# Observations of direct excitation of the betatron spectrum by mains harmonics in RHIC

Peter Cameron, BNL, Upton, NY 11973, USA

Marek Gasior, Rhodri Jones, CERN, Geneva, Switzerland

Cheng-Yang Tan, FNAL, Batavia, IL 60439, USA

Abstract

With the advent of significant improvement in the sensitivity of
observation of the betatron spectrum\[1\], the appearance of strong
spectral lines at harmonics of the mains power frequency has been
observed in the PS and SPS at CERN, the Tevatron at FNAL, and RHIC at
BNL. **These lines are problematic for the operational implementation of
accurate tune tracking and tune feedback in RHIC**. We discuss the
possible origins of these lines, and present data to support our
discussion. This note expands upon an earlier published paper\[2\].

This note is organized into six sections. After the introduction, we
present preliminary observations that revealed the presence of mains
harmonics on several different pickups. This is followed by the
definitive observations, which demonstrated that the observed signals
are not spurious, and further that there is some sense in which they can
be associated with the main dipole power supply. The results of a simple
simulation suggest in slightly more detail a specific mechanism that
might be causal. The effect on tune tracking is then discussed. Finally,
we briefly present an overall discussion and conclusions.

## introduction

Identification of the source of mains ripple in beam spectra is often
problematic. The difficulty is to clearly demonstrate that the observed
ripple originates in the beam, rather than entering the signal path
spuriously. Data collected at the CERN PS and SPS, the Tevatron at FNAL,
and RHIC at BNL suggests that the beam is being directly excited **at
the betatron resonance** by high harmonics (h \> 100) of the mains
frequency.

![](media/image1.jpeg){width="3.2743055555555554in"
height="2.2020833333333334in"}

**Figure 1:** Spectrum with BBQ excitation and 60Hz lines

Figure 1 shows the spectrum obtained from a 1m stripline pick-up looking
at Copper ions in RHIC, using the Direct Diode Detection Analog Front
End (3D AFE)\[1\] of the BaseBand Tune (BBQ) measurement system\[3\].
The horizontal axis spans \~1.2KHz, centered on the betatron resonance
at \~18.65KHz. The vertical axis spans \~30s, with the most recent time
at the bottom. The BBQ is locked on the betatron resonance, which can be
seen to shift by \~.002 when the quadrupole currents are changed and
then returned to their original values. The 60Hz lines don\'t move. This
illustrates the conundrum - what mechanism might cause high harmonics of
the mains frequency to appear in the vicinity of the betatron resonance,
yet not be sidebands of the betatron line? The obvious conclusion is
that the beam is being directly excited at these frequencies. This
interpretation was met with considerable scepticism from accelerator
physicists and power supply specialists, the question being what
mechanism might generate magnetic field ripple at such relatively high
frequencies. The data presented in this note clearly shows that the
appearance of the ripple in the betatron spectrum is not spurious, that
the betatron resonance is in fact being directly excited by high
harmonics of the power line frequency. The mechanism of this excitation
is not yet fully understood. Some of the means employed to rule out
spurious sources included:

-   Batteries - AFE electronics were powered from batteries, with no
    change in the observed spectrum.

-   Electronics location - AFE was situated immediately adjacent to the
    pickup in the tunnel, and then \~70m away in the instrumentation
    room, with no change in the observed spectrum.

-   Isolation transformers - AFE was operated with and without isolation
    transformers in the signal path, with no change in the observed
    spectrum.

-   High pass filtering - 70MHz high pass filtering was inserted between
    pickup and AFE, with no change in the observed spectrum.

-   Pickup movement - no spectral variation was seen with large (\~1cm)
    changes in the position of a moveable pickup, suggesting the cause
    is not non-linearity of the 3D AFE.

-   Intensity variation - no spectral variation was seen with large
    changes in bunch charge, again indicating against non-linearity.

-   Different pickups - mains harmonics were observed from a homodyne
    detection AFE, a 245MHz resonant pickup, and a million-turn BPM, yet
    again indicating against non-linearity.

All testing indicated that the apparent mains excitation was not
spurious and that the beam was truly being excited at the betatron
frequency by high harmonics of the mains frequency.

## preliminary Observations

Figure 1 is representative of data taken with the 3D AFE. In the effort
to confirm that the mains frequency harmonics were not due to the
interaction of some spurious source with the 3D AFE, a comparison was
made with spectra obtained from other pickups. From these observations
we conclude that the presence of mains harmonics in the betatron
spectrum has been an on-going feature of the spectrum, one which had
been frequently overlooked prior to the availability of the improved
sensitivity of the 3D AFE.

### **Homodyne Detector**

The upper portion of Figure 2 shows the spectrum in the vicinity of the
betatron line as seen by the 3D AFE, while the lower portion shows the
same beam as seen by a homodyne detector.

![](media/image2.jpeg){width="3.2423611111111112in"
height="1.9770833333333333in"}

**Figure 2:** Spectra from 3D and homodyne AFEs

The homodyne signal was obtained using the sum signal from a H9 hybrid
to mix down the difference signal from the same hybrid. The
instantaneous power levels were such that saturation of the hybrid or
mixer was unlikely. The spectra shown in Figure 2 are clearly very
similar, which reinforces the notion that the mains harmonics are not an
artifact somehow generated by the 3D AFE.

### **245MHz Resonant Pickup**

Simultaneous data was also taken with the 245MHz resonant pickup used in
the then-operational RHIC PLL system, and is shown in Figure 3.

![](media/image3.jpeg){width="3.2430555555555554in"
height="1.617361111111111in"}

**Figure 3:** Spectra from 3D and 245MHz resonant pickup

The upper images show signals from the 245MHz pickup, and the lower from
the 3D AFE. RHIC was at store and the gap cleaner was operating when
this data was taken. The broad peak which occupies the left 2/3 of the
images results from beam excitation by that kicker. Mains harmonics are
clearly visible in both planes and in the signals from both detectors,
in the right 1/3 of the images. These harmonics had never been noted in
the 245MHz signal during the many earlier years of RHIC running. It
requires some effort to observe them, as they are present only when the
197MHz storage cavities are on and produce shorter bunches, so extending
the coherent spectrum up to the 245MHz pickup frequency. In this
circumstance it is difficult to avoid saturation of the sensitive
front-end electronics. This data again reinforces the notion that the
mains harmonics are not an artifact somehow generated by the 3D AFE.

### **Million Turn BPM**

Several of the RHIC BPMs have added memory to permit acquisition of
turn-by-turn data for one million turns. These BPMs were used in the
study of transition

instabilities during the 2004 Copper run.

![](media/image4.jpeg){width="3.24375in" height="1.6347222222222222in"}

**Figure 4:** Spectra from 3D AFE and MTurn BPM

With its excellent sensitivity and immunity to saturation, the 3D AFE
also proved an excellent tool for these studies. Figure 4 shows data
taken at the same time near transition (but on different ramps, with
slightly different tune values). The pattern of the mains harmonics
(repeating every 720Hz, with 3 strong lines spaced by 180Hz) is
essentially identical for these two systems. This data once again
reinforces the notion that the mains harmonics are not an artifact
generated by the 3D AFE.

## definitive Observations

While the ubiquitous presence of mains harmonics in data from four
unrelated pickups strongly suggests that these signals are indeed on the
beam, the possibility of similar spurious leakage into the electronics
of all four pickups cannot be completely ruled out.

### **Coupling Scan**

The clue leading to the first definitive observation came from the
Tevatron, where a change in the relative amplitudes of the observed
mains harmonics in the horizontal and vertical planes was seen when the
beam separation helix was turned on. The helix is known to introduce
coupling. This prompted a brief experiment at RHIC, in which the
relative amplitudes of the mains harmonics in the two planes were
monitored while coupling was varied.

A single RHIC skew quad was scanned from zero to \~10^-3^ m^-2^. The
result is shown in Figure 5. The spectral power of the mains harmonics
in the horizontal plane is uncorrelated with coupling strength. Power in
the vertical plane is function of the coupling strength, and is almost
entirely absent when the machine is well decoupled.

![](media/image5.jpeg){width="3.2402777777777776in"
height="1.8423611111111111in"}

**Figure 5:** Power in the mains harmonics as a function of coupling
strength

This conclusively demonstrates that the mains harmonics are on the beam,
and further that the excitation is in the horizontal plane.

**Beam Spectrum during Ramping**

There are two independent 12-phase power supplies for the RHIC dipoles,
a 30V/5500A 'hold' supply for injection and store, and an additional
400V/5500A supply that is switched in to provide the field time
derivative needed for ramping.

![](media/image6.jpeg){width="3.2645833333333334in" height="2.30625in"}

**Figure 6:** RHIC Spectrum during an acceleration ramp

Figure 6 shows the beam spectrum in the vicinity of the betatron line
during tune tracking of a 31GeV ramp (tune and coupling feedbacks were
off) of polarized protons in RHIC Run 6, as seen by the 3D AFE.

The horizontal axis spans \~5KHz, centered at \~21.3KHz (the revolution
frequency in RHIC is \~78KHz). The vertical axis spans \~50 seconds,
with the most recent time at the bottom. The excitation at 2 second
intervals results from the firing of the conventional tune meter kicker.
The onset of strong 60Hz harmonics about 20 seconds into the ramp
coincides with the turning on of the ramping power supplies, and the end
of the harmonics with their turning off. The harmonics have a pattern
that repeats every 720Hz, with strong lines spaced by 360Hz. The time
correlation suggests that the source of strong mains harmonics during
ramping is the ramping power supply. During ramping the strongest mains
harmonics are \~80dB above the 3D AFE noise floor. With only the 'hold'
supply they are \~40dB above the noise floor. The damaging effect of the
mains harmonics on the quality of the tune tracking is evident.

**Power Supply Balancing**

Dedicated Accelerator Physics EXperiment (APEX) time was devoted to
investigation of the effect of balancing (or unbalancing) the 12 phases
of the main dipole power supply. Figure 7 shows beam spectra observed at
injection while changing timing of one of the phases of the main dipole
'hold' supply. The spectra at 755am and 817am (references to time
throughout this note are the times at which FFT images were dumped to
the APEX elog\[4\]) are baseline spectra, and in principle should be
identical. The 811am spectrum results from a timing change of the 12
phase power supply. The effect of the 811am timing change differs in
each of the lines shown in the figure.

![](media/image7.jpeg){width="3.2604166666666665in"
height="2.0215277777777776in"}

**Figure 7:** Baseline and tweaked spectra

The relative amplitudes of the spectral lines exhibit distinct changes
at the time when of one of the phases of the 12-phase main dipole supply
is changed. This can be seen by examining Figure 8. The top of the
figure is the spectral pattern of the baseline, the middle corresponds
to the 811am timing change, and the bottom of the figure shows the
return to the baseline timing. The abrupt changes in the spectral
pattern are clear.

![](media/image8.jpeg){width="3.2430555555555554in"
height="1.5027777777777778in"}

**Figure 8:** Abrupt spectral changes due to timing changes

A second feature of the spectra in Figure 7 is a frequency shift. If one
looks closely it can be seen that the 811am data set is slightly shifted
in frequency relative to the other two data sets. This shift is
uncorrelated with timing changes of the dipole power supply, but rather
results from continuous small variation of the 60Hz power line
frequency, multiplied up by the high harmonic number (h\~340 in Figure
7). A typical sample of this frequency drift, taken at store during RHIC
Run 6, is shown in Figure 9. The horizontal axis corresponds to
frequency, with a span of \~152Hz, centered at the betatron line at
24.65KHz (h\~411). The vertical axis is time, spanning about 2 minutes
from top to bottom. During this time the mains harmonics drift by about
10Hz. This corresponds to a drift of \~0.025Hz at 60Hz.

![](media/image9.jpeg){width="3.1993055555555556in"
height="1.3805555555555555in"}

**Figure 9:** Continuous mains frequency drift

This drift complicated the effort to analyze the data. The mains
harmonics spectral lines are extremely sharp, with widths much less than
1Hz. The resolution of the archived FFT data sets was 2.5Hz. Frequency
drifts of the order of the FFT resolution therefore make it difficult to
apply conventional spreadsheet correlation tools to the data. To
overcome this problem the peak values of each of the spectral lines were
recorded for each of the timing settings of the main dipole power
supplies. The resulting data sets, used in the following correlation
analysis, are plotted in Figure 10.

![](media/image10.jpeg){width="3.2430555555555554in"
height="1.8388888888888888in"}

**Figure 10:** Data set used for correlation analysis

The sequence of events for this data (as the interested reader can
confirm by examining the elog\[4\]) is:

1.  755am -- baseline

2.  806am -- large timing change, observable effect

3.  807am -- return to 755am baseline

4.  811am -- return to 806am settings

5.  817am -- return to 755am baseline

These data sets were subjected to correlation analysis, using the
standard Microsoft Excel CORREL function.

![](media/image11.jpeg){width="2.977777777777778in" height="1.61875in"}

This definition is in agreement with the commonly accepted
definition\[5\] of the correlation function.

Using the correlation function, a correlation matrix was generated for
the data sets, as shown in Table 1.

![](media/image12.jpeg){width="3.240972222222222in"
height="1.082638888888889in"}

**Table 1:** Correlation matrix

The matrix is symmetric. The diagonal elements are ones, corresponding
to the fact that they measure the correlation of a given data set with
itself. Brief examination of the matrix shows that the baseline data
sets are strongly correlated with each other, and weakly correlated with
the intermediate data sets in which the timing was changed, and that the
intermediate data sets are fairly strongly correlated with each other.

![](media/image13.jpeg){width="3.2444444444444445in"
height="1.0756944444444445in"}

**Table 2:** Coefficients of determination

The statistical function which is most intuitively useful when examining
correlation is not the correlation function, but rather the coefficient
of determination, which is defined\[6\] as the square of the correlation
function. The coefficient of determination is simply the proportion of
variation in common between two data sets. This is shown in Table 2.

So, for instance, the proportion of variation in common between the
three baseline data sets is between 94 and 97 percent. If the timing
change were perfectly reproduced, nothing else in the machine drifted,
and the measurement was without noise, the proportion of variation in
common between these data sets would have been 100 percent. The
proportion of variation in common between the baseline data sets and the
intermediate timing change data sets is between 7 and 13 percent. For
the 16 element data sets (the 16 elements correspond to the 12 spectral
peaks in the 720Hz span of the repetitive mains harmonics spectrum plus
2 additional peaks on either side) used in this analysis, the
probability\[6\] of arriving at the results in Table 2 with random data
sets having the same standard deviations as the measured data sets is
considerably less than one part in 10^5^.

Measurements similar to those presented above were made with many
different timings. The total spectral power remained approximately
constant during these changes, even though the spectral pattern changed.
In addition, the timing changes required to produce the observed
spectral changes were large. Our preliminary conclusion from these
measurements was that, while there was an observed causal relationship
between power supply balancing and spectral content, it was not clear
that improved balancing will significantly reduce the mains harmonics.

Additional filtering was added to the ramping supplies during the last
week of Run 6 \[7\] in hope of reducing these harmonics. This filtering
may have given some improvement, but the results were not clear enough
to permit us to definitively state that this is true.

## simulation results

A crude schematic of the RHIC 12 phase main dipole poser supply is shown
in Figure 11. The 30 degree phase shift between the A and B bridges is
accomplished not by the more conventional 'delta-wye' technique, but
rather by adjusting parameters of the transformer windings.
Consequently, the phase shift between the two bridges is voltage
dependent.

![](media/image14.jpeg){width="3.245833333333333in" height="2.81875in"}

**Figure 11:** RHIC 12-phase Power Supply

A simple MathCAD program was written to simulate the effect of shifting
one or more of the phases of the power supply. To first order, the
physical power supply has 12 free/adjustable parameters, namely the
turn-on time of each of the 12 SCRs. The firing of a given SCR also
controls the turn-off of the preceeding SCR. This overlap generates fast
transients, which in theory are smoothed by what are commonly called
'snubbers'. The MathCAD simulation had 24 free parameters; the turn-on
time of each of the 12 pulses, and the length of each pulse. Shifting
the phase of the B bridge relative to the A bridge by \~14μsec (which
incidentally is also approximately the SCR rise time) resulted in a
familiar spectral pattern. This pattern is shown in Figure 12, aligned
with the spectra of Figure 4.

![](media/image15.jpeg){width="3.2402777777777776in"
height="2.1118055555555557in"}

**Figure 12:** Spectra from Figure 4 with Simulation

While many variations in spectral patterns have been seen in RHIC, that
shown in Figure 12 is the most common. This further suggests that the
observed excitation of the betatron spectrum results from phase shifts
in the 12 phase power supply.

The upper portion of Figure 13 shows the same million-turn BPM data as
Figure 12, with the span opened to cover the frequencies from DC to
20KHz. A puzzling feature of this spectrum has been the minimum in the
vicinity of 10KHz.

![](media/image16.jpeg){width="3.245138888888889in"
height="1.3104166666666666in"}

**Figure 13:** Spectra showing minimum at \~10KHz

The lower portion of Figure 13 shows the simulation of the spectral
pattern resulting from SCR overlap between phases. In this case the
overlap was \~70μsec. In the actual power supply operation such a
spectral feature might result from a combination of SCR overlap and the
diminishing amplitude midway between two peaks of the 12 phase supply.

## Effect on tune tracking

The excellent sensitivity of the 3D AFE is a major step forward in
realizing reliable operational tune feedback in large hadron colliders.
However, the mains harmonics revealed by this sensitivity have the
potential to disrupt efforts to utilize it to full advantage. This
disruption has the following consequences:

1.  emittance blowup -- reliable tune tracking in the presence of the
    mains harmonics requires excessive beam excitation, resulting in
    excessive emmitance growth, and preventing use of the BBQ for
    reliable tune measurement and feedback during normal operations.

2.  system evolution -- because the BBQ cannot be utilized for reliable
    tune measurement and feedback during normal operations, the natural
    system evolution that results from ongoing utilization is not
    present. On the occasions when the BBQ is called upon for ramp
    development, considerable tuning by system specialists is needed to
    adapt to changes in beam conditions since its last use.

3.  operator confidence -- the perturbing effect of mains harmonics
    causes erratic performance of the BBQ when operation is attempted by
    non-experts, and sometimes even when operated by system specialists.
    This diminishes confidence in the system, and retards the effort to
    make the system fully operational.

We illustrate these consequences with two brief examples, one at
injection and one during ramping.

Figure 14 shows the tracking performance of the BBQ in the vicinity of
mains harmonics as the BBQ reference phase is manually swept. The lower
portion of the figure shows that the BBQ excitation is \~12dB to \~18dB
above the adjacent mains harmonics. The upper portion shows that,
despite this significantly greater excitation power, the PLL still
locked to the mains lines at times of close proximity.

![](media/image17.jpeg){width="3.2395833333333335in"
height="2.236111111111111in"}

**Figure 14**: BBQ tracking during a phase sweep

Figure 15 shows BBQ performance during an acceleration ramp of polarized
protons to 31GeV/c. The upper portion of the figure presents the same
data as that shown in Figure 6 (with a different orientation and aspect
ratio). The lower portion of the figure shows the in-phase (I) and
quadrature signals (Q) from the BBQ during the ramp. When the tune
tracking phase loop is locked I is approximately equal to the amplitude
of the loop response, and Q to the phase.

During the early portion of the ramp, before the ramping supply switches
on, both the tune and the I and Q signals are reasonably clean, and the
primary perturbation comes from the firing of the conventional tune
kicker. When the ramping supply comes on and the amplitude of the mains
harmonics increases by \~40dB, the quality of the phase lock is greatly
degraded, and as the tune approaches a strong mains harmonic near the
end of the ramp the I and Q data indicate that lock has been lost. This
data is typical of the effect of mains harmonics on the BBQ during
ramping. Sometimes the effect is not so bad. Sometimes it is worse.

![](media/image18.jpeg){width="3.2444444444444445in"
height="2.6131944444444444in"}

**Figure 15**: BBQ performance during a ramp

## Discussion and Conclusions

We estimate the amplitude of the observed mains harmonics excitations to
be several hundreds of nanometers at injection and store, and tens of
microns during ramping. We estimate the 3D AFE noise floor to be \~10nm.
Because the mechanism responsible for the observed excitation is not
understood, it is not possible to make anything better than very crude
estimates of the strength of the source term. If the excitation
originates in the ring dipoles, a very crude estimate suggests that
field variation of a few parts in 10^7^ would be sufficient to cause the
observed effect during ramping. During injection and store the ripple
would be about a factor of 100 less. Ripple of such small magnitude
cannot be observed by conventional monitoring of bus currents. The 3D
AFE is the primary diagnostic for this signal.

There are two particularly puzzling aspects of the data presented here.
The first is that the data exists at all, that there is some as-yet
unidentified mechanism that permits this excitation of the beam at the
betatron frequency, not only in RHIC, but also in the CERN PS and SPS,
and in the Fermilab Tevatron. The second is that these lines are \~40dB
stronger in RHIC than in the other machines.

Regarding the mysterious excitation mechanism, it is likely that the
mechanism is the same in all the machines in which these mains harmonics
have been observed. This suggests that their source is not some
machine-specific device, but rather something common to all machines.
That fact, plus the time correlation of intensified mains harmonics with
the switching in of the ramping power supplies in RHIC, together with
the observed and simulated effects of timing changes of the 12 phase
main dipole power supply, suggests that this source is in fact the main
dipole power supply.

Regarding the fact that these lines are \~40dB stronger in RHIC than in
the other machines, the reason for this is not presently understood, and
is the subject of active investigation. **It is essential to operational
non-specialist implementation of the BBQ and its associated feedback
loops that causes and cures of these harmonics be thoroughly
investigated.**

The data presented here is a very small portion of the accumulated mass
of mains harmonics data, both at RHIC and at other machines. Hopefully
the selection and presentation of the data is adequate to permit the
reader to develop a reasonably clear understanding of what is presently
known about this phenomenon in RHIC.

## acknowledgements

The authors thank Al DellaPenna for his contributions to the design,
implementation, and operation of the RHIC BBQ, and Carl Schultheiss for
making the timing changes that resulted in the data presented in the
Power Supply Balancing subsection of this note.

## References

\[1\] M. Gasior and R. Jones, "High Sensitivity Tune Measurement by
Direct Diode Detection", DIPAC 2005, Lyon.

<http://dipac2005.web.cern.ch/dipac2005/default.htm>

\[2\] P. Cameron et. al., "The Effects and Possible Origins of Mains
Ripple in the Vicinity of the Betatron Spectrum", ibid.

\[3\] P. Cameron et. al., "Simultaneous Tune and Coupling Feedback in
RHIC, and Possible Implications for LHC Commissioning", submitted to
PRST-AB. Also available as C-A/AP/xxx at

[http://www.rhichome.bnl.gov/AP/ap_notes/cad_ap_index.html](http://www.rhichome.bnl.gov/AP/ap_notes/cad_ap_index.html  )

\[4\] The elog for this APEX experiment can be viewed at
<http://www.cadops.bnl.gov/cgibin/elog/view.pl?elog=rhicpp_2006&shiftlog=Wed_Jun_14_2006_6:30:00_AM>

\[5\] for instance, see

<http://en.wikipedia.org/wiki/Correlation>

\[6\] R.J. Rummel, "Understanding Correlation", available at
<http://www.mega.nu:8080/ampp/rummel/uc.htm>

\[7\] C. Schultheiss, private communication.