Reconstruction of Pressure Profile Evolution during Levitated Dipole Experiments
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1 Reconstruction of Pressure Profile Evolution during Levitated Dipole Experiments M. E. Mauel, A. Boxer, J. Ellsworth, D. Garnier, J. Kesner ICC Conference: Reno, Nevada (June 24, 28) 1
2 Abstract Magnetic levitation of the LDX superconducting dipole causes significant changes in the measured diamagnetic flux and what appears to be fascinating temporal evolution of plasma diamagnetic current. This poster describes the reconstruction of plasma current and plasma pressure profiles from external measurements of the equilibrium magnetic field, which vary substantially as a function of time. Previous free-boundary reconstructions of plasma equilibrium [1] showed the plasma to be anisotropic and highly peeked at the location of the cyclotron resonance of the microwave heating sources. Reconstructions of the peaked plasma pressures confined by a levitated dipole incorporate the small axial motion of the dipole (+/- 5 mm), time varying levitation coil currents, eddy currents flowing in the vacuum vessel, constant magnetic flux linking the superconductor, and new flux loops located near the hot plasma in order to closely couple to plasma current and dipole current variations. [1] I. Karim, et al., Equilibrium reconstruction of anisotropic pressure profile in the levitated dipole experiment. J. Fusion Energy, 26 (27) 99. 2
3 Key Points During magnetic levitation, vertical motion of the superconducting dipole, changes in the levitation control coil current, and induced eddy currents couple to magnetic diagnostics. We self-calibrate the magnetics using levitation current ramps and pre-programmed jogs of dipole s vertical position. Using data from the calibration shots, the induced eddy currents are calculated (and digitally removed ) by inverting coupled linear ODEs. This allows Use of previous magnetic reconstruction methods. 3
4 Magnetic Detectors 4
5 Reconstruction 5
6 (1) Previous Results High beta plasmas created like those found in magnetosphere Anisotropic Required x-ray imaging to determine peak pressure Ring current Plasma Stored Energy (W p 17 (J/kA) I p ) 6
7 Ring Current: Trapped, High-β Protons (15-25 kev) Greatly intensified during geomagnetic storms Ti ~ 7Te and P ~ 1.5 P Monthly storms: ~5 MA. (LDX: 3-4 ka) 1 MA storms few times a year. Current centered near L ~ 4-5Re; L ~ 2.6Re wide and z ~ 1.6Re; Not axisymmetric. Curlometer during storms: JRC ~ 25 na/m2 (Cluster II, 25) AMPTE/CCE-CHEM Measurements Averaged over 2 years (De Michelis, Daglis, Consolini, JGR, 1999) 7
8 Dst and the Dessler-Parker-Sckopke Relation Disturbed Storm Time Index (Dst): Solar Wind Pressure (Burton, McPherron, Russell, JGR, 1975) BH = (µ/2) IRC/Rrc measured near equator plus Earth s induction fields! (LDX: IF.25 Irc) Solar Wind Convection Field Dessler-Parker-Sckopke: Energy =.54 GJ/A IRC (LDX:.12 J/A) Dst 5 MA 1-5 Days 8
9 Centrally-Peaked Proton Pressure (Even with Plasma Sheet, Outer-Edge, Source!) AMPTE/CCE-CHEM Measurements Quiet Conditions IRC ~ 1 MA (De Michelis, Daglis, Consolini, JGR, 1999) P ~ L -3.3 beta 9
10 Where is the Ring Current? 8 flux loops 9 normal-b sensors 9 tangential-b sensors Constant flux constraint on superconducting dipole Isotropic now (P > P in future) 26 measurements; 3 unknowns: (p, ψ, g) (I. Karim, 27) ( ) α ( ) 4g ψ ψfcoil ψ p(ψ) = p ψ ψ fcoil ψ J = B P Plasma B 2 + B κ Current B 2 (P P )
![45 GHz 551329 2]//TableForm= Parameter Χ 2 Ip If p P perp P R peak Γ Γ 5 3 Press Rpeak J Centroid Moment A m 2 Max Perp Β Perp Β](/docs-images/88/117750816/images/11-2.jpg "Rpeak Avg Perp Β Plasma Volume Energy J E Ip J ka Fit Value 14.5942 3356.57 738.437 2 5.716667 2.4741 1.44444 594.78 1.23389 5251.")
11 Best Fit Anisotropic Equilibrium: Supported Dipole 1. Peak pressure in-between 2.45 and 6.4 resonance GHz ]//TableForm= Parameter Χ 2 Ip If p P perp P R peak Γ Γ 5 3 Press Rpeak J Centroid Moment A m 2 Max Perp Β Perp Β Rpeak Avg Perp Β Plasma Volume Energy J E Ip J ka Fit Value Steep Gradient! High!! GHz Radius (m) Pressure Contours Current Contours 11
12 Where is the High-β Plasma? X-Ray E > 4 kev J. Ellsworth 12
13 Abel Inversion (Equatorial) Show Profiles Highly Peaked Near 2.45 GHz Resonance 3 S s _f6rs.tif m ECRH Res ΕEmission Profile s R m Light Inversion (Afterglow) ECRH Res Emission Profile 57111_f6rs.tif m X-Ray Inversion (2.45 GHz only) R m 13
14 High β Anisotropic Pressure Produced when Dipole is Mechanically Supported (a) Profile Fitting Parameters 4 P! /P 5 3 g GHz (b) X-Ray Image Analysis R peak (m) 57111, GHz GHz Pressure Contours Fig. 1. Contours of the reconstructed pressure profiles superimposed onto the X-ray images measured during (top) 2.45 GHz heating and (bottom) 6.4 GHz heating. Journal of Fusion Energy, Vol. 26, Nos. 1/2, June 27 ( 27) GHz Current Contours Radius (m) 14
15 Newly Installed Internal Flux Loops Couple Better to Plasma Currents Flux Loop 1 Flux Loop 11 Flux Loop 12 g Existing w/new Loops R (m) 15
16 (2) Self Calibration With a levitated dipole, flux loops respond to control fields Control coil only: mutuals and induced eddy currents Dipole vertical displacement: mutuals 16
17 Typical Levitation External flux loop Internal flux loop 1 ka turn variation of levitation control 4 mm motion of 1.1 MA turn dipole Question: What is the plasma contribution to magnetic signals? Flux Loop #5 (mv s) Flux Loop #1 (mv s) Levitation Control (ka Turns) Dipole Position (mm) S HEI Burst Plasma Current Causes Dipole to Rise ECRH Power (kw) time (s) 17
18 Response from Levitation Control Coil Response from steady levitation current determines mutual inductance Response during constant current-ramp drives a constant eddy current Flux Loop #1 (mv s) Flux Loop #5 (mv s) Flux Loop #1 (mv s) Levitation Control (ka Turns) No plasma; No dipole. S time (s) 18
19 Induced Eddy Currents Constant control current ramp drives a constant eddy current We need to find the mutual between eddy current and detector & the wall eddy decay time, τ W Flux Loop #1 (mv s) Flux Loop #5 (mv s) Flux Loop #1 (mv s) d(i-control)/dt (ka Turn/s) S83216 The ratio of eddy current pick-up, M E I E, to di L /dt is equal to τ w M E K LE Levitation Control (ka Turns) time (s) 19
20 Eddy Decay 1..5 d(flux Loop #5)/dt (mv) S Time (τ w ) [-Me Ie - (tau K Me) d(i-cntr)/dt] (mv).5 Take the numerical derivative of (M E I E ) Find the ratio of this derivative to the eddy-drive shown below d(i-control)/dt (ka Turn/s) τ w 71 msec for Flux Loop #5. dm E I E dt = 1 τ w [ (M E I E ) (τ w K L M E ) di ] L dt Levitation Control (ka Turns) time (s) 2
21 Dipole Vertical Jog Without plasma, program a vertical displacement of dipole. After subtracting direct response from control coil, determine the response due to δz Flux Loop #1 (mv s) Flux Loop #5 (mv s) Flux Loop #1 (mv s) Dipole Position (mm) No plasma; Yes dipole. S For Flux Loop #5,.11 mv s/mm Levitation Control (ka Turns) time (s) 21
22 Measured Coupling Coefficients Flux Num ML (µh) KLME (µh) τw (ms) Gz (mv s/mm) (5 turns) (1 turns) (3 turns) ,96 14 (5 turns) ,71 22
23 (3) How Much Dipole Current? Dipole current must be known for equilibrium reconstruction. We measure dipole current using gravitational force balance. Measured weight of dipole is 565 kg Control current required for levitation is Measured dipole position (z ) gives dipole current of MA turn 23
24 F-Coil Charge m F g = dm FL dz (I F () M FL I lev /L F )I lev ka w M = 565 kg ka w M = 565 kg MA turns Charge 24
25 (4) How Much Plasma Current? Plasma Response Total Response 2-2 Flux Loop #5 (mv s) S Compute the direct and induced contributions from control coil and dipole displacement Least-squares best fit to find plasma dipole moment and location of diamagnetic current profile Flux Loop #1 (mv s) Levitation Control (ka Turns) Dipole Position (mm) ECRH Power (kw) time (s) 25
26 (4) How Much Plasma Current? Control-coil pickup is large for coils located nearby, at top of vessel High-power levitated discharges have large diamagnetic currents I p 9 ka, 3 larger than previous!! Plasma stored energy more than 1 kj Flux Loop #5 (mv s) Flux Loop #1 (mv s) Plasma and Dipole Current (ka) Diamagnetic Current Centroid (m) Levitation Control (ka Turns) Dipole Position (mm) S ECRH Power (kw) time (s) 26
27 (5) Plasma Equilibrium with Levitated Dipole First reconstructions with levitated dipole show best fit profiles are isotropic Plasma volume is 4% smaller (less stored energy) Best fit isotropic profile is broad for full heating power example: 1 GHz GHz GHz Tuesday, June 24, 28 28
28 Example Reconstruction Anisotropic Pressure p Isotropic Pressure p 1. Peak Pressure at Innermost Closed Field Line Parameter Fit Value Χ Ip If p P perp P 1 R peak.75 Γ 1.25 Γ Press Rpeak J Centroid Moment A m Max Perp Β Perp Β Rpeak Avg Perp Β Plasma Volume Energy J E Ip J ka All Magnetics t Tuesday, June 24,
29 Best Fits Χ 2 Contours p Parameter w/anisotropy Isotropic! Fit Value Fit Value Fit Value Χ Ip If p 1 2 P perp P R peak Γ Γ Press Rpeak J Centroid Moment A m Max Perp Β Perp Β Rpeak Avg Perp Β Plasma Volume Energy J E Ip J ka Γ Γ Γ R m Χ 2 Contours p R m Χ 2 Contours p Tuesday, June 24, R m 3
30 Remaining To Do List Finalize free-boundary equilibrium calculations. (Almost finished...) Compare equilibria during supported and nonsupported operation. Is plasma pressure isotropic during levitation? Complete eddy-current structure modeling to improve accuracy Incorporate additional external and internal magnetic probes. 27
31 Summary Magnetic reconstruction of the plasma current during dipole levitation requires subtraction of direct and induced pick-up from control coils and dipole position. A self-calibration procedure using preprogrammed control currents is used to measure the coupling coefficients Plasma currents are measured to exceed 9 ka, representing stored energy greater than 1 kj!! 29
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