Magnetic noise magnet ×∇Bf = µ∇B

force

torque

magnetization×∇B

F = µ⇥rBN = µ⇥B

Forceonmagnet->forceonmirrorF1 = �µmag · grB

F2 = µmag ·�(rB)

rB· grB

F3 =�m

µ0Vmir · eB ·rB

F4 =�m

µ0Vmir ·B · grB

(magneticmomenttolerance)

(magneticfieldnonuniformity)

(magnetizationofsubstrate)

(magnetizationofsubstrate)

N1 = �µmag · grB · xmag

N2 = µmag ·�(rB)

rB

· grB · xmag

N3 = µmag · grB · �xmag

Forceonmagnet->torqueonmirror(magneticmomenttolerance)

(magneticfieldnonuniformity)

(magnetpositionerror)

Torqueonmagnet->torqueonmirrorN4 = �µmag · eB

N5 = µmag ·�B

B· eB

(magneticmomenttolerance)

(magneticfieldnonuniformity)

magnet ×BN = µ B

parameter valuemagneticmomettolerance:δµ/µ 0.2

magneticfieldnonuniformity :

δB/B0.1

magnet positionerror:δx 1mm

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

0.1 1 10 100 1000 10000

Dis

plac

emen

t Noi

se [m

/rtH

z]

Frequency [Hz]

F1 : δµ × ∇BF2 : µ × δ(∇B)F3 : χ × BF4 : χ × (∇B)N1(yaw) : δµ × ∇Β × xN1(pitch)N2(yaw) : µ × δ(∇B) × xN2(pitch)N3(yaw) : µ × ∇Β × δxN3(pitch)N4(yaw) : δµ × BN4(pitch)N5(yaw) : µ × δBN5(pitch)requirement(BS)

parameter valuemirror mass

M[kg] 18.9

magneticmoment ofmagnets :µ[A・m2] 0.074

magneticfieldB[T] 4.7×10-5

fluctuationofBB[T/rtHz]

5×10-13@10Hz

magneticfieldgradient∇B[T/m] 4.7×10-5

fluctuationof∇B∇B[T/m/rtHz]

5×10-13@10Hz

Magnetic noise for BS

~

~

(force)magneticfieldgradientununiformity δ(∇B)~0.1(∇B)

(force)magneticmomenttoleranceδµ~0.2µ

(torque)magneticfieldgradientununiformity δ(∇B)~0.1(∇B)

(torque)magneticmomenttoleranceδµ~0.2µ

(torque)magnetpositionaccuracyδx~1[mm]

(force)magnetizationofthemirror

(torque)magneticmomenttoleranceδµ~0.2µ

(torque)magneticfieldununiformity δB~0.1B

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

0.1 1 10 100 1000 10000

Dis

plac

emen

t Noi

se [m

/rtH

z]

Frequency [Hz]

F1 : δµ × ∇BF2 : µ × δ(∇B)F3 : χ × BF4 : χ × (∇B)N1(yaw) : δµ × ∇Β × xN1(pitch)N2(yaw) : µ × δ(∇B) × xN2(pitch)N3(yaw) : µ × ∇Β × δxN3(pitch)N4(yaw) : δµ × BN4(pitch)N5(yaw) : µ × δBN5(pitch)requirement(PRM)requirement(SRM)

Magnetic noise for PRM/SRMparameter valuemirror mass

M[kg] 10.8

magneticmoment ofmagnets :µ[A・m2] 0.074

magneticfieldB[T] 4.7×10-5

fluctuationofBB[T/rtHz]

5×10-13@10Hz

magneticfieldgradient∇B[T/m] 4.7×10-5

fluctuationof∇B∇B[T/m/rtHz]

5×10-13@10Hz

~

~

(force)magneticfieldgradientununiformity δ(∇B)~0.1(∇B)

(force)magneticmomenttoleranceδµ~0.2µ

(torque)magneticfieldgradientununiformity δ(∇B)~0.1(∇B)

(torque)magneticmomenttoleranceδµ~0.2µ

(torque)magnetpositionaccuracyδx~1[mm]

(force)magnetizationofthemirror

(torque)magneticmomenttoleranceδµ~0.2µ

(torque)magneticfieldununiformity δB~0.1B

10-26

10-2510-24

10-23

10-2210-21

10-20

10-1910-18

10-17

10-16

10-1510-14

10-13

10-1210-11

10-10

0.1 1 10 100 1000 10000

Dis

plac

emen

t Noi

se [m

/rtH

z]

Frequency [Hz]

F1 : δµ × ∇BF2 : µ × δ(∇B)F3 : χ × BF4 : χ × (∇B)N1(yaw) : δµ × ∇Β × xN1(pitch)N2(yaw) : µ × δ(∇B) × xN2(pitch)N3(yaw) : µ × ∇Β × δxN3(pitch)N4(yaw) : δµ × BN4(pitch)N5(yaw) : µ × δBN5(pitch)requirement

Magnetic noise for ITM/ETMparameter valuemirror mass

M[kg] 22.7

magneticmoment ofmagnets :µ[A・m2] 0.0027

magneticfieldB[T] 4.7×10-5

fluctuationofBB[T/rtHz]

5×10-13@10Hz

magneticfieldgradient∇B[T/m] 4.7×10-5

fluctuationof∇B∇B[T/m/rtHz]

5×10-13@10Hz

~

~

(force)magneticfieldgradientununiformity δ(∇B)~0.1(∇B)

(force)magneticmomenttoleranceδµ~0.2µ

(torque)magneticfieldgradientununiformity δ(∇B)~0.1(∇B)

(torque)magneticmomenttoleranceδµ~0.2µ

(torque)magnetpositionaccuracyδx~1[mm]

(force)magnetizationofthemirror

(torque)magneticmomenttoleranceδµ~0.2µ

(torque)magneticfieldununiformity δB~0.1B

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

0.1 1 10 100 1000 10000

Dis

plac

emen

t Noi

se [m

/rtH

z]

Frequency [Hz]

FIMrequirement(BS)

Magnetic noise from IM(Intermediate Mass)

magnets of BS suspension system

parameter valueIM massMIM [kg] 36.5

magneticmoment ofmagnets :µ[A・m2] 0.69

fluctuationof∇B∇B[T/m/rtHz]

5×10-13@10Hz~

magnets

・NOcancellationbetweenmagnets・largermagnetsthanthemagnetsonthemirror

forceononemagnet

10-24

10-23

10-22

10-21

10-20

10-19

10-18

10-17

10-16

10-15

10-14

10-13

10-12

10-11

10-10

0.1 1 10 100 1000 10000

Dis

plac

emen

t Noi

se [m

/rtH

z]

Frequency [Hz]

FIMrequirement(PRM)requirement(SRM)

Magnetic noise from IM(Intermediate Mass)

magnets of PRM/SRM suspension system

parameter valueIM massMIM [kg] 15.6

magneticmoment ofmagnets :µ[A・m2] 0.69

fluctuationof∇B∇B[T/m/rtHz]

5×10-13@10Hz~

magnets

forceononemagnet

・NOcancellationbetweenmagnets・largermagnetsthanthemagnetsonthemirror