# Presentation: 158479

##  Orbit Length Stabilization Project

- Paul Lebrun, with much help and guidance from  Martin Hu, Cons Gattuso, Stan Pruss......
- June 22 + 7 = 29, 2005

## Outline

- Status of the software
- Current studies
- Principle
- 4-bump Optic checks
- 4-bump correction shape and amplitude, scans.
- 5-bump scans, local and non-local
- Caveat: Seemingly random VDQ Phase jumps
- Fixed, June 27 !!!
- Beam Physics Issues
- QCL vs 4 or 5-bump correction
- Interpretation of current results
- Plans & future studies
- Dedicated timeline
- Parasitic, leftover pbars (once cold)
- Moderate stash, cooling performance.
- Other ramps

## Status of the software 

- VDQ28 Fitting OAC
- Just running fine, stable.  Saving individual Snapshot, typically for every three ramps.
- And fitting, writing to local files, reporting to ACNET
- Controlling the Ramp cards,
- Only the F(t) table,
- I promise, I won’t change anymore the interrups or pointer tables! (there was need to..)
-  4-bump coded up, has been easily be extended to a 5-bump, or multiple bumps, if need be.
- Utility script to scan versus ramp parameter.
- Offline Analysis: sometimes done in Java, lately in C++/Root
- A detail you don’t need to know, unless you want to do some analysis on this data... (Help is always welcome..)
- I try to complete the e-log with offline plots, because scans can not be interpreted without this offline analysis step.
- Left to implement, if need be:
- Automate search for a minimum of the fitted peak to peak oscillation..
- “Adaptive algorithm”

## Principle, Online Plot. 

- Use proton (few days ago) or leftover pbar after  shots to Tev. ~ 5 to 10 e10, (pbar) or 40 e10 (proton). If pbar, long emitt ~ 10 eV.sec.
- Place the pbar or proton beam in a linear bucket, typical r.f ramp time of ~ 4.8 sec
- With QCLP on, peak to peak oscillation of VDQ of ~ .25 to .3 degrees, on 0x23
- Turn QCLP off!, turn on the 4-bump designed by Stan and Meiquin.
- Watch these devices: MI ramp,  bump setting, BPM reading at 520, record VDQ28 traces. Fit VDQ28 real time. Record all parameters of this fits in files on compute node dce08.
-  Then, play with the parameter of the 4-bump during 0x23 cycles, varying both the shape and amplitude.

- I:IB : MI ramp current
- R:H518T : 4-bump value, at 518
-   ( R:H520, R:H522, R:H524 follow the same shape, value set to be closed orbit.)
- R:HP520 : Hor. BPM at 520.
- R:VDQ28 : Phase Oscillation bunch/r.f., “in degrees of 53 MHz “

## Type of scans, Cost for HEP 

- On the 0x23 cycles
- 4-bump vs 5-bump
- Versus amplitude of the bump.  Up to ~ 1 cm bump
- ... asymmetric amplitude up/down ramp
- .... start time with respect to the MI ramp
- .....  duration of the bump
- This is tedious ( I’ll show scan results in a few slides... )
- Cost to HEP ( so far!) 10.8 e10 pbars (yesterday, 16:30).
- Little or no excuse! (I had my tea and my cookies 1⁄2 hour before)
- The beam was too cold and/or bucket width too small
- I tried to place a bigger bump, to increase synchroton motion
- At +2.75 Amps for H518, I was too far, stopped it, while coming back down, the C453 cards updated themselves, sequentially, such that this large bump became non-local, and I scrape it..
- Fix is easy: not going past 1.5 Amps at H518, re-heat the beam if need be, and perhaps make the transition smoother (complicated, I don’t control the timeline!)

## Bump Shapes studied on Summer Solstice. (yesterday) 

- Bipolar			One bump

## 4-Bump, Horizontal Plane, 518-520

- Courtesy – Meiqin Xiao..  This bump is made a location where little or no change of betatron tune is expected, e.g., no sextupole feed-down.  We are making progress at refining the 940 microns estimate.

- Orbit length difference: dll=0.00898mm

- 940 +- 10 m

## Check that this bump is closed: 

- Left: Horizontal Orbit, with the ~ 6 mm 4-bump, left, difference with 4-bump On/Off. Check made on June 17, 06:45 A.M.

## Check that tune across the 0x23 cycle, No QCL (1)   

- No 4 bump.  Tune moves, orbit is only partially corrected for the MI ramp.

## Check that tune across the 0x23 cycle, No QCL (2)   

- With 4 bump.  Tune moves more or less in the same way (This is what we wanted!)

## Check that tune across the 0x23 cycle, With QCL    

-  Without 4 bump, but QCL is On Tune are moving more, and crossing. To be avoided....

## Results,  Example 

- Shown on the left is a real-time plot (D44) of the fitted peak to peak maximum VDQ28 (R:VDQPPA) vs time , as we change the ramp, scanning various parameters (bump height, duration, time delay... (Also shown is the fitted frequency (R:BDQFRA), R:Beam, and Long Long emit. Not shown is the set value of the scan.
- Shown on the right is the result of offline analysis, filtering off the non 0x23 events, selecting the fits with acceptable synchrotron frequency. The Peak to Peak max. amplitude, of VDQ28, fitted, is shown versus the bump current. Done with Pbar, On Saturday June 11.

- Red mark =
- QCLP

## Quality of the data from such scans, Reproducibility?  

- Shown are two consecutive scans for the bipolar bump, as shown on slide 4, versus the amplitude of this bump.  The error bar comes from a straight statistical analysis of the ~ 30 to 40 ramps taken at each setting.  The green and red sets don’t agree, setting to setting. However, in average, the optimum current seems to be consistent, around 1.5 Amps.

## Unaccounted variations. 

- Top: the average of the maximum/minimum of  VDQ28  phase during a 0x23 cycle, fitted.  This quantity is the “average” phase. Bottom: the difference between the max/min, e.g., the fitted peak to peak oscillation amplitude, also data logged as “R:VDQPPA.  During these 4 minutes, the setting on the 4-bump, or any other known setting changed. (Of course, one can not monitor everything that goes on in the tunnel, but to the best of my knowledge, nothing changed).

- Time !

- <Phase>

- Peak to
- Peak
- Phase
- variation

## VDQ28 Phase Slippage.. 

- A known feature. Martin Hu and Paul J. attempted to fix the problem by replacing the front-end computer board, no success.
- Brian C will help...
- Could affect the real beam longitudinal motion, via the phase damper, at the system tries to damp out its own glitch.
- A real nuisance if we want to reduce the VDQ28 oscillation below a few degree (peak to peak!), reliably.
- Lengthens considerably the time it takes to do a scan..

- Fixed by B. Chase...

- Fixed by R.F. experts.. (B. Chase..)

## Implication: Repeat Measurements...

- In these scans, taken yesterday late morning, we look for the optimum amplitude for the 5-bump (non-local), asymmetric, which mimics the QCLP type of bump.
- On the X axis is the current at H518. On the Y axis the average, fitted peak-to-peak amplitude for the 0x23 cycles
- The color code:
- Blue dot, taken just before this scan, at relatively high emittance
- Black : first part of the scan
- Magenta: 2nd part, back down in current.
- Green: fine steps, taken later.
- Good agreement on what the optimum current is.. (~ 0.42 +- 0.04 Amps.

## Results for the “One Bump”  

- Results for the “One Bump”

- Left: Fitted peak-to-peak oscillation amplitudes versus the start time of the 5-bump, non-local, asymmetric, bipolar  in the 0x23 cycle. The ramp starts at 0.48 seconds. The duration of the bump was 0.1 for the first pulse, 0.45 seconds for the second one.  seconds, up/down time 0.1 seconds).  A clear minimum is observed..
- Right: Fitted peak to peak amplitudes versus the size of the 5-bump, local, symmetric (duration 0.45 sec)  (Amps, at 518).  This scan is incomplete and not accurate..

- I bump =
-  0.41 amps

- tStart

- I_bump.
- At H518

## Scans done so far.... Bottom line  

- Trouble is: No QCL / with QCL for the small intensity,  small long. emittance is only ~ 0.5 degree.  In fact, on slide, 10, there are no significant difference between QCL and the bipolar 4-bump. Note that the smallest synchrotron oscillation amplitude depends on many other factors, such linear bucket properties, and long. Emittance. Thus, scans can not be directly compared to one an other.
**Optimum Shape: bipolar symmetric!! **
- The bipolar 4-bump requires about 1.5 Amps at H518, which corresponds to ~ 5.2 mm/H520, and 7.8 mm at H522  bump -> could work.
- The 5-bump, non-local, needs only I_H518 = 0.45 Amps -> relatively bigger change for smaller transverse bump, but unknow.. Un-intentional study...
- The 5-bump, local, does NOT need a 2 Amps at H518, optimum seems to be below 1 Amps -> good.
- Next step: repeat the correct 5-bump, local, and perhaps check that it is indeed close and the tunes looks good. If bump is small enough at the optimum current, use the 5-bump.

## Beam Physics Issues: Motivation

- But, do we understand, quantitatively, why a ~ 6 mm 4-bump, corresponding to ~ 450 microns path length difference works?  What is the scale of the perturbation? Why and how does a bipolar correcting transverse bump works ? Why is it “pseudo-inductive” e.g., correction is ~ B/t
- I was asked to write an “adaptive algorithm to minimize VDQ28 oscillations “automatically”...Not to do beam physics!
- This “adaptive” bit is a bit vague, and therefore hard, so this is why I started to do these scans without automated search for a extremum. We have the software tools and the computing resources to implemented automated search for extrema, but exploring this multi-parameter space is tedious and slow... Given the “phases glitches” and the smallness of the effect, this is even more tedious!
- Perhaps we can try to understand the physics a bit better, and eliminate solutions that have no chance to work. Let us go through a bit of beam physics modeling, explore possibilities...

## Recap: What is VDQ28, how much orbit length? 

- The “28” is a currently a misnomer.
- It measures the synchrotron phase of the bunch with respect to revolution marker, at the base bad – 89 kHz, in degree
- Therefore, this fitted peak-to-peak VDQ28 Amplitude A_s satisfies
- L/L  = (A_s/360) f_s/f_r
- Where L is the orbit length, f_s is the synchrotron frequency (~ 1 Hz)  and f_r is the revolution frequency.
- Without QCL, without 4-bump, we observe A_s ~ 0.7 degree, or s L of 62 m, per turn
- When either QCL or 4-bump is used, one reduce these oscillation by ~0.3  degree, which is ~30 m, per turn.
- (The ~0.3 degree is for a ~ 4.8 microsecond bucket long! )
- With the 4-bump, 6 mm transverse deflection, the orbit changes length by only ~ 450 m, per turn !
- How do we relate the synchrotron amplitude to the perturbation? Is there a glaring discrepancy between the ~ 30 microns (Synchrotron amplitude) and the 450 microns (linear optics)

## Solving the 2nd order differential equation of motion..

- nus = 1.0;
- omega1SQ = 4*Pi * Pi * nus*nus;
- veffrf1 = -1.0 *omega1SQ;
- kDamp = -0.2;
- periodPerturb = 5.2;
- Phase0 = 0.48;
- sigmaRamp = 1.177*0.2;
- sigR2 = 2.0 * sigmaRamp*sigmaRamp;
- myPerturb = Sum[D[Exp[-(x-periodPerturb*i-Phase0)*(x-periodPerturb*i - Phase0)/sigR2],x],{i,0,23}];
- lengthSuper = periodPerturb * 22; (* 22 0x 23 cycles per super cycles assumed *)
- lengthStudy = lengthSuper + 30.;
-  YPhiSol1 = NDSolve[{y''[x] Š veffrf1 * y[x] +y'[x]*kDamp +  .5* myPerturb, y[0] == 0.0, y'[0] == 0.}, y, {x, 0., lengthStudy}, MaxSteps ® 500000]

- Simple Mathematica stuff..... Here, we simulate/solve a complete 2 min long supercycle.  The perturbation is assumed to be the derivative of a Gaussian, e.g., bipolar. (perhaps wrong!!...)

## Preliminary Mathematica result

- The way a forced, damped oscillator works...

- 1 Super cycle, 120 sec.
- Blue is the perturbation,
- Green is the response...

- 1 ramp.. Note: response has been multiplied by a factor of 20 !!!

## Modeling the longitudinal perturbation... 

- While the scale of the perturbation  and the response of the system are plausible, we still need to understand the dynamics in a bit more details:
- Model a : The change in the orbit due to residual MI B field is only partly compensated by local bumps, ~ MI ramp current. There is an overall orbit length change.  QCL can correct for this because it also produce a global dipole field.   If the 4-bump is applied in a straight section, the sign of the transverse bump should not matter.  Luckily enough, the 4-bump is applied partly where the beam bends   we can shorten or lengthen the path length! (V. Lebedev, Stan,... )
**However, one then expect a correcting 4-bump pulse proportional to the MI B field, not it’s derivative. ******** pulse shape is wrong.. **

## Modeling the longitudinal perturbation...(ii)  

- A variant
- Model b : The very low permeability of the shielding distorts, or “delay” the B field inside the RR beam pipe-> expect a different f(t)... Delayed by ~ 80 mSec, from a previous study done by  S. Nagaitsev.  Can this model support a bipolar correcting pulse ?
- The tStart scan done yesterday does not support this model strongly..
- Model c : The MI acts as a transformer on the RR, we induce current .. -> inductive recipe is O.K. (P.L. ).  In this case, changing the orbit length, turn after turn, make sense, because the energy of the beam stay put. (only magnetic perturbation and correction are applied).

## Modeling the longitudinal perturbation...(iii)  

- Modeling...
- Model d: A bit more remote: Can the M.I./RR act as a really crummy Induction Linac ? That is, dB/dt inside the beam pipe (~ few (< 10) Gauss/sec or a up to ~2 10-3 Tesla) translates into ~ 2 10-3 V/m2 induction. Integrated over a path length determined by the size of the beam pipe, we get ~ E ~ 2 10-5 V/M.  Summing over the length of the ring,  up to 0.02 V/M per turn, at most.  But the a 450 micron path length difference (or ~1.5 picosecond)  in the 4.8 sec, +- 1kV linear ramp translates to 0.3 mV per turn.  So the scales could match!
- Conclusion: A correction proportional to B and/or dB/dt is plausible.

## Do we care? What’s the specs?   

- The replacement of the QCL correction by a known 4-bump taught us that the magnitude of the required correction: per turn, only ~ 450 microns path length, per ramp, ~ 24 m (~75 ns) !!!!
- The bunch length is ~ 400 ns long, for ~30 eVsec, dP ~ 4 MeV
- Conclusion: Yes, we care!...( And now I finally understood what the problem is...)

## Will this work?  

- Yes, sort o, if,
- A. The perturbation is “ B field”, correcting the orbit length makes perfect sense, we are correcting the same physical quantity: the path length, or time of arrival of a given particle with respect to the r.f. All good!
- B. If “truly inductive”, E field,
- In a linear bucket, one still could improve by lengthening/shortening the orbit. As the synchrotron period is unique (~ 1 Hz) one can make a significant correction, during each 0.6 ns ramp, by adjusting the path length difference to a change in momentum. But not perfectly, the synchrotron period is too short (or we are taking intto account for the slip factor in the correct way.
- In a square bucket, I don’t understand how correcting the orbit length will work.  The r.f. will not restore the momentum after correcting path length at random times!.

## Wrapping up: More Studies !! 

- More scans, with left-over pbars. (at least finish the incomplete 5-bump bipolar symmetric scans for the one bump..)
- Measure again the response function to a single (e.g. one cycle) perturbation.   Control the time-line. Needs at least 10 to 20 seconds between cycles  Costly. (Needs more than a few ramps, to mitigate the other unknown perturbation, and glitches)
- Use the 4-bump correction, bipolar ~ 1.2 Amps, instead of QCL, on the 0x23, for regular shots.
- Or the 5-bump, bipolar symmetric, once optimum amplitude is
- Extend to the other cycles...