MEDSI 2004, JR Chen1
Mechanical Effects on Beam Stability
June-Rong ChenNational Synchrotron Radiation Research Center, Hsinchu
MEDSI’04, ESRF, May 24, 2004
MEDSI 2004, JR Chen
Outline
I. IntroductionII. The Effects on Beam Orbit and Beam SizeIII. Thermo-mechanical EffectsIV. Mechanical DesignV. Sensors
MEDSI 2004, JR Chen3
I. Introduction
1.1 Beam Instability Frequency Domain1.2 Heat Sources and Frequency Domain1.3 Vibration Sources and Frequency Domain1.4 Power Spectra Density
MEDSI 2004, JR Chen4
Machine Instability Frequency Domain
SR users’ most concern
Frequency (Hz)109
GHz106
MHz103
kHz1
Hz10-310-610-9
yr day secminhr
RF fr
eque
ncy
Betat
ron os
cillat
ion
Revo
lution
freq
uenc
y
Sync
hrotr
on os
cillat
ion
Dampin
g tim
e, Ex
citati
on ti
me
AC lin
e volt
age (
60Hz)
Traff
ic (~
4Hz)
Ocean
wav
e (~7
sec)
Daily S
unsh
ine
Four
Sea
son
Thermal EffectVibration EffectBeam Effect
Ground Settlement
Beam
lifet
ime (
hrs)
MEDSI 2004, JR Chen5
Major parameters of the TLS storage ring:Lattice type Combined function Triple Bend Achromat (TBA)Operational energy 1.5 GeVCircumference 120 mRevolution frequency 2498.27 kHzOrbital period 400.277 nsRF frequency 499.654 MHzHarmonic number 200Bending field 1.43TBending radius 3.495 mInjection energy 1.5 GevNatural beam emittance 2.56 x 10-8 rad-mNatural energy spread 0.075%Momentum compaction factor 0.00678Damping time
Horizontal 6.959 msVertical 9.372 msLongitudinal 5.668 ms
Betatron tunes horizontal/vertical 7.18/4.13Natural chromaticities
Horizontal -15.292Vertical -7.868
Synchrotron tune (RF 800KV) 1.06*10-2
Bunch length (RF 800KV) 0.92 cmRadiation loss per turn (dipole) 128 keVNominal stored current (multibunch) 200 mANumber of stored electrons (multibunch) 5*1011
MEDSI 2004, JR Chen6
Mechanical Effect on Beam Orbit and Size
II. Pedestal
Beam Orbit Distortion, Emittance/Size Blowup
III. Girder
IV. Magnet/BPM etc.
⇑
⇑
I. Ground⇑
Ground Vibration
Heat (Air/Water)
Coolant Vibration
Displacement am
plified
⇑
MEDSI 2004, JR Chen7
Girder
An unstable girder will move all the components on it.
Girder Displacement
Pedestal
Ground
MEDSI 2004, JR Chen8
Heat Sources and Frequency Domain
1. Four Season: 1y2. Tunnel warm up (first start up after long shutdown): ~1w3. Sunshine: 1d4. Beam current decay (lifetime): ~ 10 hr5. Re-injection (energy ramp-up/down): ~ 1 hr6. Temperature “jitter”: ~ min
MEDSI 2004, JR Chen9
Vibration Sources and Frequency DomainA. Natural
1. ATL: PSD(f) ~ 1/f 22. Tide: 7 sec (Ocean wave)3. Moon gravitation force (high/low tide): ~12 hour (long wavelength)4. Earthquake5. Wind: 0.03-0.1 Hz, Plane wind ground bending (HERA)6. Long-term noise (BG): 1/f 47. Ground settlement
B. Traffic1. Traffic: ~ 4 Hz (hump on road), tens Hz (peak at 30Hz, SLS)
C. Facility Equipment1. Pumps, motors: tens Hz (15-70 Hz)2. Water vibration : tens Hz (30 Hz, ESRF)3. LHe flow:700-1500Hz (45g/s, SSC)
MEDSI 2004, JR Chen10
Ground vibration (A. Seryi, APAC2001)
Power spectrum of absolute ground motion measured at different sites. Smooth curves show modeling spectra. The high noise level at HERA is caused by cultural noise and, supposedly, by resonances of the clay/sandy site itself.
MEDSI 2004, JR Chen11
Spectrum of Coherence C(f) of two signals x(t), y(t)
X(f), Y(f) are Fourier transformations of x, y.
PSD (dimension: power in unit frequency band)
, Unit: µm2/Hz
Power Spectra Density (vibration)
2
0
2)(2lim)( ∫ −
∞→=
T fti
Tx dtetxT
fS π
dffSfff
f xrms ∫=2
1
)(),( 212σ
⟩⟩⟨⟨⟩⟨
=)(*)()(*)(
)(*)()(fYfYfXfX
fYfXfC
MEDSI 2004, JR Chen12
II. Effects on Beam Orbit and Size
2.1 Orbit Distortion2.2 Emittance and Beam Size Blowup2.3 Stability Requirement for Beam Orbit
and Size
MEDSI 2004, JR Chen13
(amplification factor, K≈30 for TLS)
Orbit Distortion
The rms closed orbit distortion σco(s) at an azimuthal position s is
with betatron tune ν, focal length F, uncorrelated transverse rms quadrupole misalignment σq, and number N of identical FODO cells. The average <β> is taken at the quadrupoles.
NF
ss q
CO
σπνββ
σsin2
)()(
⟩⟨=
qCO Ks σσ =)(
MEDSI 2004, JR Chen14
Emittance and Beam Size Blowup
2xx x )/)(()((s) EEss δηβεσ +=
constant'x)('xx)(2x)( 22 =++= sss βαγε
2/'βα −= βαγ
21+=
εε k≅y 0.1)~k coupling,(k <=
)((s) yy y sβεσ =
2xx x' )/)('()((s) EEss δηγεσ += )((s) yy y' sγεσ =
Couplings: H V: by skew quads, orbit in sextupoles, resonanceslongitudinal transverse: , scattering etc.E/E∆x ∆=η
MEDSI 2004, JR Chen15
Emittance and Beam Size Blowup (conti.)
Transverse emittance growth due to fast (turn to turn) dipole angular kicks δθ produced by bending field ΔB/B fluctuations in dipole magnets or by fast motion of quadrupolesσq which has a rate of
where f0 is the revolution frequency, Δνis fractal part of tune, Sδθ is the PSD of δθ= σq /F.
20 )/()2/1( FNf qq σβγ ⟩⟨≈
)()2/1(/ 02
0 fSfNdtd qN νβγε δθ ∆⟩⟨=
(V. Shiltsev, EPAC 96)
MEDSI 2004, JR Chen16
ESRF
MEDSI 2004, JR Chen17
Stability Requirement on Beam Orbit and Size
Intensity fluctuation after aperture: <0.1%(some experiments require < 0.01%)
Beam orbit fluctuation < 0.05 beam sizeBeam size fluctuation < 0.01 beam size
(Gaussian beam size) (aperture full dimension = 1x beam size)
MEDSI 2004, JR Chen18
MEDSI 2004, JR Chen19
A
Synchrotron light from bending magnet
Focusing mirror(3:1)
Pin-hole: 50 µm diameter
Photo-diode
Photon Beam Intensity Fluctuation(ΔI Monitor)
Oct.2002 Nov.2002 Jan.2003 Feb.20030.00
0.05
0.10
0.15
0.20
0.25
0.30
e-BPM noise reduced
AC line voltage regulated, PS-Q4 Noise reduced
photon beam monitor, ∆ I/I, improved
dI /
I (%
)
Time
ΔI/I ≈ 0.06%i.e. orbit fluctuation <2µmbeam size fluctuation <0.1µm(for Gaussian Beam)
MEDSI 2004, JR Chen20
III. Thermo-mechanical Effects
3.1 Dynamic Mechanical Considerations 3.2 Sources, Routes and Sensitivity of the
Thermo-mechanical Effects3.3 Temperature Control
MEDSI 2004, JR Chen21
Dynamic Mechanical Considerations*Sources of Noise
--- Air Temperature--- Water Temperature--- Synchrotron Light--- Electrical Power (electrical heating)
**Mechanical Effects--- Girder--- Vacuum Chamber--- RF Cavity--- Monitors
***Sensors and Control--- Temperature/Position Sensors--- Control Systems
MEDSI 2004, JR Chen22
Sources, Routes and Sensitivity of the Thermo-mechanical Effects
• Air Temperature Fluctuation• Synchrotron Light Irradiation• Power Supply and Electrical Heating• Water Temperature Fluctuation
(magnet, rf cavity, etc.)
MEDSI 2004, JR Chen23
Propagation chart from heat sources to the fluctuations in beam orbit and beam size (TLS)
Beam orbit / beam size fluctuation
Sources of Noise Utility System Accelerator Components
Synchrotron light Outdoor temp. Machine setting AC voltage
CTW / CHW Electrical heating
AHUs Cable heating
Air temp. (expt area) Air temp. (tunnel) Air temp. (core area)
DIW (BL) DIW (VAC) DIW (mag, rf, ps)
Photon monitor Vacuum chamber
e-BPM Girder
Operation Technique
Magnet RF System PS (magnet)
Feedback System
MEDSI 2004, JR Chen24
Monitor reading Beam orbit / beam size fluctuationFeedback
Magnet RF cavity PS (magnet)
Girdere-BPM
Photon monitor Vacuum chamber
Air temp. (expt area)
DIW (BL) DIW (VAC) DIW (mag, rf, ps)
Air temp. (tunnel) Air temp. (core area)
Outdoor temp. Machine setting AC voltage
Electrical heatingCTW / CHW
AHUs
Synchrotron light
Cable heating
e-beam& wave
Air Temperature Fluctuation -- Girder Displacement --
MEDSI 2004, JR Chen25
Girder
An unstable girder will move all the components on it.
Girder Displacement
MEDSI 2004, JR Chen26
Girder Displacement
• Main cause: air temperatureSensitivity to air temp.: ~10 μm / ℃Induced beam orbit drift: 20-100 μm / ℃
• Current status: < ± 0.1 μm per 8 hr shiftAir temp. : < ± 0.1℃ (utility control system improved)Thermal insulator jacket
-200 0 200 400 600 800 1000 1200 14000.92
0.94
0.96
0.98
1.00-200 0 200 400 600 800 1000 1200 1400
24.0
24.5
25.0
25.5
26.0
Beam Position
mm
min
Air Temperature
Deg
ree
(C)
0 25 50 75 10024
25
26
27
28
Disp
lace
men
t (µ
m)
Tunnel Air Temp. Girder Disp. Outer Girder Disp. Inner
Time (Hours)
Tem
pera
ture
()℃
-20
-15
-10
-5
0
MEDSI 2004, JR Chen27
Non-uniform Temperature Distribution
Temp(oC)Temp(oC)
Air OutletAir OutletAir ReturnAir Return
MEDSI 2004, JR Chen28
Monitor reading Beam orbit / beam size fluctuationFeedback
Magnet RF cavity PS (magnet)
Girdere-BPM
Photon monitor Vacuum chamber
Air temp. (expt area)
DIW (BL) DIW (VAC) DIW (mag, rf, ps)
Air temp. (tunnel) Air temp. (core area)
Outdoor temp. Beam energy AC voltage
Electrical heatingCTW / CHW
AHUs
Synchrotron light
Cable heating
e-beam& wave
Synchrotron Light Irradiation-- Expansion of Vacuum Chamber --
MEDSI 2004, JR Chen29
Expansion of Vacuum Chamber
The expanded vacuum chamber moves the components touched or connected to it. The force transferred to the girder.
MEDSI 2004, JR Chen30
Expansion of Vacuum Chamber
• Caused by synchrotron light irradiation.Sensitivity to water temp.: ~10 μm / ℃Move the girder (~0.3μm/℃) and BPM (~1μm/℃) Induced beam orbit drift: ~10-30 μm / ℃
• Current statusVacuum cooling water temp.: ~ ± 0.5℃(Should be greatly improved after adopting Top-up Injection)
0 6 12 18 2419.5
20.0
20.5
21.0
21.5 Girder Displacement Beam Current
Time (Hours)
Disp
lace
men
t (µ
m)
0
100
200
Bea
m C
urre
nt (m
A)
0 200 400 600 800 1000 1200 1400-0.08-0.06-0.04-0.02
0 200 400 600 800 1000 1200 14000.51.01.52.0
0 200 400 600 800 1000 1200 14002425262728
0 200 400 600 800 1000 1200 14000
100200
Beam Position
mm
min
BPM Displacement
um
Vac-chamber Temp
Tem
p (C
)
Beam Current
mA
MEDSI 2004, JR Chen31
Monitor reading Beam orbit / beam size fluctuationFeedback
Magnet RF cavity PS (magnet)
Girdere-BPM
Photon monitor Vacuum chamber
Air temp. (expt area)
DIW (BL) DIW (VAC) DIW (mag, rf, ps)
Air temp. (tunnel) Air temp. (core area)
Outdoor temp. Machine setting AC voltage
Electrical heatingCTW / CHW
AHUs
Synchrotron light
Cable heating
e-beam& wave
Power Supply and Electrical Effect (1)
MEDSI 2004, JR Chen32
Power Supply and Electrical Heating (1)
• Transient after injection or shut downHeat source: mainly dipole-cables
• Transient time~ 0.5 hr (after injection, insignificant after injector energy
increased from 1.3 GeV to 1.5 GeV)ΔT: > 0.5℃ ΔT: < 0.2℃
~ 12 hr (after shut down), it’s better not to turn PS off ΔT: >1.5℃
0.0 6.0 12.0 18.0 24.022
23
24
25
Beam
Cur
rent
(mA
)
Tem
pera
ture
()℃
Time (Hours)
Beam Current Tunnel Air Temp.
0
100
200
6 8 10 12 14 16 18 2026.2
26.3
26.4
26.5
Tunnel Air Temp. Beam Current
Time (Hours)
Tem
pera
ture
()℃
0
100
200
Beam
Cuu
ent (
mA
)
(after shutdown) (re-injection)
MEDSI 2004, JR Chen33
Monitor reading Beam orbit / beam size fluctuationFeedback
Magnet RF cavity PS (magnet)
Girdere-BPM
Photon monitor Vacuum chamber
Air temp. (expt area)
DIW (BL) DIW (VAC) DIW (mag, rf, ps)
Air temp. (tunnel) Air temp. (core area)
Outdoor temp. Machine setting AC voltage
Electrical heatingCTW / CHW
AHUs
Synchrotron light
Cable heating
e-beam& wave
Power Supply and Electrical Effect (2)
MEDSI 2004, JR Chen34
Power Supply and Electrical Heating (2)
9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.022
24
26
Bea
m O
rbit
(mm
)
Vol
tage
(V)
Tem
pera
ture
()℃
Time (Hours)
Core Area Temp. Quadrupole Power Beam Orbit
205.52
205.56
205.60
205.64
0.97
0.98
0.99
1.00
• Phenomenon AC line voltage air temperatureAC line voltage output of DC-PS Sensitivity: ~ 5 μm / ℃
• Current StatusAir temperature (core area): ~ ± 0.3℃A.C. line voltage fluctuation : ~ ± 1.5%(~ ± 0.05% for PS-Q4)
Temperature
AC Line Voltage
AC Line VoltageTransmitter Water Temp.horizontal beam size
(Beam size): ~ 1 μm/Volt
MEDSI 2004, JR Chen35
Monitor reading Beam orbit / beam size fluctuationFeedback
Magnet RF cavity PS (magnet)
Girdere-BPM
Photon monitor Vacuum chamber
Air temp. (expt area)
DIW (BL) DIW (VAC) DIW (mag, rf, ps)
Air temp. (tunnel) Air temp. (core area)
Outdoor temp. Machine setting AC voltage
Electrical heatingCTW / CHW
AHUs
Synchrotron light
Cable heating
e-beam& wave
Water Temperature Fluctuation-- Magnet & RF cavity --
MEDSI 2004, JR Chen36
Magnet (Water Temp.)
100 200 300 40022
24
26
28 Mag-Water Temp. Beam Position
Time(min.)
Tem
pera
ture
()℃
0.22
0.23
0.24
0.25
0.26
Posit
ion
(mm
)
Caused by the temperature fluctuations of magnet cooling waterMagnet deformed ~10μm/℃Induced beam orbit drift: 5-50 μm / ℃
Current statusCooling water temp.: ~ ± 0.1℃
MEDSI 2004, JR Chen37
Beam Size FluctuationInduced by RF-Water Temp.
11.5 12.0 12.5
35
36
37
38
Bea
m S
ize(µ
m)
Tem
pera
ture
()℃
Time (Hours)
Beam Size (X) DIW Temp. of the Rf Cavity
320
360
400
• Phenomenon Water temperature beam size (x) Sensitivity: ~20 µm/℃ (hor.)
• Current StatusWater temperature (rf): < ± 0.02℃
MEDSI 2004, JR Chen38
~1 µm/℃-~0.3µm/℃-10-30µm/℃~ ±0.5℃Water Temp.(vac-outlet)
---~20 µm/℃(hor.)-< ±0.02℃Water Temp.
(rf)
-~10µm/℃--5-50 µm/℃< ±0.1℃Water Temp.(magnet)
--~10 µm/℃(ver.)-20-100µm/℃< ±0.1℃Air Temp.
BPMMagnetGirderBeam sizeBeam orbit
Amplification factor(component displacement)Amplification factorCurrent
Temp. Fluctuation
Heat source
Sensitivity of the fluctuations in beam orbit, beam size and the displacements of main components
to the fluctuations in the air and water temperatures
MEDSI 2004, JR Chen
Water Temperature Control• Controlled step by step:
CTW CHW(&HTW) (± 0.3℃) DIW (± 0.1℃)
• Device linearity and resolution (e.g. valves)Two smaller valves with better resolution, instead of one.
• Variable frequency controllerTo control the stability of water pressure (flow rate)
• Buffer tank (or heater + mixing heat exchanger)To further smooth the temperature fluctuation (± 0.01℃)
• Capacity (heat exchanger)
MEDSI 2004, JR Chen40
Water Pressure Control: Fluctuation: <1%Sensor: Pressure Gauge Pump: Variable Frequency Controller
Water Temperature Control: Fluctuation: < ± 0.1℃Sensor: ThermocoupleValve: Electrical Actuator
MEDSI 2004, JR Chen41
Water Pressure Control: (same as Cu-water system)
Water Temperature Control:Buffer Tank: MixingFluctuation: < ± 0.01℃Sensor: high resolution temperature sensorValve: Electrical Actuator
MEDSI 2004, JR Chen
Air Temperature Control
• AHU System• Temperature Uniformity• Thermal Insulator
MEDSI 2004, JR Chen
CHW & HTW Temperature Control: Fluctuation: < ± 0.3℃
Air Temperature Control: Fluctuation: < ± 0.15℃Sensor: Thermocouple (SR)Valve: CHW valve
AHU System (TLS)
X (H)
Air to SR tunnelX
(C)
Air return from SR tunnel
Temperature Sensor
Hot WaterChilled Water
Temperature Sensor
Outdoor Air (IN)
Exhausted air
Temperature Sensor (in SR Tunnel)
MEDSI 2004, JR Chen44
Air Flow Uniformity Control (ID)
MEDSI 2004, JR Chen45
Girder with thermal insulation. Transient time constant Longer (smoothing effect)
MEDSI 2004, JR Chen46
IV. Mechanical Design
4.1 Ground4.2 Structure of Girder Magnet Assembly
MEDSI 2004, JR Chen47
Ground• Ground Motion
settlement: ESRF, PLS (~2mm/year)Site selection (underground composition)Same Base (move as a whole)No Underground Hollow
• Ground wave isolationTrench around the structure: ESRF 3m deepExpansion jointDamping of soil and concrete slab
• Vibrating Equipment Vibration Reduction/IsolationAway from Light source
Ground Motion (PLS)(In Soo Ko, APAC2004)SR TUNNEL ELEVATION SURVEY
(Dev From '93.06 To '03.07)
-26
-22
-18
-14
-10
-6
-2
2
6
10
14
18
22
26
1 2 3 4 5 6 7 8 9 10 11 12
Cell No.
Dev(mm)
' 93.08' 94.08' 95.07' 96.07
' 97.07' 98.07' 99.07' 00.07' 01.07' 02.08
' 03.07
MEDSI 2004, JR Chen49
Ground Vibration at TLSInj
ection
tunn
el
Utility
tunn
el
MEDSI 2004, JR Chen50
Ground wave isolation – ESRF“ESRF foundation phase report”, 1987
MEDSI 2004, JR Chen51
Location of Utility and Cryogenics System at TLS
Liquid N2 Dewar
He gas storage tank
He Compressor
Refrigerator and
AirHandleUnits
To Utilities
d > 80m
d > 60m
MEDSI 2004, JR Chen52
Structure of Girder Magnet Assembly
1. Interaction of Ground Waves with Beam2. Vibration Suppression
MEDSI 2004, JR Chen53
Interaction of Ground Waves with BeamFactor 1: Damping factor of soil and concrete slab (Section 4.1)Factor 2: Amplification factor of Girder Assembly
(Ground vibration Pedestal Girder Magnet)Factor 3: COD Amplification factor
(Magnet Beam) (Section II)Factor 4: Attenuation factors of Fast Feedback System
The characteristic wavelengths of slow ground motions are far greater than betatron wavelength, the dynamic effects to the beam can be neglected.
Betatron wavelength λβy=C/νy = 120 m / 4.13= 29 mλβx=C/νx = 120 m / 7.18= 16.7 m
Assume υ= 500 m/s (soft ground)fβ = υ/ λ= 17 Hz --- vertical
= 30 Hz --- horizontalFor frequencies << fβ, the effects to the beam can be neglected.
MEDSI 2004, JR Chen54
Vertical orbit distortion (no amplification in GA)
where, Φnis the vertical betatronphase advance between the obsevationpoint and the nth magnet. β0, and are the values of the β-function at observation point, focusing and defocusing quads.
due to a single vertical ground wave with amplitude , phase , angular frequency ω=2π f, velocity υ, wavelength λ= υ/f and direction of incidence θω:
}Re{ˆ)()]cos([ 0 wn
Cti
n eytyθθ
λφω −++
=∆
)]}cos(
)cos(ˆ[
ˆsin2
Re{)(
)/cos()/(12
1
)/cos()/(2
2
)(0 0
ynCi
N
n
ynCi
N
n
ti
yc
wyn
wyn
e
e
eFyty
πνβ
πνβ
πνβ
θνλ
θνλ
φω
−Φ−
−Φ×
=
−Φ−
=
−Φ
=
+
∑
∑(
y
0φ
β β(
(A. Chao and M Tigner, “Handbook of Accelerator Physics and Engineering”, Ch-5.13, 1999.)
MEDSI 2004, JR Chen55
The ratio of the COD to the amplitude of plane ground wave is
where Jp the Bessel function and
Cp becomes resonant for |p| = |m|N± ν y (ν= Nµ/2π). Withδνy the distance of νy from the closet integer [νy], the maximum of the resonant term can be expressed as 1/
21
234341414
2242444
0
}])()(
])()({[2ˆ
ˆ
−−−
∞
−∞=−
−−
∞
−∞=
−+
−==
∑
∑
pppp
p
pppp
pc
y
CCJCCJ
CCJCCJfy
yR
λλ
λλβ
)}(cos]2
)1(cos[ˆ{)
2sin(
)1( 1
ww
p
p pN
Np
NpC θπβµθπβµπ −−−−
+×
−
−=
+ (
)sin( yNδνπ
The Bessel function Jp differs significantly from zero only for argumentsC/λ> p. Thus Ry is small for small C/λ and rises in a step-like manner at C/λ= [νy], N-[νy], N+[νy], 2N-[νy], etc..
MEDSI 2004, JR Chen56
21
234341414
2242444
0
}])(')('
])(')('{[2ˆ
ˆ
−−−
∞
−∞=−
−−
∞
−∞=
−+
−==
∑
∑
pppp
p
pppp
pc
CCJCCJ
CCJCCJFx
xRx
λλ
λλβ
}Re{)cos(ˆ)()]cos([ 0 wn
Cti
wnn extxθθ
λφω
θθ−++
×−=∆
Horizontal orbit distortion due to a single vertical ground wave
MEDSI 2004, JR Chen57
Vibration Suppression• Resonant frequency of mechanical structure
-- Equation of Motion-- Design Considerations
• Damping design
Purpose: To reduce the amplification factor (transmissibility) of Girder Magnet Assembly
(Ground vibration Pedestal Girder Magnet)
MEDSI 2004, JR Chen58
Resonant frequency of the system:
, for viscous damping, for hysteretic damping
where, m: mass, k: spring constant, y0: excitation, c: damping constant, loss factor:
Equation of Motion
0))(1( 0 =−++ yyikym η&&0)()( 00 =−+−+ yykyycym &&&&
EnergyStoredTotalCycleperLossEnergy
=η
π2/0 mkf =
(A. Chao and M Tigner, “Handbook of Accelerator Physics and Engineering”, Ch-5.14, 1999.)
MEDSI 2004, JR Chen59
2
0
22
0
2
0
0 )2(])(1[
)2(1
ff
ff
ff
YY
aa
a
ς
ς
+−
+=
The steady-state amplitude Y of the system in response to a base excitation y0= Y0 cos(2πfat) is
222
0
2
0 ])(1[
1
η
η
+−
+=
ffY
Y
a
)2(2 0fmcπ
ς =
(hysteretic)
(viscous)
where, and π2/0 mkf =
MEDSI 2004, JR Chen60
H1
H2
L1 W2
W1W0
VEM
π2/0 mkf =
VEM
VEM
1. As the amplitude of the excitation source increases at lower frequencies, the resonant frequency of the MGA system should be as high as possible.
2. m: Mass of magnets is the most dominant mass in the system but hard to change. To use hollow box structure with ribs to reduce the weight of girder but keep the strength. k: It is crucial in designing the dimensions of the girder assembly and selecting the material of pedestal and girder. (H1, H2, L1-- as small as possible; W0, W1, W2-- as large as possible)
3. Damping design (ViscoElasticMaterial, VEM) is quite effective to reduce the amplification factor.
Design Considerations
MEDSI 2004, JR Chen61
Damping Design
• Damping Materials
• Cases StudyAPS - Damping PadESRF - Damping LinkTLS - Composite Damping Material
MEDSI 2004, JR Chen62
0.1 to 50000.001 to 10Rubber, plastic
10,000 to 30,0000.01 to 0.05, 0.1 for dry sand
Sand, granularmedia
5000 to 250000.01 (oak) to 0.02 (cork)Wood, cork,plywood
10 x 103 to 100 x l030.001 (light) to 0.05 (dense)Concrete10 x 1060.002Cu30 x 1061 x 10-4 - 6 x 10-3Steel, Fe10 x 10610-4AlModulus (E) [psi]Loss Factor, ηMaterial
Table 1 Relevant material properties
Damping Material (I)
(A. Chao and M Tigner, “Handbook of Accelerator Physics and Engineering”, Ch-5.14, 1999.)
MEDSI 2004, JR Chen63
Pedestal High Strength Concrete(S. Seko et al., APAC2004)
Concrete: high stiffness & low transmissibility of acceleration.
MEDSI 2004, JR Chen64
Table.2 Properties of viscoelastic damping material(VEM) at 50 to 100°F and 5 - 15 Hz frequency range————————————————————
VEM η G [psi] ————————————————————
3M ISD 112 0.8 20 - 1003M NPE 3128 0.6 - 1 10 - 70Anatrol AN 217 0.7 - 1 20 - 70Anatrol AN 218 0.5 - 1 40 - 300
————————————————————G = E/2(1+µ) (µ: Possion’s ratio, µ≈0.5 for VEM)
Damping Material (II)
(A. Chao and M Tigner, “Handbook of Accelerator Physics and Engineering”, Ch-5.14, 1999.)
MEDSI 2004, JR Chen65
VEM• The property of VEM is environmental
dependent.(temperature, frequency, strain amplitude, static pre-strain, radiation dose)
• Must be carefully used.
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)1( VEMVEMVEM ikK η+=
VEMISYM KKK111
+=
VEMISYM KKK +=
steel
steelsteel t
baEk = ]))(2
(1[ 2
VEMVEM
VEMVEM tab
bat
baEk+
+=
steel
steelsteel t
baGk =VEM
VEMVEM t
baGk =
Damping Pad
In shear:
In compression:
(series)
(parallel)
MEDSI 2004, JR Chen67
Damping Pad – APS(D. Mangra et al., MEDSI 2000)
Damping pads under the pedestals can reduce the displacement magnification by a factor of 4-6. The peak displacements at natural frequencies can be reduced by more than one order of magnitude.
Damping pads provide a more cost-effective solution for reducing vibration levels than increasing the support stiffness.
The damping pads should be installed closer to the ground in order to intercept the ground excitation before it is magnified by the weaker elements of the support system (e.g. alignment jacks).
Damping pad:Anatrol 217 films: (2x)Stainless plates16”d-3/4”t,12”d-1/8”t, 12”d-1/2”t
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APS
MEDSI 2004, JR Chen69
Damping Link - ESRF (L. Zhang et al., SSIELS-2001 )
(Al+VEM+Al)
Why damping links in ESRF? Damping pad had weak stiffness in horizontal. (e.g. 0.6mm displacement) The damping links are compatible with
the alignment operation. (2mm tolerance)
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ESRF
(wf: water flow on, wd: with damping links)
MEDSI 2004, JR Chen71
Frequency Response H1(Signal 1,hammer) - Input (Magnitude)FFT- template : Input : Input : FFT Analyzer
0 4 8 12 16 20 24 28 32 36 40 44 48
-180
-170
-160
-150
-140
-130
-120
-110
-100
[Hz]
[dB/1.00 (m/s²)/g] Frequency Response H1(Signal 1,hammer) - Input (Magnitude)FFT- template : Input : Input : FFT Analyzer
0 4 8 12 16 20 24 28 32 36 40 44 48
-180
-170
-160
-150
-140
-130
-120
-110
-100
[Hz]
[dB/1.00 (m/s²)/g]
Frequency Response H1(Signal 1,hammer) - Input (Magnitude)FFT- template : Input : Input : FFT Analyzer
0 4 8 12 16 20 24 28 32 36 40 44 48
-190
-180
-170
-160
-150
-140
-130
-120
-110
[Hz]
[dB/1.00 (m/s²)/g] Frequency Response H1(Signal 1,hammer) - Input (Magnitude)FFT- template : Input : Input : FFT Analyzer
0 4 8 12 16 20 24 28 32 36 40 44 48
-190
-180
-170
-160
-150
-140
-130
-120
-110
[Hz]
[dB/1.00 (m/s²)/g]
Frequency Response H1(Signal 1,hammer) - Input (Magnitude)FFT- template : Input : Input : FFT Analyzer
0 4 8 12 16 20 24 28 32 36 40 44 48
-140
-130
-120
-110
-100
-90
-80
-70
-60
[Hz]
[dB/1.00 (m/s²)/g] Frequency Response H1(Signal 1,hammer) - Input (Magnitude)FFT- template : Input : Input : FFT Analyzer
0 4 8 12 16 20 24 28 32 36 40 44 48
-140
-130
-120
-110
-100
-90
-80
-70
-60
[Hz]
[dB/1.00 (m/s²)/g]
CDM
CDM
CDM
Composite Damping Material - TLS(D.J. Wang et al., APAC 2004)
Composite damping material (CDM) -- a mixing of epoxy and sand
(similar to polymer concrete) -- high stiffness-- peak shifts 24Hz 35Hz
with CDM
w/o CDM
with CDM& Water
filled withwater
MEDSI 2004, JR Chen
• Hydrostatic Leveling System • Potentiometer• LVDT• Accelerometer• Vibrometer• Autocollimator
V. Sensors
MEDSI 2004, JR Chen73
Positioning and Positioning Monitoring System (SLS)(S. Zelenika et al., MEDSI 2000)
Dynamic Alignment(A) mover + encorder(B) HLS(C) HPS
(A)
(B)
(C)HLS: hydrostatic leveling systemHPS: horizontal positioning system
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Features:Stability ±10µmSettling time ~5 minLong term drift
Hydrostatic Leveling System
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Measurement Setup (TLS)
LVDT Granite Stand
Potentiometer
MEDSI 2004, JR Chen
Potentiometer
outin
Lininac
bcout
VVLdntDisplaceme
R,VLdV
RRV
×=⇒
∞=×=×=
ResistanceWiper
Shaft
Spring
Envelope
Terminal
Vin
abc
RL
Vout
carb
on b
rush
d
MEDSI 2004, JR Chen
• Signal : DC Max. 14 V (GEFRAN PY2)Linearity : ± 0.3%
• Resolution : Depends on the resolution of AD/DA card• Noticeable friction load• Need for a contact with the object• Low speed• Friction and excitation voltage cause heating• Low environment stability
MEDSI 2004, JR Chen
LVDT
• Len’s Law : E = L(dI/dt)• Input Voltage : AC, Vref
• Output Voltage : AC, Vout = V1 – V2
• Displacement = k Vout (DC)
V1 V2Vout = V1- V2
Vref
MEDSI 2004, JR Chen
• Linearity : ±0.1%• Resolution : 0.1 μm• Very little friction resistance• Hysteresis is negligible (mechanical and electric)• Output impedance is very low• Low susceptibility to noise and interferences• If LVDT is put in the high electromagnetic field, the
measurement of noise is increased.
MEDSI 2004, JR Chen
Accelerometer
• eo : output voltage• : acceleration• : time constant, RC, s• : sensitivity , V/cm• : natural frequency• D : d/dt
• Piezoelectric accelerometer : The electric charges output of piezo is proportional to the force.
• Transfer function
)1/D2/D)(1D(D)]C/(K[
)D(xe
n2n
2
2nq
i
o
+ωξ+ω+τ
τω=
&&
ix&&τ
CKq
nω
mass
Spring
Piezoelectriccrystal stack
Vibration Surface
MEDSI 2004, JR Chen
• Measurement range : 2.5g pk (PCB-393C)Range : 0.025-800 HzNon-Linearity : ≦ 1 %Sensitivity : 100mV/g
• Generally the range of Piezoelectric accelerometer is from 2 to 25kHz.
• Below 1 Hz must be carefully, always the signal is not so reliable.
• Mount the sensor assembly to the prepared test surface by “rocking” or “sliding” it into place.
MEDSI 2004, JR Chen
LLaser
Braggcell
OBJ
SIG OUT
+ -
RF IN
BS1 BS2
BS3
D2
D1
Vibrometer• Laser Doppler Vibrometer : two head, one for
reference, one for measurement.• Mach-Zehnder interferometer
I(1)=1/2 A2 (1+cos(2π(fB + 2△z/λ)))I(2)=1/2 A2 (1- cos(2π(fB + 2△z/λ)))SIG OUT voltage u=K cos(2π(fB + 2△z/λ)) △z : Displacement fB : frequency shift by Bragg cell
• The Doppler effect : RF signal : θRF = 4π△z/λDoppler shift fD = 2△z/△t/λ = 2 v/λfout = fB + fDThe sign of v denotes the moving direction.
MEDSI 2004, JR Chen
Autocollimator• High-precision instrument for measurement
of angular settings.• The autocollimator projects the image of a
reticle marking in collimated beam path to the mirror. When the mirror is titled with an angle α, the reflected beam is shifted △Y from the center.
• The angle of tilt : α= △Y/2f• f : focal length of the autocollimator
MEDSI 2004, JR Chen
Moller-WedelElcomat-2000
D (angle)25 Hz0.05arcsec±100arcsec(~ 7500mm)
Autocollimator
PolytecOFV-2200
V250 kHz0.5μm/s100 mm/sVibrometer
PCB-393CA0.025-800 Hz0.1mg(rms)
2.5g(peak)Accelerometer
TESAGT21
D60Hz0.1μm±0.2mmLVDT
GEFRANPY2F
D5Hz1.15μm(16 bits)
10mmPotentiometer
RemarkAcceleratorVelocity
Displacement
Frequencyrange
ResolutionRangeSensor