SSX summary: helicity balance and Ohms law

Workshop on Magnetic Self-OrganizationNSF Center meeting, Aug 4-6, 2004

Michael BrownC. 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-handedSpheromak

Left-handedspheromak 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

PART 1

Helicity balance

Spheromak formation

Complete merging: FRC formation

Right-handedSpheromak

Left-handedspheromak

FRC

Helicity conservation leads to a null helicity structure

The SSX Laboratory

10kV/100kAPulsed power

Cylindrical flux conservers andvacuum chamber (=0.40m, L=0.65m)

Coaxial magnetized plasmaguns 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

Distributed probe array

12 probe stalks: 4 toroidally at three axial positions

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 50s, but toroidal fields remain•Midplane flux profile consistent with RS/√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=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)

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PART 2

Generalized Ohm’s Lawand 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 propertiesEnergetic particles

3D magnetic probe array

600 coils, 558 array

~2 cm spacing

25 three channel 8:1multiplexer/integratorboards

10 eight channel 8-bitCAMAC digitizers

Full probe readoutevery 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 Ohm’s 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)

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

SummarySpheromak 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)