MI Note 0257 Status and Issues for Main Injector Momentum and Tune Control Bruce C. Brown 2 June 1999 Present momentum and tune control in the Main Injector is an outgrowth of design efforts specific to the Main Injector combined with practices developed through the years of Main Ring operation. We seek to provide a design which in principle has complete control of the tune (no uncontrolled parameters which change the tune) and in practice we believe we need to (at least) control the difference between requested and achieved tune to about 0.003. We must achieve precise (and repeatable) momentum control for both low field and high field transfers but we have not identified reasons why those momenta must be accurate. The momentum broadcast by MECAR is used for control by the LLRF. It appears that the control range of this system is sufficient despite current large errors. We have not established goals for control of momentum but perhaps its effect on tune control will be the most limiting. We have found some problems which limit our ability to control tune. We have also discovered some problems in specifying the desired momentum ramp. I would like to outline these problems in conjunction with a status report which may help others to identify what we may expect to discover as further limitation. We include here a discussion of issues is followed by a specific list of questions which need to be addressed in improving the present momentum and tune control of the Main Injector. Momentum Control We specify momentum ramps on application page I2 by a series of time segments on which the derivatives of the momentum are specified (first, second, and third). These derivatives along with an initial value determine the dipole ramp. Continuity at the breakpoints is required for the values (continuity of the magnet current) and first derivative (continuity of the magnet voltage). Higher derivatives are permitted to have discontinuities. However, in the Main Ring, it was shown that the breakpoints between these segments were clearly observable looking only at beam measurements; the beam responded to discontinuities in the derivatives of the bend field. We concluded that smoother ramps were required. The currently implement solution involves calculating points from the ramp specification, sparsifying these points in I2 in a pattern thought to match the requirements, and passing these sparsified points to MECAR. In MECAR, a FIR filter smoothes these points before constructing the ramp (a sequence of points at 1440 Hz). For the nine months of commissioning, a low pass filter with a cutoff frequency of 20 Hz was used. In May 1999, it was noted that the learning bandwidth of MECAR was 15 Hz, so it seemed foolish to pass in data which is above the design bandwidth of the regulation system. The filter was modified to pass signals below 10 Hz. We had noticed that the momentum ramp was causing currents to change earlier than the time specified for the first parabola segment. At the time we were running $29 cycles which started acceleration at 0.5 seconds whereas the momentum started changing near 0.475 seconds. At that point, it was considered and implementation details of the FIR filter were discovered to be significant. We noted that the implementation used can be described as a convolution with a center delay of zero. Unlike real time FIR filters which must delay the signal, this algorithm symmetrically modifies the signal, causing about half of the change to occur before the breakpoints in the unfiltered signal. Moving the band pass down to 10 Hz makes the time span grow to about 100 ms (50 ms early and late)! Operationally we should expect difficulties and misunderstandings for everyone tuning due to the large disconnect between the specified ramp segments and the ramp which is created for MECAR regulation. In light of requirements to achieve rapid cycling of the Main Injector for such applications as pbar production, we recognize the demand to avoid excess time in ramp segments. The present FIR filter situation, when applied to a ramp designed with a 50 or 100 ms flattop segment will result in no significant flat portion of the current. This situation will demand attention before rapid cycling is required by the operations schedule. We can attempt to empirically determine FIR filter parameters which provide operationally satisfactory results. This may not satisfy the esthetic that unachievable requirements are not requested of the MECAR regulation system. Having recognized these difficulties, it seems wise to seek an alternative system for specifying ramps which provides a smooth specification to match the regulation capabilities of MECAR while providing a user interface for I2 which creates intuitive timing expectations In addition to (and independent of) the above issues, the initial goal of providing a dipole current specification which produces the specified momentum ramp still lacks important implementation features. The results are not apparent to the casual Main Injector operator since the LLRF system successfully controls the orbit as requested. However, the error signals available from the LLRF clearly demonstrate a significant error between the specified and achieved momentum. To address this we need to change the description of hysteresis used in I2 (which was provided in Summer 1998) with a more precise description published at PAC99. Parameters used in the present software are based on measurements of a single MI dipole. We expect to fit to a suitable average of the full set of measurements to provide the final operational parameter set. Tune Control Assumptions The present tune control system provides a specification of the quadrupole current regulation signal for each of the two main quadrupole buses based on the momentum program and the specified tunes. The fundamental assumption of the control algorithm is that the momentum of the beam to be focused is correctly described by a (B * rho) determined from the net bend of the main dipoles. This prescription can be complete if the following assumptions are valid: 1. The correction quadrupoles do not change the tune. 2. The net bend of the horizontal dipole correctors is zero. 3. The orbit places the beam in the centers of all quadrupoles and sextupoles. (Understanding the effects of known violations of this requirement is a fundamental concern of this note.) Quadrupole Corrector Concerns By design, the harmonic correctors provide no (significant) net tune change. The extraction quadrupoles do change the tune but should be off except at the extraction times. However, we achieve the harmonic correction using individually powered quadrupoles controlled with 'MULT' tuning on parameter pages. Currently no hardware or software is available to assure that the the correction quadrupoles do not modify the injection or low field tune. Below we will discuss the large tune changes which can be create by net bend effects. The orbit distortions required at all Lambertson magnet locations are large. The tune effects from these should be considered. Tune Changes from Corrector Bending As discussed in the PAC99 tune regulation paper, we control the quadrupole current by matching a specified signal to the quantity I_q - 0.4 * I_b. The beam tune is governed by the ratio of focusing to bending strength. Using a linear approximation locally, one sees that the tune is governed by the quadrupole to dipole ratio QBRAT = I_q/(0.4*I_b) where the 0.4 (4000/10000) gives a ratio near 1. From the design lattice and the linear term in the strength vs current for the dipole and quadrupole fields we calculate that a ratio change dQBRAT gives a tune change dnu = 40 * dQBRAT. (Compare 40 to the 25.4 or 26.4 one might naively guess.) Tune calibration efforts on January 10, 1999 achieved a match between requested and measured tune of better than 0.01 for many points up the momentum ramp. Time prevented final adjustment/measurement for all points and some were wrong by up to 0.02 or so. Observations in May 1999 reveal that the fractional tune requested for various ramps at injection range up to 0.46 - 0.48 whereas the measured tune is 0.38 - 0.4. After much deliberation, it was realized that the orbit smoothing process permits one to monotonically increase the average bend provided by the horizontal correctors. The I50 application program will provide individual and average values for the 104 correctors in amperes or micro-radians. The values can be measured at the breakpoint times used for the dipole corrector ramps. Examining each breakpoint up to 120 GeV in mid-May 1999 reveals an average up to 100 micro-radians (value at injection). The formulas above permit one to calculate the expected effect on tune due to the average corrector bend. At injection, the correctors provided a net bend of 10.4 milli-radians. Since the total bend controls the momentum and, for circulating beam, the total remains at 2 pi radians, the correctors provide about 0.166% of the bend (dQBRAT = -0.00166). This is equivalent to reducing the QBRAT ratio at a given time by this amount so we expect the achieved tune to be lower by 0.066 which is comparable to the observed discrepancy. How well should be expect to control this? The vertical correction has all the limitations (correctors and beam position detectors of similar capability) of the horizontal corrections except for the coupling to momentum error. Since we have from 2 to 5 micro-radian average corrections vertically, we should be able to control the average horizontal corrector bend to 4.5 micro-radians which will affect the tune by about 0.003. While tune measurements on the Main Injector have roughly confirmed the magnitude of the net dipole effects described above, the trivial example of a 3-bump appears to contradict this conclusion. In the MI lattice (90 degree cells), the standard 3-bump achieves a change in position while closing to no net bend error by using two dipoles of the same polarity and a small correction at the point in the middle from the third dipole. The net angle of the dipoles is cancelled by bending in the quadrupole field governed by the displacement of the beam at the quadrupole. The angles from the dipoles and the quadrupole together create no net effect on the total bend of the beam and we should not have to consider them when setting the main dipole current. Orbit correction algorithms which correctly account for these concerns probably exist and we will find them. It will, nevertheless, be useful to better understand appropriate language for clarifying the above dichotomy. Other Tune Control Effects The tune control design attempted to address all issues which must exist in a machine: required main dipole and quadrupole currents in the face of hysteresis; and design and perhaps measured tune sensitivity matrix. In the question list below we will address other tune effects which need to be considered, measured and addressed if significant. Ramping Problems from Mixed Ramp Requirements In addition to other problems, the requirements for mixing 120 and 150 GeV ramps have been shown to induce problems of current errors. In particular, the following situation has been documented. An 80 second super-cycle started with a 150 GeV ($21) cycle which was followed by 4 cycles of $29 ramps to 120 GeV. Current errors were plotted at low currents (near injection). It was found that the dipole error (I:MBIERR) was similar on all ramps. The errors on the quadrupole bus (I:MHIERR, I:MVIERR) were found to be typical for the $21 and the last two $29 ramps, where typical quad regulation on the low energy parabola is less than 0.1 A error. The first 120 GeV ramp after the 150 GeV ramp had a consistent negative error. The error grows linearly up the ramp, reaching about 0.25 A at 0.9 Sec (near 70 GeV). The next $29 ramp over-corrects for this and produces a positive error. We have not examined the machine operation carefully to find what tune effect are induced or whether we can successfully adjust the machine so that this tune excursion does not affect beam operation. Questions To Be Answered Consider the following questions in light of the above discussion. 1. What fundamental requirements need to be placed on the ramps which are generated for MECAR to control? If optimized (minimum time) ramps are essential to meet program (HEP) requirements, what are the fundamental limits on the ramps? Is a limit on the frequency components really the correct thing to specify. Do we apply them on current?, on voltage? 2. What are the correct operational considerations for a ramp design (specification) system? The flat portions of the ramp must surely be specified in a obvious way to facilitate specification of injection and extraction operations? RF and magnet voltage limitations are more subtle. The consequences of ramps design choices outside of the flat portions must be made clear for experts, but they are less likely to require interpretation for routine operational changes. 3. The evidence for problems associated with polynomial ramp segments has been described but not documented carefully. Are the specifics known? (remembered?) From the viewpoint of the RF systems, can specific comments be made as to what is important? Are momentum effects likely to be the only concerns or should we have a separate list of reasons for considering smoothness requirements on tune (quadrupole) curves? MI studies which vary the FIR filter parameters can be formulated to clarify these issues as appropriate. 4. We have evaluated above our sensitivity to dipole error effects due to net bending from the horizontal dipole correctors. It suggests that we are sufficiently sensitive that we should employ a carefully analyzed algorithm for orbit smoothing which avoids this problem. The current I50 orbit smoothing program includes some options which can partially avoid this problem but we should obtain (or create) a definitive algorithm which eliminates this problem. 5. The correct description of the bend effects from quadrupoles, including the interactions between correctors and quadrupoles for standard 3-bumps requires more consideration than has gone into the present ramp and orbit control systems. A suitable viewpoint may make all of this more obvious than we currently find it. Will such a viewpoint change our view of a correct orbit smoothing program? There can be net bending from the quadrupoles. Since we have employed a design which makes use of quadrupole position bumps to distort the orbit at Lambertson locations, we should evaluate this effect and integrate this knowledge into our design for tune control. How carefully must we deal with the altered locations of beam position detectors associated with quadrupole moves? 6. Since desired positions (intentional orbit distortions) are quite large (up to 30 mm), the sextupoles may also create some significant effects. Sextupole are located in positions with significant dispersion whereas the Lambertson locations are typically at low dispersion locations. It is still worth documenting the answers to the following questions. Do sextupoles create significant net bending? How large a net effect do they have on the machine tune for a given sextupole current? (or perhaps for a given chromaticity change?) 7. Tune correction quadrupoles are used only for extraction. Have we confirmed that they are not on during other parts of the ramp? Have we compared their tune effects to the design? 8. The harmonic correction quadrupoles are designed to create no net tune change. Have we checked our tuning to see that it conforms to this design specification? Have measurements been done to determine the actual machine response? Should we add software to avoid unpleasant surprises due to inappropriate tuning? 9. We find that $29 ramps which closely follow $21 ramps are not well regulated. With the requirement for having two $21 (150 GeV) ramps in close succession, we must address this regulation problem to provide good operation for the fixed target run. Summary As we attempt to place control of Main Injector in the hands of the operations crews, we must identify issues such as those above which subject us to potential mis-tuning. Only by providing tools which either avoid problems by design or expose problems (and cures) in convenient ways, will operators and specialists be able to understand all the right issues. Ramp optimizations to achieve high ramp rates will impose additional constraints on our ability to operate this machine without stress. Answering the above questions will improve our ability to achieve the goal of trouble-free operation. Input if desired from many directions to provide guidance in resolving these problems. Please contact the author or other interested parties with your comments and suggestions. References: 1. Many entries in the Main Injector Electronic Log illustrate the points addressed in this note. 2. B.C. Brown, C. M. Bhat, D. J. Harding, P. S. Martin, and G. Wu. Design for Fermilab Main Injector Magnet Ramps Which Account for Hysteresis. PAC97, Also available as FERMILAB-Conf-97/147. 3. Bruce C. Brown. MI Power Supply Control Issues for Magnets with Hysteresis. Main Injector Note MI-0211 Ver 1.1, Fermilab, June 1997. 4. Bruce C. Brown. Some Additional Information for Dipole and Quadrupole Power Supply Control. Main Injector Note MI-0245 Ver 1.1, Fermilab, September 1998. 5. G. Wu et. al., Tune Control in the Main Injector, PAC99, Available as Fermilab Conf-99/73, April 1999.