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.
Download ReportTranscript 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.
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 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?) DR DR time DR Conditions: IMPOSSIBLE (for species s) if E vs B 0 SECTP LANL GSFC UMD Electric Field Equations z x Electron eqn. of motion 1 m e ve E ve B Pe ve ve ne e e t vi B m v 1 1 j B Pe e e v e ve nee ne e e t At reconnection site 1 Pxy Pyz Pyy me Ey ne e x z y e important? SECTP v y ve v y t small, limited by me? 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 Normal Magnetic Flux: 0 F Bz (x, z 0)dx X normal magnetic flux 4.0 3.5 3.0 2.5 2.0 mi/me = 9 mi/me = 25 mi/me = 64 mi/me = 100 1.5 1.0 0.5 0.0 0 5 10 15 20 i t 25 30 35 40 evolution electron-mass independent! => Local electron physics adjusts to permit large scale evolution SECTP LANL GSFC UMD mi/me=9, i t = 18 Compare extremes along dashed lines - ion quantities - electron quantities SECTP mi/me=100, i t = 16 LANL GSFC UMD Large (ion) Scale Features Bz magnetic field 0.60 ion v x 1.0 100 0.40 Bz(9) Bz(100) 5.0 0.20 vix(9) vix(100) 10-1 0.00 0.0 100 -0.20 -0.40 -5.0 10-1 -0.60 -0.80 0 5 10 15 shif ted x 20 -1.0 100 25 0 5 10 15 shif ted x 20 -> Ion scale features approx invariant. SECTP LANL GSFC UMD 25 Small (electron) Scale Features electron v 6.0 100 4.0 100 x vex(9) vex(100) vex(9) 2.0 100 0.0 100 -2.0 100 -4.0 100 -6.0 100 0 SECTP 5 10 15 shif ted x 20 25 LANL GSFC UMD Pressure Tensor P xye 6.0 10-2 4.0 10-2 2.0 10-2 0.0 100 -2.0 10-2 -4.0 10-2 pxye(9) pxye(100) -6.0 10-2 0 p vx Pxy ~ z x SECTP 5 10 15 shif ted x 20 25 LANL GSFC UMD Pxye Pyze SECTP LANL GSFC UMD Sample Electron Distribution (Pxye) 10.0<x< 11.0 -0.5<z< 0.5 log f 0.076 0.4 -0.739 0.2 -1.555 uy 0.0 -2.370 -0.2 -3.185 -0.4 -4.000 -0.4 -0.2 0.0 0.2 0.4 ux Thermal inertia (nongyrotropic pressure)-based dissipation seems key to anti-parallel reconnection SECTP LANL GSFC UMD Can be explained by trapping scale: “bounce motion” [Horiuchi and Sato, 1996] 2meTe z 2 2 e (Bx / z ) 1/ 4 [Biskamp and Schindler, 1971] => Estimate of reconnection electric field E 2me Te v x' SECTP [Hesse et al., 1999] [Kuznetsova et al., 2000] LANL GSFC UMD realistic electron mass Ricci et al. SECTP 3D – no LHD, kink, … Zeiler et al. LANL GSFC UMD 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 -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 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= 2Lz= 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 - 100x106 particles - 800x800 grid Results averaged over 60 plasma periods SECTP LANL GSFC UMD SECTP LANL GSFC UMD Change of symmetry By SECTP P. Pritchett LANL GSFC UMD Parallel electric field it=16 …also analytic theory by Drake et al. SECTP LANL GSFC UMD Electric Field Equations z x Electron eqn. of motion E ve B vi B 1 m v Pe e e ve ve ne e e t m v 1 1 j B Pe e e v e ve nee ne e e t At reconnection site 1 Pxy Pyz Pyy me v y E y Ell ve v y ne e x z y e t important? small, limited by me? SECTP LANL GSFC UMD Magnitude of Bulk Acceleration Contribution Time derivative of (negative) electron velocity in y direction: SECTP LANL GSFC UMD Pxye Pyze SECTP LANL GSFC UMD -(vezBx-vexBz) 1 Pxye Pyze ene x z -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 vx vy LANL GSFC UMD ..pressure tensor nearly(?) gyrotropic Pe Peg Peng p|| p Peg p 1 BB 2 B But: p|| p p|| p Peg | y By B B By 0 2 2 B B if Bx, Bz=0 -> nongyrotropy important. How to estimate? SECTP LANL GSFC UMD Scaling the pressure tensor evolution equation T Pe T e ve Pe Pe ve Pe ve Pe B Pe B Q t me Q v P P e P L L Assume e1 , L / v Pii Pij ignore heat flux… SECTP LANL GSFC UMD Pressure tensor approximations Pxxe vey Bz Pyze Pyye Pxxe e x By Pzze vey Bx Pxye Pyye Pzze e z By Hesse, Kuznetsova, Hoshino, 2001 SECTP LANL GSFC UMD Electron Pressure Tensors from simulation approximation Pxye Pyze Pxye Pyze critical difference at reconnection site! SECTP LANL GSFC UMD P yze 0.004 at x=13.15, t=16 0.003 0.002 0.001 0 -0.001 -0.002 -0.003 -0.4 -0.2 0 z SECTP 0.2 0.4 coll. skin depth LANL GSFC UMD Pxxe vey Bz 1 Qxxye Qxyze Pyze Pyye Pxxe e x By e x z P vey B 1 Qxyze xxe Pyye Pxxe z e x By e z Qxyze Qxxye Pyza approximation SECTP LANL GSFC UMD Heat Flux Tensor Time Evolution Q m s d 3 u (u v)( u v)( u v) f s lots of work Qijk t l l es ms SECTP (ijkl Pkl vi v j Pil v j v k Pjl vi v k Qijk vl ) xl Qlij v k Qljk vi Qlik vj xl xl xl l l r s [Qijs Br Qijr B s ] rsk [Qiks Br Qikr B s ] rsj 0 [Q B Q B ] jks r jkr s rsi LANL GSFC UMD Approximations for Qxyze x,y,x component: (2 Pxl v x v y Pyl v x v x Qxyxvl ) xl l 0; neglect t Qlxy l v x Qlyx v x Qlxx vy xl xl xl l l e 2Qxyy Bz 2Qxyz By Qxxx Bz Qxxz Bx 0 me Assume near gyrotropy, By>>Bx, Bz Qxyz 1 y 2 2 P v v 0 . 5 P v P v v 0 . 5 P v xy x xz x y yz x x xx x y z Leading order, Pii>>Pjk Qxyz SECTP Pxxvy vx 1 ( Pxxvxv y ) y x y x LANL GSFC UMD Approximations for Qxyze From simulation: Qxyze and approximation, x=13.15 0.008 Q 0.006 xyze Q xyze approximation 0.004 0.002 0 Approximation: -0.002 -0.004 -0.006 -0.008 -0.4 -0.2 0 0.2 0.4 z Ok in center, difference due to 4-tensor? SECTP LANL GSFC UMD Scaling of diffusion region me v y 1 B0vz me c2 1 c2 1 | Einertial |~ vz ~ 2 B0vz | Econvection | 2 2 2 e x L1 0 e ne w pe L1 w pe 2 L12 Pxxe vey Bz 1 Pxxv y vx Pyze Pyye Pxxe e x By e z y x | E pressure 1 1 2 Pxxv y vx 1 1 2 Pxxv y vz |~ ~ nee e z 2 y x nee e z 2 y z 2 1 P 1 r ~| Einertial | 2 xx2 | Einertial | L 2 L2 y ne me L2 => 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 3D Modeling M. Scholer et al.: Formation of “2D” channel J. Drake et al.: Buneman modes, electron holes, anomalous resistivity 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 -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 •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 - 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 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 me=1 SECTP me=1/256 LANL GSFC UMD large run, By=0. SECTP LANL GSFC UMD large run, By=0.8 SECTP LANL GSFC UMD large run, By=0. large run, By=0.8 Reconnection rates similar to GEM problem SECTP LANL GSFC UMD By, both large runs, t=40 initial By=0. initial By=0.8 no quadrupole or quadrupolar modulation! SECTP LANL GSFC UMD large run, By=0., t=40 SECTP Pxye vix Pyze jiy LANL GSFC UMD large run, By=0.8, t=40 SECTP Pxye vix Pyze jiy LANL GSFC UMD Electric Field Equations z x Electron eqn. of motion E ve B vi B 1 m v Pe e e ve ve ne e e t m v 1 1 j B Pe e e v e ve nee ne e e t Approximate representation in MHD: 1 E vi B Pi ni e SECTP LANL GSFC UMD Additional slides SECTP LANL GSFC UMD By jye jyi 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= 2Lz= 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 - 50x106 particles - 800x400 grid 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 Magnitude of Pressure Tensor Contribution Pyze ne SECTP 1 1 Pyz Ey Pe | y ene ene z 1 0.5E 2 ~ 0.18 0.35 8E 2 LANL 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? Relevance: me straight acceleration -> v e vey e 1 thermalization -> Pe ene Approach: Integrate 104 electron orbits in vicinity of reconnection region SECTP LANL GSFC UMD kinetic energy change as function of delta y delta y-component of kinetic energy vs. delta y 2 2 y = -2.5605e-05 - 0.17785x R= 0.98882 y = -0.027939 - 0.16877x R= 0.9873 1.5 1.5 1 1 0.5 delta Eyk 0.5 delta Ek 0 0 -0.5 -0.5 -12 -10 -8 -6 -4 -2 delta y Ekin 1.78y Ekin, y 1.67y SECTP 0 2 -12 y -10 Ekin -8 -6 -4 -2 0 2 delta y eE y Approximately 6% of energy is thermalized LANL GSFC UMD orbit( 6293): x-z plane 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 13.15 13.2 13.25 13.3 x 13.35 13.4 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 13.2 13.25 13.3 13.35 13.4 13.45 x SECTP LANL GSFC UMD 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 Scaling the pressure tensor evolution equation T T e ve Pe Pe ve Pe ve Pe B Pe B 0 me , y x z ve Pxy Pxx x v y Pxz z v y Pxy x vx Pxy x vx Pyz z vx x Pxz z Pyy Pxx y Pyz 0 xy component near reconnection site: B y B x , B z Pii Pij SECTP LANL GSFC UMD magnetic flux normal to current sheet 3.5 3 recflux/0.0 recflux/0.4 recflux/0.8 2.5 2 1.5 1 0.5 0 0 5 10 15 20 25 30 time Reconnection faster for smaller guide fields SECTP LANL GSFC UMD