Newtonian noise mitigation by using mini-sogros

Transcription

1 Nwtonan nos mtgaton by usng mn-sogos Ho Jung Pa /8/6 Sn SOGO s a vry snstv gravty stran gaug on may b ab to mpoy sad- and rmov t down SOGOs n pa of a arg array of ssmomtrs to drty masur Nwtonan nos NN afftng t ntrfromtr tst masss. Hr w nvstgat t possb- << L. ty of mtgatng t NN n ntrfromtrs by usng mn-sogos wt arm-ngt Prnp of NN mtgaton ayg wavs ar tdd to domnat t NN at f ~ H []. W onsdr a ayg wav travng aong a drton wt an ang wt rspt to t as. T dspamnts of a fr tst mass at gt abov t ground aong y and ar gvn [ 3] by Gρ Y sn Gρ Gρ wr s t vrta dspamnt drty bnat t tst mass.83 s a fator tat aounts for parta anaton for NN from surfa dspamnt 5 m/ /s and 3. m/s s t spd of wavs at t ground v and undrground y sn s t poston of t tst mass aong t drton of wav propagaton and ρ s t man mass ground dnsty. In t prsn of a GW and ayg wavs t ntrfromtr masurs L Ly L [ ] [ Y y Y y ] wr and Y y rprsnt t NN-ndud dspamnts aong t and y as summd ovr mutp wavs at t tst mass poston and y rsptvy. At H t ayg wavngt boms λ ~ 5 m << L ausng and Y to b ompty unorratd wt on anotr. Hn w nd to masur or Y for a tst mass by usng a sparat mn-sogo o-oatd wt t as sown n Fg.. T stran tnsor tat a mn-sogo dtts Fg.. Four mn-sogos ooatd wt four an b sown [3] to b tst masss of a asr ntrfromtr. a b

2 sn sn sn sn 3 j j sn Gρ. By omparng Eq. 3 wt Eq. a w fnd 3 Y 5 wr was gnord sn t s ompty domnatd by t NN. Trfor t NN n t ntrfromtr tst mass aong t y as oud n prnp b mtgatd by o-oatng a mn-sogo wt t s Fg. and orratng t - 3- omponnt of t mn-sogo wt t ntrfromtr output and subtratng t orratd part. W sov Eq. 5 for and substtut t nto Eq. to obtan [ L Ly ] [ ] [ 3 y 3 y ]. 6 L L L T snstvty rqurd for mn-sogo to rovr s tn gvn by L 7 wr t numra fator am from t nornt sum of t nos n t four mn-sogos. Fgur sows t snstvty goas of Advand LIGO aligo and Enstn Tsop ET []. T sadd rgon rprsnts t paramtr spa domnatd by t NN. A worty mtgaton goa for aligo woud b rjtng t NN by a fator of 5 to 3 H / at H. Wt L m Eq. 7 yds H / Fg.. Snstvty goas of aligo and ET. T sadd at H. rgon s domnatd by t NN. To b ab to mtgat t NN by usng ts orraton mtod t SOGO output must b gy orratd wt t NN-ndud dspamnt of t tst mass. T mtgaton fator S s ratd to t orraton btwn t snsor and t tst mass C SN [] as S C SN. 8 To av S 5 on nds C SN.98. Ts rqurs.8 m and a SOGO must b oatd wtn.8 m of t ntrfromtr tst mass []. Su a sma SOGO woud ardy av noug snstvty and oud not b brougt to su promty to t ntrfromtr tst mass.

3 3 Two mn-sogos symmtray oatd W onsdr t possbty of oatng two argr basn mn-sogos symmtray on t oppost sds of a tst mass and avragng out t unorratd parts. Fgur 3 sows t four tst masss of t two mn-sogos on t oronta pan at t sam as t ntrfromtr tst mass M. For smpty t four vrta tst masss ar not sown. W oos t orgn to b at M. Tn t NN-drvn dspamnt of M aong t as s 9 wr /. T -omponnts of t mn-sogo and rspons ar gvn by [ ] [ ] { } a [ ] [ ] { } 3 b wr j and j ar t and postons of tst mass j. From Fg. 3 w fnd sn a. 3 b Substtutng Eqs. and nto Eqs. w obtan t rspons of mn-sogo and : sn sn a. sn sn b T sum ovr t two mn-sogos boms. sn Y Surprsngy t oronta as trms an out and ony t vrta as trms ontrbut. Fg. 3. Four mn-sogo tst masss surroundng an ntrfromtr tst mass.

4 Now w suprpos ayg wavs omng from a drtons. Equatons 9 and ar modfd nto d Y sn. d In t mt / << sma Y d and t orraton btwn and Y approas unty as td. wr T orraton btwn t doub mn-sogo and ntrfromtr tst mass s gvn by Y C SN d Y * d * dy Y * Substtutng Eqs. 8 and 9 nto Eq. 7 w obtan C SN sn. 9 d sn d d sn wr s a funton of wt random amptud and pas. Equaton sows tat t pas dos not ontrbut to C SN. Fgur sows C SN omputd as a funton of. In ordr to obtan C SN.98 w nd.. At f H.5 m and 9.5 m. Trfor t unorratd parts of t NN oud ndd b avragd out by symmtray oatd mn-sogos wt a argr basn 9.5 m nstad of.8 m for S 5. Fg.. Corraton btwn t doub mn- SOGO and ntrfromtr tst mass vrsus.

5 Tab. Proposd dttor paramtrs and dttor nos of mn-sogo. Paramtr SOGO Mtod Empoyd Ea tst mass M.5 3 g Nb squar tub Arm-ngt L m Ovr a rgd patform Antnna tmpratur T. K Lqud um or ryooor SQUID tmpratur T SQ. K H 3 /H duton rfrgrator DM rsonan frquny f D H Magnt vtaton DM quaty fator Q D 7 Surfa posd pur Nb Pump frquny f p 5 H Tund apator brdg transdur Ampfr nos numbr n Nary quantum-mtd d SQUID Dttor nos S / f H / Computd at f H Tab sows dttor paramtrs tat oud mt t SOGO snstvty rqurmnt. Ea tst mass wgs.5 tons and t basn s m. It woud b suffnt to oo t tst masss to. K as ong as t SQUIDs ar ood sparaty to. K to ra t rqurd nos v of. A wt nos v of at. K as bn dmonstratd by usng a two-stag d SQUID [5]. T Q rqurmnt for t tst masss s modst. T ntrns nos sptra dnsty omputd for ts paramtrs s pottd n Fg. 5. T tota dttor nos at H s H / satsfyng our rqurmnt for S 5. A sng mn-sogo oatd undr a tst mass Fg. 5. Dttor nos of a -m SOGO ood to. K and oupd to a SQUID. W oud avod t ompty of usng two mn-sogos for a ntrfromtr tst mass f a mn-sogo oud prsy b o-oatd wt a tst mass. W oud furtr smpfy t f w oud dspns wt t two tst masss tat masur t ratv vrta araton ndud by and 3. Du to nonnarts n t suprondutng rut vrta rsonan frquns of vtatd suprondutng tst masss rman g H. In prnp t suprondutng ngatv sprng tat as bn dmonstratd wt SGG [6] oud b appd but t atua mpmntaton woud b vry angng. Normay t anguar rspons of t two tst masss on t oronta arm and tat of t two tst masss on t vrta arm ar dffrnd to rjt t CM anguar araton of Fg. 6. A sng-arm mn-sogo oatd undr a tst mass. 5

6 t patform. If t patform oud b suffnty w soatd from t ssm nos of t ground on woud not nd su dffrnng. Fgur 6 sows a sng-arm mn-sogo oatd undr a ntrfromtr tst mass. T patform oud b suspndd as a pnduum from ts md-pont. Undr su suspnson t patform woud b ompty soatd from t ground tt. By png ts anguar rsonan frquny about t as to mh t anguar araton about t as woud b soatd by 8 at H. A typa ssm nos v at saow dpt ~ m s ~ 7 m s H / [7]. To ra t ntrns nos v of H / t nar araton nos must b rjtd by at H. T mn-sogo oud b dsgnd to av a tota CM nar araton rjton rato of. Tr s onrn tat t undrground avty w ouss t mn-sogo may aus ayg wavs to sattr n a way tat produs NN sgnas for t SOGO tst masss tat ar not ompty orratd wt t NN tat affts t ntrfromtr tst mass []. Ts probm nds to b studd. frns [] M. G. Br t a. Improvng t snstvty of futur gravtatona wav obsrvators n t H band: Nwtonan and ssm nos Gn.. Grav [] J. Harms t a. Low frquny trrstra gravtatona wav dttors Pys. v. D [3] H. J. Pa Mtgaton of Nwtonan nos usng a tnsor gravtatona wav dttor unpubsd nots 6. [] J. Harms prvat ommunatons. [5] P. Fafr t a. ћ SQUID ampfr for aoust gravtatona wav dttors App. Pys. Ltt [6] J. W. Par H. J. Pa H. A. Can and M. V. Moody "Snstvty Enanmnt of Inrta Instrumnts by Mans of a Suprondutng Ngatv Sprng" n t Prodngs of t t Intrnatona Cryogn Engnrng Confrn dtd by H. Coan P. Brgund and M. Krusus Buttrwort Surry 98 p.36. [7] M. G. Br t a. Nwtonan nos and ambnt ground moton for gravtatona wav dttors J. Pys. Conf. Sr