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

SECTPLANL GSFC UMD 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

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

SECTPLANL GSFC UMD Electric Field Equations Electron eqn. of motion At reconnection site small, limited by m e ?important? x z

SECTPLANL GSFC UMD Results for anti-parallel reconnection: Brief review

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

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

SECTPLANL GSFC UMD Compare extremes along dashed lines - ion quantities - electron quantities

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

SECTPLANL GSFC UMD Small (electron) Scale Features

SECTPLANL GSFC UMD Pressure Tensor

SECTPLANL GSFC UMD

10.0<x< <z< log f u y u x Sample Electron Distribution (P xye ) Thermal inertia (nongyrotropic pressure)-based dissipation seems key to anti-parallel reconnection

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

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

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

SECTPLANL GSFC UMD …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!

SECTPLANL GSFC UMD 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

SECTPLANL GSFC UMD Simulation Setup - 1-D “Harris” Equilibrium, L x = 2L z = 25.6 c/  pi - Flux function: A = -ln cosh(z/  ) - normal magnetic field perturbation (X type, 2.5% of lobe field) - 0, 40, 80% guide field - Sheet Full-Width  = c/  pi - T i /T e = 5 - m i /m e = x10 6 particles - 800x800 grid Results averaged over 60 plasma periods

SECTPLANL GSFC UMD

ByBy P. Pritchett Change of symmetry

SECTPLANL GSFC UMD Parallel electric field  i t=16 …also analytic theory by Drake et al.

SECTPLANL GSFC UMD Electric Field Equations Electron eqn. of motion At reconnection site small, limited by m e ?important? x z

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

SECTPLANL GSFC UMD P xye P yze

SECTPLANL GSFC UMD -(v ez B x -v ex B z ) -m e (v e.grad v ey )/e

SECTPLANL GSFC UMD Electron Distribution Functions F(v x,v y )F(v x,v z )F(v y,v z ) vxvx vyvy vxvx vzvz vyvy vzvz

SECTPLANL GSFC UMD..pressure tensor nearly(?) gyrotropic But: if B x, B z =0 -> nongyrotropy important. How to estimate?

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

SECTPLANL GSFC UMD Hesse, Kuznetsova, Hoshino, 2001 Pressure tensor approximations

SECTPLANL GSFC UMD Electron Pressure Tensors from simulation approximation P xye P yze critical difference at reconnection site!

SECTPLANL GSFC UMD coll. skin depth

SECTPLANL GSFC UMD Q xxye Q xyze P yza approximation

SECTPLANL GSFC UMD Heat Flux Tensor Time Evolution lots of work

SECTPLANL GSFC UMD Approximations for Q xyze Assume near gyrotropy, B y >>B x, B z Leading order, P ii >>P jk x,y,x component:

SECTPLANL GSFC UMD Approximations for Q xyze From simulation: Approximation: Ok in center, difference due to 4-tensor?

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

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

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

SECTPLANL GSFC UMD P. Pritchett: inertia important

SECTPLANL GSFC UMD …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!

SECTPLANL GSFC UMD 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?

SECTPLANL GSFC UMD 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

SECTPLANL GSFC UMD GEM-size run, no B y

SECTPLANL GSFC UMD GEM-size run, no B y m e =1 m e =1/256

SECTPLANL GSFC UMD GEM-size run, B y =0.8

SECTPLANL GSFC UMD GEM-size run, B y =0.8 m e =1 m e =1/256

SECTPLANL GSFC UMD large run, B y =0.

SECTPLANL GSFC UMD large run, B y =0.8

SECTPLANL GSFC UMD large run, B y =0.large run, B y =0.8 Reconnection rates similar to GEM problem

SECTPLANL GSFC UMD initial B y =0.8 initial B y =0. B y, both large runs, t=40 no quadrupole or quadrupolar modulation!

SECTPLANL GSFC UMD large run, B y =0., t=40 P xye P yze v ix j iy

SECTPLANL GSFC UMD large run, B y =0.8, t=40 P xye P yze v ix j iy

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

SECTPLANL GSFC UMD Additional slides

SECTPLANL GSFC UMD P xye P yze j yi j ye ByBy A tour of the reconnection region…

SECTPLANL GSFC UMD Mass Dependence of Electron Diffusion Region: Simulation Setup - 1-D “Harris” Equilibrium, L x = 2L z = 25.6 c/  pi - Flux function: A = -ln cosh(z/  ) - normal magnetic field perturbation (X type, 5% of lobe field) - Sheet Full-Width  = c/  pi - T e /T i = m e /m i =1/9-1/100 -  pe /  ce =5 - 50x10 6 particles - 800x400 grid

SECTPLANL GSFC UMD m i =m e, B y =1 rate slightly reduced due to higher plasma mass

SECTPLANL GSFC UMD Additional Material

SECTPLANL GSFC UMD P yze Magnitude of Pressure Tensor Contribution nene

SECTPLANL GSFC UMD Particle Picture: Straight Acceleration and Thermalization Question: Are electrons transiently accelerated while crossing the diffusion region, or is some of the energy thermalized? Approach: Integrate 10 4 electron orbits in vicinity of reconnection region Relevance: straight acceleration -> thermalization ->

SECTPLANL GSFC UMD kinetic energy change as function of delta y delta Ek y = e x R= delta y delta y-component of kinetic energy vs. delta y delta Eyk y = x R= delta y Approximately 6% of energy is thermalized

SECTPLANL GSFC UMD orbit( 6293): x-z plane x orbit( 6293): z-x acceleration phase z x

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

SECTPLANL GSFC UMD V max = 0.65 V max = 2.8

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

SECTPLANL GSFC UMD Reconnection faster for smaller guide fields