Charging & Charge Control for Proof-Masses in Space Effects of free charge • Lorentz force • Electrostatic forces from mirror charges • Spring Constants • Forces from applied voltages Charging Estimates • Rates • Timelines Charge Management • Measurement procedures • Discharge procedures LISA Symposium – PSU 24/07/2002
25
Embed
for Proof-Masses in Space Charging & Charge Controlcgwp.gravity.psu.edu/lisa/presentations/sumner.pdfJafry, Sumner & Buchman - 96 Jafry & Sumner - 97} GEANT3 ~16 charges/sec. Modeling
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Charging & Charge Controlfor Proof-Masses in Space�Effects of free charge
• Lorentz force
• Electrostatic forces from mirror charges
• Spring Constants
• Forces from applied voltages
�Charging Estimates
• Rates
• Timelines
�Charge Management
• Measurement procedures
• Discharge procedures
LISA Symposium – PSU 24/07/2002
Lorentz force noise
LISA Symposium – PSU 24/07/2002
BvQFl ∧= HallEQ−
MetallicEnclosure(Blaser)
BvQFl ∧=η
( ) ( ) ( )222 vBQBQva nnn ηδδη +=
Lorentz force noise
LISA Symposium – PSU 24/07/2002
)Hz(10 C 104 HzT/ 105.2 4-15
11−
−
×≤⇒×
= çQf
Bnδ
antinsignific term2 HzC/ 2
25.2 nd⇒≈
f
QeQn πδ
&
See later!
( ) ( ) ( )222 vBQBQva nnn ηδδη +=
Electrostatic forces
LISA Symposium – PSU 24/07/2002
FE
k
C
kV
Q
C
C
k
Q
CV
C
kki
i ii
i
n
= − = + −∑ ∑=
∂∂
∂∂
∂∂
∂∂
1
2 22
2
21
−∆≈
∂
∂+
∂
∂==
232
2
2
2
2
2 4
222 d
Ad
d
A
C
Q
k
C
k
C
C
Q
k
C
C
QF lrk
εδε∂∂
( ) spaceparameter - sconstraint 4
2 32
22
dTdd
A
mC
tQta d ∆⇒
∆≈⇒ε&
( ) ( )2
32
2
2
332
22 442
14
2
∆+
∆+≈⇒ dd
A
mC
QQdd
d
A
Cd
A
mC
Qa n
nn
εδδ
εε
( )
∆+≈⇒ 2
332
2 421
4
2d
d
A
Cd
A
C
Qk
εε
Electrostatic forces
LISA Symposium – PSU 24/07/2002
FE
k
C
kV
Q
C
C
k
Q
CV
C
kki
i ii
i
n
= − = + −∑ ∑=
∂∂
∂∂
∂∂
∂∂
1
2 22
2
21
( )
2
2
2
2
2
222
nr
cmr
rn
rnn
kk
CV
mC
Q
k
CV
k
C
mC
Q
k
CV
mC
Q
k
CV
mC
Qa
δ
δδ
∂
∂+
∂
∂∆
∂
∂+
∂
∂+
∂
∂∆≈⇒
Common-mode voltage effects disappear to first order in force
Differential-mode voltages used for charge measurement – see later
2
2
2 k
CV
C
Q
k
CV
k
C
C
Qk r
cmr
∂
∂+
∂
∂∆
∂
∂≈⇒
Summary of Charge Limits
LISA Symposium – PSU 24/07/2002
10 µV/√HzδVn
10µm∆d
Assumptions!!
3x10-11Potential (noise) (1Vcm)
10-24Potential (noise)
4x10-13Stiffness (1Vcm)
10-8Stiffness (∆Vdm)
3x10-12Stiffness (assymetry)
1.4x10-11 (10-4 Hz)Charge Noise (∆d)
4x10-11Displacement Noise
4x10-11 (10-4 Hz)Lorentz Noise
Limit (C)Effect
Charging Rates
Jafry, Sumner & Buchman - 96
Jafry & Sumner - 97 } GEANT3
~16 charges/sec
Modeling of Charging (LTP)
LISA Symposium – PSU 24/07/2002
•Compare rates using GEANT4 with low-E extension
•Get charging timelines
Modeling of Charging (LTP)
LISA Symposium – PSU 24/07/2002
Modeling of Charging (LTP)
LISA Symposium – PSU 24/07/2002
Modeling of Charging (LISA)
LISA Symposium – PSU 24/07/2002
Modeling ofCharging(LISA)
LISA Symposium – PSU 24/07/2002
‘…the hadron-inducedfluorescence isvery badlyimplemented.So we switchedit off …’
LISA Symposium – PSU 24/07/2002
Modeling of Charging (LISA)
LISA Symposium – PSU 24/07/2002
Modeling of Charging (LISA)
LISA Symposium – PSU 24/07/2002
Charge Management System
LISA Symposium – PSU 24/07/2002
�Charge Measurement using applied dither force intransverse direction with capacitive sensing of test-mass response.
�Discharge technique using differential illuminationof surfaces with UV illumination, with bias voltageenhancement if needed.
Cd
AQEFd
ε2=
Charge Measurement
Dither Technique•Different gaps in eachdirection give differentmeasurement authority
•Need to see ditherabove residual drag-freeposition noise
•Assume transversedither with 1nm/√Hzposition noise