aser nerferomeer Sace Anenna SA Tme-elay nerferomery wh Movng Sacecraf Arrays Massmo Tno Je Proulson aboraory, Calforna nsue of Technology GSFC JP 8 h GWAW, ec 7-0, 00, Mlwaukee, Wsconsn
WM Folkner e al, CQG, 4, 54, 997
Unequal-arm nerferomeers P aser P ν 0, φ φ n h n h = = φ φ M Tno, & JW Armsrong, Phys Rev, 59, 000 999 : ] [ ] [ where n h n h Ψ Ψ = = φ φ ] [ ] ][ [ ] ][ [ ] [ ] [ n h n h = φ φ SV hurandhar, KR Nayak, and J-Y Vne, Phys Rev, 65, 000 00 φ = wo-way hase measuremens
* n r l * l o n r Tme-delay nerferomery l n r * M Tno: Phys Rev, 5, 554 996; Phys Rev, 58, 000 998 JW Armsrong, FB Esabrook, and M Tno: A J, 57, 84 999 FB Esabrook, M Tno, & JW Armsrong, Phys Rev, 6, 0400 000 M Tno, A Shaddock, J Sylvesre, & JW Armsrong: Phys Rev 67, 00 00 s bes o hnk of SA as a closed array of sx one-way delay lnes beween he es masses Ths aroach allows us o reconsruc he unequal-arm Mchelson nerferomeer, as well as new nerferomerc combnaons, whch offer advanages n hardware desgn, n robusness o falures of sngle lnks, and n redundancy of daa
Unequal-arm nerferomeers Con = [ φ φ ] [ φ φ ] One can acually regard as gven by he nerference of wo beams ha roagae whn he wo arms of SA, each exerencng a delay equal o s acually a zero-area Sagnac nerferomeer, synheszed by roerly combnng measuremens from each arm A Shaddock, M Tno, FB Esabrook & JW Armsrong, Phys Rev, 68, 060 R 00
Sx-Pulse aa Combnaons α, β, γ, ζ α = η η η η η η,,,, ζ = η η η η η η,,,, --??,, = GW Secondary,,,, noses A Shaddock, M Tno, FB Esabrook & JW Armsrong, Phys Rev, 68, 060 R 00
Egh-Pulse aa Combnaons, Y, Z Unequal-arm Mchelson P, Q, R Beacon Monor E, F, G U, V, W Relay
Movng sacecraf Arrays and Clocks Synchronzaon The analyss above assumed he clocks onboard he SA S/Cs o be synchronzed o each oher n he frame aached o he SA array n a roang reference frame, he Sagnac effec revens he mlemenaon of he Ensen s Synchronzaon Procedure, e synchronzaon by ransmsson of elecromagnec sgnals GPS s a good examle of hs roblem! To accoun for he Sagnac effec, one nroduces an hyohecal neral reference frame, and me n hs frame s he one adoed by he sacecraf clocks! n oher words, he onboard recevers have o conver me nformaon receved from Earh o me n hs neral reference frame SSB N Asbby, The Sagnac effec n he GPS Sysem, h://dglanderlbero/solcclos/ M Tno, FB Esabrook, & JW Armsrong, gr-qc/0007, Ocober 6, 00
Movng sacecraf Arrays and Clocks Synchronzaon Con n he SSB frame, he dfferences beween back-forh delay mes are very much larger han has been revously recognzed The reason s n he aberraon due o moon and changes of orenaon n he SSB frame Wh a velocy V=0 km/s, he lgh-rans mes of lgh sgnals n oosng drecons, and wll dffer by as much as V a few housands km They wll also change n me due o roaon 0 m/s; hs however s sgnfcanly smaller han he sacecraf relave velocy 0 m/s
T wh Movng sacecraf Arrays The frs-generaon T exressons do no accoun for: The Sagnac Effec Tme-deendence velocy of he arm lenghs n he T exressons he Flex-effec Boh effecs reven he erfec cancellaon of he laser frequency flucuaons n he frs-generaon T combnaons Wh a laser frequency sably of 0 Hz/Hz / he remanng laser frequency flucuaons could be as much as 0 mes larger han he secondary nose sources A Shaddock, Phys Rev : o aear; gr-qc/0065 Cornsh & Hellngs, Class Quanum Grav 0 No November 00 485-4860 A Shaddock, M Tno, FB Esabrook & JW Armsrong, Phys Rev, 68, 060 R 00
The Sagnac Effec and he Sagnac Combnaons α, β, γ n resence of roaon, he amoun of me sen by a beam o roagae clockwse s dfferen by he me sends o roagae counerclockwse along he same arm =>,,,,, The Sagnac effec revens he erfec cancellaon of he laser frequency flucuaons n he exsng exressons of he Sagnac combnaons α, β, γ, ζ @ 0 - Hz he laser frequency flucuaons remanng n α, β, γ, ζ would be abou 0 mes larger han he secondary nose sources r r ' ' ' = 4 Ω Α 4 km α, β, γ α, α, α
Flexy A Shaddock, M Tno, FB Esabrook & JW Armsrong, Phys Rev, 68, 060 R 00
Sysemac Aroach s here a general rocedure for dervng he nd generaon T combnaons? YES! M Tno, FB Esabrook, & JW Armsrong, gr-qc/0007, Ocober 6, 00 ], [ ' ' ' ' ' ' ' j j j j j j j V V Ψ Ψ Ψ =Ψ Ψ
Sysemac Aroach Con η, η, η, η η η η η ;' ; = [ ] ' = [ ] ' = [ ] η η [ ] η η ' ;' ' ; = [ ][ ] [ ][ ] ' ' ' ' = 0 η η η η ; ;' η η η η ;' ; ;' ;' = [ ] ' ' = [ ] ' ' = [ ][ η η η η ' ' ; ;' [ ][ η η η η ' ' ;' ; ;' ;' ] ] 0
How oes he SA Sensvy Change? Once he laser frequency flucuaons are removed, he correcons o he sgnal and he secondary noses ocal ah, roof-mass, ec, nroduced by he exra delays due o he Sagnac 4 km and flexy ~ 00 m effecs, are many orders of magnude below he sgnals and secondary noses deermned by he s generaon T exressons: ] [ ~ ~ f e f f = = π