**Booster damper logbook part 2****\
**progress notes by Bill Ashmanskas\
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**[2008-07-11]{.underline}****[\
]{.underline}****[\
]{.underline}**Today\'s goal is to make the horizontal coordinate damp.\
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graph26: coarse timing, horizontal damper. 

![](media/image1.png){width="5.490277777777778in" height="4.55in"}

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graph28: horizontal damping.  This doesn\'t look nearly as impressive as
vertical damping.  The damper struggles to excite the beam, doesn\'t
excite a very large oscillation, and then damps it.  The damping time is
faster than the decoherence time, but the decoherence time is far faster
than in the vertical plane.  On the top plot, red is damper on, black is
damper off, after initially exciting the beam.  The bottom plot is
zoomed out a bit, to show that it is not so easy to excite the beam
horizontally.

![](media/image2.png){width="4.55in" height="4.620138888888889in"}

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So I declare this a partial success.  I will have to check with Eliana
to see whether the horizontal decoherence time makes sense here.  Also,
it would be interesting to try to reduce the tune spread and look to see
how things differ.

## [2008-07-11]{.underline} 

((246.1 - 110.7) + ((207.756 - 170.095) / 0.29979)) / 18.8 = 13.884\
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I see that horizontal kicker cable is (246.1-110.7) ns longer than
vertical, and is (207.756-170.095) m upstream of vertical.  So
horizontal kick should be emitted by damper board 13.9 RF ticks before
vertical kick.  In fact, it is (after empirical optimization) emitted 14
buckets before vertical kick.  Neat!\
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+++ collection of random facts written down after re-reading my 2006
notes on this project +++\
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HOR_DAMP: betax=6.641m, mux=2.441 periods, Dx=2.768m, s=170.095m\
cable length 246.1ns\
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VER_DAMP: betay=20.960m, muy=2.957 periods, alpha_y=0.126, s=207.756m\
cable length 110.7ns\
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PICK_UP: betax=6.417m, mux=2.980 periods, alpha_x=-0.290, Dx=2.336m\
betay=20.757m, muy=2.965 periods, alpha_y=0.077, s=208.756m\
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amp input to vertical kicker fanback \~ 318ns\
=\> amp input to beam \~ 205ns\
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Qx=6.720, Qy=6.779\
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so delta mu_y (PU to VD) = 6.712, sine = -0.97\
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L=474m\
gamma(400 MeV)=1.43\
gamma(8 GeV)=9.53\
gammaT=5.47\
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hf0 = 38.0 MHz, 52.3 MHz, 52.8 MHz at injection, transition, extraction\
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Wildman\'s amplifier (AR 500A100) is flat to +/- 10 degrees from 10 kHz
to \>100 MHz; good for 500 watts; gain \~ 57 dB (max)\
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2005-08-01 plan was\
1.  show that damper board can handle frequency sweep\
2.  acquire data up the ramp\
3.  repeat #2 with reduced tune spread to see instability growth rate\
4.  implement variable delay up the ramp, such that we can apply a kick
that follows a given bunch up the ramp\
5.  show that you can remove one bunch by anti-damping\
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seeing the notch on the beam on signal vs. turn vs. bucket is nice\
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I committed booster_dampers on 2006-08-05, with changes as of
2006-02-24;\
previous changes had been 2006-02-21.\
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Quartus 4.1 to avoid SHARC woes.\
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I can run vmware player (free) on whitespace.  Can connect to it with
VNC.\
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Run Quartus 4.1, compile damper project.\
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P = V\*\*2(rms)/R.  500W into 50 ohms =\> Vrms = 158V.\
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( c, s \\\\ -s+g, c) (y \\\\ theta) = ( cy + s theta \\\\ c theta +
(g-s) y)\
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=\>\
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y(N+1) = c y(N) + s theta(N)\
theta(N+1) = c theta(N) + (g-s) y(N)\
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cos(2 pi nu) = \<y(N) y(N-1)\> / \<y(N)\*\*2\>\
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ytwiddle = y/sqrt(beta)\
thetatwiddle = sqrt(beta)\*y\' + (alpha/sqrt(beta))\*y\
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2006-08-07\
my \"simulation\" uses feedback coefs for 3 turns =\
(gain/d)\*(sin(phi), cos(phi), -sin(phi)-cos(phi))\
where phi=0.67\*2\*pi\
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100% gain \~ 10-15 turns growth (doubling time); phz=22 maximizes
effect\
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I think transition is at turn \~ 10000.  Should be 9500 turns after
injection (and f=52.21 MHz) using my program booster_gen_freq_curve.py\
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back in Sep 2006, damper T1/2 \~ 10-15 turns, while decoherence T1/2 \~
220 turns, at turn \~ 16000\
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frequency essentially sweeps from 52.3 to 52.8 MHz above transition:
52.2 to 52.8 MHz in 16 ms.\
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injection occurs at damper turn \~ 900, so 10400 is where damper should
see transition.  17ms after injection.\
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\-\--   \-\--\
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**[2008-07-15]{.underline}****[\
]{.underline}****[\
]{.underline}**Bill Ashmanskas, Nathan Eddy\
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We installed the spare Recycler damper (100 watt) amplifier to drive one
plate of the Booster vertical damper.  We still have both (500 watt)
amplifiers from the MI driving the two plates of the Booster horizontal
damper.  I had to adjust the kick timing, because the 100W and 500W
amplifiers have different delays.  Jim Crisp measured the 100W
amplifier\'s delay to be 22.2 ns.  I had a crude guess that the delay of
the 500W amplifier was 90-100 ns, based on adding up propagation delays
measured in 2006.  But after adjusting the timing with the scope in the
usual way (set D4YFIR:=0x777, D4YPHA:=0, etc.), I found that I needed a
1.5 bucket adjustment, not the 4 bucket adjustment I originally
guessed.  So it appears that the delay of the 500W amplifier is about 50
ns.  This should be confirmed at some point with a direct measurement.\
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The vertical damper now works, with the 100W amplifier!  Damping time
appears to be about 9 turns.

![](media/image3.png){width="4.6in" height="4.55in"}graph29.png\
The two vertical bars are 9 turns apart; the two horizontal bars are a
factor of 2.71828 apart.

![](media/image4.png){width="4.6097222222222225in"
height="2.8402777777777777in"}graph30.png\
Fitting an exponential to error\*\*2 gives a decay time of about 4
turns, which implies about 8 turns for rms error signal.\
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Again, this is vertical plane, one plate, 100W amplifier.\
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Bill Pellico increased longitudinal quadrupole damper gain and decreased
horizontal chromaticity for us on the \$17 cycles. (See today\'s Booster
logbook for the details of what was adjusted in the Booster.)  **We saw
that the damper is really able to damp instabilities!!!  This is
fantastic!!**\
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![](media/image5.png){width="4.6402777777777775in"
height="4.729861111111111in"}

In the above graph, damper is ON in the top half and OFF in the bottom
half.  What is graphed is the horizontal error signal vs. turn.\

![](media/image6.png){width="4.7in" height="4.559722222222222in"}

Here is a close-up, showing just the end of the cycle; otherwise same as
previous graph.  I do not understand why the damper is not able to
suppress the activity at the very end of the cycle (turn 20300 or so).

![](media/image7.png){width="4.620138888888889in" height="4.5in"}

Here is another pair of pulses (damper ON for top and OFF for bottom),
with expanded scale.\

![](media/image8.png){width="8.540277777777778in"
height="6.909722222222222in"}

Dampers ON for the above multiwire profile\

![](media/image9.png){width="8.540277777777778in"
height="6.909722222222222in"}

Dampers OFF for the above multiwire profile.

![](media/image10.png){width="4.479861111111111in"
height="4.6097222222222225in"}

This may be worth investigating further.  When the X damper is OFF, I
can see the blowup on the vertical pickup too.

![](media/image11.png){width="4.659722222222222in"
height="4.559722222222222in"}

The above graph is vertical error signal vs turn.  In both cases,
horizontal damper is OFF, but vertical damper is ON for top half and OFF
for bottom half.  So vertical damper can damp out what spills over into
V plane from H instability shown earlier.  I see this ON/OFF difference
reproducibly on several OFF and several ON pulses.  But if the
horizontal damper is on, the vertical blowup doesn\'t occur.\
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I\'m going to call it a day.  I think the most urgent thing to do
tomorrow is to add some devices that can be graphed via ACNET Fast Time
Plot to show the summed absolute value of the error signal, summed over
bunches for some number of turns (1 turn?  256 turns?).  (There are
600-900 revolutions in a 720 Hz tick.)  Then the same for the kick
signal.  Nathan suggests that we should also put out the maximum value
seen for any bucket within the interval, so that saturation can be
detected.\
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I\'d also like to put a 20dB coupler onto each DAC output so that we can
run a copy of each amplifier input into the oscilloscope.\
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