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Workshop on Magnetic Self-Organization NSF Center meeting, Aug 4-6, 2004 Michael Brown C. D. Cothran, J. Fung, A. O Murchadha, Z. Michielli, M. Chang Swarthmore College Collaborators: M. Schaffer (GA), W. Matthaeus (Bartol), D. Cohen (Swarthmore), E. Belova (PPPL) Research supported by US DOE grants ER54604 and ER54490 SSX summary: helicity balance and Ohms law

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Outline A brief tour of the Swarthmore Spheromak Experiment (SSX) Device, diagnostics, plasma parameters Full merging and self-organization to large scale (magnetic helicity conservation, FRC, doublet CT) Local 3D magnetic reconnection studies (generalized Ohms law, Hall terms, energetic ions)

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Full merging: FRC formation Right-handed Spheromak Left-handed spheromak Large scale structure (FRC)

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Magnetic structure consistent with FRC/doublet-CT full data m=0 dominates Other modes are present

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Magnetic reconnection in three dimensions

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Reconnection in SSX-FRC

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Ensemble average of 36 identical shots

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Research program at the Swarthmore Spheromak EXperiment Complete merging Magnetically restricted merging Partial (mechanically restricted) merging magnetic reconnection FRC/doublet-CT formation and stability (B )

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PART 1 Helicity balance

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Spheromak formation

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Complete merging: FRC formation Right-handed Spheromak Left-handed spheromak FRC Helicity conservation leads to a null helicity structure

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Why Field Reversed Configurations (FRC)? Fusion 1 compact toroid Purely poloidal fields Natural divertor at the ends Can be translated …but must be stable in the MHD fluid limit Experiment (kinetic) says yes Theory/simulation says no

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Testing stability at large s (fluid MHD limit) s minor radius / ion gyroradius Counter-helicity spheromak merging leads to… Higher flux (4 mWb) Moderate temperature (<100 eV) High s (>10) …thanks to Y. Ono, TS-3 device, U. Tokyo

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Recent FRC stability predictions Yu. Omelchenko et al Phys. Plasmas 8, 4463 (2001) Hybrid simulation Self-generated toroidal field (from axially sheared toroidal electron flow) stabilizes the tilt mode even for fluid FRCs …but see also E. Belova et al Phys. Plasmas 7, 4996 (2000)

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External midplane coils for control of reconnection and B Analytic solution (P. Parks, GA) Numerical Grad-Shafronov equilibrium (M. Schaffer et al, GA) 8.0 kA 13.0 kA Increasing midplane field limits merging How much toroidal field is necessary for stability? …is this doublet-CT (two magnetic axes) interesting?

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The SSX Laboratory 10kV/100kA Pulsed power Cylindrical flux conservers and vacuum chamber ( =0.40m, L=0.65m) Coaxial magnetized plasma guns on each end (1 mWb)

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Diagnostics at SSX 600 channel 1.25 MHz data acquisition system Magnetic probe arrays Langmuir triple probe He-Ne quadrature interferometer 0.2 m VUV monochrometer Bolometer Retarding Grid Energy Analyzers (RGEA) Soft x-ray photodiodes (SXR) Directional (Gundestrup) Mach probe

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SSX-FRC parameters

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Distributed probe array 12 probe stalks: 4 toroidally at three axial positions

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SSX-FRC design and numerical equilibrium /

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Magnetic structure consistent with FRC/doublet-CT m=0 (toroidal mode) component Reversed field Very little midplane toroidal field Axially antisymmetric B 70 G RCC field (on axis)

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Magnetic structure consistent with FRC/doublet-CT full data m=0 dominates Other modes are present

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Peak poloidal flux and radial flux profile Ends reach 3-4 mWb immediately (3-4 amplification) Midplane flux grows to match ends Reconnection rate 0.04 No private flux after 50 s, but toroidal fields remain Midplane flux profile consistent with R S /2: high FRC 70 G RCC field (on axis)

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Axisymmetric helicity estimate Poloidal flux = 3 mWb (east and west) Toroidal flux = +/- 3 mWb (east and west) Helicity = 2x10 mWb^2 east – 2x10 mWb^2 west = zero total Rate = 2(1 kV)(1 mWb) x 10 s = 20 mWb^2

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m=0,1 toroidal and poloidal energy densities

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m=1 component late in time: tilted CT Geometric axis of CT is perpendicular to the flux conserver axis

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Elena Belova 2D simulation

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3D simulation showing tilt instability

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Full data (70 G on axis)

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m=0 (70 G on axis)

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m=1 (70 G on axis)

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RCC field restricts reconnection

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Magnetic energy, density indicate high

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Full data (350 G on axis)

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Co-helicity Rapid tilt (by 50 s) Very long lifetime compared to counter-helicity

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Mode analysis: magnetic energies co-helicity m=0m=1 m=0 counter-helicity east midplane west

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SSX-FRC prototype: midplane walls removed from SSX FCs 5 cm annulus remaining (passive RCC)

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Nonzero helicity is observed in tilted final state

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PART 2 Generalized Ohms Law and Energetic Ions

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3D magnetic reconnection experiments Brown et al Astrophys. J. Lett. (9/02) Brown et al Phys. Plasmas 9, 2077 (2002) Brown et al Phys. Plasmas 6, 1717 (1999) Kornack et al Phys. Rev. E 58, R36 (1998) Magnetic probe array RGEAs Large slots cut into FC rear walls define the reconnection region 3D magnetic properties Energetic particles

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3D magnetic probe array 600 coils, array ~2 cm spacing 25 three channel 8:1 multiplexer/integrator boards 10 eight channel 8-bit CAMAC digitizers Full probe readout every 0.8 s

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Reconnection in SSX-FRC Catch reconnection early (< 32 s) then FRC forms

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Generalized Ohms Law and Curl E + vxB = ηJ + (JxB – grad P)/ne + J/t Curl (vxB + div P) = B/t + Curl ηJ + Curl (JxB)/ne + Curl (J/t)

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Hall term dominates electric field during shot

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Ensemble average of 36 identical shots

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Terms in curl of Ohms law (single shot)

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Generalized Ohms Law magnitudes E + vxB = ηJ + (JxB – grad P)/ne + J/t Ohmic and electron inertia terms are small From near pressure balance and unity, we know that JxB and grad P are comparable Only grad P can contribute at the neutral line

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In plane magnetic field (ala min variance)

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Out of plane magnetic field

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Merger of left and right handed tori

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Side view

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Cross section

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In plane JxB force (ala min variance)

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Out of plane JxB force (slingshot)

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Flux conservers for partial merging

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Poloidal and toroidal view Outer field lines Poloidal and toroidal view Inner field lines

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Outer reconnection region

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Inner reconnection region

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Flux tube interaction for counter-helicity spheromaks

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Co- and counter-helicity merging Counter-helicity: rapid reconnection Co-helicity: no apparent reconnection t = 32 s t = 64 s

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Current density J = B/ 0 and RGEA response

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Current channel formation correlates with RGEA activity

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RGEA raw signals

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Average peak signal for the out-of-plane RGEA Fit to a thermal distribution with drift: T=33±11eV and V=86±20eV

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Preliminary soft x-ray detector analysis

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Summary Spheromak merging in SSX forms large scale, self-organized structure Reconnection is fully 3D Merging results in self-organized structure Helicity conservation implies null helicity Hall terms dominate electric field in Ohms law Study dynamics of doublet-FRC Study flow with Mach probe, ion doppler Need computational/theoretical support Local SSX reconnection is fully 3D, generates energetic particles, flow, and heat

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Plans for the near future Implement IDS at midplane of SSX-FRC (use with Mach probe) Compare flow results with Belova code Helium glow discharge cleaning for density control (lower density, larger c/ pi )

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