ESS 154/200C Lecture 2 Upper Atmosphere/Ionosphere

Date Day Topic Instructor Due ESS 200C Space Plasma Physics ESS 154 Solar Terrestrial Physics M/W/F 10:00 – 11:15 AM Geology 4677 Instructors: C.T. Russell (Tel. x-53188; Office: Slichter 6869) R.J. Strangeway (Tel. x-66247; Office: Slichter 6869) Date Day Topic Instructor Due 1/4 M A Brief History of Solar Terrestrial Physics CTR 1/6 W Upper Atmosphere / Ionosphere CTR 1/8 F The Sun: Core to Chromosphere CTR 1/11 M The Corona, Solar Cycle, Solar Activity Coronal Mass Ejections, and Flares CTR PS1 1/13 W The Solar Wind and Heliosphere, Part 1 CTR 1/15 F The Solar Wind and Heliosphere, Part 2 CTR 1/20 W Physics of Plasmas RJS PS2 1/22 F MHD including Waves RJS 1/25 M Solar Wind Interactions: Magnetized Planets YM PS3 1/27 W Solar Wind Interactions: Unmagnetized Planets YM 1/29 F Collisionless Shocks CTR 2/1 M Mid-Term PS4 2/3 W Solar Wind Magnetosphere Coupling I CTR 2/5 F Solar Wind Magnetosphere Coupling II; The Inner Magnetosphere I CTR 2/8 M The Inner Magnetosphere II CTR PS5 2/10 W Planetary Magnetospheres CTR 2/12 F The Auroral Ionosphere RJS 2/17 W Waves in Plasmas 1 RJS PS6 2/19 F Waves in Plasmas 2 RJS 2/26 F Review CTR/RJS PS7 2/29 M Final

The Gravitational Field Kepler’s laws of planetary motion Planets move in ellipses with the Sun at a focus. Planet-Sun line sweeps out equal areas in equal times. Square of period proportional to cube of semi-major axis. Newton’s universal law of gravity Potential Energy Kinetic Energy

Physics of Collisional Gases Particles have cross sections Average separation Particle flux Time variation due to spatial variation In 3 dimensions, the continuity equation

Thermal Pressure Thermal pressure (internal, static, scalar) is the mean net transport of momentum through a surface per square meter per second produced by the thermal motion of the gas. Assume that all particles have the same speed c and 1/6 of the particles move in each of the 6 directions. The particles that can contribute to momentum transfer from volume 1 to 2 are in the x range c ∆t. The momentum transfer from 1 to 2 is Φ1,2 is 1/6 (c ∆t A) n (c m)/A ∆t =1/6 nmc2 The momentum transfer from 2 to 1 is Φ 2,1 = – 1/6 nmc2 The net momentum transfer is Φ1,2 – Φ2,1= 1/3 nmc2 Note dynamic pressure involves non-random velocity and is nmu2 where u is the bulk velocity.

Altitude Variation: Troposphere Pressure falls off with altitude. This gradient in pressure just balances the force of gravity on that volume element of the atmosphere or dp=mgn(h)dh, if m (mass of atom) and g are constant , if T constant n = no exp (-h/H), where H = kT/mg But equation of state, pρ-γ = constant, links T and n through T = constant nγ-1 At high altitudes, the temperature stops falling.

Altitude Variation: Lower Atmosphere As we go further upward in the lower atmosphere, the temperature rises again. This region is the stratosphere. The boundary between the troposphere and the stratosphere is called the tropopause The top of the stratosphere is the stratopause. Above this point the temperature again falls. Clearly there is heating at the stratopause. The region of temperature decrease is called the mesosphere. It ends at the mesopause where the atmosphere again begins to warm reaching about 1000 K at 300 km altitude The heat for the thermopshere comes from the magnetosphere. Planets without magnetospheres do not have a thermosphere Below 100 km altitude the atmosphere is well mixed or homogeneous because the atmosphere is very dynamic. Above 100 km the atmosphere becomes heterogeneous.

Atmospheric Nomenclature The atmosphere can be divided into many different zones according to its various properties. Temperature: Affected by heating, radiation, convection and conduction. Chemical composition: Homogeneity maintained by mixing. Vertical transport: By convection, diffusion, ballistic trajectories. Gravitational binding: Collisional versus collisionless motion Ionization: Density and temperature vary.

The Structure of the Heterosphere Above about 100km the diffusion of particle species through each other becomes faster than eddy diffusion due to parcels of air interchanging. Soon the scale height becomes inversely proportional to the mass of each of the species. 40Ar falls off faster than 32O2 that falls off faster than 28N2 that falls off faster than 4He. Note that the neutral density greatly exceeds the ionospheric density until very high altitudes.

Collision Frequency in the Heterosphere Cross section Area covered by targets encountered in depth l is 1/l nn = s The mean free path of a particle (l) is (σnn)-1 where σ is the cross section and nn is the number density. The collision frequency ν1,2 is the thermal speed divided by the mean free path, vth σ nn, where vth is measured in the reference frame of the gas. The collision frequency drops rapidly with altitude changing from about 1010 times per second at the surface of the Earth to once per second at 400 km. The mean free path (l1,2 here) varies from 0.1 microns to 100 km over the same distance.

Distribution Function If we wish to calculate the escape flux we need only to know the speed distribution independent of direction We integrate over all directions and obtain a normalized speed distribution function The most probable speed is (2 kT/m)1/2; mean speed, (8 kT/πm)1/2 and rms speed, (3 kT/m)1/2 For 1000K H atoms at the exobase, there are some escaping atoms In the fluid approximation, we use a distribution function to describe the spatial variation (in configuration space) and the velocity distribution In its equilibrium state a gas can be described by a maxwellian distribution in velocity space where

Atmospheric Escape Flux Neutrals in the exosphere consist of : 1) ballistic non-escaping particles 2) orbiting particles 3) escaping particles 4) accreting particles 5) transient particles To determine if an atmosphere is stable over the life of the planet we must calculate the escape flux over the life of the planet. We can use the distribution function to calculate the escape flux at the exobase, EB, the so called called Jeans escape flux in terms of the escape parameter X Φes = n(hEB) cw/(2π1/2) (1+X) (exp (-X)) where X = (ces/cw)2EB = rEB/HEB where HEB = kT∞/(mgEB) Note: EB is exobase; es is escape; cw is most probable thermal speed The escape parameter for hydrogen in the Earth’s atmosphere is about 7 and it escapes in less than 105 years but helium with X = 28 is stable over the lifetime of the Earth

Energy from the Sun Photosphere temperature is 5780K. Temperature first drops and then rises slowly in the chromosphere. Rapid rise of temperature in the transition region. Temperature reaches over 106 K in the corona. UV comes from the upper photosphere; Ca II, Ha, K, H emissions from chromosphere; EUV, X-ray and radio waves (10.7cm) from the corona. Energy of sun is produced by nuclear fusion. This energy is transported upward by radiation and then by convection when it becomes more efficient. Convection makes the Sun's photosphere turbulent, drives the Sun's dynamo and introduces short time scales into solar variations. Photosphere is the layer from which 50% of the photons can escape the Sun without being absorbed.

Solar Radiation Spectrum Radio emissions at wavelengths produced in coronal near the location of EUV production have large variations that are moderately but not perfectly well correlated with EUV variations. Upper atmosphere absorbs EUV and part of UV spectrum and is heated significantly by this radiation. Solar EUV flux can vary by up to a factor of 4. When ozone in the stratosphere is destroyed, UV radiation can reach the surface of the Earth causing an increased risk of skin cancer. Most of the radiance from the Sun is in visible wavelengths. That is why we use it to see. Sun is most variable at X-ray and EUV wavelengths and moderately variable at UV wavelengths.

Waves in the Atmosphere Acoustic waves are pressure fluctuations that travel at the speed of sound vs As illustrated here pressure gradients accelerate the gas back and forth. A standing wave would have zero velocity at the peaks and troughs. A traveling wave as illustrated here has gas velocity 90 deg out of phase with pressure forces. Buoyancy oscillations occur in the vertical direction at the Brunt-Vaisala frequency If speed of sound or temperature is constant, ωg = g (cpT)-½ If we combine buoyant and compressional effects, we get gravity waves illustrated here. Waves at frequencies above ωa = γg/2vs are called acoustic gravity waves. Waves below the Brunt-Vaisala frequency are called internal gravity waves.

Photoionization 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.

Photoionization – Details Intermediate steps in deriving peak production location: Rewriting in terms of height (h), rather than path distance (s): Density at peak production altitude: To determine integrated column density, rewrite density in terms of s: Optical depth:

Chapman 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

Particle 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. Note: In this context nn(s) is a mass density

Particle 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 Assume Solving for Then Curves here are for mono-energetic beams. In practice, sum over a distribution of energies.

Bremsstrahlung/ 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-

Ionospheric 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 becomes

The 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.

Day/Night Density Profiles Density profiles from International Reference Ionosphere Solid lines – Summer Dashed lines – Winter Upper plot – high sunspot number Lower plot – low sunspot number Note: Units are #/m3, = 106 x #/cm3 0.09 0.28 0.9 2.8 9 MHz

Collision 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.

Conductivity Parallel equation of motion Perpendicular equation of motion Conductivity tensor Pedersen conductivity (along E┴) Hall conductivity (along -E x B) Parallel conductivity