Osamu Miyakawa Hiroaki Yamamoto March 21, 2006 LSC meeting

March 2007, LSC meeting, Osamu Miyakawa 1LIGO-G070129-00-Z

Osamu MiyakawaHiroaki Yamamoto

March 21, 2006 LSC meeting

Modeling of AdLIGO arm lock acquisition

using E2E time domain simulation


Introduction

Is it possible to acquire lock FP arms of AdLIGO?

» Complicated Quad-suspension

» Weak actuation force ~100N due to Electro Static Drive (ESD)

» High finesse ~1200

» Radiation pressure due to high power (0.8MW)

First fringe lock for arm is a minimum requirement for full 5DOFs lock of RSE according to the 40m’s experiment.


Parameters in this simulation

4km single arm cavity AdLIGO Quad suspension

» Local damping (6 DOFs on Top Mass)» Maximum actuation force: 200mN for UIM, 20mN for PM, 100N for TM» LSC UGF: 8Hz for UIM, 40Hz for PM, 180Hz for TM

Error signal from reflected RFPD. Feedback to test mass only during lock acquisition, then feedback to lower 3 masses after locked. Higher order mode up to TEM01, 10 implemented

For maximum mirror speed test No seismic motion Very low power ~1kW stored in arm to avoid radiation pressure Initial given mirror speed at TM

There might be better parameters because it’s a big parameter space.


Lock acquisition using Raw error signals

Lockable mirror speed ~ 25nm/sec Ringing causes no lock acquisition.

» Cavity length, Finesse, Mirror speed

0.1 0.2 0.3 0.4 0.50

500

1000

[W]

Power

0.1 0.2 0.3 0.4 0.5

-0.1

-0.05

0

0.05

0.1

Time[s]

[W]

Raw error signal

0.1 0.2 0.3 0.4 0.50

500

1000

[W]

Power

0.1 0.2 0.3 0.4 0.5

-0.1

-0.05

0

0.05

0.1

Time[s]

[W]

Raw error signal

0.1 0.2 0.3 0.4 0.50

500

1000

[W]

Power

0.1 0.2 0.3 0.4 0.5

-0.1

-0.05

0

0.05

0.1

Time[s]

[W]

Raw error signal

0.1 0.2 0.3 0.4 0.50

500

1000

[W]

Power

v=30nm/s

DC

0.1 0.2 0.3 0.4 0.5

-0.1

-0.05

0

0.05

0.1

Time[s]

[W]

Raw error signal

v=30nm/s

DC

v=20nm/sec v=25nm/sec v=30nm/sec Locked Locked after a fringe passed No lock


0.1 0.2 0.3 0.4 0.50

200

400

600

800

[W]

Power

0.1 0.2 0.3 0.4 0.5-2

-1.5

-1

-0.5

0

0.5

Time[s]

[W]

Raw error signal

Lockable mirror speed ~25nm/sec No advantage for lock acquisition time even normalization applied. Ringing flips sign for both raw/normalized error signal.

Initial LIGO algorithm ~ normalized by transmitted light

0.1 0.2 0.3 0.4 0.50

500

1000

[W]

Power

0.1 0.2 0.3 0.4 0.5-2

-1.5

-1

-0.5

0

0.5

Time[s]

[W]

Raw error signalNormalized signal

0.1 0.2 0.3 0.4 0.50

500

1000

[W]

Power

0.1 0.2 0.3 0.4 0.5-2

-1.5

-1

-0.5

0

0.5

Time[s]

[W]

Raw error signalNormalized signal

0.1 0.2 0.3 0.4 0.50

200

400

600

800

[W]

Power

0.1 0.2 0.3 0.4 0.5-2

-1.5

-1

-0.5

0

0.5

Time[s]

[W]

Raw error signal

Normalized

Raw error

Normalized signal

v=20nm/sec v=25nm/sec v=30nm/sec Locked Locked after a fringe passed No lock

Linearizedarea


0.2 0.4 0.6 0.8 10

200

400

600

800

1000

Time[s]

[W]

Power

0.2 0.4 0.6 0.8 1-0.5

0

0.5

Time[s]

[W]

Raw error signal

0.2 0.4 0.6 0.8 1-5

-4

-3

-2

-1

0

1

2

x 10-8

Time[s]

[m]

Relative position

predicted

actual

0.2 0.4 0.6 0.8 1

-200

-100

0

100

200

Time[s]

[N]

Actuation force

UIM(mN)

PM(mN)

TM(uN)

Guide lock

This “guide lock” algorithm was originally proposed by Matt Evans.

Raw error signal of first fringe at 0.2 sec is used to estimate the mirror direction and position.

Applying maximal force to return it to the fringe at low speed where locking servo can catch it, even though the arm power is low and the demod signal is oscillating.

Initial fringe approach speed can be maximized up to 280 nm/s (x11 times faster than the speed with raw/normalized error signal).


Optimization for Guide lock parameters

0.1 0.2 0.3 0.4 0.50

500

1000

[W]

Power

0.1 0.2 0.3 0.4 0.5-0.5

0

0.5

[W]

Raw error signal

0.1 0.2 0.3 0.4 0.5

-2

-1

0

x 10-8

Time[s]

[m]

Relative position

predicted

actual

0.2 0.4 0.6 0.8 10

500

1000

[W]

Power

0.2 0.4 0.6 0.8 1-0.5

0

0.5

[W]

Raw error signal

0.2 0.4 0.6 0.8 1

-2

0

2x 10

-8

Time[s]

[m]

Relative position

predicted

actual

70nm/sec with no optimization 230nm/sec with optimization


10-1

100

101

10-15

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

10-6

10-5

Frequency [Hz]

No

ise

[m

/rtH

z]

Seismic noise

.ITM.ground.x(78)

.ITM.sus.x(72)

.ITM.m0.x(41)

.ITM.m1.x(47)

.ITM.m2.x(53)

.ITM.m3.x(59)

Lock acquisition limited by mirror speed due to micro seismic

• Upper 10% of noisy time• Mirror speed is limited around 0.2-0.3Hz micro seismic.• It produces 1e-6m/s between test masses.


Suspension Point Interferometer (SPI)

Y. Aso Ph.D thesis (2006)

•SPI reduces displacement noise at least 10 times at low frequency


0 20 40 60 80 100-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1x 10

-6

Time[s]

[m/s

]

Velocity between test masses

DayNightSPI/DaySPI/Night

Cavity velocity

• Day: upper 10% of noisy time• Night: 1/5 motion of the day time• SPI: reduce mirror speed 10times at low frequency (0.1Hz zero and 1Hz pole)

Lock range byGuide lock

Lock range byRaw/Normalized

error signal


Arm LSC Summary

Possibility of lock acquisition when mirrors pass through a resonant point

Guide lock can replace SPI.

» Can lock arm but not easy to lock full 5DOF in the day time with one of the guidelock or SPI.

» May lock full 5DOFs in the night with one of the guidelock or SPI

» May lock full 5DOFs in all day with guidelock and SPI.

Lockable mirror speed

Day Night SPI/Day SPI/Night

Raw error 25nm/sec 9.5% 32% 56% 98%

Normalized 25nm/sec 9.5% 32% 56% 98%

Guide lock 280nm/sec 68% 99% 100% 100%


Difficulty

Bias of alignment was assumed to be zero, and mode matching was assumed to be perfect

» Causes mistriggering guide lock in real experiment

Peak does not corresponds to the real resonant point. Peak is delayed due to the limit of the speed of light.

Mirror should be pushed to cross the resonant point if the seismic noise is too small, but should not be too fast.

» If you take 20sec to cross resonant point, mirror speed will be about 50nm/sec, enough slow.


Lock acquisition with radiation pressure

Radiation pressure causes a disturbance of lock acquisition

60nm/sec :enough slow to acquire lock for LSC

Full power : 0.7MW

Lock can be acquired with less than few kW

Following 40m method: ~30% input light makes 1kW inside arm with CARM offset

» 125W x 0.3 x 0.5(BS) x 0.07(TPRM) x 770(FP) = 1kW

Locked

Locked

No lock


0 1 2 3 4 50

1

2

3

4

5

6

7

8x 10

4

Time[s]

[W]

Power

TEM00TEM01(pit) x10TEM10(yaw) x10

0 1 2 3 4 5-3

-2

-1

0

1

2

3x 10

-6

Time[s]

[m]

Position

0 1 2 3 4 5-2

-1.5

-1

-0.5

0

0.5

1x 10

-6

Time[s]

[ra

d]

Pitch

ITM.m0ITM.m1ITM.m2ITM.m3ETM.m0ETM.m1ETM.m2ETM.m3

0 10 20 300

1

2

3

4

5

6

7

8x 10

5

Time[s]

[W]

Power

Angle stability with/without ASC due to radiation pressure

ITM ETM

Radiationpressure

LSC

LSC

LSC

1.3e-5 m

ASC

ASC

ASC

ASC Controlling M3 through M2 leads full power(0.7MW)

f 3 filter

Boost at 2Hz

10Hz control band width

Pitch motion due to Radiation pressure breaks lock with 10%(70kW) of full power if there is no ASC


102

103

104

105

106

107

Pitch opto-mechanical(suspenstion) TF

Gai

n

0Wcommdiff

100

101

-180-135

-90-45

04590

135180

Frequency [Hz]

Pha

se[d

eg]

102

103

104

105

106

107

yaw opto-mechanical(suspenstion) TF

Gai

n

0Wcommdiff

100

101

-180-135

-90-45

04590

135180

Frequency [Hz]P

hase

[deg

]

Opt-mechanical (suspension) TF

TF from M2 actuator to WFS error signal, simulated in time domain.

Low frequency gain and peak are suppressed.

» Needs compensating gain for full power

Optical spring in differential mode at 4.5Hz for pitch and 4.1Hz for yaw.

Control BW must be higher than optical spring frequency.

Optical spring Optical spring


Positive g factorOpt-mechanical (suspension) TF

Transfer function from penultimate mass actuator to WFS error signal. ITM ROC = ETM ROC = 55.4km, g1 = g2 = +0.927 (see P030055-B) instead

of ITM ROC = ETM ROC = 2.076km , g1 = g2 = -0.927 A dip exists in yaw-differential mode. Phase has more delay than negative g factor case.

102

103

104

105

106

107 Pitch opto-mechanical(suspenstion) TF for positive-g

Ga

in

100

101

-180-135

-90-45

04590

135180

Frequency [Hz]

Ph

ase

[de

g]

0Wcommdiff

101

102

103

104

105

106

107 yaw opto-mechanical(suspenstion) TF for positive-g

Ga

in

100

101

-180-135

-90-45

04590

135180

Frequency [Hz]P

ha

se[d

eg

]

0Wcommdiff


Conclusion and Next step

At least, there is a path to acquire arm lock with current design parameters, but real world is more difficult than simulation world.

The next major step: lock acquisition for full DRFPMI

» simulation time : real time = 10 : 1 for single FP cavity

= 200 : 1 for DRFPMI with length motion

= 400000 : 1 for DRFPMI with length/angle motion

First trial; 40m method, with radiation pressure, no angle motion

1. Lock 3DOFs of central part (MICH, PRC, SRC)

2. Lock 2DOFs of arms with CARM offset to keep arm power low

3. ASC on

4. Reduce CARM offset

5. Full RSE

Noise study (electronic noise, vacuum noise)

Future plan; includes FFT results

» thermal, mirror surface, loss distribution


AdLIGO on E2E

Documents

Osamu Miyakawa Hiroaki Yamamoto March 21, 2006 LSC meeting