
# Research Glossary

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The following terms are listed in alphabetical order. Entries without a description are meant as placeholders which I will fill in as I have time. If you notice anything, anywhere on this page, that could be improved, please do not hesitate to let me know. (Thanks!)

Abel Inversion
In observational astronomy, an Abel inversion is a technique for inferring something (usually electron density) from a solar or stellar occultation. This technique uses an Abel Transform, which assumes spherical symmetry. Because of this assumption, it is usually not as accurate near the terminator due to the presence of strong horizontal (not spherically-symmetric) structure, including clouds and winds.
Ambipolar Diffusion
Ambipolar diffusion is a process in which a polarization electrostatic field develops due to gravitational settling, and "ions and electrons move as a single gas under the influence of gravity and the density and temperature gradients." (Schunk & Nagy 2000, pg. 117)
Ampère Force
The Ampère force is one name for the mutual attraction or repulsion between two given segments of current.
Appleton Anomaly
Also known as the equatorial ionization anomaly, this refers to twin bands of plasma circling Earth's equator at roughly ±17° latitude above and below the magnetic equator.
Boltzmann Collision Integral
For binary, elastic collisions, the Boltzmann collision integral quantifies the effect of collisions on the time evolution of the distribution function. This is the $\frac{\delta f_{s}}{\delta t}$ term in the Boltzmann equation. This integral takes the following form (Schunk & Nagy 2000, pg. 49): $$\frac{\delta f_{s}}{\delta t} = \int \int d^3 v_{t} \; d \Omega \; g_{st} \; \sigma_{st}( g_{st},\theta) \left( f_{s}^{\prime} \; f_{t}^{\prime} - f_{s}\; f_{t} \right)$$ where \begin{aligned} d^3 v_{t} \quad = \quad & \text{velocity-space volume element for target species }t \\ g_{st} \quad = \quad & \left| \vector{v}_{s}-\vector{v}_{t}\right| \text{is the relative speed of the colliding particles }s\text{ and }t \\ d \Omega \quad = \quad & \text{element of solid angle in the colliding particles' center-of-mass }\\ & \text{reference frame} \\ \theta \quad = \quad & \text{center-of-mass scattering angle} \\ \sigma_{st}( g_{st},\theta) \quad = \quad & \text{differential scattering cross section, defined as the}\\ & \text{number of molecules scattered per solid angle }d\Omega\text{, per unit}\\ & \text{time, divided by the incident intensity} \\ f_{s}^{\prime} f_{t}^{\prime} \quad = \quad & f_{s} (\vector{r},\vector{v}_{s}^{\prime},t) \; f_{t} (\vector{r},\vector{v}_{t}^{\prime},t)\text{, where the primes indicate the distribution} \\ & \text{functions are evaluated with the particle velocities }\textit{after}\text{ the collision.} \\ \end{aligned}
Boltzmann Equation
The Boltzmann equation describes how a particular distribution function $f_{s}$ (for species $s$) evolves in time. If the effect of collisions can be reduced to $\frac{\delta f_{s}}{\delta t}$, then the Boltzmann equation takes the following form (Schunk & Nagy 2000, pg. 49): $$\pder{f_{s}}{t} + \vector{v}_{s} \cdot \vector{\nabla} f_{s} + \vector{a}_{s} \cdot \vector{\nabla}_{v} f_{s} = \frac{\delta f_{s}}{\delta t}$$
Charge Neutrality
Charge neutrality is a approximation in which there are equal numbers of positive charges ("ions") and negative charges (almost always just electrons) in a given bulk sample or region. (Mathematically stated, $n_e = n_i$.) In many atmospheres, this is a decent assumption because if there were a separation of charges, there would be a net electric field which would exert a force on charged particles to move them towards oppositely-charged particles (that is, towards charge neutrality).
Importantly, charge neutrality does not prevent currents from flowing in a fluid. This is related to the difference between position and velocity.
Climate
Climate is the long-term average weather of a given region.
Collisionless Plasma
An approximation of plasma physics in which particles do not collide with each other. This is valid when the collisional mean free path is much larger than the length scale at which density changes. (Schunk & Nagy 2000, pg. 16)
Coriolis Parameter
The Coriolis parameter (also called the Coriolis frequency or Coriolis coefficient) is given by the following equation: $f = 2 \Omega \sin\phi$, where $\phi$ is the latitude. Therefore, the Coriolis parameter is zero at the equator, $+2\Omega$ at the north pole, and $-2\Omega$ at the south pole.
Coulomb Collisions
Coulomb collisions are binary, elastic collisions involving two charged particles which inteact via their mutual electric field. In plasmas, where the particle's kinetic energy is large, Coulomb collisions typically result in small deflections. (Coulomb Collision, Wikipedia)
Coulomb Logarithm
The Coulomb logarithm (usually designated $\lambda$ or $\ln \Lambda$)is a value derived from collision/scattering theory (for Coulomb collisions) that indicates whether small-angle collisions or large-angle collisions are more effective. In plasmas, high kinetic energies typically result in small deflections, yielding Coulomb logarithm of roughly $\ln \Lambda \sim 5 - 15$. (Coulomb Collision, Wikipedia)
Cyclostrophic Wind Balance
Cyclostrophic wind balance is an idealized balance of forces which results in a steady-state wind. In this balance, centripetal acceleration is caused entirely by the pressure-gradient force, which may be thought to balance the centrifugal force. Because the Coriolis force and any (surface?) frictional forces are neglected, flow folows isobars. These flows tend to form roughly circular cyclones, as in tornadoes, dust devils, and/or waterspouts. The force balance (per unit mass) is: $$\frac{v^2}{r} = -\frac{1}{\rho} \frac{\partial p}{\partial n} \text{,}$$ where \begin{aligned} v \quad = \quad & \text{the flow speed perpendicular to the pressure gradient (e.g. along isobars)} \\ r \quad = \quad & \text{the radius of curvature of the fluid's centripetal accelration} \\ \rho \quad = \quad & \text{the fluid density} \\ p \quad = \quad & \text{the pressure} \\ n \quad = \quad & \text{a unit vector normal to the isobaric pressure surface, pointing outward from the center of the resulting centripetal acceleration} \\ \end{aligned}
D Layer
The innermost layer of Earth's dayside ionosphere is the D layer, at roughly 60–90 km altitude. Ionization is primarily due to Lyman-alpha radiation (λ = 121.6 nm) ionizing nitric oxide (NO), but high solar activity can generate "hard" X-rays (λ < 1 nm) that ionize N2 and O2. Importantly, high recombination rates cause there to be relatively less ionization in this layer than other layers, and without the sun's photoionization, this layer all but disappears at night. ("Ionosphere: D Layer", Wikipedia)
Distribution Function
A function that describes the distribution of particles in physical space, velocity space, and time. It can also be thought of as a continuous probability function for an ensemble of particles. Each constituent species $s$ in the ensemble has its own distribution function of the form $f_{s}(\vector{r},\vector{v}_{s},t)$, where $f_{s}$ is the number of particles of species $s$ at time $t$ that are located in a volume element $d^3 r$ about position $\vector{r}$ in physical space and have velocities in a volume element $d^3 v_{s}$ about velocity $\vector{v}_{s}$. (Schunk & Nagy 2000, pg. 47) The distribution function is the basis of the Maxwell-Boltzmann transport equations, kinetic theory, and statistical mechanics.
Dungey Cycle
The Dungey Cycle is a circulation model of magnetospheric plasma proposed by Dungey (1961) in which solar winds are strong enough to penetrate the magnetopause, allowing reconnection to occur on the daytime side of the planet (provided the solar wind has an oppposite orientation to the planet's field). The reconnection event converts the planet's outermost closed field lines into open field lines and the solar wind "convects" (or, perhaps more properly, advects) the associated plasma and its field lines over the poles and toward the magnetotail. This stretches and lengthens the field lines, storing energy therein. This energy can be released during a second reconnection event, just as it does in the Vasyliūnas Cycle, when these stretched field lines "pinch off" in the magnetotail. The inward, now-closed, field lines created by the reconnection event pull backwards toward the planet and the outward field lines eject plasma outward. (Paraphrased from Eastwood et al. 2015).)
Dynamic Pressure
In the context of gases, dynamic pressure is the kinetic energy per unit volume. It is one of the primary terms in the Bernoulli equation.
E Layer
The middle layer of Earth's ionosphere is the E layer, also known as the "Kennelly-Heaviside layer" or the "Heaviside layer". At roughly 90–150 km altitude, ionization is primarily due to "soft" X-rays (λ ∼ 1–10 nm) and far UV solar ionization of O2. The thickness of this layer depends on the balance between ionization and recombination, so the E layer weakens at night and reaches a maximum around noon. ("Ionosphere: E Layer", Wikipedia)
Solar wind also influences this layer by pressing it closer to Earth during the day and stretching it further from Earth at night. Medium-frequency radio waves can reflect off this layer to communicate beyond the horizon ("Kennelly–Heaviside layer", Wikipedia).
Edward V. Appleton received the 1947 Nobel Prize in Physics for demonstrating its existence.
Equatorial Electrojet
The equatorial electrojet (or EEJ) is a thin region of eastward-flowing current in the equatorial regions of Earth's lower ionosphere. ("Equatorial Electrojet", Wikipedia)
Equatorial Fountain
The equatorial fountain refers to an upward motion of plasma near the equator during the day due to an upward E×B drift. At night, the motion is downward instead. This fountain lifts plasma from the equator until the pressure gradient force and gravity become more important, at which point the plasma is transported poleward and downward along magnetic field lines to about ±17° magnetic latitude, creating the equatorial ionization anomaly regions.
See also: Section 1.1 of the PREASA Program description web page, and references therein.
Equatorial Ionization Anomaly
The equatorial ionization anomaly (EIA), also known as the Appleton Anomaly, refers to two low-latitude bands of higher-than-surrounding electron densities centerred around 17° above and below Earth's geomagnetic equator. It is understood to be caused by the equatorial fountain transporting plasma from lower in the ionosphere upward and then poleward along magnetic field lines.
See also: Section 1.1 of the PREASA Program description web page, and references therein.
Equatorial Jet
An equatorial jet is a relatively strong and somewhat narrow zonal wind pattern at or very near the equator of a planetary body.
Equatorial spread-F (ESF) is a general term referring to plasma irregularities in the F Layer of Earth's ionosphere and near the equator. These often occur on broad length and time scales which sometimes span as much as 5-6 orders of magnitude. (McDaniel, 2000; Ossakow, 1981, pg. 437)
Exobase
The transition altitude at which "nutral densities become so low that collisions become unimportant and, hence, the upper atmosphere can no longer be characterized as a fluid" (Schunk & Nagy 2000, pg. 28). The exobase is essentially the top boundary of the thermosphere and the bottom boundary of the exosphere.
Exosphere
The exosphere is the region above the thermosphere in which neutral particles are scarce enough as to "behave like individual ballistic particles" (Schunk & Nagy 2000, pg. 28).
F Layer
The outermost layer of Earth's ionosphere is the F layer, or the Appleton-Barnett layer, at roughly 150 to 800 km altitude. This region has the highest number density of electrons and ions in the atmosphere. ("F region", Wikipedia) Because of this, signals penetrating this layer escape the atmosphere. ("Ionosphere: F Layer", Wikipedia)
During the day, the F layer splits into the F1 and F2 regions. At night, the F1 and F2 regions merge back together. ("Ionosphere: F Layer", Wikipedia)
Generalized Ohm's Law
In plasma physics, one can treat a partially ionized plasma as three species of fluid: an ion species, a neutral species, and an electron species. When one combines the three equations of motion and the continuity equation for electrons, making several approximations along the way, one can derive an equation of motion for the electrons, which many term the generalized Ohm's law (Leake et al. 2014, pg. 121). Due to the nature of the approximations taken, different authors get somewhat (slightly?) different versions of this law. Several versions of the generalized Ohm's law can be found in the following works: Leake et al. 2014 (pg. 121); Song et al. 2001; Koskinen et al. 2014.
Geostrophic Wind Balance
Geostrophic wind balance is an idealized balance of the pressure-gradient force and the Coriolis force, resulting in steady-state flow. Geostrophic winds flow along isobars at constant height and leads to the following equations of motion: $$\vec{v}_g = \frac{\hat{k}}{f} \times \vec{\nabla}_p \Phi_G$$, where \begin{aligned} \vec{v}_G \quad = \quad & \text{the horizontal velocity vector} \\ \hat{k} \quad = \quad & \text{the vertical unit vector} \\ f \quad = \quad & \text{the Coriolis parameter} \\ \vec{\nabla}_p \quad = \quad & \text{the gradient operator in pressure coordinates} \\ \Phi_G \quad = \quad & \text{the } \href{http://en.wikipedia.org/wiki/Geopotential_height}{\text{geopotential height}} \end{aligned}
Gyroscopic Pumping
A persistent, axisymmetric, azimuthal force can drive meridional flows. This effect, known as gyroscopic pumping, comes from a balance in the angular momentum equation. (Paraphrased, from Acevedo-Arreguin et al., 2013).
Heterosphere
The heterosphere is the region of an atmosphere in which the constituent gasses separate by molecular mass and molecular diffusion dominates over eddy diffusion. Heterospheres tend to include the ionosphere, thermosphere, and beyond.
Homopause
The homopause is a dividing point in an atmosphere, below which the atmosphere is said to be "well-mixed" (this region is the homopsphere). Above the homopause, each chemical species has its own scale height. It is often defined to be the level at which eddy diffusion is balanced by molecular diffusion. On Earth (at least?), it is lower in the daytime than at night (source).
Homosphere
The homopsphere is the region of an atmosphere in which the chemical composition is relatively uniform and eddy diffusion dominates over molecular diffusion. The homosphere tends to include the troposphere, stratosphere and even the mesosphere.
Inertial Wind Balance
Inertial wind balance is an idealized balance of forces resulting in steady-state flow. For inertial winds, pressure is assumed to be uniform in a given region, so there is no pressure-gradient force. Furthermore, flow is assumed frictionless (no surface friction?), and external, driving winds (sources of pressure gradients) have died down. Therefore, the Coriolis force alone dictates bulk motion and causing rotation. Because of these idealizations, inertial flows are more commen in dense and (nearly?) imcompressible fluids, like oceans, than in atmospheres.
Interplanetary Magnetic Field (IMF)
Stellar wind drags the stellar magnetic field outward from the host star. The resulting structure, usually in context of distances further from the star, is called the interplanetary magnetic field.
Ionization
Ionization is the general name for a group of processes that remove or add a charge to an atom or molecule. In the context of atmospheric chemistry, ionization usually refers to the removal of an electron from an atom or molecule.
Ionosphere
The ionosphere is the region in which particles are generally ionized. On Earth, the ionosphere is located from roughly 60 to beyond 1000 km above the surface. It includes the thermosphere and some of the mesosphere and exosphere (Ionosphere, Wikipedia).
Jeans Escape
Jeans escape is a mechanism that explains how gasses can escape an atmosphere. In any molecular distribution function, a few molecules will have much more energy than the rest. If these higher-than-average-energy particles are near the top of the atmosphere, and their kinetic energy is sufficiently high (such that their velocity is above the planetary body's escape velocity), then they leave the atmosphere simply by not colliding with another particle and losing energy. This typically occurs above the level where the molecule's mean free path exceeds its scale height (Atmospheric escape, Wikipedia). Because of this relationship, particles with lower mass escape more easily than particles with greater mass.
Joule Heating
Joule heating is the mechanism by which a wire heats up when current runs through it. The energy produced is measured in units of power per unit volume. In differential form, $\frac{\partial P}{\partial V} = \vec{j} \cdot \vec{E}$.
See also: Vasyliunas & Song 2005 for a discussion on what exactly constitutes "Joule heating".
Kinetic Tensor
A chemical species $\alpha$ has a kinetic tensor $\tensor{\kappa}_\alpha$ equal to $$\tensor{\kappa} = \rho \vector{v} \vector{v} + \tensor{P}$$ for that species (Vasyliunas, 2012).
Magnetic Reconnection
Magnetic reconnection is a processes that bring magnetic lines together, drastically changing the topology of a given magnetic field. This can happen when two objects or regions with strong, opposing magnetic fields are brought in close proximity, such as when solar wind encounters a strong planetary magnetic field, or (probably) in the creation of solar flares. This process is often highly localized in time and space, converting magnetic energy to kinetic and thermal energy. (Magnetic reconnection, Wikipedia)
Magnetization
There are evidently (at least) two meanings of magnetization:
Magnetohydrodynamics
Magnetohydrodynamics is the study of how magnetic fields interact with conducting fluids, like plasmas. When a conducting fluid flows through a magnetic field, the charges inside the fluid experience forces from the magnetic field that can change the bulk flow of the fluid. The moving charges in the fluid can also induce their own magnetic and electric fields. These processes cause many nonlinear and complicated interactions, for which there are often no analytic solutions.
Magnetopause
A planet's magnetopause is the boundary layer separating "the magnetized stellar wind plasma in the magnetosheath from that confined by the [planet's] magnetic field". The location of the magnetopause is roughly deteremined by the balance of the stellar wind's dynamic pressure and the magnetic pressure of the compressed planetary magnetic field lines. (Schunk & Nagy 2000, pg. 23)
Magnetosheath
The region inward of a planetary bow shock in which the stellar wind is decelerated, heated and deflected around the planet. (Schunk & Nagy 2000, pg. 21)
Magnetosphere
The region inward of the magnetopause, where the planetary magnetic field has a larger influence on dynamics than the interplanetary magnetic field.
Magnetospheric Convection
The solar wind interacts with a magnetosphere causes a bulk flow of plasma down the magnetotail via magnetic reconnection and viscous processes. This flow is called "convection" in the context of magnetospheres, though it is a misnomer (source) because convection in fluid dynamics usually refers to bulk fluid overturning due to a gravitationally unstable thermal gradient (or "convective heat transfer"; though there are other mechanisms as well). That said, the word "convection" can (evidently) refer to any fluid motion, regardless of cause, in the context of fluid mechanics, according to a Wikipedia article here.
Major Ion
In the context of atmospheres, a major ion is a positively charged ion species with a number density comparable to the electron number density—in other words, it is one of the most populous ion species.
Maxwell-Boltzmann Velocity Distribution Function
When colliisons dominate, as is the case when the system is in thermodynamic equilibrium, the Maxwell-Boltzmann distribution function emerges (Schunk & Nagy 2000, pg. 55): $f_{s}^{MB}(\vector{r},\vector{v}_{s},t) = n_s(\vector{r},t) \left[ \frac{m_s}{2 \pi k T_{s}(\vector{r},t)}\right]^{3/2} \exp \left( - \frac{m_{s} \left[ \vector{v}_s - \vector{u}_s(\vector{r},t) \right]^{2}}{2 k T_{s}(\vector{r},t)} \right)$
Maxwell Molecule Collisions
"Maxwell molecule collisions correspond to an interaction potential of $V \sim 1/r^4$ and $\sigma_{st} \sim 1/g_{s}$." (Schunk & Nagy 2000, pg. 82), where $V$ is the interaction potential, $\sigma_{st}$ is the collisional cross section between species $s$ and species $t$, and $g_{st} \equiv \left| \vector{v}_{s}-\vector{v}_{t}\right|$ is the relative speed of the colliding particles $s$ and $t$. Such collisions greatly simplify the momentum transfer integral (among other things?).
Mesopause
The upper boundary of the mesosphere. Atmospheric temperature typically decreases with altitude in the mesosphere down to a minimum value located at the mesopause. This is the coldest region of the Earth's atmosphere ($T \simeq 180 \; \text{K}$).
Mesoscale
The mesoscale is 2 km–2000 km. In this regime, gravity waves, thunderstorms, tornados, cloud clusters, local winds and urban air polution are relevant phenomena. (Jacobson 1999, Table 1.1)
Mesosphere
The atmospheric layer above the stratosphere. On Earth, the mesosphere is located roughly 45 to 95 km above the surface. In this layer, temperature decreases with altitude.
Microscale
The microscale is 2 mm–2 km. In this regime, eddies, small plumes, car exhaust and cumulous clouds are relevant phenomena. (Jacobson 1999, Table 1.1)
Minor Ion
In the context of atmospheres, a minor ion is a positively charged ion (trace) species with a number density much less than the electron number density.
Molecular Scale
The molecular scale is anything much less than 2 mm. In this regime, molecular diffusion and molecular viscosity are relevant phenomena. (Jacobson 1999, Table 1.1)
Oversaturation
Oversaturation is when a chemical species' partial pressure is greater than the vapor pressure at "the cold trap temperature". (Yelle et al. 1993, pg. 38)
Parallel Conductivity
The parallel conductivity ($\sigma_{\parallel}$) is the conductivity in the direction of the magnetic field in a plasma.
Pedersen Conductivity
The Pedersen conductivity ($\sigma_{P}$) is the conductivity in the direction of the electric field in a plasma.
Photodissociation
Also called "photolysis" or "photodecomposition", photodissociation is a chemical reaction in which light breaks apart a chemical compound. Higher-energy photos are typically responsible. These reactions or processes are often known as "photolytic" reactions or processes. Two terrestrial examples of photolytic processes are photosynthesis and sunlight breaking apart water molecules into oxygen and hydrogen in Earth's atmosphere.
Planetary Scale
The planetary scale is anything greater than 10,000 km. In this regime, global wind systems, Rossby (planetary) waves, stratospheric ozone reduction and global warming are relevant phenomena. (Jacobson 1999, Table 1.1)
Polarization Electrostatic Field
Gravity causes heavier ions to settle below lighter electrons. This charge separation sets up an electrostatic field, called the polarization electrostatic field, which itself prevents further charge separation. (Schunk & Nagy 2000, pg. 117)
Recombination
Ion recombination is the general name for a group of processes that bring a negatively-charged particle together with a positively-charged one, such that the product has a neutral charge.
Refractory Compounds
Refractory compunds are a group of chemical compounds which have relatively high boiling points. These typically include heavier compounds such as metals, minerals, silicates, and more. In differentiated planetary bodies, refractory compounds tend to sink toward the core.
Solar Occultation
A solar occultation is a special case of a stellar occultation in which the star being occulted is the Sun. These occultations presumably give better results than stellar occultations due to how much better we know our sun than other stars, and how much brighter it is.
Stellar Occultation
"A stellar occultation occurs when the light from a star is blocked by an intervening body (such as a planet, moon, ring, or asteroid) from reaching an observer. The main reason for observing stellar occultations is that they can be used to probe ring systems and atmospheres in the outer solar system with spatial resolutions of a few kilometers-several orders of magnitude better than the resolution of any other Earth-based method." (Source: MIT Planetary Astronomy Lab; alternative link here).
Stratopause
The upper boundary of the stratosphere. Atmospheric temperature typically increases with altitude in the stratosphere up to a maximum value located at the stratopause.
Stratosphere
The atmospheric layer above the troposphere. On Earth, the stratosphere is located roughly 10 to 45 km above the surface. In this layer, temperature increases with altitude.
Supersaturation
Supersaturation is when a chemical species' partial pressure is greater than the vapor pressure at the local temperature. (Yelle et al. 1993, pg. 38)
Synoptic Scale
The synoptic scale is 500 km–10,000 km. In this regime, high- and low-pressure systems, weather fronts, tropical storms, hurricanes, and Antarctic ozone holes are relevant phenomena. (Jacobson 1999, Table 1.1)
Temperature Inversion
Ordinarily, Earth's atmosphere gets colder with increasing altitude. (This is in part because pressure and density decrease with altitude and because the ground warms due to Solar radiation.) Under special circumstances, however, this reverses and temperature increases with altitude. This phenomenon is known as a temperature inversion. Temperature inversions are more common at night, when the ground radiatively cools (causing near-surface atmosphere to cool as well), but it can also happen during a cold front or result from cool sea breezes creeping underneath a warmer land air mass.
Thermal Velocity
The thermal (or random) velocity is the velocity of an individual particle with respect to that of the bulk fluid's drift velocity. It can be quantified as $\vector{c}_s = \vector{v}_s - \vector{u}_s$, where $\vector{c}_s$ is the random velocity, $\vector{v}_s$ is the total velocity of the particle, and $\vector{u}_s$ is the drift velocity of the fluid. Thermal velocity is more useful than total velocity for defining transport properties in atmospheres or ionospheres where large relative drifts between species is commonplace. (Schunk & Nagy 2000, pg. 51)
Thermal Wind
The thermal wind is a vertical wind shear created by a balance between the Coriolis and pressure-gradient forces.
Thermocline
A thermocline is a thin layer of a fluid separating two layers of different temperatures. It is marked by a much larger temperature gradient above and below it. In the context of atmospheres, it can also refer to a nighttime inversion layer.
Thermosphere
The atmospheric layer above the mesosphere. On Earth, the thermosphere is located roughly 95 to 500 km above the surface. In this layer, temperature increases with altitude up to a max value ($T \simeq 1000 \; \text{K}$ on Earth), then levels off to a constant value.
Transfer Collision Integrals
Transfer collision integrals are simply velocity moments of the Boltzmann collision integral. If $\xi_{s}(\vector{c}_s)$ is a generic velocity moment (taking values of $1$, $m_{s} \vector{c}_{s}$, $\frac{1}{2} m_{s} c_{s}^{2}$, $m_{s} \vector{c}_{s}\vector{c}_{s}$, and $\frac{1}{2} m_{s} c_{s}^{2} \vector{c}_{s}$, and so on), then the corresponding moment of the transfer integral is: (Schunk & Nagy 2000, pg. 78) $\int d^3 c_s \; \xi_{s}(\vector{c}_s) \frac{\delta f_s}{\delta t} = \int \int \int d^3 c_{s} d^3 c_{t} \; d \Omega \; g_{st} \; \sigma_{st}( g_{st},\theta) \left( f_{s}^{\prime} \; f_{t}^{\prime} - f_{s}\; f_{t} \right) \xi_{s} \text{,}$ where variables are defined as in the glossary entry for the Boltzmann collision integral.
Tropopause
The upper boundary of the troposphere. Atmospheric temperature typically decreases with altitude in the troposphere down to a minimum value located at the tropopause.
Troposphere
The atmospheric layer closest to the planetary surface. On Earth, this 10 km thick layer is where most atmospheric weather occurs.
Weather
Weather is the current state of the atmosphere in a given region.
Vlasov Equation
The Vlasov equation is a special case of the Boltzmann equation in which collisions are neglected, such that $\tder{f_{s}}{t} = 0$. In this case, the transport equation reduces to (Schunk & Nagy 2000, pg. 48): $$\pder{f_{s}}{t} + \vector{v}_{s} \cdot \vector{\nabla} f_{s} + \vector{a}_{s} \cdot \vector{\nabla}_{v} f_{s} = 0$$