MRX research in the context of Princeton Max-Planck collaboration
Masaaki Yamada Princeton Plasma Physics laboratory Princeton University
January 14, 2013 With MRX Staff: H. Ji, R. Kulsrud, E. Lawrence, T. Tharp + Graduate students Magnetic Reconnection
• Topological rearrangement of magnetic field lines! • Magnetic energy => Kinetic energy! • Key to stellar flares, coronal heating, particle acceleration, star formation, energy loss in lab plasmas!
Before reconnection After reconnection Outline! !Magnetic reconnection! – Leading issue in space, astro- and fusion plasma physics – A major question was: Why does it occur so fast? – New question: How does energy flow from magnetic field to plasmas?
• Generation of a reconnection layer on MRX => Local analysis • Two fluid physics analysis!
Recent Emphasis:! • Energy conversion processes from B2 to ions and electrons! • A new series of experimental campaign and the recent results! – Plasma jog experiment: Addresses heating and acceleration of ions and electrons – Guide field effects on two-fluid reconnection – Reconnection in partially ionized plasmas – Solar flare relevant plasma arcs
Plans for Princeton-MPPC collaboration! Magnetic Reconnection Experiment Primary objectives of MRX is to create a proto-typical reconnection layer and study it experimentally with cross- validation with numerical simulations
Experimentally measured flux evolution!
13 -3 ne= 1-10 x10 cm , ! Te~5-15 eV, ! B~100-500 G, ! S < 1000! Reconnection layer Profile changes with Collisionality: Experimentally measured field line features in MRX
• Manifestation of Hall effects • Electrons would pull magnetic field lines with their flow Two-fluid physics dictates reconnection layer dynamics
(a) (b) R • Out of plane magnetic field is generated during reconnection. • Electron acceleration and heating with mirror- Plasma Electron Outflow trapped electrons. Current • Parallel electron y conduction determines Z PlasmaPlasma potential profile! InflowInflow
Sheath width ~ c/ωpi In-plane Potential Profile
Karimabadi et al, 2007
Wygant et al. 2005
MRX, 2012 • A large bipolar electrostatic field (BEF) exists in the reconnection layer due to two-fluid effects. • It can accelerate ions generating a pair of counter-streaming ion beams in the diffusion layer. Ion Acceleration (Mach probe)
• Clear ion acceleration by the in-plane electric field. • Asymmetry in the ion inflow is caused by asymmetry in the upstream density. Both flows and temperature of electron and ion measured by plasma jogging
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50 468.45 468.5 468.55 468.6 468.65 468.7 Wavelength (nm) J. Yoo, 2012 Ion acceleration data and simulation results
Goldman et al., 2012
Wygant JGR 2005 Drake et al., 2009 Downstream Ion Heating3
Φ (V) J ⋅E (W/cm3) (a) p (b) i (a) (b)
60 40 20 T 25 (R,Z) = (37.5,0) i
42 42 V 50 30 80 (R,Z) = (37.5,15) 15 V 15
iZ iz (km/s) 40 40 20 10 5 40 (eV) i 38 38 10 T 30 60 5 −5
R (cm) R (cm) 0 36 36 20 0 −15 −10 0 5 10 15 34 34 Z (cm) 10 −20 40 (c) 20 25 32 32 0 −30 V
Number of photons 15 15 0 5 10 15 0 5 10 15 iz Z (cm) Z (cm) (km/s) 20 10 5 (eV) i T 5 −5 FIG. 3. (a) In-plane ion flow vector measured by Mach probes 0 0 −15 468.55 468.6 468.65 30 35 40 45 together along with contours of Φp and Ψ.Theflowvectors λ (nm) R(cm) are measured every 1 cm along R and every 3 cm along Z. The maximum ion velocity is 16 km/s. As ions flow across • Ions are heated downstream. FIG. 4. (a) Spectra of He 4686 Aat(˚ R, Z)=(37.5, 0) (black) the separatrices, they are accelerated by Ein and turn into • Classical viscous heating under the assumption of unmagnetized ions and at (R, Z)=(37.5, 15) (green). Solid lines are from fitting the outflow direction. (b) Work done by the electric field on the spectra cannot explain into the the sum observed of 13 Gaussianion heating. functions. Both ion ions. It is dominated by the strong Hall field. heating• Downstream and acceleration ion thermalization are observed is due at (toR, re-magnetization Z)=(37.5, 15). (b) Axial (NumericalTi and V simulations)iZ profiles at R =37.5cm.ForZ>9 cm, the ion temperature rises significantly while ViZ begins the above equation at Z = 0 leads to to saturate. (c) Radial Ti and ViZ profiles at Z =15cm (downstream). The ion temperature profile is peaked at the ∗ ER (VeY V )BZ , (2) center of the layer while the outflow profile is broader. ≈− − eY ∗ where VeY = (1/eneBZ )∂pe/∂R is the electron diamag- netic drift velocity.− The diamagnetic drift term is not negligible due to strong electron heating near the cur- V/m). Furthermore, its spatial scale is smaller than the rent sheet that cannot be explained by classical Ohmic ion skin depth δi = c/ωpi ( 9cm).Thus,assoonasthe ∼ heating [27]. The radial electric field reverses sign at the ions see the strong Ein, they are accelerated toward the X point where the sign of BZ also reverses. This indi- outflow direction. Figure 3-(a) shows the ion flow vector cates that the bipolar radial electric field is the result of profile measured by Mach probes along with contours of electron force balance [28]. Since VeY contains the dia- Φp. Considerable changes in the ion flow occur near the magnetic component, Eqn. (2) implies that the electron boundary. The corresponding large difference between diamagnetic drift does not contribute to ER; only pure the ion and electron in-plane flow profiles produces the acceleration by EY plays a role [29]. By integrating the well-known quadrupole out-of-plane magnetic field [30]. right-hand side of Eqn. (2) along R, the radial potential It is worth noting that the stagnation point of the ion profile can be estimated. The electron drift velocity is flow is shifted to the inboard side (R<37.5), which is obtained by Ve = J/ene + Vi = B/µ0ene + Vi. caused by the upstream density asymmetry [31]; the out- As shown in Fig. 2-(b),− the estimates−∇ × by Eqn. (2) (the board side (R>37.5) has about 2–3 times larger density blue line) agree with the measured values (red asterisks). than the inboard side due to radial symmetry-breaking Similarly, the electron momentum equation along the processes in the earlier phases of the discharge [32]. outflow direction at R =37.5 cm yields Figure 3-(b) shows the profile of the work done by ∗∗ the electric field on the ions per unit volume and unit EZ (VeY VeY )BR, (3) ≈ − time, Ji E. The in-plane electric field is calculated by ∗∗ E · where V = (1/eneBR)∂pe/∂Z is the electron dia- in = Φp and the out-of-plane reconnection electric eY − −∇ magnetic drift from the pressure gradient along Z.As field is estimated by EY =(∂Ψ/∂t)/2πR.Theworkdone electrons flow out of the EDR with high VeY ,theycreate by EY is fairly uniform over the measurement region, 3 a further potential decrease along the outflow direction which is inside of the IDR, with values of 2–8 W/cm . Z. The amount of the further potential decrease can be On the other hand, the work done by Ein is localized 3 estimated by integrating Eqn. (3) along Z, which agrees downstream with higher values of 20–50 W/cm . This with the measured values as shown in Fig. 2-(c). Due to means that ions gain energy mostly from the Hall electric the high mobility of electrons, the potential drop around field, which agrees with recent simulation results [22, 33]. the EDR is conveyed along magnetic field lines, creating In addition to ion acceleration, we also observe ion astrongEin near the separatices as shown in Fig. 2-(a). heating downstream. Figure 4-(a) shows measured He The strong Hall electric field ballistically accelerates 4686 A˚ spectra at the X point [(R, Z)=(37.5, 0), blue] ions near the separatrices where the ions are unmagne- and downstream [(R, Z)=(37.5, 15), red]. Clear broad- tized. The magnitude of Ein near the boundary can ex- ening (heating) and shifting (acceleration) exist in the ceed 700 V/m, which is much larger than EY ( 200 spectrum at Z = 15 cm. Figure 4-(b) shows the axial ∼ Electron Heating
• Strong increase near the electron diffusion region. • Inboard side has higher electron temperature. A jog experiment on MRX (2011)!
NASA MMS Satellite to be launched in 2014
In collaboration with UNH, MMS, UC-Berkeley. Hall Effects on Guide Field Reconnection in MRX
Effects of Guide Fields on Collision-less Reconnection
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There isn’t a simple analytic model for this, but measurements qualitatively match two-fluid simulations
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R (cm) −120 R (cm) 35 35 35 35 R (cm) 35 −40 −40 −160 −160 −160 −160 −160 −40 −40 −40 −220 −220 −220 −220 −220 −300 −300 −300 −300 −300 −140 −140 −140 −140 −140 30 30 30 30 30 −60 −180 −180 −180 −180 −180 −240 −240 −60 − 60 −60 −60 − 240 −240 −240 −10Z−10 (cm)Z− 10(cm) +10Z− 10(cm) +10Z −(cm)10 +10 Z +10(cm) − +1010Z−10 (cm)Z− 10(cm) +10Z− 10(cm) +10Z −(cm)10 +10 Z +10(cm) − +1010Z−10 (cm)Z− 10(cm) +10Z− 10(cm) +10Z −(cm)10 +10 Z +10(cm) − +1010Z−10 (cm)Z− 10(cm) +10Z− 10(cm) +10Z −(cm)10 +10 Z +10(cm) − +1010Z−10 (cm)Z− 10(cm) +10Z− 10(cm) +10Z −(cm)10 +10 Z +10(cm) +10
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Simulations performed by A. Bhattacharjee, B. Sullivan, and Y. Huang at UNH. Recent (2D) Simulations Find Multiple Flux Ropes in Collisionless Plasmas
Bhattacharjee et al. (2009):MHD Daughton et al. (2009): PIC
The Sweet-Parker layer breaks up to form plasmoids when S > ~104 => Multiple flux ropes =>Turbulent reconnection? 17 => MRX-U Conceptual Designs Are Almost Complete [Ji et al, 2013]
Parameters MRX LRX
Device diameter 1.5 m 3 m
Device length 2 m 3.2 m
Flux core diameter 0.75 m 1.5 m
Stored energy 25 kJ 4 MJ
Plasma heating No OH (10MW)
S (anti-parallel) 600-1,400 5,000-16,000
λ=(Z/δi) 35-10 100-30
S (guide field) 2900 100,000
λ=(Z/ρS) 180 1,000 18 Current layer observed to disrupt over a fast timescale in MRX
Current Layer Disrupts over a short time period
“Disruption:” Impulsive reconnection event in which Jy drops and Ey peaks Line-tied magnetic flux rope experiments
• The MRX flux ropes are magnetized partial-toroidal arc discharges formed between two copper electrodes
• Magnetic probes and a fast camera are used to quantitatively analyze the evolution of the flux rope discharges
Magnetic Axis Equilibrium Reconstruction
Shot 108312 Shot 108307 Reconnection in Partially Ionized Plasmas
• Electron-neutral collisions increase classical resistivity • Ion-neutral drag can effectively increase the ion 1/2 1/2 mass: VA→VA (ρi/ρn) ; c/ωpi→c/ωpi(ρn/ρi) ‣ Length scale: Predicted to increase for fast Hall reconnection (Zweibel ApJ 1989 739:72, Malyshkin et al ApJ 2011). ‣ Key physics: Often treated as ambipolar diffusion, but multi-fluid approach may be needed to see all effects.
E. Lawrence et al PRL 2013 Current sheet and out-of-plane B field unaffected
Ionized case (ni/nn~12%; ηen~0.5ηei; νen, νei<<νce)
Weakly ionized case (ni/nn~0.9%; ηen~ηei; νen, νei<<νce) 2D Ion Outflow Profiles
13 -3 Ionized case (ni~2×10 cm ; ni/nn~12%; L/λin~2)
Contours show magnetic flux
13 -3 Weakly ionized case (ni~2×10 cm ; ni/nn~0.9%; L/λin~50)
Outflow channel broadens Ion outflow speed is reduced to Alfvén speed based on total (ion+neutral) mass density. Summary • Recent progress in study of reconnection layer in MRX! – Transition from collisional MHD to two-fluid regime changes profiles of the neutral sheets – Hall effects verified – Multiple flux ropes observed with larger S – Emphasis shifted to study of particle heating and acceleration; Role of potential profiles!
• New experiments initiated: related to solar atmosphere! – Effects of guide field – Reconnection in partially ionized plasmas – Stability of line tied flux rope : Global reconnection Research Plans on MRX with MPPC • Effects of Guide Field! – Reconnection dynamics A scaling on reconnection rate – Effects on particle heating and acceleration – Exchange visits
• 3D Study of Reconnection layer! – Characteristics of flux ropes
• Study the role driving term! – Global and local effects
• Reconnection process in tokamaks and solar flares!