The purpose of phasing linac klystrons is to transfer the maximum amount of energy from the klystron's RF output to a beam pulse in the linac. The process of phasing is a system of trial-and-error measurements used to empirically determine the phase-shifter position for that klystron which results in maximum energy being transferred.
A klystron's RF output forms a travelling longitudinal wave in the disk-loaded waveguide. Its amplitude with respect to time at a specified location is sinusoidal. The disk-loaded waveguide is designed so that the phase velocity of the RF (i.e. the traveling velocity of the wave crests) is equal to the speed of light.* Since the beam in the linac is highly relativistic, its speed is also c. Hence, if the beam pulse arrives at the beginning of an RF section "on crest" (i.e., when the RF amplitude there is maximum), it will stay on-crest as it travels through the length of that RF section. This is the case that results in maximum energy transfer from the RF to the beam.
The beam arrival time at a given RF section is determined by the timing system's interaction with upstream components. We can't delay a beam pulse at the start of an individual RF section until it corresponds to maximum amplitude of the longitudinal wave there. We must do it the other way around: adjust the phase of a klystron's RF output to correspond properly to the beam's arrival time at that waveguide section.
The klystron's output phase is directly dependent on the phase of the drive signal that is fed into the klystron from the subbooster. Before it reaches an individual klystron, however, the drive signal passes through a phase-shifter and attenuator unit called an I-Phi-A. The I-Phi-A's mechanism for phase shifting is a stepper motor-driven device called a FOX phase shifter.**
Each subbooster is also equipped with its own phase shifter, contained in the subbooster drive unit (SBDU) hardware chassis. This phase shifter can be used to move the phase of the subbooster output drive signal that feeds the eight klystrons in that sector. Consequently, moving this phase will move the phase of every klystron in the sector by the same amount.
It is important to understand that phase is a relative measure, not an absolute one. When we measure the phase of an RF signal from a subbooster or klystron, we do so with respect to a stable reference phase. In terms of how much energy is transferred to the beam in the linac, the only thing that matters is the phase of the RF in the disk-loaded waveguide with respect to the arrival time of a beam pulse there. It makes no difference at all how much or how little the RF is phase-shifted before that point. As an example, suppose we happen to know that the drive signal coming from a subbooster into a specified klystron is out-of-phase with respect to the beam arrival time at that klystron's waveguide section by +90 degrees. In theory, we could move the klystron's phase by -90 degrees to properly phase it. Or, we could phase-shift it by +270 degrees, or -450 degrees... the beam in the linac would never know the difference.
We could also choose to correct the mis-phasing of the klystron in the above example by using the subbooster's phase shifter to shift the klystron's incoming drive signal by +270 degrees. The problem with this solution is that in doing so, we would move the phases of all seven other klystrons in the sector by +270 degrees as well. So it is not a viable solution to move a subbooster's phase in order to maximize energy transferred to the beam from an individual klystron. And since the beam is impervious to how much or how little the RF is phase-shifted before it reaches the disk-loaded waveguide, there is no such thing as a "right" or "wrong" subbooster phase. There are only right and wrong klystron output phases.
That being said, there are times when we choose to simply phase a subbooster rather than phasing all eight klystrons in a sector individually. To do so, we vary the subbooster phase shifter in order to experimentally determine a "best" value. The best subbooster phase shift will be the one that averages out the individual mis-phasings of the klystrons, such that the sum of their energies transferred to the beam is highest. Even though the overall energy gain from the sector can be increased by this method, some klystrons in the sector will most likely end up more mis-phased with respect to the beam than they were when you started. Thus it will not achieve the maximum energy possible from the sector. Subbooster phasing is therefore only useful as a quick-and-dirty method for gaining some energy from a sector that is badly mis-phased. If you want to achieve the maximum possible energy from the sector, you must phase all eight klystrons individually. The subbooster phase is then simply an initial condition, and so it is automatically correct and there will be no need to change it.
When we phase a klystron, we are looking for the phase that gives the most energy to the beam in the linac. The phase of the klystron's RF output is directly dependent on the phase of the drive signal coming into the klystron. This drive signal comes from the subbooster, but before reaching the klystron, it can be phase-shifted by a FOX phase shifter inside the klystron's associated I-Phi-A hardware chassis. To change the klystron's [RF output] phase, we can change the position of the FOX phase shifter.
Like many other procedures, the best way to determine the optimal phase is by trial-and-error: manipulate the FOX phase shifter to move the klystron's phase around, and see what value gives the most energy to the beam. Since the RF amplitude is a sine function, by moving the phase around we should see the energy downstream of the klystron increase and decrease sinusoidally.
Unfortunately, we don't have a machine component that can simply detect a passing beam pulse in the linac and read out its energy in MeV. On the other hand, we don't actually need to know the beam's total energy for this process-- we only need to know its relative energy for different klystron phases, and look for the maximum. To do this, we can make use of the fact that beam pulses of higher energy are bent less by a given bending magnet. Consequently, beam position at a particular point in a bending region will vary according to energy. We can choose a BPM in a downstream bending region and sample the beam's position there for different klystron phases. The measured position will be sinusoidal when sampled over a large phase range.
If you display vector on an energy feedback, you will notice that its measurements, used to calculate the energy state, are simply BPM readings. That is because the feedbacks use the same method for determining the beam energy, as operators use for phasing RF. The feedback measures the beam's position in the plane of bending inside of a bending region. Consider the FFTB beam, which is bent downward into the FFTB tunnel. The energy feedback looks at the beam's y-position on a BPM in the downward bending region. If the beam's position measures too positive in y, then it is being under-bent, so its energy is too high, and the feedback will lower its energy. If the y-position has a negative offset from optimal, the feedback will raise the energy.
Depending on the location of the klystron we wish to phase, we must choose a BPM to sample in a downstream dispersive region. For klystrons in the first few sectors of the linac, the PEP extraction regions (where the LER and HER beams are bent out of the linac and into the bypass lines-- in sectors 4 and 10, respectively) are possible choices. The LI11 chicane is another option. For klystrons in sectors 11 through 19, the scavenger extraction region (where the scavenger beam is bent toward the positron vault) is a good choice. For klystrons everywhere after sector 19, the only beam that can be used is beamcode 3 (in the current setup). If the beam is being sent to the A-line or parked in the north arc, we can use the region in the BSY where it is bent out and away from the straight-ahead line. If beamcode 3 is going to the FFTB, we can use the dispersive region at the very end of the BSY where the beam is bent downward into the FFTB tunnel.
Once we've decided what dispersive region to use, there are two methods for choosing a particular BPM in that region to sample. One way is to use the online machine model to find a BPM at a point of high dispersion. Here is a basic example of how to do this (follow along on the SCP if you want to):
Suppose we want to choose a BPM in the scavenger extraction line to phase the RF in sector 15. From the SCP main index, go to the Model Systems index. Since we're using the scav beam, select beamcode 10. The region of interest to select will be the e- NRTL PTGT, which covers the area from the North Damping Ring ring-to-linac transport line up to the positron target. Then go on to the Model Application Panel. The model type should be TWISS. Select the model subsystem SCVEXT, and hit the Optics button. Refresh the loaded model using the Run DIMAD button. Toggle the SELECT TWISS PARAM button to ETA (which is dispersion), and hit the PLOT TWISS PARAM button. This will show a plot of dispersion in both x and y in the region we've selected. As you can see, the dispersion function is mostly flat; the only interesting part is at the end, in EP01 where the electrons are bent strongly toward the target. Go to the plot option panel. In the lower right, toggle the Axis button to x and the Mode button to Value. Then enter lower limits and upper limits that will zoom in the x-axis on the area of interest (say, 1850-2000). To make the plot use the values you enter, you must then toggle the Mode button back to Select, and then select both the Lower and Upper Limit buttons by clicking on them (toggle to white bars). Hit the plot button to the left to replot. Use the same process to zoom in on the y-axis to a useful scale. Next, we can change the plot to show BPM numbers along the x-axis. Toggle the PLOT MAGNET/UNITS button in the lower left-hand corner to UNITS. Then de-select any selected magnet types in the middle-right portion of the panel, and select only BPMS, then replot. We can see here that there are a number of good options of BPMs in EP01 with high dispersion (175, 185, 190, 210, etc.) Any of these should work, and of course, it can't hurt to sample more than one.
Another good way to find an appropriate BPM to sample is to see which one is being used by the energy feedback in that region. For example, if you display the vector for the scavenger energy feedback, you can look for BPMs that have large values in x, such as 175 and 185. Recall that these two also showed up as high-dispersion using the model). These are probably good choices. You can also go to the feedback calibration and diagnostic panel and display the feedback's measurement matrix, to see exactly which BPMs are being used for the calculation of the energy state, and what their coefficients are. Some energy feedbacks use just a single BPM, and others use several.
The above method of using a BPM as the sample variable requires that the energy feedback in a region be put to Compute. Consequently, when we change the beam energy by moving a klystron phase, its trajectory through the rest of the accelerator will be affected. Thus it will be quite disruptive to any program using beam that passes through that area if the klystron is active on that beamcode. An alternative method that should cause minimal disruption to programs is to leave the energy feedback on, and instead of sampling a BPM, use the energy feedback's command value as your sample variable. As we move the klystron out-of-phase, the feedback's measurement will show less energy, and the feedback will therefore add energy to keep the state equal to its setpoint-- so its command will be increased. At the optimal klystron phase, the feedback will measure maximum energy, and its command will be at a minimum.
Here are some tips for setting up a correlation plot to phase a klystron. The step variable will be the klystron's FOX phase shifter. Your sample variable will either be one or more BPMs you have chosen (feedback-off method) or an energy feedback's command value (feedback-on method).
The FOX phase shifter has control system secondary name KPHR. For example, if you want to phase klystron 12-4, your primary step variable entry would be KLYS LI12 41 KPHR. The subbooster step variable is entered the same way, but the unit number is always 1; for example, SBST LI12 1 KPHR. The phase shifter is controlled in units of degrees. In other words, a range of -180 to +180 should correspond to one full period (360 degrees) of the klystron or subbooster's phase.
There are two schools of thought on how big of a phase range to use. One is to use a very large range (one or more full periods worth). You can then fit the resultant data with a sine function. The other method is to scan over only a small range (maybe 60 degrees total or so). In this case, you must first be in the vicinity of the optimal klystron phase. The resulting data should then be essentially parabolic. Fitting the data with a parabola in correlation plot has the notable advantage of allowing the user to "Accept Best Value", which will move the step variable actuator (in our case, the FOX phase shifter) to the position that corresponds to the parabola's max or min.
If you're using the feedback-off method, it's a good idea to sample more than one BPM, since the correlation plot will take the same amount of time no matter how many you sample, and you can simply choose the one that worked best. An example of the database structure for entering a BPM as a sample variable would be BPMS EP01 175 X. If you're using the feedback-on method, note that you must add sufficient settle time for the feedback to converge at each step of the phase shifter. It is a good idea to sample both the feedback command and its state; the state should be consistent (flat) across the span of data points. If it isn't, then the feedback either became maxed at some point or was not able to converge in the alloted time, and you must fix the problem by adding a klystron upstream (don't forget to LEM), or adding more settle time.
As is true for most applications of correlation plot, your data will be more accurate if you factor in some averaging at each step. If you're using BPMs, you can use the BPM/TOROID AVRG option to tell it how many readings to take per sample. Or, you can simply enter TIME as a secondary step variable. The Range button will then prompt you for the number of steps (which defines how many data points will be collected at each step of the primary step variable), and the increment of time between samples, in seconds.
The klystron phase display summary button on the SCP shows several phase-related readback values for the subbooster and klystrons in that sector: PRAW, PPAD, GOLD, GOLD+MSTR, PHAS, PDES, PCON, and P-SHFTR.***
The phase of a klystron or subbooster is measured by a phase-and-amplitude detector (PAD). For klystrons, the PAD pickup is located just after the SLED cavity on the RF output. For subboosters, it is on the subbooster's output drive signal. The phase measurement from the PAD is displayed as PRAW, in terms of raw counts. The PAD software then converts this measurement into degrees, displayed as PPAD.
P-SHFTR represents the phase shifter's postion in terms of degrees. The FOX phase shifters have a maximum range of 720 degrees. If a phase shifter is close to its outer limit, its position can be centered using the FOX HOME button on the klystron's Diagnostic panel. A phase trim will then move the phase shifter to the nearest appropriate value to correct the station's phase.
The PAD's measurements are output to the klystron or subbooster's PIOP module, which processes the measurements along with the Gold value and a MSTR measurement to determine the station's phase (PHAS) in degrees, and sends this value to the control system. MSTR is a measurement taken at an upstream location that is used to calculate a phase offset coming into the sector. This factor (which may be set to NONE, in which case its value is zero) is added to the Gold and displayed as GOLD+MSTR.
PDES, similar to BDES for magnets, represents the desired value of the phase for a particular station. When a station's Gold value is updated, PDES is automatically set to zero, to serve as a convenient reference value. When a phase trim is performed, the PIOP module compares the measured PHAS with the PDES, calculates how much the phase shifter must move in order to make PHAS equal to PDES, and sends the appropriate command to that phase shifter. PDES can be changed at any time via the SCP, either by typing in a value using the ENTER PDES button, or by assigning it to a knob. The PDES will then read a non-zero number until the station is re-golded.
The tolerance limit for a given station's phase is a database variable that can be set by the user on the Klystron Enter panel (but should normally never be changed). The tolerance limit can be seen on the PIOP DATA display for a given station. For most sectors in the linac, it is set to +/-2.50 degrees. The tolerance is set smaller for sectors in the beginning part of the linac, where phase is more critical because of the beam's relatively low energy. The VAX only requests a trim when the PHAS is out-of-tolerance with respect to PDES, and only if auto-trimming is enabled for that station. There is also the option to set the station to a TOUCH-UP mode, in which small auto-trims can be implemented, but are inhibited if the phase value is too far out-of-tol or the phase jitter value is too great. Since phasing a station involves moving its phase to different values, an auto-trim could potentially come through and mess up the process. In this case you might wish to disable auto-trim until you are finished. Its mode can be toggled from the Special Klystron Functions panel.
When phasing a klystron or subbooster, since your step variable is a phase shifter, the phase shifter position value is represented on the x-axis. If you are using the parabola-fit method, you can use the "accept best value" feature to automatically move your phase shifter to the best position. You can then set PDES to match the current PHAS at that location. This eliminates the danger of an auto-trim moving the phase back to its initial value. If you are unable to use "accept best value", then you must take note of the phase-shifter's best position and, using the phase display, change PDES and trim until the phase shifter is in the proper position. When you have set PDES to the ideal phase value for the station (or all stations in the sector), you want to re-gold that station or sector to zero the PDES at this place. From the main klystron index, go to the *New* K Gold panel, and from there to the OLD KLYS Gold panel. In the lower right, hit the button that says UPDATE GOLD ONLY, and follow the prompts to re-gold the proper station or sector.
* Interestingly, in a plain cylindrical waveguide, the phase velocity is actually greater than c. The disk-loadedness of the disk-loaded waveguide is what slows down the phase velocity to make it equal to c. An explanation of this phenomenon can be found in some accelerator physics texts.
** For more information on the I-Phi-A, FOX phase shifter, SBDU and other RF-related hardware, see the Linac RF site.
*** More information on phase-related database variables is available here.
This document is illustrated with photos my father took in Baja, Mexico.