Evaluation of disturbances due to test mass charging for LISA and LISA Pathfinder. DNA Shaul, HM Araujo, GK Rochester, TJ Sumner, PJ Wass

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1 Evaluation of disturbances due to test mass charging for LISA and LISA Pathfinder DNA Shaul, HM Araujo, GK Rochester, J Sumner, PJ Wass 5 th International LISA Symposium, ESEC, Wednesday 14 th July 004

2 alk Outline Electrostatic analyses (LP GRS) - FE model of entire GRS - FE CM submodels + Comparison to // plate COULOMB Charging Disturbance Estimates LISA & LISA PF Solar Max & Min LORENZ Method to Cope with Charging

3 Why do Ms charge up? Ms can charge up due to: Galactic cosmic rays Solar particles Solar Flare (RACE) Crab Nebula More in later talks

4 Why does charging matter? Charging of Ms disturbs their geodesic motion Unwanted forces from: Coulomb interactions with surrounding conductors of GRS Charge-dependent Coulomb accn: a Qk = Q C m + QV mc Q mc N 1 i= 1 V i i,n => erms ~ k => erms~ V & V k Lorentz interactions as it moves through magnetic fields Lorentz accn: ( Q m) V B a L = Sun IMF Ulysses (GSFC) Earth

5 Main charging Disturbances 1. Acceleration Noise (from fluctuations in: charge, M position & velocity, voltages, magnetic field). Modification of stiffness (from position dependence) 3. Coherent Fourier components (as Q(t) ~t) Parasitic coupling arget LISA Strain Noise Stray forces x Courtesy: S. Vitale Q(t) t

6 Electrostatic FE model of LP GRS Coulomb accn is capacitance and hence geometry dependent 1 C C k C k = 0 + Move in 1 DOF, Sym => ( ) ( ) a Detere energy in system for given geometry & voltage distribution using FE analysis (ANSYS software) Change V distribution => capacitances between specific conductors Change M position => capacitance derivatives YZ-injection sensor design* (LISA PF LP GRS EM design) Qk = Q C k m C k C x + QV mc Q mc = 1.15 ± 0.01µ F/ m N 1 i= 1 V i i,n % > than ANSYS (1σ errors # ~ 1%) // plate ( = 0) = 33.7 ± 0.pF 30% 1% 46mm side M Gaps: X face: 4 mm sens Y face:.9 mm sens, 4 mm inj Z face: 3.5 mm sens, 4 mm inj z x * B Weber et al. 03 SPIE y C y C z =.50 ± 0.03µ F / m = 1.6 ± 0.03µ F / m # Shaul & Sumner 04 CNME 1% 7%

7 LP M CM: 1 Plunger, 4 stoppers & corresponding M recesses, per z face. (Plunger tip level with recessed, injection electrodes during science mode) (1) Pyramidal plunger & baseball-glove-shaped stoppers (ht 1.5mm)* OR () Pyramidal plunger & alternative, elongated stoppers (l gth 1mm, ht 1mm) * For either set of features, C & C unchanged to within 0.4σ & 1.σ respectively z * D Smart, S obin et al.

8 Submodel CM => estimate CM influence more accurately Positions of borders chosen as compromise between model size & distance from RoI => imise effect on couplings of interest. BCs were not derived from the full model => avoid confounding models accuracies Plunger Baseball glove stopper Alternative, elongated stopper Reduced model complexity (effects results only at the ~1% level) Sign depends on which side of the sensor the feature is located C M,CM: ( ± ) ± ( 1.10 ± 0.01) z + ( 3334 ± 58) z ( ± ) ± ( ± 0.01) z + ( 660 ± 6) z ( ± ) ± ( 9.31± 0.03) z + ( 879 ± 137) z Figures represent the properties of CM, NO increase in capacitance when CM added as not compared no CM case Other capacitances will be affected by the inclusion of CM. hese figures indicate CM level of influence.

9 Comparison of CM to full sensor otal C M,CM < 3% C for both types of stopper otal C < 4% & 9% for CM with bbg stoppers & elongated stoppers a Qk M, CM z C z Only 0.7% from plungers In dc /dk, this gets multiplied by M offset from the centre of opposing features C ease the positioning Q N 1 QV C Q Ci,N = + V => erms ~ z => requirements of the i C m mc mc i= 1 z retracted CM (E.g. M offset of 50µm from the centre of the plungers => contribution of ~3% of that when the M is offset 10µm wrt entire sensor) M, CM z < 9%, 6% & 14% of that of a single z-face, sensing electrode for a pyramidal plunger, a bbg stopper & an elongated stopper Q N 1 i,n a Qk =... Vi => erms ~ mc i= 1 => Need to maintain a high level of uniformity in the CM surfaces, to imise work function differences, as patch effects could multiply these gradients into significant effects Similarly, to imise the CM contribution to stiffness, the mean voltage of opposing features should also be imised. i z V i

10 Magnitude of Charging Disturbances (using ANSYS results for sensitive x-axis)

11 Net charging rate (GEAN GCR) (+e/s) "Worst case" net charging rate assumed (+e/s) Effective charging rate, R eff (+e/s) e x (t) (S/N) Stiffness, s Qx (s - ) Displacement noise (ms - Hz -0.5 ) Voltage noise (ms - Hz -0.5 ) Lorentz noise (ms - Hz -0.5 ) otal noise (ms - Hz -0.5 ) Charging Rates 4, Assume worst case charging conditions: f x (t) (S/N) + error margin of ~30% l x (t) (S/N) e/s+ (may ~cancel in the actual sensor) 100 ~30% on the GEAN GCR 7.35 charging rates e/s for kinetic low-energy secondary 0.57 electron 0.30 emission E E E-16 1.E-16 6.E-16 max , E E-18.39E E E , E E E E E-16 Within Limit? max , E E-18 Charge Rate of noise SEP (ms events - Hz -0.5 ) expected to be low 3.97E-16 enough that 3.07E-16 data acquisition 4.04E-16 could be suspended for their duration, but needs to be verified [δq (CHz -0.5 ) = (R eff ) 0.5 e/πf] 3.09E-16.5E E E-16 For f ~ 10-4 Hz charging & Lorentz noise and coherent component estimates largest LISA: Araujo H et al submitted to Astroparticle Physics, arxiv:astro-ph/ LISA PF: Wass P et al in preparation. ~

12 e x (t) (S/N) f x (t) (S/N) l x (t) (S/N) Coherent Charging Signals For f ~ 10-4 Hz estimates largest (τ = 1 yr; = 1day) S/N Stiffness, is the s Qx ratio (s - ) of the charging signal to -1.11E-08 the acceleration -5.7E-09 noise -1.00E-08 budget -4.93E-09 for LISA Displacement noise (ms - Hz -0.5 ) Charge noise (ms - Hz -0.5 ) Voltage noise (ms - Hz -0.5 ) Lorentz noise (ms - Hz -0.5 ) otal noise (ms - Hz -0.5 ) e f k (t) Θ t k QV & t mc k ( t) Ξkt t C m x f (Hz) 1E-04 1E-03 1E-0 1E-01 1E+00 resultant Q& Qt & mc N 1 V i= 1 i in () ( t Φ t ηq& t m)[ V B ] xˆ x e x (t) Accn noise l x (t) I f x (t) l IP 1E-09 1E-11 1E-13 1E-15 1E-17 (ms-hz-0.5) 4, E E-16 Acceleration spectral density 4.6E-16 1.E-16 6.E-16 Q(t) max, E E-16.39E E E-16 4, E E E E E-16 Within Limit? max, f (Hz) 1E-04 1E-03 1E-0 f x (t) Sens S/N = 5 Magnitudes plotted 1E-19 at primary peaks of sinc functions e x (t) WDB 8.0E E-16.5E E E-16 1E-0 1E-1 1E- 1E-3 1E-4 ~ Coulomb signals dependent on: k (10µm), V (1mV), V (100mV), V (100mV) Lorentz signal dependent on mean B IP (~ 0.5n -> ~ 40n; median ~6n). Even 40n < accn noise) (η = 0.01) Exact spectral shape depends on discharging scheme & variability of e.g. mean charging rate (Shaul et al, CQG 04) t Equivalent strain in space

13 Stiffness, s Qx (s - ) Stiffness: GRS Requirement: -x10-8 -> 8x10-8 s E-08 max -5.7E E-08 Within Limit? max -4.93E-09 s Qk = m a Qk N 1 1 C, QV C Q C Q C N i N C i, N QV C Vi + V + 3 i i= 1 C C C i= 1 C Q = C ~V (100mV) erms that doate are ~ independent of k ~V (100mV) Q C C Independent of voltage

14 For f ~ 10-4 Hz (Charge noise~1/f) Displacement noise (ms - Hz -0.5 ) Charge noise (ms - Hz -0.5 ) Voltage noise (ms - Hz -0.5 ) Lorentz noise (ms - Hz -0.5 ) otal noise Qk (ms - Hz -0.5 ) δa Qk a N 1 a = δk + k i = 1 Vi aqk 1 = m s Qk Qk δx =.5nmHz δv 0.5 a 1 N = + 1 Qk Q C V C Q C m mc mc i= 1 aqk Q Q p, = C p N, V mc mc p N Coulomb Noise i aqk + Q V Doant term i i, δv = 10 / δq N 1.70E E E-16 1.E-16 6.E-16 µ VHz 0.5 max 8.54E E-16.39E E E E E E E E-16 max 8.0E E-16.5E E E-16 : all terms same order of magnitude ~

15 For f ~ 10-4 Hz (Lorentz noise~1/f 1.6 ) Lorentz noise (ms - Hz -0.5 ) Lorentz Noise max max 1.E E E E-17 B IP = δb IP = Hz 0.5 B SC = δb SC = Hz 0.5 Lorentz accn: ( η Q& tvi BIP + ηqt & VI δbip + ηqt & δvi BIP + Qt & δvsc BSC + ηδqvi BIP ) m a L m Fluctuations in B IP Fluctuations in M velocity Charging shot noise Doant term by > 3 orders of magnitude so ~ insensitive to range of B IP Accn Noise

16 Charge noise (ms - Hz -0.5 ) Voltage noise (ms - Hz -0.5 ) Lorentz noise (ms - Hz -0.5 ) otal noise (ms - Hz -0.5 ) Magnitude of Charging Disturbances Net charging rate (GEAN GCR) (+e/s) "Worst case" net charging rate assumed (+e/s) Effective charging rate (+e/s) e x (t) (S/N) f x (t) (S/N) l x (t) (S/N) Stiffness, s Qx (s - ) Displacement noise (ms - Hz -0.5 ) , E E E E-16 1.E-16 6.E-16 max , E E E-16.39E E E , E E E E E E Noise Allocation =0% of LISA noise budget = ( f /3mHz) Within Limit? max , E E E-16.5E E E-16 [ ] 0. 5 ms Hz Reduce by ~ hrs => noise within spec If no contribution of secondaries -> net charging rate, total noise ~10-0% If V=1mV, the e(t) ~55%, stiffness ~90%, total noise ~0-30% ~

17 Comparison to //plate // plate approx overestimates Coulomb noise, stiffness, e x (t) by ~10% f x (t) by ~40% BU LEVEL OF AGREEMEN IS DEPENDEN ON SENSOR GEOMERY E.g. For similar rento torsion sensor design, FE results (validated in expt: Carbone et al 003 Physical Review Letters ) & // plate approx give similar levels of agreement But if exclude guard rings for this design, agreement : C (FE) = C (//) x 1.56 (from 1.30) agreement of nd derivatives wrt x, y & z ~same (~0-30%) //plate approx overestimates: noise, stiffness, e x (t) by ~30-40% f x (t) by ~110% guard rings imise fringing fields exact level of agreement between derived quantities also dependent on other parameters e.g. V => USE CAUION WHEN EMPLOY // PLAE APPROX

18 Management of disturbances UV light => discharge the Ms via pe effect. Noally, ~ 1 day => accn noise & stiffness within budget But coherent charging signals above noise target o remove charging signals: spectral analysis? continuous discharging of the Ms at a rate exceeding the charging rate? Disadvantage = increased noise 7.0E-16 Variation of total noise for LISA, with discharging rate, assug Q=0 Acceleration noise (ms - Hz -0.5 ) 6.5E E E E E E-16 hank-you Discharging rate (-e/s) Discharging rate = ~6 x Charging rate, to reach noal noise budget Variation in charging rate between & max ~ 50% => plausible that discharging rate could be set high enough to cope with variations in the GCR flux, without exceeding budgets Still need to quantify e.g. impact of restoration of equilibrium of charging and discharging currents following changes in the mean charging rate