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The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC SECTP LANL GSFC UMD The Collisionless Diffusion Region: An Introduction Michael Hesse NASA GSFC SECTP LANL GSFC UMD

Overview: Diffusion region basics The (electron) diffusion region for anti-parallel reconnection The (electron) diffusion Overview: Diffusion region basics The (electron) diffusion region for anti-parallel reconnection The (electron) diffusion region for guide-field reconnection An avenue toward fast MHD reconnection without Hall terms Acknowledgements: J. Birn, M. Kuznetsova, K. Schindler, M. Hoshino, J. Drake SECTP LANL GSFC UMD

Magnetic Reconnection: Dissipation Mechanism (How does it work? ) Conditions: IMPOSSIBLE (for species s) Magnetic Reconnection: Dissipation Mechanism (How does it work? ) Conditions: IMPOSSIBLE (for species s) if SECTP LANL GSFC UMD

Electric Field Equations z x Electron eqn. of motion At reconnection site important? SECTP Electric Field Equations z x Electron eqn. of motion At reconnection site important? SECTP small, limited by me? LANL GSFC UMD

Results for anti-parallel reconnection: Brief review SECTP LANL GSFC UMD Results for anti-parallel reconnection: Brief review SECTP LANL GSFC UMD

Magnetic field and ion-electron flow velocities P. Pritchett M. Hoshino SECTP LANL GSFC UMD Magnetic field and ion-electron flow velocities P. Pritchett M. Hoshino SECTP LANL GSFC UMD

Normal Magnetic Flux: evolution electron-mass independent! => Local electron physics adjusts to permit large Normal Magnetic Flux: evolution electron-mass independent! => Local electron physics adjusts to permit large scale evolution SECTP LANL GSFC UMD

Compare extremes along dashed lines - ion quantities - electron quantities SECTP LANL GSFC Compare extremes along dashed lines - ion quantities - electron quantities SECTP LANL GSFC UMD

Large (ion) Scale Features -> Ion scale features approx invariant. SECTP LANL GSFC UMD Large (ion) Scale Features -> Ion scale features approx invariant. SECTP LANL GSFC UMD

Small (electron) Scale Features SECTP LANL GSFC UMD Small (electron) Scale Features SECTP LANL GSFC UMD

Pressure Tensor SECTP LANL GSFC UMD Pressure Tensor SECTP LANL GSFC UMD

SECTP LANL GSFC UMD SECTP LANL GSFC UMD

Sample Electron Distribution (Pxye) 10. 0<x< 11. 0 -0. 5<z< 0. 5 log f Sample Electron Distribution (Pxye) 10. 0

Can be explained by trapping scale: “bounce motion” [Horiuchi and Sato, 1996] [Biskamp and Can be explained by trapping scale: “bounce motion” [Horiuchi and Sato, 1996] [Biskamp and Schindler, 1971] => Estimate of reconnection electric field [Hesse et al. , 1999] [Kuznetsova et al. , 2000] SECTP LANL GSFC UMD

realistic electron mass Ricci et al. SECTP 3 D – no LHD, kink, … realistic electron mass Ricci et al. SECTP 3 D – no LHD, kink, … Zeiler et al. LANL GSFC UMD

But, some questions remain… Sausage mode, Buechner et al. SECTP Kink, LHD, Ozaki et But, some questions remain… Sausage mode, Buechner et al. SECTP Kink, LHD, Ozaki et al. Ion sound mode… LANL GSFC UMD

…and other limitations, such as -Finite (small) system size -Finite (small) ion/electron mass ratio …and other limitations, such as -Finite (small) system size -Finite (small) ion/electron mass ratio -Finite (small) speed of light -Periodicity …there is work to be done! SECTP LANL GSFC UMD

What changes in the presence of guide field? if guide field strong enough electrons What changes in the presence of guide field? if guide field strong enough electrons are magnetized no bounce orbits no nongyrotropic pressures(? ) bulk inertia dominant(? ) Method: Theory and PIC simulations SECTP LANL GSFC UMD

Simulation Setup - 1 -D “Harris” Equilibrium, Lx= 2 Lz= 25. 6 c/wpi - Simulation Setup - 1 -D “Harris” Equilibrium, Lx= 2 Lz= 25. 6 c/wpi - Flux function: A = -ln cosh(z/a) - normal magnetic field perturbation (X type, 2. 5% of lobe field) - 0, 40, 80% guide field - Sheet Full-Width a= c/wpi - Ti/Te = 5 - mi/me=256 - 100 x 106 particles - 800 x 800 grid Results averaged over 60 plasma periods SECTP LANL GSFC UMD

SECTP LANL GSFC UMD SECTP LANL GSFC UMD

Change of symmetry By SECTP P. Pritchett LANL GSFC UMD Change of symmetry By SECTP P. Pritchett LANL GSFC UMD

Parallel electric field Wit=16 …also analytic theory by Drake et al. SECTP LANL GSFC Parallel electric field Wit=16 …also analytic theory by Drake et al. SECTP LANL GSFC UMD

Electric Field Equations z x Electron eqn. of motion At reconnection site important? SECTP Electric Field Equations z x Electron eqn. of motion At reconnection site important? SECTP small, limited by me? LANL GSFC UMD

Magnitude of Bulk Acceleration Contribution Time derivative of (negative) electron velocity in y direction: Magnitude of Bulk Acceleration Contribution Time derivative of (negative) electron velocity in y direction: SECTP LANL GSFC UMD

 Pxye Pyze SECTP LANL GSFC UMD Pxye Pyze SECTP LANL GSFC UMD

-(vez. Bx-vex. Bz) -me(ve. grad vey)/e SECTP LANL GSFC UMD -(vez. Bx-vex. Bz) -me(ve. grad vey)/e SECTP LANL GSFC UMD

Electron Distribution Functions F(vx, vy) vy F(vx, vz) vz vx SECTP F(vy, vz) vz Electron Distribution Functions F(vx, vy) vy F(vx, vz) vz vx SECTP F(vy, vz) vz vx vy LANL GSFC UMD

. . pressure tensor nearly(? ) gyrotropic But: if Bx, Bz=0 -> nongyrotropy important. . . pressure tensor nearly(? ) gyrotropic But: if Bx, Bz=0 -> nongyrotropy important. How to estimate? SECTP LANL GSFC UMD

Scaling the pressure tensor evolution equation Assume ignore heat flux… SECTP LANL GSFC UMD Scaling the pressure tensor evolution equation Assume ignore heat flux… SECTP LANL GSFC UMD

Pressure tensor approximations Hesse, Kuznetsova, Hoshino, 2001 SECTP LANL GSFC UMD Pressure tensor approximations Hesse, Kuznetsova, Hoshino, 2001 SECTP LANL GSFC UMD

Electron Pressure Tensors from simulation approximation Pxye Pyze critical difference at reconnection site! SECTP Electron Pressure Tensors from simulation approximation Pxye Pyze critical difference at reconnection site! SECTP LANL GSFC UMD

coll. skin depth SECTP LANL GSFC UMD coll. skin depth SECTP LANL GSFC UMD

Qxyze Qxxye Pyza approximation SECTP LANL GSFC UMD Qxyze Qxxye Pyza approximation SECTP LANL GSFC UMD

Heat Flux Tensor Time Evolution lots of work SECTP LANL GSFC UMD Heat Flux Tensor Time Evolution lots of work SECTP LANL GSFC UMD

Approximations for Qxyze x, y, x component: Assume near gyrotropy, By>>Bx, Bz Leading order, Approximations for Qxyze x, y, x component: Assume near gyrotropy, By>>Bx, Bz Leading order, Pii>>Pjk SECTP LANL GSFC UMD

Approximations for Qxyze From simulation: Approximation: Ok in center, difference due to 4 -tensor? Approximations for Qxyze From simulation: Approximation: Ok in center, difference due to 4 -tensor? SECTP LANL GSFC UMD

Scaling of diffusion region => 2 Scale lengths: SECTP Collisionless skin depth Electron Larmor Scaling of diffusion region => 2 Scale lengths: SECTP Collisionless skin depth Electron Larmor radius in guide field LANL GSFC UMD

Physical Mechanism: Larmor orbit interacts with “anti-parallel” B components SECTP LANL GSFC UMD Physical Mechanism: Larmor orbit interacts with “anti-parallel” B components SECTP LANL GSFC UMD

3 D Modeling M. Scholer et al. : Formation of “ 2 D” channel 3 D Modeling M. Scholer et al. : Formation of “ 2 D” channel J. Drake et al. : Buneman modes, electron holes, anomalous resistivity SECTP LANL GSFC UMD

P. Pritchett: inertia important SECTP LANL GSFC UMD P. Pritchett: inertia important SECTP LANL GSFC UMD

…and other limitations, such as -Finite (small) system size -Finite (small) ion/electron mass ratio …and other limitations, such as -Finite (small) system size -Finite (small) ion/electron mass ratio -Finite (small) speed of light -Periodicity …there is work to be done! SECTP LANL GSFC UMD

Results from GEM reconnection challenge: • Hall effect (dispersive waves) speeds up reconnection rate Results from GEM reconnection challenge: • Hall effect (dispersive waves) speeds up reconnection rate • Reconnection rate otherwise independent on model • MHD models with simple resistivity show only slow reconnection rates Question: Are Hall effects the only way to include fast reconnection in MHD models? SECTP LANL GSFC UMD

Approach: • Hall effect result of ion-electron scale separation • Eliminate scale separation by Approach: • Hall effect result of ion-electron scale separation • Eliminate scale separation by - Choosing equal ion and electron mass - Choosing equal ion and electron temperatures • Simple and cheap…, includes ion and “electron” kinetic physics • “Small” GEM runs with and without guide field • “Large” runs, with and without guide field SECTP LANL GSFC UMD

GEM-size run, no By SECTP LANL GSFC UMD GEM-size run, no By SECTP LANL GSFC UMD

GEM-size run, no By me=1 SECTP me=1/256 LANL GSFC UMD GEM-size run, no By me=1 SECTP me=1/256 LANL GSFC UMD

GEM-size run, By=0. 8 SECTP LANL GSFC UMD GEM-size run, By=0. 8 SECTP LANL GSFC UMD

GEM-size run, By=0. 8 me=1 SECTP me=1/256 LANL GSFC UMD GEM-size run, By=0. 8 me=1 SECTP me=1/256 LANL GSFC UMD

large run, By=0. SECTP LANL GSFC UMD large run, By=0. SECTP LANL GSFC UMD

large run, By=0. 8 SECTP LANL GSFC UMD large run, By=0. 8 SECTP LANL GSFC UMD

large run, By=0. 8 Reconnection rates similar to GEM problem SECTP LANL GSFC UMD large run, By=0. 8 Reconnection rates similar to GEM problem SECTP LANL GSFC UMD

By, both large runs, t=40 initial By=0. 8 no quadrupole or quadrupolar modulation! SECTP By, both large runs, t=40 initial By=0. 8 no quadrupole or quadrupolar modulation! SECTP LANL GSFC UMD

large run, By=0. , t=40 Pxye Pyze SECTP vix jiy LANL GSFC UMD large run, By=0. , t=40 Pxye Pyze SECTP vix jiy LANL GSFC UMD

large run, By=0. 8, t=40 Pxye Pyze SECTP vix jiy LANL GSFC UMD large run, By=0. 8, t=40 Pxye Pyze SECTP vix jiy LANL GSFC UMD

Electric Field Equations z x Electron eqn. of motion Approximate representation in MHD: SECTP Electric Field Equations z x Electron eqn. of motion Approximate representation in MHD: SECTP LANL GSFC UMD

Additional slides SECTP LANL GSFC UMD Additional slides SECTP LANL GSFC UMD

jye jyi By A tour of the reconnection region… Pxye SECTP Pyze LANL GSFC jye jyi By A tour of the reconnection region… Pxye SECTP Pyze LANL GSFC UMD

Mass Dependence of Electron Diffusion Region: Simulation Setup - 1 -D “Harris” Equilibrium, Lx= Mass Dependence of Electron Diffusion Region: Simulation Setup - 1 -D “Harris” Equilibrium, Lx= 2 Lz= 25. 6 c/wpi - Flux function: A = -ln cosh(z/a) - normal magnetic field perturbation (X type, 5% of lobe field) - Sheet Full-Width a= c/wpi - Te/Ti = 0. 2 - me/mi=1/9 -1/100 - wpe/wce=5 - 50 x 106 particles - 800 x 400 grid SECTP LANL GSFC UMD

mi=me, By=1 rate slightly reduced due to higher plasma mass SECTP LANL GSFC UMD mi=me, By=1 rate slightly reduced due to higher plasma mass SECTP LANL GSFC UMD

Additional Material SECTP LANL GSFC UMD Additional Material SECTP LANL GSFC UMD

Magnitude of Pressure Tensor Contribution Pyze ne SECTP LANL GSFC UMD Magnitude of Pressure Tensor Contribution Pyze ne SECTP LANL GSFC UMD

Particle Picture: Straight Acceleration and Thermalization Question: Are electrons transiently accelerated while crossing the Particle Picture: Straight Acceleration and Thermalization Question: Are electrons transiently accelerated while crossing the diffusion region, or is some of the energy thermalized? Relevance: straight acceleration -> thermalization -> Approach: Integrate 104 electron orbits in vicinity of reconnection region SECTP LANL GSFC UMD

kinetic energy change as function of delta y-component of kinetic energy vs. delta y kinetic energy change as function of delta y-component of kinetic energy vs. delta y 2 2 y = -2. 5605 e-05 - 0. 17785 x R= 0. 98882 y = -0. 027939 - 0. 16877 x R= 0. 9873 1. 5 1 1 0. 5 delta Eyk 0. 5 delta Ek 0 0 -0. 5 -12 -10 -8 -6 -4 delta y -2 0 2 -10 -8 -6 -4 -2 0 2 delta y Approximately 6% of energy is thermalized SECTP LANL GSFC UMD

orbit( 6293): x-z plane 0. 06 0. 04 0. 02 0 -0. 02 -0. orbit( 6293): x-z plane 0. 06 0. 04 0. 02 0 -0. 02 -0. 04 -0. 06 -0. 08 13. 15 13. 25 13. 3 x 13. 35 13. 45 orbit( 6293): z-x acceleration phase 0. 06 0. 04 0. 02 z 0 -0. 02 -0. 04 -0. 06 -0. 08 13. 15 13. 25 13. 35 13. 45 x SECTP LANL GSFC UMD

Contours of Poloidal Magnetic Field Scale length related to electron Larmor radius SECTP LANL Contours of Poloidal Magnetic Field Scale length related to electron Larmor radius SECTP LANL GSFC UMD

Vmax= 0. 65 Vmax= 2. 8 SECTP LANL GSFC UMD Vmax= 0. 65 Vmax= 2. 8 SECTP LANL GSFC UMD

Scaling the pressure tensor evolution equation xy component near reconnection site: SECTP LANL GSFC Scaling the pressure tensor evolution equation xy component near reconnection site: SECTP LANL GSFC UMD

Reconnection faster for smaller guide fields SECTP LANL GSFC UMD Reconnection faster for smaller guide fields SECTP LANL GSFC UMD