Proposal for Low frequency damping system in Tevatron

• Why do we need it? Maybe not?

• Can our current correctors handle the job?

• How should the system look?

• Problems or issues?

Horizontal Beam motion

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200400

200

0

200

400T:ORBACH position in microns

Time (4.898 msec)

posit

ion (m

icron

s)

233.417

220.503

Xi

2.027 1030 i

0 5 10 15 20 25 30 35 40 45 500

20

40FFT of T:ORBACH position data

Frequency (Hz)

mic

ro m

eter

s 2 XFi

N

i204

N

.

Beam Signal while cycling T:HA49 correctors at 15 Hz

0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200500

0

500T:ORBACH position

Time (4.898 secs)

micro

mete

rs Xi

i

0 200 400 600 800 1000 1200 1400 1600 1800 2000 22002

1

0

1

2

Time (4.898 sec)

Curre

nt in

Corre

ctor (

Amps)

Ii

i

0 5 10 15 20 25 30 35 40 45 500

100

200FFT of T:ORBACH position data

Frequency (Hz)

micr

o m

eters 2 XFi

N

i204

N

.

0 5 10 15 20 25 30 35 40 45 500

0.5

1

1.5FFT of reference Current for Corrector

Frequency (Hz)

micr

o m

eters 2

IFi

N

i 207

N

Since at 15 Hz we can generate a 174 micron kick we shouldBe able to generate at least a 131 micron amplitude kick at 20 Hz which is much stronger than the strongest signal of 32 micronsobserved at 12 Hz. So the correctors are able to damp all oscillationsbelow 20 Hz if driven correctly.

How should the system look?

BPM 1

BPM 2

ProcessingCorrector 1

Corrector 2

CDF

D0D1

B1

Algorithm for orbit correction

0 5000 1 104

1.5 104

2 104

2.5 104

3 104

3.5 104

4 104

4.5 104

5 104

5.5 104

6 104

6.5 104

7 104

7.5 104

8 104

8.5 104

9 104

9.5 104

1 105

1 104

0

1 104

Z n 0

n

.

0 5 10 15 20 25 30 35 40 45 500

2 105

4 105

cxn2

N

n

N 21 106

Simulated beam response to applied kick 0.5 micro-rad kick of 20 Hz at D0 low beta quad as measured at A0 yield 30 micro-meter oscillations. Turn-by-turn (top) and frequency (bottom)

0 5000 1 104

1.5 104

2 104

2.5 104

3 104

3.5 104

4 104

4.5 104

5 104

5.5 104

6 104

6.5 104

7 104

7.5 104

8 104

8.5 104

9 104

9.5 104

1 105

0Z n 0

n

.

0 5 10 15 20 25 30 35 40 45 500

4 105

cxn2

N

n

N 21 106

Simulated beam response with damping feedback turned on. Now beam motion down to < 2E-20 meters at A0. Turn-by-turn (top) and frequency (bottom). The correctors are running < 0.8 micro-rad which would require cycling correctors at .324 Amps much less than the 1.2 Amps we were able to produce at 15Hz. If quad motion was located at B0 the optics are very similar and simulations produce similar results.

A detail schematic of a single orbit correction node

BPM 1HB11

BPM 2HB13

Corrector 1 HB19

Corrector 2 HB13

Sample And HoldCard

Sample And HoldCard

Op-amp x A

Op-amp x B

Op-amp x C

SUM

Beam sync trigger

1-200 Hz filter

1-200 Hz filter

Op-amp x D

SUM

A more detailed schematic of the damping system. Here Gains A,B and C are determined by the optics, voltage to position ratio of BPMs and voltage to Amp ratio for the correctors reference voltage. We have BPM transfer function of 12V/m, corrector transfer ratio of 2.54-rad/Amp and controlled by reference voltage transfer function 5 Amps/volt. This gives a total BPM voltage to reference voltage multiplicative factor as (1/12)x(1/2.54E-6)x(1/5) = 6561.67. The optics factor are Fa=1.88E-5, Fb= -0.021, Fc= -0.039, and Fd=-

2.371E-4. So a first estimate has A = 0.1233, B = -137.7, C = -255.9 and D = -1.555.

Issues to worry about? Phase shift?

Is this a real phase shift??? The snap shot time stamp says yes. But calculations from skin effect of stainless steel beam pipe say no.

0.61637 38.817

0.738 40.738

1.2 54.842

Current (Amps) Phase Diff. (degrees)

assuming the harmonic time dependence exp[iwt] and the spatial dependence of exp[ikx] for a simple slab geometry. Where our wave number k can be approximated with

k 1 1i( )

f f

With resistivity 75 106 cm

K become (1+i)*0.023√f . With a beam pipe thickness ~ .32 cm the phaseshift becomes

0.00736 f f

Or 1.63 degrees at 15 Hz.

Even if this does turn out to be a problem we can look to solutions used atThe APS where a simple phase and amplitude compensation circuit are used toCompensate phase shifts due to electronic and skin effects of aluminum beam Pipe yielding phase shifts in excess of 90 degrees.