Exploring reconnection physics in SSPX and NIMROD Lawrence Livermore National Laboratory Livermore, CA Center for Magnetic Self Organization La 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 Hooper with thanks to: LLNL SSPX and Theory Teams U. Wisc. NIMROD Team

2 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

3 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 B z steps up Mode amplitudes drop

4 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

5 SSPX reconnection –– A second current peak into an existing spheromak –– B poloidal 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

6 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

7 NIMROD Buildup 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

8 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

9 Fieldline evolution as the discharge develops Initial bubble blowing Toroidal field growth During early formation stages, the fieldlines evolve without chaos Fieldline puncture plot

10 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 =µ 0 j/B (azimuthally averaged) is patchy and non-monotonic (shown later) Azimuthally-averaged poloidal flux

11 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

12 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

13 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

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

15 Helicity (K) and magnetic energy (W) decay times depend differently on with NIMROD finds large (factor of 10) spatial variations in – including sheets of negative current Energy losses depend quadratically on –– W 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

16 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

17 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 jB 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