Research supported by the NSF Aeronomy & CEDAR Grants

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1 Large-Scale Simulations of Farley- Buneman Turbulence in 2D and 3D and Hybrid Gradient Drift Simulations by Meers Oppenheim, Yakov Dimant, Yann Tambouret Center for Space Physics, Boston University, Boston, MA, USA Lars Dyrud Center for Remote Sensing, Arlington, VA, USA Research supported by the NSF Aeronomy & CEDAR Grants Boston University Center for Space Physics

2 Overview Background on E-region Farley-Buneman (FB) Turbulence What have we done? Developed EPPIC (Electrostatic Parallel Particle-in-Cell) Code Large Kinetic 2D simulations Farley-Buneman turbulence Fully 3D simulations So What? See high-resolution 2D Spectra Compare to Radar and Rocket Data Learn the physics of 2D FB turbulence Learn about V ph and spectral width Study 3D FB turbulence Compare to 2D Learn about electron heating Important for interpreting radar measurements and conductivities! New Hybrid Gradient-Drift Simulations Gradient Driven Waves in the E-region

3 Background: E-region Plasma Waves E-region ionosphere (9-14 km altitude): Region with strong electric fields Electrons magnetized: Hall drift V d ~= ExB/B 2 drifting with occasional collision with neutral Ions demagnetized by collisions: Pedersen drift Waves: Perpendicular to B Driven by polarization electric field: called Farley-Buneman or modified two stream instability Damped by diffusion Type 1 coherent radar echoes Heat the electrons Modify the conductivities B E δn > Ions δe Electrons δe δn _ + _ + _ + + _ + _ + _ + _ + _ + _ + _ + δ n < δn < V n V Ph > 2 = E B B V Coherent Radar Image

4 Simulation Method: Particle-In-Cell 1. Gather to determine charge density, ρ Particle Trajectories Charge Density Electron Ion 2. Calculate Electric field: 3. Update velocities: v E v = v dvi qi = dt m dx v dt i 4. Update Positions: = vi 5. Collide particles with neutrals 6. Go to Step 1 v i ρ ε v [ E( x, t) + v B( x, t) ] i v i r i

5 Old 3D Simulations Parameters PIC electrons & Ions 128x128x mx1.2mx12m m i /m e = 625 i e Psi=.5 (Altitude=15km) 2.1 Billion PIC particles X-Y Cro oss Secti ion direction E 1 12 Density <E 2 > (V/m) 2 Avg and Max Turbulent E-field Energy Density X-Z Cross Section ion B direct Time (s) 1 ExB Direction (m)

6 Comparable 2D Simulation Problem in 2D Resolution! Insufficient! 1 Density ection E dire 1 ExB Direction (m)

7 Solution: Better Parallel Supercomputing Mesh Parallelization: Particle Trajectories Charge Density -1-1 Processor Processor EPPIC Domain Decomposition: Particle Trajectories Processor 1 Processor 3 New Code Applies both techniques Processor 2 Processor 4 Efficiently uses multi- thousand processor supercomputer Electron Ion

8 Fully Kinetic 2-D 17 Simulations Simulations Parameters: 2-D Grid: 496 by 496 cells 4cm by 4cm Altitude ~15km in Auroral region Driving Field: ~1.5 Threshold field (5 mv/m at high latitudes) Artificial e - mass: m e:sim = 44m e ; m i:sim =m i Perpendicular to geomagnetic field, B,, only 4 Billion virtual PIC particles Timestep: dt = 3μs s (< cyclotron and plasma frequencies) E dire ection ExB Direction (m) 17 Avg and Max Turbulent E-field Energy Density E 2 (V/ m) 2 Time (s)

9 496x496 Simulation with billions of PIC particles E direct tion (m) ExB direction (m)

10 2D wave phase velocity (1/s) omega Total Spectral Energy: n( k,w).26 E 2 V d /(1+ Ψ) C sa C smax.26 E k (1/m).26 E 4

11 What a fixed k radar sees? Velocities: E/B = 1 m/s V linear = 77 m/s C s = 44 m/s

12 2D Spectral Widths at 3 wavelengths Center for Space Physics

13 3D simulations 256x256x512 Grid Lower Altitude (more collisional) 41 Driving Field: ~4x Threshold field (15 mv/m at high latitudes) Artificial e - mass: m e:sim = 44m e ; 4 Billion virtual PIC particles 2D looks the same! 12 E dire ection (m) Potential (x-y cross-section) B directio on (m) Potential (x-z cross-section) ExB direction (m) 12 ExB direction (m) 12

14 Temperatures 2D vs. 3D 3D Electron RMS Velocity 2D Electron RMS Velocity Center for Space Physics

15 Movie from 512x512x124 Simulation 12 Density (x-y cross-section) 24 Density (x-z cross-section) E n (m) direction X --- ExB direction (m) 12 X --- ExB direction (m) 12

16 Spectral evolution from large simulation n(k, t) for k z = n(k, t) for k z =2π/(51 m) k y k x k x

17 Spectral evolution from large simulation n(k, t)for k y = n(k, t) for k y =2π/(8.5 m) k z k y k x k x Center for Space Physics

18 Identical 2D simulation 12 Density --- n(x,y) Spectral Density --- n(k x,k y ) Y --- E directi ion (m) K Y --- E dire ection (m m) X --- ExB direction (m) 12 K --- ExB direction (m) X

19 Higher altitude 3D simulation electrons: First Moment (RMS Of V e ) Ions: First Moment (RMS Of V i ) 2-D Te emps 3-D Temps

20 New EPPIC code Large scale 2D simulations cos θ V ph =C smax cos C smax Conclusions C smax is the largest estimate t of C s possible θ is the angle at the max growth rate: close to between V d and the wave direction spectral width = (C smax -ΔV ) sin θ +Δ V ΔV is the spectral width at θ= ΔV spectral width First 3D pure PIC simulations of the Farley-Buneman instability: HEATING!!!! Can explore differences between 2D and 3D: Turbulent Fields Turbulent Heating Sufficient to produce good spectral resolution Great tool for exploring instabilities, waves and tubulence Meers Oppenheim, Lars Dyrud, and Yakov Dimant Center for Space Physics

21 Gradient Drift Simulation Fluid Electrons (domain decomposed) Kinetic (PIC) Ions Initial gradient Sub-critical E field Objectives: Watch evolution from 1km 1m scale Understand coupled FB-GD waves Energy dissipation

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23 Spectrum at 6m Normalized Power of 3m waves Spectral Width of 3m waves (two methods of calculating)

24 Gradient Drift Conclusions Preliminary Work: Need to start with longer initial waves More realistic parameters needed

25 Temperatures and Acoustic speed Electrons: First Moment (RMS Of V e ) Ions: First Moment (RMS Of V i ) Original C =4m/s Original C s =4m/s Wave heated C s =~ 5m/s

26 Comparing 2D and 3D Turbulent Fields 2D same size and parameters as 3D Avg and Max Turbulent E-field Energy Density 3D Avg and Max Turbulent E-field Energy Density 2D 2 (V/m) 2 E 2 Time (s) Time (s)

27 Wave Heating in the high latitude E-region: A brief overview Electron Temperatures Raised from a ~5K to ~25K Observations: First report: Schlegel and St. Maurice, [JGR, 81] Elevated drift velocities of coherent echoes [Nelson and Schlegel, 85; Farley and Providakes, 89; Williams, et. al., 92 and others] Measurement of T e and E driver simultaneously [Foster and Erickson, GRL ] Theory: Turbulence drives small E E drives electrons Electrons collide with neutrals and heat [Robinson,86; St.- Maurice, 9, Dimant, 95] If E known, can estimate T e [Milikh and Dimant, 23] ature (K) Electron Temper Ion Drift Velocity (m/s)

28 Boundary Conditions (BC) Simulations of all types require BC BC introduce limitations and, sometimes, error Example: Periodic is the simplest BC The right side connects to the left The top to the bottom Particles leaving the Left reenter on the Right and visa versa Particles leaving the top -> bottom Ion

29 3D vs. 2D Simulation Temps Electron Moments <V x,y,z2 > Ion Moments <V x,y,z2 > Temp 2-D T D Temp 3-D Time (s) Time (s) 3-D Simulations get hotter!

30 Supercomputing Parallelization Mesh Parallelization Each Processor Contains whole mesh Complete PIC Code N processors Particles differ Communications i Sum charge density arrays MPI Library: 1 call Processor 1 Processor 2 Particle Trajectories Charge Density N total Processors

31 Higher Resolution 2D 124x124 Shows turbulence 4 E direc ction Electric Potential 2D Electron moments ExB Direction (m) 3D Electron moments 4 2D Temp (k) 3D Temp (k) Time (s) Time (s)

32 What a fixed k radar sees? 1 V/ Driver 1mV/m Di Velocities: E/B = 2 m/s Vlinear=154 m/s Cs = 55 m/s /

33 3D Farley Buneman Simulations Simulations Parameters: Altitude ~1km in Auroral region Driving Field: ~4 x threshold (14 mv/m at high latitudes) Artificial e - mass: m e:sim = 44m e ; m i:sim =m i 2-D Grid: 128x128x64 cells of.8mx.8mx.8m

34 Fixed k Spectra for 3D Notes: Velocities: E/B = 26 m/s = 6 m/s C s

35 Simulation Method: Particle-In-Cell 1. Gather to determine charge density, ρ Particle Trajectories Charge Density Electron Ion 2. Calculate Electric field: 3. Update velocities: v dv dt v dxi dt Update Positions: = vi 5. Collide particles with neutrals 6. Go to Step 1 i v E v = ρ ε qi v v r = E( xi, t) + i B( xi, t) m v i [ ]