Exploring reconnection physics in SSPX and NIMROD

Lawrence Livermore National Laboratory Livermore, CA 94526

Center for Magnetic Self OrganizationLa Jolla, March 2-3, 2005

Work performed under the auspices of the U. S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.

Bick Hooperwith thanks to:

LLNL SSPX and Theory TeamsU. Wisc. NIMROD Team

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SSPX is a gun driven spheromak –– a strong arc is established

in bias flux between a cathode and flux conserver The magnetic pressure due to the current drives a bias magnetic flux into the flux conserver – generating toroidal magnetic field and flux

• The plasma pinches and non-axisymmetric modes grow generating local poloidal field but no net poloidal flux

• When the mode amplitudes become large nonlinear coupling generates an axisymmetric field

• Reconnection is required to generate net poloidal flux

Flux “bubble” in NIMROD

Note: Nimrod is up-side-down relative to SSPX

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The correct geometry, vacuum flux, and gun current yield good agreement between NIMROD and SSPX

SSPX NIMROD

Reconnection is required for topology change – Voltage spikes are reconnection “events”

Reconnection when:

• Gun voltage spikes

• Bz steps up

• Mode amplitudes drop

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Experimental reconnection is best demonstrated by an “isolated” event

Reconnection during startup in the experiment is “messy”

• The breakdown process is highly non-symmetric so that the azimuthal modes have initial large amplitudes

• It is difficult to analyze the processes in detail during this process

After the plasma is established, mode amplitudes can become small

• A new current pulse is applied and the mode grow in a more “controlled” manner

• The resulting reconnection event is relatively well defined

Magnetic fluctuation history

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SSPX reconnection –– A second current peak into an existing spheromak –– Bpoloidal at the flux conserver midplane does not start to increase until the peak of the second current pulse

I, V, 90° midplane and bottom probes Azimuthal array shows this at all angles

Note the spike in voltage after 1.4 ms

Probe p17 (FC bottom) increases from 1.3 ms

Note the break in dI/dt at ≈ 1.48 ms

Probe p09 (FC midplane) flat until 1.4 ms

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Contours of |B| show the column is pinched during the current rise and relaxes during the event

During current rise

t = 1.38 ms

During current decay

t = 1.52 ms

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NIMRODBuildup starting with low amplitude magnetic modes

When NIMROD is started with low amplitude, non-symmetric modes –– helicity and magnetic energy injection forms a nearly axisymmetric configuration

• There is little or no conversion of toroidal flux into poloidal flux until the modes (especially n=1) grow sufficiently large that nonlinear coupling generates an axisymmetric magnetic field

• Flux conversion requires a change in field topology –– A reconnection event occurs, very similar to that seen in SSPX

– We study this event to gain insight into the physics occurring during reconnection in spheromaks

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NIMROD –– Mode growth from a low “seed” delays initial reconnection processes until after the current peaks

Energy in n=0 grows until higher n modes become large

Mode energy takes 100 µs to grow from 10–8 J

Not shown:

Toroidal current and flux drop during the initial reconnection event

A voltage spike appears on the cathode, much as in the experiment

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Fieldline evolution as the discharge develops

Initial “bubble

blowing”

Toroidal field

growth

During early formation stages, the fieldlines evolve without chaos

Fieldline puncture plot

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After the burst of magnetic modes, azimuthally-averaged flux contours are formed (a “good” mean-field spheromak) but fieldlines are chaotic

All fieldlines are open –– chaos is apparent

• All fieldlines exit the flux conserver

• =µ0j/B (azimuthally averaged) is patchy and non-monotonic (shown later)

Azimuthally-averaged poloidal flux

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Fieldline evolution –– reconnection is needed for topology change

At other times (not shown) the 5 fieldlines (1 cm spaced cross at the flux conserver) diverge significantly from one another

Note the knot in the fieldline bundle

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Fieldline evolution (cont.) –– fieldlines initially close together can follow very different paths –– a clear sign of chaos

Shown are 4 (of 5) fieldlines from an initial cross on the flux conserver, with one-centimeter spacing

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Current sheets with < 0 –– are associated with reconnection

Fieldlines which pass close to the current sheets are very sensitive to their precise location –– as expected for generation of chaos

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Large velocity flows perpendicular to B are associated with the current layers

Perpendicular speed

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Helicity (K) and magnetic energy (W) decay times depend differently on

€

τW =W

dW dt=

B2dV∫

2η ||λ

2

μ0

B2∫ dV+ 2μ0 j⊥⋅E⊥dV∫

€

τK =K

dK dt=

B2dV∫2

η ||λ

μ0 λ−1B2dV∫

€

−1 = K 2μ0Wwith

NIMROD finds large (factor of 10) spatial variations in – including sheets of negative current

• Energy losses depend quadratically on –– τW is reduced significantly by these variations

• Helicity losses depend linearly on so the variations tend to cancel (“conservation of helicity”) –– however, the variations are so large that cancellation is not perfect

SSPX formation efficiencies [~ 18% (energy) and ~ 33% (helicity)] are likely due to enhanced losses associated with current layers

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Summary of results to date• NIMROD does a good job of matching the experiment

• Reconnection is needed to convert toroidal flux to poloidal flux

• In NIMROD we find:

– Initial injection of current is nearly axisymmetric

– Non-symmetric modes grow until nonlinearities are large enough to generate n=0 fields

– Reconnection then occurs with strong effects on topology

• Examination of details in NIMROD identifies current sheets as a major “player” in reconnection

– Inductive electric fields reverse in the current sheets

– “Collisions” of fieldlines with these sheets generate chaos

– Ohmic dissipation due to large variations in are a candidate for inefficiencies during formation

• Reconnection is accompanied by magnetic chaos

– This plays an essential role in the formation of the spheromak, e.g. allowing current (and flux) to penetrate throughout the volume

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Plans for probing SSPX to see if the negative current layers actually exist

A post doc – Carlos Romero-Talamás – is joining the SSPX experiment to do internal measurements with the goal of better understanding the reconnection and other processes

• One experiment will be to use probes near the X-point of the mean-field spheromak

• The NIMROD calculations suggest that the signature of reconnection will be negative j•B

• The location of the dominant reconnection is expected to be locked to the n=1 mode

Both magnetic and Rogowski probes will be required to explore the expected physics – a fast camera will be used to image the plasma and help guide interpretation of the probes

NIMROD modeling will be used to help interpret and guide the experiment –– AND the measurements will help (in)validate the code and to guide its use