Demonstration of a HERO/LERO BPM "Dropout"

HVS 01/05

On this page I will try to demonstrate the effect of a BPM dropout on the HERO or LERO feedback.

To do this I use a simple mockup¹ of the feedback kick calculation using SCP orbitfit routine. I choose for simplicity to do this only for the HER and only for the X plane. While such is not completely representative of the HERO and LERO calculations, such is sufficient for a simplified demonstration of BPM dropout effects.

I have constructed several reference orbit files for this purpose. For each of these orbits, I'll demonstrate using SCP orbit fit (configured to include only the HERO BPMs for fitting) the HERO kick change which results from dropping HERO measurement 9122. This is the same effect that would result from 9122 BPM readout dropping out (due to NoQ etc.) with HERO's "number of bad measurements allowed" parameter set to allow one bad measurement.

To provide for visual aid; in the pictures which follow I've left the TMIT bar present only for BPM units used by HERO. Pictures for the fits which have BPM 9122 excluded show TMIT for BPM 9122 as red.

Again; in the pictures which follow, all PR02 X BPMs are displayed, but the fit shown is based only upon the BPMs used by HERO.


Orbit Information sent to orbitfit (click on item to go to pictures with a discussion)	Change in kick calculation with 9122 BPM dropout
An orbit which reads all zeros.	none
An orbit which reads all zero plus 100um RMS noise superimposed	-0.12uR
An orbit which includes a pure (model generated) betatron oscillation originating outside of IR2.	+0.1uR
An orbit which includes a pure (model generated) betatron oscillation originating outside of IR2 plus 100um RMS noise superimposed.	+1.25uR
An orbit which includes a pure (model generated) betatron oscillation originating outside of IR2 plus a 10uR kick at HERO corrector HCOR1R.	+0.12uR
An orbit which includes a pure (model generated) betatron oscillation originating outside of IR2 plus a 10uR kick at HERO corrector HCOR1R plus 100um RMS noise superimposed.	+1.1uR
An orbit which includes a pure (model generated) betatron oscillation originating outside of IR2 plus a 10uR kick at HERO corrector HCOR1R plus an additional 10uR kick at (a strategically selected²) IR region corrector 7022.	+0.05uR
An orbit which includes a pure (model generated) betatron oscillation originating outside of IR2 plus a 10uR kick at HERO corrector HCOR1R plus an additional 10uR kick at (a strategically selected²) IR region corrector 7022 plus 100um RMS noise superimposed.	+0.59uR
An orbit which includes a pure (model generated) betatron oscillation originating outside of IR2 plus a 10uR kick at HERO corrector HCOR1R plus an additional 42uR kick at (a strategically selected²) arc corrector 9102.	+4.81uR

¹ The mockup has two flaws:

The mockup overly simplifies the calculations performed by HERO. HERO fits for two kicks per plane; one at the IP phase and another at HERO corrector's phase. Separation between these two is close to 90 degrees. While HERO can only correct one of these phases, the other is still fitted. SCP orbit fit can only fit one kick location.
Towards not having this drawback corrupt the result, I'll only include kicks which are at the same phase as the HERO corrector.

HERO fitting includes the out of plane information (Y measurements for X calculations) due to the IR region coupling. For simplicity I choose to ignore this (relatively small) effect.

² These correctors are strategically chosen (due to the first mockup flaw listed above) since their betatron phase is quite near that of HERO's corrector 8020.

An orbit which reads all zeros:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

This example is profoundly uninteresting. All the measurements read zero, so a fitted parameter is going to come back as zero. The fitted kick is zero regardless of which BPMs are included in the fit. This is the condition immediately after regolding the feedback loop.

An orbit which reads all zeros plus 100um RMS noise:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

This example shows that with small noise signal included in the BPM readout, the kick angle result changes in a way which is not meaningful. Remember the noiseless condition would be zero kick angle. Notice the residuals are of about the same size as the measurements. Neither the measurements nor the resultant fit are physically meaningful. Notice that a change in fitted kick of 1.2 uR occurs if BPM 9122 drops out.

An orbit which reads a pure betatron oscillation originating outside of IR2:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

Since the model which generated the (purely external) betatron oscillation is the same as the model which does the orbit fitting for IP kick, it would be expected that zero kick is returned from the orbit fit routine; and such is seen here. The small orbit residuals (~10um) are due to to roundoff error and mockup flaw #2. The difference in fitted kick due to a dropout is small (~0.1 uR) since all of the measurements are consistent with an purely external oscillation with no kicks within the fitted region.

An orbit which reads a pure betatron oscillation originating outside of IR2 plus 100um RMS noise:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

So again I've thrown noise on top of what is otherwise a perfect fit to perfect data. Again the non-zero kick angle determination is not physically meaningful (remember that the noiseless data corresponds to zero kick angle). The residuals are small (same as the noise amplitude) compared to the values of the measurements. If BPM 9122 drops out, the change in fitted kick is only about 1.3uR. Again; the kick would be zero if the noise (and roundoff errors and mockup flaw #2) were removed.

An orbit which reads a pure betatron oscillation originating outside of IR2 plus 10uR kick at HERO corrector HCOR1R (8020):

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

This time I've provided to the orbit fitting routine some data (model generated) which should fit exactly to an external oscillation plus kick at the desired fit point. The residuals are small. The kick angle determination is the same as expected from the data provided. If BPM 9122 drops out, the change in fitted kick angle is small (0.12 uR entirely due to roundoff error and mockup flaw #2) since again all of the data is perfectly consistent with the what the fit is trying to extract from the data.

An orbit which reads a pure betatron oscillation originating outside of IR2 plus 10uR kick at HERO corrector HCOR1R (8020) plus 100um RMS noise:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

In this case the noiseless data would provide a perfect result for the kick angle. The noise on top of the data corrupts that determination by about 0.5 uR. The residuals are the same size as the noise. A dropout of 9122 BPM only changes the readout by ~1.1uR.

An orbit which reads a pure betatron oscillation originating outside of IR2 plus 10uR kick at HERO corrector HCOR1R (8020) plus another 10uR kick at XCOR 7022:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

This case starts to look interesting.

In this case we have given the orbit fit routine a set of data which has an additional kick which it does not have provision to fit. It turns out however that the two kicks I put in the data (+10uR each at XCOR 7022 and XCOR 8020) have quite nearly 180 degrees betatron phase difference.

Notice the fitted kick amplitude at XCOR 8020 is only ~5.6 uR (just over half of the 10uR put into the dataset). Since the two correctors have 180 degrees phase difference the two kicks tend to cancel.

With β_x at 8020 = 620m and β_x at 7022 = 114m, the β_x ratio is about 5.5:1 and their relative strengths are 2.3:1. XCOR 8020 is 2.3 times as "strong" as XCOR 7022. So XCOR 7022 corrects only 1/2.3 =0.43 of the orbit change made by XCOR 8020. This leaves 1.0 - 0.43 = 0.56 (precisely the amount shown) of the XCOR 8020 effect visible to the HERO fit.

Notice the residuals are small everywhere except for the region between the correctors† (where the data is known to be different than what we expect to fit). Dropping BPM 9122 has only a tiny (0.05uR) effect on the kick calculation since the data and the calculation are perfectly consistent except for the (modulo 180 degree) location of the kick being provided to the fit.

†What happens to the beam trajectory inside the region between the two correctors? Consider the efforts of the "second incarnation of LERO" and "PR02FFWD" in the parent link to this page for some thoughts about why the correction HERO makes should coincide with the sources of the kicks HERO is intended to correct.

An orbit which reads a pure betatron oscillation originating outside of IR2 plus 10uR kick at HERO corrector HCOR1R (8020) plus another 10uR kick at XCOR 7022 + 100um RMS noise:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

In this case the added noise causes a dropout of BPM 9122 to have a small (0.6uR) effect on the "combined" kick determination. Size of residuals outside the region between the two correctors are on the order of the noise signal.

An orbit which reads a pure betatron oscillation originating outside of IR2 plus 10uR kick at HERO corrector HCOR1R (8020) plus another 42uR kick at XCOR 9102:

All HERO BPMS used for fit

HERO BPM 9122 excluded from fit

This result is very interesting. We've again provided data comprising two kicks; one at the fit point and one out in the arc where the BPM measurements are. With all BPMs included the residuals are poor. This is due to the fact that we have given the fit a set of data which is inconsistent with the solution parameters which have been specified for the fit. The kick at HERO's corrector is largely mis-estimated (should be 10 uR fit returns ~5 uR).

If BPM 9122 is dropped from the fit the kick determination changes by 4.8uR (which is large).

What happens when BPM 9122 is dropped from the fit? The residuals clean up (except for BPM 9122) and HERO's kick determination recovers to what was provided in the data. Reader will now feel "set-up" in that I deliberately choose a kick (XCOR 9102) whose influence on the trajectory/kick/problem is eliminated if BPM 9122 is eliminated. A kick at XCOR 9102 is not seen (appears only as a global betatron oscillation) without BPM 9122.

So one begins to recognize three important things about HERO's suseptability to BPM dropouts in the presence of orbit deviations from gold:

Trajectory kicks originating inboard of HERO's arc BPMs are treated as kicks at HERO's kick fit point(s). The component of this deviation whose phase is the same as HERO's corrector will be corrected, leaving an orbit excursion between the deviation source and the HERO corrector. The HERO "solution" is happy with this; the residuals are small, and suseptability to BPM dropouts is no different than if the orbit were not deviated.
Random BPM noise does have an effect on the kick determination, but the effect is not more dramatic when the overall differences to gold increase in a way consistent with what HERO's fit extracts from the data (i.e. when the residuals still remain small).
Orbit kicks originating within the arcs which comprise HERO's measurements introduce a condition which HERO (by design) is not equipped to deal with. The kick at HEROs corrector will be mis-evaluated, and the fit residuals will increase. In this condition a BPM dropout changes the HERO kick determination causing HERO to steer undesirably.

Therefore the criteria for regolding of HERO/LERO (to avoid suseptability to BPM dropouts) should be based upon the size of the fit residuals. As long as the residuals remain small, this suseptability will remain small.