective shunt impedance of 0.81 M?.PinReff = PsimRsim (2.5)There are several reasons that the effective shunt impedance of our cavity ismuch lower than our theoretical shunt impedance. The geometry of the cavityis slightly different from the cavity model used in GPT, which is mainly due toadjustments made when tuning the cavity to the correct resonant frequency. Thequality factor of the cavity is also much lower than the theoretical value of 10,000 and was last measured as 5400.While I have not calculated error bounds for this value as it is a first estimateand we would require more data to obtain proper error bounds, it is important topoint out that this number will never be quite accurate either, due to differences inthe beam parameters in real life and in the GPT simulation. While I tried to copythe experimental set-up exactly in GPT, there will undoubtedly be differences,resulting in the input voltage of the cavity needing to be slightly different to getthe same deflection. However, this estimate should be a reasonable starting pointfor further data collection.The Buncher CavityFigure 2.14 demonstrates some results from the GPT simulation with the de-flector turned on and the buncher off, at nominal power, and finally at a higher32(a) Buncher OFF(b) Buncher at 10.2W (Nominal Power)(c) Buncher at 35WFigure 2.14: GPT Simulation Results- Effect of the buncher operating in thebunching phase on the screen output at DB1.33power. We can see that at the nominal power, the spread in the y direction isminimized, and then moving to a higher power, the vertical spread is increasedagain, reflecting the fact that the buncher is over-focusing.We have already determined experimentally what the nominal buncher poweris for optimal focusing at the deflector. By comparing this nominal bunchingpower with the value determined using the GPT simulation, we can determine theeffective shunt impedance of the bunching cavity, exactly as was done with thedeflector cavity in the preceding section. This was determined to be 10.2W?1.6Win the GPT simulation. The error in this number could be reduced with furthersimulations.Comparing this value with our experimentally determined value of 48.5W, thisis significantly lower. This discrepancy arises from several factors, including thefact that space charge (the repulsion between like charges) is neglected in the cur-rent GPT model. This will have a large effect on bunching as more power will berequired to focus the electrons when space charge is considered. Similarly to thedeflector, there is also the fact that the actual RF characteristics of the buncher(Q factor, geometry factor) are not the ideal values used in the GPT simulation.Finally, with the values for the actual and simulated input power required foroptimal bunching, we can determine that the effective shunt impedance of thebunching cavity is 0.326 M? using equation 2.5 again. Knowing the effectiveshunt impedance, we can use this to determine the input power required to obtainoptimal focusing (minimized bunch length) for any point along the beamline.Once again, there are no error bounds provided on this value, as not enoughdata is available. However, this value can now be used to focus further data col-lection in the right range of buncher input powers.34Chapter 3ConclusionsThis project set out to measure the beam bunch length for the ARIEL electronlinear accelerator. This required determining the RF characteristics, in particularthe effective shunt impedance, of the deflector cavity which in turn provides arelationship between vertical spread after the deflector and bunch length. In ad-dition, work was done to determine the effective shunt impedance of the bunchingcavity, so as to provide a relationship between the optimal focusing distance andinput power.To accomplish these objectives, a significant part of this project was settingup the experimental apparatus. This involved adjusting the settings of the beamoptics and RF devices in the injection line, as well as inserting collimators toobtain a tightly focused beam at the diagnostic box used for data collection. Theexperimental procedure was provided by Bob Laxdal, the project sponsor, andwas then adjusted as the data collection proceeded. Both the experimental set-upand procedure developed during this project will be useful when taking furtherdata collection. In addition, the tools developed while analyzing the data suchas the GPT simulation, will be relevant for future work on this project as well asother projects relating to the injection line.Having collected and analyzed the first round of data, the effective shuntimpedance of the deflecting cavity as installed in the beamline was determinedto be 0.81M?. This is significantly different than the ideal shunt impedance of1.6M?, but this is expected due to differences in the computer model of the de-flector and the actual deflector cavity. Error bounds are not available for thisvalue, but can and should be obtained by collecting more data points. The valueobtained for the effective shunt impedance can then be used to determine therelationship between vertical spread at DB1 and bunch length. This will allow usto use the deflector cavity as a powerful diagnostic device, giving us the lengthof the beam bunch in the injection line. Such a measurement is important foraccelerator engineers in optimizing the acceleration and focusing of the beam, aswell as to downstream users who require this type of information when conductingtheir experiments.The effective shunt impedance of the buncher cavity was determined to be350.326M?, compared with a simulated (theoretical) value of 1.55M? for a ? = 0.51particle. The discrepancy in this value is expected not only due to differences inthe ideal buncher and the buncher as installed in the beamline, but also due tothe absence of effects such as space charge in the current GPT simulation model.The repulsion between electrons will mean that we expect to obtain a lower shuntimpedance as it is harder to focus the electron bunch. We can use this valuefor the shunt impedance to determine the power required for optimal focusingof the bunch at any point in the beamline, allowing us to provide small, tightlyconcentrated bunches of electrons to users downstream, a desirable quality in abeam.36Chapter 4Project DeliverablesThe following deliverables are to be transferred to the project sponsor. Notethat the results obtained are a first estimate, and should be confirmed with furtherdata collection (see chapter 5).1. Effective shunt impedance of the buncher cavity2. Effective shunt impedance of the deflector cavity3. General Particle Tracer simulation code and results4. The raw experimental data collected5. All other plots, images and animations resulting from the data collectionand analysis6. A final report documenting the project, including recommendations for fu-ture work37Chapter 5RecommendationsWhile a significant amount of work has been accomplished in the last four months,there is still much to do to obtain a robust program for beam bunch length mea-surement, as well as to fully characterize the bunching cavity, necessary for optimaltemporal focusing of the bunch. Now that the groundwork has been laid, futurework can build on this to solidify the results obtained and apply them in a usefulmanner.1. One of the main objectives achieved during this project was the developmentof the experimental set-up and procedure. In conjunction with the dataanalysis tools developed during the project (GPT simulations, MATLABscripts, etc), this has greatly facilitated data collection and analysis. Withthe framework in place, this project is at the stage where more data shouldbe collected to confirm the results obtained, and set error bounds on thesevalues.2. The GPT input beam parameters are not actually up to date, and were ob-tained using an older gun design. While it was assumed that the differencesin beam characteristics would be small, it would be beneficial to obtain themost up to date results from the electron gun simulations.3. The original objective of this project was to produce a computer programthat could analyze an image and in combination with user input of some ofthe RF and beam parameters, the program would output the beam bunchlength. The results of this project have brought us much closer to this objec-tive by characterizing the RF cavities involved and providing a relationshipbetween the spread in time and the vertical smear after the deflector. Thenext step would be to use these results in developing this program.4. As part of the analysis, it would be convenient to determine the relationshipbetween the current of the solenoid after the deflector, VLBT1 SOL1, andthe rotation of the beam axes. This may not be possible if this relationshipdepends on the beam properties, but it could be worth investigating. Inparticular, if this relationship were determined, it could be used in conjunc-tion with the new feature in the viewscreens that allows the user to rotatethe images obtained.38Chapter 6AcknowledgmentsThis project is part of a much larger goal to characterize the entire VECC injectionline, and as such I had the opportunity to work with several accelerator physicistsand engineers at TRIUMF while completing this project. I would like to thank allof these individuals for the incredible amount of assistance and guidance I receivedand acknowledge their crucial role in the completion of this project. Withouttheir contributions, from characterizing the solenoids to helping me take data toreviewing my work, I could not have completed any of this. In particular, I wouldlike to thank:? Bob Laxdal, head of the superconducting RF group at TRIUMF, who hasbeen an excellent supervisor, providing inspiration and much guidance andexpertise throughout the project.? Chris Gong, graduate student at TRIUMF, who assisted in the collection ofdata and was always on hand to discuss questions pertaining to beam opticsand the GPT simulations.? Yu-Chiu Chao, beam optics researcher at TRIUMF, who is spearheadingthe initiative to characterize the VECC beamline elements and was thus animportant contributor to the project in providing the input parameters forthe GPT simulations as well as the models for some of the other beamlineelements.? Vladimir Zvagintsev, SRF Engineering at TRIUMF, designed the deflectorcavity and provided the electromagnetic field distribution results from RFsimulations of the cavity, which are necessary for the beam dynamics sim-ulations. He was also on hand to answer questions regarding the deflectorand buncher cavities.? Philipp Kolb, graduate student at TRIUMF, has proven very useful forbouncing ideas off of and answering endless questions.I also greatly appreciated the support of the electrical, EPICS, and low levelRF groups at TRIUMF.39Bibliography[1] Belomestnykh, S., Bazarov, I., Shemelin., V. Sikora, J., Smolenski, K.,Veshcherevich, V. ? Deflecting Cavity for Beam Diagnostics at Cornell ERLinjector?, Nuclear Instruments and Methods in Physics Research A, vol. 614,2010, pages 179-183.[2] Fliller, R., Edwards, H., Ruan, J. ? Start to End Simulations of Transverseto Longitudinal Emittance Exchange at the A0 Photoinjector?, Proceedingsof EPAC08, Genoa, Italy, 2008, pages 3002-3004.[3] Mastuba, S., Honda, Y., Miyajima, T. ?Deflecting Cavity for Bunch LengthDiagnostics at Compact ERL Injector?, Proceedings of IPAC?10, Kyoto,Japan, pages 951-953.[4] Shemelin, V., Belomestnykh, S. ?RF Design of the De-flecting Cavity for Beam Diagnostics in ERL Injector?,http://www.lns.cornell.edu/public/ERL/2007/ERL07-2/ERL07-2.pdf, 2007.[5] Zhou, F., Adolphsen, C., Ding, Y., Li, Z., Vlieks, A. ? X-Band PhotoinjectorBeam Dynamics?, Proceedings of IPAC?10, Kyoto, Japan, 2010.40Appendix ABuncher Cavity PowerCalculations41Buncher Power DeterminationFor a buncher with shunt impedance, Rsh, and transit time factor, T0, we candetermine the approximate power required for optimal focusing after a given driftlength.In the operational mode, RF electric fields propagating in the buncher arein the z direction (direction of travel of the beam), and have a sinusoidal timedependence. We only want to operate in the ascending, linear region of the sinu-soidal wave, as depicted by figure 1. Electrons that are lagging behind the centerof the bunch will undergo positive acceleration, while leading electrons will bedecelerated.Figure 1: Operating RF Regime of Buncher CavityTo optimize the buncher we want the particles at the extremities of the bunchto undergo acceleration such that by the end of the subsequent drift, d, the beamis focused in the longitudinal direction. The particle at the center of the beamundergoes no acceleration, so ? = ?0. Let?s consider the voltage required for anelectron at a phase offset of ?0 (relative to the RF of the buncher) from the centerof the beam to reach the point d in the same time as the center of the bunch.Start by solving for the ? required. Initially the longitudinal spread is given by:?L = ?0?0? ?0c (1)Where ?0 is the resonant frequency of the bunching cavity. For ?L to be 0 by the1end of a drift, d, we need (assuming we are using a sin wave and that the middleof the bunch reaches the buncher at ? = 0):ttravel|?=0 = ?t+ ttravel|?0 (2)? d?0c= d?c +?0?0c?0?c(3)Solving for ? gives:? = ?0 +?0c?20?0d(4)Given ?, we can find the change in energy required:?EE =(?0?0)2? ? ?0?0=(?0?0)2?0?0c?0d(5)The change in energy of a particle in an electric field, ?E, in eV, is given by thevoltage, V . We can determine the required Veff , making the following approxi-mation as we are operating in the linear regime of the sinusoid:V = Veff sin?0 ? ?0Veff (6)? Veff =?E?0(7)? Veff = (?0?0)3E0c?0d(8)For our buncher, ?0 = 2pi ? 1.3E9, and with the current experimental setup,E0 = 511keV , ?0 = 0.5147, ?0 = 1.166 and our drift length is the distance fromthe buncher to the deflector cavity (where we are actually measuring the timespread, even if the result only shows up at the diagnostic box after the deflector).This distance is d = 1.53m, assuming a perfect trajectory (centered). Substi-tuting these values into equation 8, we find that our required effective voltage is2approximately 2.65kV.Having solved for the effective voltage, we need to convert this to the actualrequired cavity voltage, V0 which will depend on the transit time factor of thecavity, T0:V0 =VeffT0(9)? T0 =????E(? = 0, z) exp(i?0 z?c) dz????E(? = 0, z) dz(10)This transit time factor will depend on the speed of the electrons. Using equa-tion 10, and substituting in the values mentionned above, we obtain T=0.82 fora ? = 1 particle, and T=0.47 for a ? = 0.5147 electron.Finally, we can use the shunt impedance to find the required input power to thecavity. Note this needs to be divided by 2 if Rsh is given using the 2P definition.Pin =V 20Rsh(11)The shunt impedance for this buncher cavity (EMMA buncher) was determinedexperimentally to be 3.27M? using the 2P definition. Therefore, the nominalbunching power required for optimal focusing of the bunch at the deflector cavityis:Pin =V 202Rsh= (5.64kV)22 ? 3.27E6 ? = 4.87W (12)3Appendix BBeam Optics Settings for DataCollection45Time:     Mon Nov 26 19:00:57 2012Login ID: veccops (VECC Ops User)Eff  UID: 1372Group ID: 24Keywords: Comments: Type:     AbsoluteDirectory /epicsserver/usr1/local/epics/projects/veccReq File: /usr1/vecc/burt/vecc.reqRO VGUN:BIAS1:RDCUR.VAL 1 1.367208361943999e-02RO VGUN:BIAS1:RDVOL.VAL 1 8.505378805218586e+04RO VGUN:BIAS1:DRVBIT.RVAL 1 1.000000000000000e+00VGUN:BIAS1:VOL.VAL 1 8.500000000000000e+04RO VGUN:CHT:RDCUR.VAL 1 1.263980463980464e+03RO VGUN:CHT:RDVOL.VAL 1 6.520146520146520e+00VGUN:CHT:VOL.VAL 1 6.399999999999999e+00VGUN:CHT:CUR.VAL 1 1.485720000000000e+03RO VGUN:CATHB:RDCUR.VAL 1 2.122100122100122e+00RO VGUN:CATHB:RDVOL.VAL 1 1.015873015873016e+02VGUN:CATHB:VOL.VAL 1 1.000000000000000e+02VGUN:CATHB:CUR.VAL 1 5.042700000000000e+00RO VLBT:XCB1A:RDCUR.VAL 1 -6.843671320668346e-02RO VLBT:XCB1A:RDVOL.VAL 1 -3.854428931105516e-01RO VLBT:XCB1A:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:XCB1A:CUR.VAL 1 -5.999999999999989e-02RO VLBT:YCB1A:RDCUR.VAL 1 6.996261539635310e-02RO VLBT:YCB1A:RDVOL.VAL 1 1.657129777981231e-01RO VLBT:YCB1A:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:YCB1A:CUR.VAL 1 9.000000000000000e-02RO VLBT:SOL1:RDCUR.VAL 1 8.704509040970474e-01RO VLBT:SOL1:RDVOL.VAL 1 7.427786678873884e+00RO VLBT:SOL1:DRVBIT.RVAL 1 1.000000000000000e+00VLBT:SOL1:CUR.VAL 1 8.699999999999999e-01RO VLBT:XCB1B:RDCUR.VAL 1 -1.266498817425803e-02RO VLBT:XCB1B:RDVOL.VAL 1 -2.915999084458686e-01RO VLBT:XCB1B:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:XCB1B:CUR.VAL 1 -3.000000000000003e-02RO VLBT:YCB1B:RDCUR.VAL 1 -1.057450217441062e-01RO VLBT:YCB1B:RDVOL.VAL 1 -9.750514991989014e-02RO VLBT:YCB1B:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:YCB1B:CUR.VAL 1 -1.999999999999999e-02RO VLBT:SOL2:RDCUR.VAL 1 -1.358052948805982e-02RO VLBT:SOL2:RDVOL.VAL 1 -1.496910048065919e-01RO VLBT:SOL2:DRVBIT.RVAL 1 1.000000000000000e+00VLBT:SOL2:CUR.VAL 1 -1.000000000000082e-02RO VLBT:XCB2:RDCUR.VAL 1 1.149004348821241e-01RO VLBT:XCB2:RDVOL.VAL 1 4.623483634699016e-02RO VLBT:XCB2:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:XCB2:CUR.VAL 1 2.400000000000000e-01RO VLBT:YCB2:RDCUR.VAL 1 -5.630579079880980e-02RO VLBT:YCB2:RDVOL.VAL 1 -9.933623254749371e-02RO VLBT:YCB2:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:YCB2:CUR.VAL 1 -3.000000000000002e-02RO VLBT:SOL3:RDCUR.VAL 1 3.509575036240177e-03RO VLBT:SOL3:RDVOL.VAL 1 1.835660334172579e-01RO VLBT:SOL3:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:SOL3:CUR.VAL 1 2.999999999999958e-02RO VLBT:XCB3A:RDCUR.VAL 1 -8.158999008163577e-01RO VLBT:XCB3A:RDVOL.VAL 1 -5.699244678416113e-01RO VLBT:XCB3A:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:XCB3A:CUR.VAL 1 -9.350000000000003e-01RO VLBT:YCB3A:RDCUR.VAL 1 -2.186617837796597e-01RO VLBT:YCB3A:RDVOL.VAL 1 -1.661707484550240e-01RO VLBT:YCB3A:DRVBIT.RVAL 1 0.000000000000000e+00VLBT:YCB3A:CUR.VAL 1 -3.399999999999998e-01RO VLBT:FC0V:SCALECUR.VAL 1 0.000000000000000e+00VLBT:FC0V:GAIN.RVAL 1 1.000000000000000e+00VLBT:FC0V:RDVOL.SMOO 1 0.000000000000000e+00RO VLBT:FC1AV:SCALECUR.VAL 1 -6.347849971007416e-08RO VLBT:FC1A:STATON.RVAL 1 0.000000000000000e+00VLBT:FC1AV:GAIN.RVAL 1 6.000000000000000e+00VLBT:FC1AV:RDVOL.SMOO 1 0.000000000000000e+00RO VLBT:FC1B:STATON.RVAL 1 0.000000000000000e+00RO VLBT:FC3V:SCALECUR.VAL 1 4.882961516159551e-09RO VLBT:FC3:STATON.RVAL 1 0.000000000000000e+00VLBT:FC3V:GAIN.RVAL 1 1.200000000000000e+01VLBT:FC3V:RDVOL.SMOO 1 0.000000000000000e+00RO VLBT:BPM1A:X.VAL 1 -4.619000000000000e+00RO VLBT:BPM1A:Y.VAL 1 -2.793000000000000e+00RO VLBT:BPM1A:INTENSITY.VAL 1 6.808800000000001e+01RO VLBT:BPM1A:ERROR.VAL 1 0.000000000000000e+00RO VLBT:BPM1B:X.VAL 1 -3.011000000000000e+00RO VLBT:BPM1B:Y.VAL 1 -6.770000000000000e-01RO VLBT:BPM1B:INTENSITY.VAL 1 5.409800000000000e+01RO VLBT:BPM1B:ERROR.VAL 1 0.000000000000000e+00RO VLBT:IG1:RDVAC.VAL 1 1.248702831369807e-08RO VLBT:IG1:STATDRV.RVAL 1 1.000000000000000e+00RO VLBT:IG2:RDVAC.VAL 1 1.969070629206549e-08RO VLBT:IG2:STATDRV.RVAL 1 1.000000000000000e+00RO VLBT:IG3:RDVAC.VAL 1 9.999999999999999e-12RO VLBT:IG3:STATDRV.RVAL 1 0.000000000000000e+00RO VEMIT:IG1:RDVAC.VAL 1 5.252798246288538e-09RO VEMIT:IG1:STATDRV.RVAL 1 1.000000000000000e+00VLBT:BUNCH1:ASET.VAL 1 2.280000000000000e+02VLBT:BUNCH1:PSET.VAL 1 -4.621760000000000e+01RO VLBT1:MB0:RDCUR.VAL 1 4.531929503318837e-02RO VLBT1:MB0:RDVOL.VAL 1 4.206912336919204e-01RO VLBT1:MB0:DRVBIT.RVAL 1 0.000000000000000e+00VLBT1:MB0:CUR.VAL 1 0.000000000000000e+00RO VLBT1:YCB0A:RDCUR.VAL 1 1.525902189669637e-04RO VLBT1:YCB0A:RDVOL.VAL 1 4.577706569008910e-04RO VLBT1:YCB0A:DRVBIT.RVAL 1 0.000000000000000e+00VLBT1:YCB0A:CUR.VAL 1 0.000000000000000e+00RO VLBT1:XCB0B:RDCUR.VAL 1 -3.462272068360418e-01RO VLBT1:XCB0B:RDVOL.VAL 1 -2.623025864042115e-01RO VLBT1:XCB0B:DRVBIT.RVAL 1 0.000000000000000e+00VLBT1:XCB0B:CUR.VAL 1 -4.000000000000000e-01RO VLBT1:YCB0B:RDCUR.VAL 1 -3.341725795376516e-02RO VLBT1:YCB0B:RDVOL.VAL 1 -8.194094758525979e-02RO VLBT1:YCB0B:DRVBIT.RVAL 1 0.000000000000000e+00VLBT1:YCB0B:CUR.VAL 1 -1.263999999999994e-01RO VLBT1:SOL1:RDCUR.VAL 1 1.268482490272373e+00RO VLBT1:SOL1:RDVOL.VAL 1 2.271915770199130e+00RO VLBT1:SOL1:DRVBIT.RVAL 1 1.000000000000000e+00VLBT1:SOL1:CUR.VAL 1 1.300000000000000e+00RO VLBT1:FC0V:SCALECUR.VAL 1 0.000000000000000e+00RO VLBT1:FC0:STATON.RVAL 1 0.000000000000000e+00VLBT1:FC0V:GAIN.RVAL 1 2.400000000000000e+01VLBT1:FC0V:RDVOL.SMOO 1 0.000000000000000e+00RO VLBT1:FC1V:SCALECUR.VAL 1 0.000000000000000e+00RO VLBT1:FC1:STATON.RVAL 1 0.000000000000000e+00VLBT1:FC1V:GAIN.RVAL 1 4.800000000000000e+01VLBT1:FC1V:RDVOL.SMOO 1 0.000000000000000e+00RO VLBT1:IG1:RDVAC.VAL 1 1.465737388299312e-07Appendix CExperimental Procedure49Experimental Procedure- Deflector and Buncher RF Characterization Authors: Bob Laxdal, Alysson Vrielink, Chris Gong, Yu Chiu Chao November 26th , 2012  1. With the  RF deflector and RF buncher off establish a beam with low transverse emittance around the analyzing leg : a. Choose a relatively high cathode  bias to reduce the conduction angle (~100V)  and a high duty cycle (~10% -20%) . b. Align the beam and ensure it is parallel using DB1A and DB1B.   c. Insert the 1mm radius circular collimators (xy slits)  at DB1A and DB1B and use SOL1A, SOL1B and VLBT1:SOL1 to collimate the  beam ? optimize dipole magnet for maximum transmission to VLBT1:DB1 (~168mA) . The optics settings used on November 26 th , which proved effective, can be found using the save restore feature and loading 121126_1953 -vecc.snap.  d. With the collimators in, increase the RF lev el until high enough current is obtained at FC1 on the analyzing leg  but less than  1uA. e. Insert the screen at VLBT1:DB1. A djust VLBT1:SOL1 for best beam spot on the screen.  2. Setting up the deflector:  a. The LPM0  x -slit can be inserted (position at around 146.5mm) to select a certain energy slice if desired.  b. Turn on deflector to nominal power (see deflector operating procedure) at ~50 W , including the  3dB loss in input cable.  Scan phase to identify  the deflecting and non deflecting phase s using the screen. The non deflecting phase is the phase at which the y spread in the beam is minimized. Note: with VLBT1:SOL1 on, the x- y axis is rotated.  c. Scanning through t he phase, take screenshots every 30 degrees.  d. Repeat steps b) and c) for several power levels (although the deflecting phase should  be independent of input power). 3. Setting up the buncher:  a. Make sure the LPM0 x- slit isn?t inserted if the intent is to look at the effect of the buncher on energy spread of the beam.  b. Turn on buncher to nominal power (see buncher operat ing procedure) at ~48.5W, including the 1dB loss in the input cable.  Scan phase to  determine the accelerating and bunching phases. The accelerating phas e will be evident as the point where the x centroid of the beam is farthest away from the x centroid with the buncher off. The non accelerating phases should be when the beam is at approximately the same location with the buncher off.  c. To identify the bunch ing phase, turn on the deflector  at the deflecting phase . The bunching phase will show far less vertical smear than the debunching phase  if the buncher is close to the nominal power.  4. Determining the nominal buncher power  a. With the deflector tur ned on at the nominal power and at the deflecting phase, adjust the buncher setpoint, recording the FWD and REV power as read out by the power meter connected to the buncher. Determine the setpoint where the vertical smear is minimized.  5. Longitudinal Emittance Measurements  a. Use the LPM0 sli t to select a portion of the dispersed beam and use the deflector to measure the time spread b. For each slit position record profile with and without deflector on using the deflecting (0 degree) phase and power level determined in the initial set- up (step 2.) Appendix DGPT Code52################## Start bunch ####################### #   time=1.984e-09; #   setfile("beam","test.gdf"); #   settransform ("wcs","z",-0.140,"beam");      dtmax=1E-11;      omega=2*Pi*1.3*10^9;     ffac=8E3;      Eo=85;# energy in keV     G =(85+511)/511;     beta=sqrt(1-G^-2);     setparticles("beam",15000,me,qe,-6*10^-9);     setxdist("beam","g",0,0.000621286,2,2);     setydist("beam","g",0,0.000619437,2,2);     settdist("beam","u",0, 6.8E-11);     setGBxdist("beam","g",0,0.0113,2,2);     setGBydist("beam","g",0,0.01192,2,2);     setGdist("beam","g",G,0.293365/511,2,2);     SetGBxemittance("beam",2.5E-6);     SetGByemittance("beam",2.5E-6);  #Set solenoid field strength based on solenoid currents        sol1=1.03E-2;    sol2=2.24E-4;     ###################inputs#########################    zend = 1.26;#(1.26+0.15)    zdb1a=0.54123;    zdb1b=zdb1a+0.48173;    zdbvlbt10=0.34406+0.15;    zdbvlbt11=0.46196+0.51033+zdbvlbt10; ########################################################   ##################### elements############################       map1D_B("wcs","z",0.01926,"bNW.gdf","z","Bz",sol1);  #     BUNCHER: (COMMENT TO TURN OFF)       map1D_TM("wcs","z",0.59241,"bun.gdf","z","Ez",ffac,phi*Pi/180,omega);        map1D_B("wcs","z",0.91414,"bsol.gdf","z","Bz",sol2);  #     DIAGNOSTIC BOXES       rmax("wcs","z",zdb1a,1E-3,5E-3);       rmax("wcs","z",zdb1b,1E-3,5E-3);   #     screen("wcs","I",zdb1a-10E-3); #     screen("wcs","I",zdb1a);  #     screen("wcs","I",zdb1b-10E-3); #     screen("wcs","I",zdb1b);       screen("wcs","I",zend);       tout(0,1e-08,0.1e-09,"wcs"); ################## Start bunch #######################      #Set maximum step size     dtmax=1E-11; #Set field factor for deflector    ffac=2.9E-3; #  rfphase=phi;    rfphase=0;  #Set up beam at point right before dipole  avgGBx=avgBx*sqrt(1/(1-avgBx^2)); avgGBy=avgBy*sqrt(1/(1-avgBy^2)); avgGBz=avgBz*sqrt(1/(1-avgBz^2));  stdGBx=stdBx*(1/(1-avgBx^2))^3/2; stdGBy=stdBy*(1/(1-avgBy^2))^3/2; stdGBz=stdBz*(1/(1-avgBz^2))^3/2;  npar=10000;  #Assume on-axis      Eo=85;# energy in keV     G =(85+511)/511;     beta=sqrt(1-G^-2);      setparticles("beam",npar,me,qe,qe*npar);     setxdist("beam","g",0,stdx,2,2);     setydist("beam","g",0,stdy,2,2);     settdist("beam","g",0,stdt,2,2);     SetGBxdist("beam","g",avgGBx,stdGBx,2,2);     SetGBydist("beam","g",avgGBy,stdGBy,2,2);     SetGBzdist("beam","g",avgGBz,stdGBz,2,2);      SetGBxemittance("beam",nemixrms);     SetGByemittance("beam",nemiyrms);  #Set solenoid field strength based on solenoid currents        vlbt1sol=1.8E-2;     ###################inputs#########################    energy = 85; #in keV    gamma = (energy+511)/511 ; # value of gamma    zend = 1.26;#(1.26+0.15)    Rbend = 0.15; # radius of curvature of the dipole in m     angle = 90; # bending angle in degree    phiin =0 ; # entry cut angle    phiout = 0 ; # exit cut angle    dl = 0;# offset    b1 =0; # dipole fringe field coefficient    b2 =0; # ......do...................    zdb1a=0.54123;    zdb1b=zdb1a+0.48173;    zdbvlbt10=0.34406+0.15;    zdbvlbt11=0.46196+0.51033+zdbvlbt10; ########################################################    #We actually start at this point  # ---------------dipole magnet----------------------------------       beta = sqrt(gamma*gamma-1)/gamma ;       Bfield = -me*c*gamma*beta/(qe*Rbend) ;       ccs("wcs", 0,0,0.15, cos(angle/deg),0,-sin(angle/deg), 0,1,0, "bend");       sectormagnet("wcs","bend", Rbend, Bfield, 30/deg,30/deg, dl, b1, b2); #------------------------------------------------------------------  #      xymax("bend","z",zdbvlbt10,2E-3,1,5E-3);   #     DEFLECTOR: (COMMENT TO TURN OFF)      map3D_TM("bend", "z",0.51479,"TM.gdf","x","y","z","Ex","Ey","Ez","Bx","By","Bz",ffac,rfphase*Pi/180,2*Pi*1.3*10^9);   #     VLBT1 SOLENOID        map1D_B("bend","z",0.95602,"bsol.gdf","z","Bz",vlbt1sol);  #Switch co-ordinate frame again angle1=-30; ccs("bend", 0,0,zdbvlbt11, cos(angle1/deg),-sin(angle1/deg),0, sin(angle1/deg),cos(angle1/deg),0, "new");  #####################################################################################  #     screen("bend","I",zdbvlbt11);      screen("bend","I",zdbvlbt11,"new");      tout(0,1.2e-08,0.1e-09,"bend");  #screen("bend","I",zdbvlbt11); #tout(0,1.2e-08,0.1e-09,"bend"); 


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