MODELING THE EARTH’S IONOSPHERE:SAMI2 AND SAMI3

J.D. Huba and G. Joyce∗

Plasma Physics DivisionNaval Research LaboratoryWashington, DC

CEDAR WorkshopBoulder, CO

June, 2010

∗ Icarus Research, Inc.

(acknowledge M. Swisdak)

SAMI VERSIONShighlights

SAMI2-0.98; SAMI2 MPI-0.98; SAMI3 MPI-0.98SAMI2: 2D and SAMI3: 3Dmagnetic latitude: ±60◦

E ×B drifts specified (analytical or Fejer/Scherliess)magnetic field: IGRF-like

SAMI3 MPI-1.68; SAMI3 MPI-1.68CRCR: includes corotational potentialE ×B drifts calculated from potential equationmagnetic field: tilted and untilted dipole

SAMI3 MPI-2.68CRmagnetic field: untilted dipolehigh-resolution longitudinal subgrid (for ESF studies)(∆φ = 0.0625◦; ∆x ∼ 7 km)

SAMI3/LFM and SAMI3/RCMglobal code with electrodynamic coupling to themagnetospheremagnetic latitude: ±88◦

PLASMA DYNAMICSH+,O+,He+,N+,N+

2 ,NO+,O+2

ion continuity

∂ni

∂t+∇ · (niVi) = Pi − Lini

ion velocity

∂Vi

∂t+ Vi · ∇Vi = − 1

ρi∇Pi +

e

miE +

e

micVi ×B + g

−νin(Vi −Vn)−∑

j

νij (Vi −Vj)

ion temperature

∂Ti

∂t+ Vi · ∇Ti +

23Ti∇ ·Vi +

23

1nik∇ ·Qi = Qin +Qij +Qie

PLASMA DYNAMICS

electron momentum

0 = − 1neme

bs∂Pe

∂s− e

meEs

electron temperature

∂Te

∂t− 2

31nek

b2s∂

∂sκe∂Te

∂s= Qen +Qei +Qphe +QRF

NEUTRAL ATMOSPHERE MODELS

empirical models

NLRMSISE-00 (Picone et al.)provides neutral densities and temperature

HWM93/HWM07 (Hedin/Drob)provides neutral wind

first principle models

TIME-GCM (Crowley)

PHOTOIONIZATION: SOLAR FLUX MODELS

empirical models: flux φ∞(λ) is in 37 bins

EUVAC (Richards et al., 1994)function of geophysical conditions

φi = F74113i[1 +Ai(P − 80)] where

P = (F10.7A+ F10.7)/2

data/model driven (100 bins: 10A)

NRLEUV (Lean, Warren, and Mariska)FISM (Chamberlin)

photoionization/photoabsorption cross-sections tabulated

CHEMICAL REACTION RATES

HOW IS THE MODEL BUILT?Numerical Issues

transport

parallelperpendicular

grid

lagrangianeulerian

TRANSPORTmagnetic field organizes plasma motion: ⊥ and ‖ components

continuity equation

∂ni

∂t+∇ · (niVi) = Pi − Lini

∂ni

∂t+∇‖ ·

(niVi‖

)+∇ · (niVi⊥) = Pi − Lini

parallel motion (diffusion/advection)

∂ni

∂t+∇‖ ·

(niV‖i

)= Pi − Lini for t

∆t→ t∗

perpendicular motion (advection)

∂ni

∂t+∇ · (niV⊥i) = 0 for t∗ ∆t→ t+ ∆t

PARALLEL TRANSPORTconventional method: ignore ion inertia

∂ni

∂t+ b2s

∂

∂s

niVis

bs= Pi − Lini

0 = − 1nimi

bs∂(Pi + Pe)

∂s+ gs − νin(Vis − Vns)−

∑j

νij(Vis − Vjs)

procedure:→ solve for ion velocity Vis

→ substitute into continuity→ expand density ni ' ni0 + ni1

→ obtain fully implicit differencing scheme→ iterate equations to obtain a solution

advantage: large time steps (∼ 5 – 15 min)

disadvantage: complexity, stability, limited species (e.g., nomolecular transport)

PARALLEL TRANSPORTSAMI2/3 method: include ion inertia

∂ni

∂t+ b2s

∂

∂s

niVis

bs= Pi − Lini

∂Vis

∂t+(Vi·∇)Vis = − 1

nimibs∂(Pi + Pe)

∂s+gs−νin(Vis−Vns)−

∑j

νij(Vis−Vjs)

procedure:→ diffusion terms backward biased (implicit)→ advection terms use donor cell method→ obtain semi-implicit differencing scheme

disadvantage: small time steps (∼ 1 – 15 sec)

advantage: simplicity, stability, flexibility, better description athigh altitudes

PERPENDICULAR TRANSPORTgrid: lagrangian vs eurlerian

perpendicular dynamics (E ×B transport)

lagrangian grid: follow flux tube motion

eulerian grid: fixed mesh

LAGRANGIAN GRIDFollow E ×B drift of a flux tube

animate

EULERIAN GRIDorthogonal

EULERIAN GRIDnonorthogonal: finite volume, donor cell method

GRID COMPARISONlagrangian, orthogonal eulerian, nonorthogonal eulerian

SAMI3 EXAMPLE

OVERVIEW OF SAMI2/32D and 3D ionosphere models

magnetic field: tilted and untilted dipole model / IGRF-like

interhemispheric / global ±60◦ and ±88◦

nonorthogonal, nonuniform fixed grid

seven (7) ion species (all ions are equal):H+, He+, N+, O+, N+

2 , NO+, and O+2

solve continuity and momentum for all 7 speciessolve temperature for H+, He+, O+, and e−

plasma motionE×B drift perpendicular to B(both vertical and longitudinal in SAMI3)ion inertia included parallel to B

neutral species: NRLMSISE00/HWM93/HWM07 andTIMEGCM

chemistry: 21 reactions + recombination

photoionization: daytime and nighttime

SAMI2 OPEN SOURCE PROJECThttp://wwwppd.nrl.navy.mil/sami2-OSP/index.html