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

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)

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

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

Magnetic reconnection in three dimensions

Reconnection in SSX-FRC

Ensemble average of 36 identical shots

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 )

PART 1 Helicity balance

Spheromak formation

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

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

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

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)

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?

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)

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

SSX-FRC parameters

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

SSX-FRC design and numerical equilibrium /

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)

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

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)

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

m=0,1 toroidal and poloidal energy densities

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

Elena Belova 2D simulation

3D simulation showing tilt instability

Full data (70 G on axis)

m=0 (70 G on axis)

m=1 (70 G on axis)

RCC field restricts reconnection

Magnetic energy, density indicate high

Full data (350 G on axis)

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

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

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

Nonzero helicity is observed in tilted final state

PART 2 Generalized Ohms Law and Energetic Ions

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

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

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

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)

Hall term dominates electric field during shot

Ensemble average of 36 identical shots

Terms in curl of Ohms law (single shot)

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

In plane magnetic field (ala min variance)

Out of plane magnetic field

Merger of left and right handed tori

Side view

Cross section

In plane JxB force (ala min variance)

Out of plane JxB force (slingshot)

Flux conservers for partial merging

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

Outer reconnection region

Inner reconnection region

Flux tube interaction for counter-helicity spheromaks

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

Current density J = B/ 0 and RGEA response

Current channel formation correlates with RGEA activity

RGEA raw signals

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

Preliminary soft x-ray detector analysis

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

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 )