ESS200CHydrostatic EquilibriumPhotoionizationChapman Production FunctionParticle Impact IonizationParticle Energy DepositionBremsstrahlung/ Ion LossIonospheric Density ProfileThe Earth’s IonosphereCollision FrequenciesConductivityForce Balance - MI CouplingMaxwell Stress and Poynting FluxCurrents and Ionospheric DragWeimer FAC morphologyFAST ObservationsMHD FAST ComparisonsMHD FACsdB’s Scaled to Ionosphere38700 – MHD Comparison1ESS200CEarth’s IonosphereLecture 132Hydrostatic Equilibrium•The force of gravity on a parcel of air is balanced by the pressure gradient•Assume Tn is independent of height and integrate we obtain•The density of an atmosphere falls off (generally) exponentially.)(nnnnkTndhddhdpgmn −=−=]/)(exp[00 nnHhhnn −−=3Photoionization•As radiation passes through the atmosphere, it is absorbed and its intensity decreases•If this absorption is due to ion production, then•One ion pair is produced (generally) per 35eV in air•Production is a maximum when •Here•Since•So peak production occurs when or where , where Nnm is the integrated density. This is also where the optical depth is unity.IndsdInσ=−InCdsdICQnσ=−=0=dsdQdsdIndsdnInn−=nnnnnHdhdnndsdnndhdsχχχcoscos11sec=−=−=1sec =χσmnnH1=nmNσ4Chapman Production Function •Peak production is•Production as a function of height is•Let y = (h - hm) / Hn then•Below the peak y is negative and exp (-y) dominates •Above the peak y is positive and –y dominates•If we reference local production rate to maximum at subsolar point, we obtain•where)]1exp(/[cosInmmmHCInCQ χσ∞==]]/)exp[(/)(1exp[nmnmmHhhHhhQQ −−−+=)]exp(1exp[ yyQQm−−−=€ Q = Qmoexp[1− z − sec χ exp(−z)]hm= hm0+ Hnln(sec χ )Qm= Qm0cosχHhhzm/)(0−=5Particle Impact Ionization•In many situations, particle impacts can be the principal source of ionization–Solar proton events in polar cap–Auroral zone during substorms–Satellites with atmospheres in planetary magnetospheres•A primary particle can produce energetic secondary electrons that can ionize. These electrons can also produce x rays when they decelerate•Charge exchange can occur for ions producing a fast neutral•Process is very non-linear; often is numerically stimulated•Range energy relation is a good approximation. Allow calculation of stopping altitude. ∫=−⋅×+×=−⋅×=−−−−−ηξξξξ0267.10670275.0060)()502.0,(1036.51030.4)()1001,,(1005.5)(dssnRangekeVelectronscmgRkeVairprotonscmgRnNote: In this context nn(s) is a mass density6Particle Energy Deposition•Need to calculate altitude distribution of energy loss•Range-energy relation can also be written•Assume that the depth of matter traversed at x is approximated by•Where is energy particle has at point x•Solving for•Then •Curves here are for mono-energetic beams. In practice, sum over a distribution of energies.∫−=000/)(ξξξξdxddR)()(/000 locRRdxddx ξξξξξ−=−=∫locξlocξγγξξ1)]([01xAAloc−=−11))((/−−−= γξξγAdxdlocloc7Bremsstrahlung/ Ion Loss•Electrons scatter much more easily than ions.•A decelerating or accelerating electric charge produces electromagnetic energy.•This braking radiation tends to be in the x-ray range and this produces further ionization.•Once produced electrons are lost by three processes:–Radiative recombination•e+x+→x+hυ–Dissociative recombination•e+xy+→x+y–Attachment•e+z→z-8Ionospheric Density Profile•Photochemical equilibrium assumes transport is not important so local loss matches local production.•If loss is due to electron-ion collisions, we get a Chapman layer•If there is vertical transport•Treating the pressure forces of electrons and ions and assuming neutrals are stationary, we obtain•Where is the ambipolar diffusion coefficient and Hp the plasma scale height•Vertical transport velocity becomes0=−=∂∂LQtne21)/(2ααQnnLQee===hunLQtnehee∂∂−−=∂∂ )(⎥⎥⎦⎤⎢⎢⎣⎡+−=peepleHndhdnDuninieimTTkD υ/)( +=gmTTkiei/)( +⎥⎦⎤⎢⎣⎡+−=−gmnddpmnuiehTiniepl1)( υ9The Earth’s Ionosphere•The electron density in the ionosphere is less than the neutral density.•For historical reasons, the ionospheric layers are called D, E, F–D layer, produced by x-ray photons, cosmic rays–E layer, near 110 km, produced by UV and solar x-rays–F1 layer, near 170 km, produced by EUV–F2 layer, transport important•Enhanced ionization in the D-region leads to absorption of radio waves passing through because it is collisional with neutrals.•At night, ionosphere can recombine, but transport, especially from high altitudes can be important•In polar regions where field is vertical, a polar wind of light ions can form similar to the solar wind.10Collision Frequencies•Ion and electrons collide with neutrals as they gyrate. How they move in response to electric fields depends very much on the collision frequency relative to the gyro-frequency.•If the gyro-frequency is much lower than the collision frequency, ions and electrons move in the direction of the electric field or opposite to it. This will produce a current.•If the collision frequency is much lower than the gyro-frequency, ions and electrons drift together perpendicular to the magnetic field.•Since the ions and electrons have different gyro-frequencies and collision frequencies, a complex set of currents may be produced. This is treated with a tensor electrical conductivity.11ConductivityiiniuvmqE =•Parallel equation of motion•Perpendicular equation of motion•Conductivity tensor•Petersen conductivity (along E┴)•Hall conductivity (along E x B)•Parallel conductivityeeneuvmeE =−Ej0σ=⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛⎟⎟⎟⎠⎞⎜⎜⎜⎝⎛−=zyxEEEj012210000σσσσσ22222221)](1)(1[ envvvmvvvmeiinininieeneneneΩ++Ω+=σ20]11[ envmvmeiniene+=σ222222)](1)(1[ envvvmvvvmeiininiinieeneneeneΩ+Ω−Ω+Ω=σ€ q E⊥+ui× B( )= mivinu⊥i€ −e E⊥+ue× B( )= mevenu⊥e12Force Balance - MI Coupling j = ne(Ui– Ue)13Maxwell Stress and Poynting Flux14Currents and Ionospheric Drag15Weimer FAC morphology16FAST ObservationsIMF By ~ -9 nT.IMF Bz weakly negative, going positive.Questions:•Where is the dawnside open/closed boundary?•Where do the field-aligned currents go?17MHD FAST Comparisons18MHD FACs19dB’s Scaled to Ionospheredt = -411sdt = -51sTimeTimeUT and ephemeris data for FAST onlyScaled dB’s largely agree. Mapped by