Eddy Cuents and Magneti Calibations in LDX using a Coppe Plasma D.P. Boyle PPPL M.E. Mauel D.T. Ganie Columbia J. Kesne MIT PSFC
Coppe Plasma Oveview LDX Magnetis Goals Calibate magneti diagnostis positions and gains Find eddy uent deay times Coppe Plasma Opeation Theoy Analysis Results
LDX Magnetis 18 etenal magneti field sensos 9 paallel 9 nomal n 1000 tuns a 50 m 15 m length 9 etenal flu loops 5 intenal flu loops Sensos ae time integated using RC iuits
RC dt dt d RC B B na na B da B A d A da B A z B A B Z z R R k Z z R k k E k K k IR I Z R z A z z Φ Φ + Φ Φ + + + + 1 sin os ; 1 4 ˆ 0 θ θ π ϕ π μ ϕ ϕ l
Goal: Calibate Magnetis Positions of sensos z θ have been measued with ules and lase level Auay ~ 3mm / 1º Gains g of integato boads have been measued eletonially Would be bette to measue positions and total gains magnetially
Goal: Eddy Cuents Magneti levitation vetially unstable Requies ative feedbak ontol Flutuations in L-oil F-oil and plasma uent magnitude Flutuations in F-oil and plasma position Changing uents indue eddy uents in vessel Eddy uents ae piked up by magneti diagnostis Must be measued so they an be popely inluded in magneti eonstution L- and F-oil eddy uents measued in vauum shots L-oil only shots know position know uent Use L-oil to indue vetial og in F-oil measue position with lases and alulate uent fom foe balane How to estimate eddy uents due to flutuating plasma uents? Changes in plasma uent magnitude and position NOT known
Solution: Build Coppe Plasmas oils of 1 AWG oppe wie Appoimately same adius as plasma R 76 m oil - 8 tuns 91 m oil - 5 tuns Built on plywood foms foms disassembled and eassembled in vessel oils squeezed though pot Opeated in 3 vetial positions Fom midplane Z 0 ±5 m L-oil ontol system used to impose tapezoidal uent pulses 4s flattop @ 60A Rise and fall times: 0.5s 1s s Opeated with + and - polaity by swithing oil leads R 3 Z 3 times polaities 31 sensos
Photo of oppe plasma
} { Senso paametes: } { Coppe Plasma paametes: : senso Fo oppe plasma shot } { given by : positions oppe plasma paametes fo oils in 3 vetial All 3 1 3 1 3 1 1 s i i i i i i s i i i g z I Z R i I Z Z Z Z R R X θ ρ δρ ρ ρ ρ δ δ Θ Θ Θ Θ Θ z θ δz a Z ρ 1 R Θ δθ δρ R
Theoy: Calibate Magnetis By using oppe plasma with diffeent adii R at 3 diffeent heights Z an use least squaes fit to find senso alibation 6 equations to find 3 o 4 unknowns Coppe plasma paametes also not known eatly an use least squaes to find them R 3 Z 31 sensos 186 equations to find 15 unknowns s is non-linea Lineaize using measued paametes Solve linea least squaes Adust paametes and epeat Swith between solving fo and s
0 0 s s i i X f s s s i s s i s e e i i + σ σ 1 0 g i g s i e g g e i i σ σ 1 0 1 0 i i i s i X f e X X e X i i + σ σ 0 tol e σ < s0 s tol e σ < s X
Results: Calibate Magnetis Flu loops give easonable esults Calulated loations mostly within ~ m of measued Gains mostly within ~10% of measued χ goodness of fit ~10-3 Coppe plasma loation also found within 1 m of measued Magneti sensos have vey lage eos χ goodness of fit too small fo floating point Beause of poo esults not used in solving fo oppe plasma loation
Theoy: Eddy Cuents Measued voltage given by sum of all oil and eddy uents I times thei espetive Geen s funtions G In eality many eddy uent modes ou To simplify assume one dominant mode pe senso Final equation equies no knowledge of eddy uents to alulate deay time τ E 1 3 G I + E G I τ G E E I E d dt G τ E G di dt E E k + I E E di dt k E τ E di dt
Analysis: Eddy Cuents Using the I and wavefoms fom eah of the 31 sensos and 36 epeiments : Steady state Geen s funtion G is atio of flattops 0 / I0 This is the quantity used in senso alibation d/dt dominated Geen s funtion G -k E G E is atio of slopes d/dt / di/dt at some initial time τ E found by least squaes fit to Eq. 3
G I G -k E G E di/dt d/dt
-RHS LHS-RHS LHS G I τ E d G GE ke dt di dt
Unetainty Analysis Most unetainty due to integato dift Ciuits have some dift ompensation In analysis subtat initial dift befoe pulse Optionally subtat dift duing flattop and afte pulse Find aveage dift and unetainty as a funtion of time fom shots with no uent Sum shots with opposite polaity to anel out stay fields and any epoduible difts Also some unetainty due to powe supply Cuent is somewhat noisy Diffiult to fit initial d/dt on small noisy signal Feedbak system designed fo L-oil not oppe plasma Leads to inging at ones of tapezoid
dift σ dift
Results: Eddy Cuents Most sensos in ange 30-70 ms Standad deviations ove all shots 3-5 ms Consistent with peditions fom theoy Some < 10 ms o negative standad deviations as big as τ E
B B // Etenal Flu Loops Intenal Flu Loops
Summay Senso alibation and eddy uent deay time esults geneally onsistent with pevious measuements Coppe plasma epeiment did not yield an impovement in auay o peision ove pevious measuements
Suggestions fo Futue Wok Wok to edue integato dift Optimizing powe supply fo oppe plasma ould edue noise and inging Use less simplified model fo oppe plasma and sensos Multiple windings in oppe plasma Possible eos in onstution Aea and length in magneti sensos Ty moe obust fitting shemes fo alibation Impove alulation of k E G E Use diffeent pulse shape faste ise time sinsusoid Use non-linea method to solve fo both τ E and k E G E Do moe omplete analysis with multiple eddy uent modes
Aknowledgements DOE Fusion Enegy Sienes Fellowship administeed by ORISE Thanks to the LDX team fo assistane in onstution and installation of the oppe plasma