# Plasmas/Ions This is an animation comparing the ionospheric conditions during a typical day with that of a day containing an ionospheric storm. Credit: GSFC, NASA.

An ion is an atom or molecule with a net electric charge due to the loss or gain of one or more electrons.

"Above center "is an animation comparing the ionospheric conditions during a typical day with that of a day containing an ionospheric storm. An ionospheric storm is caused by a coronal mass ejection from the sun that strikes the Earth's atmosphere. These mass ejections contain large amounts of particles that smash into the ionosphere and knock electrons loose from atoms. As discussed above the loose electrons reflect radio waves from astronomical sources back into space. The addition of loose electrons as a result of a mass ejection makes observations and communications difficult. The dark blue and purple areas are the areas where the number of loose electrons is low. In these areas there are few electrons to reflect radio waves and thus lower frequency waves are able to reach the ground. As can be seen from the animations the night time and early morning hours are best for observations due to the fact that the sun is not in the sky and its ultraviolet light is not reaching the atmosphere at this time."

"The density of electrons (how many electrons there are per every cubic centimeter) is represented by the varying colors. Bands of high density that appear at high latitudes during the storm but disappear rapidly as it subsides are due to the high velocity particles smashing into the atoms in the atmosphere and knocking electrons free. These same high velocity particles produce the auroral lights."

"The lowest frequency detectable, known as the critical frequency, is related to the density of electrons by the equation:

$f=9x10^{-3}xsqrt(N)MHz.$ In this equation f is the critical frequency and N is the electron density, sqrt means to take the square root of the electron density. In the maps above the electron density ranges from 33300 electrons/cm3 (dark blue) to 249750 electrons/cm3 (green) to 552780 electrons/cm3 (red)."

## Theory of ions

Def. "[a]n atom or group of atoms bearing an electrical charge such as the sodium and chlorine atoms in a salt solution" is called an ion.

## Cosmic rays

About 89% of cosmic rays are simple protons or hydrogen nuclei, 10% are helium nuclei of alpha particles, and 1% are the nuclei of heavier elements. Solitary electrons constitute much of the remaining 1%.

## Venus The image shows Venus Express data with an artist's impression of the tear-drop shaped ionosphere. Credit: ESA/Wei et al. (2012).

In 1967, Venera-4 found the Venusian magnetic field is much weaker than that of Earth. This magnetic field is induced by an interaction between the ionosphere and the solar wind. Venus's small induced magnetosphere provides negligible protection to the atmosphere against cosmic radiation. This radiation may result in cloud-to-cloud lightning discharges.

The weak magnetosphere around Venus means the solar wind is interacting directly with the outer atmosphere of the planet. Here, ions of hydrogen and oxygen are being created by the dissociation of neutral molecules from ultraviolet radiation. The solar wind then supplies energy that gives some of these ions sufficient velocity to escape the planet's gravity field. This erosion process results in a steady loss of low-mass hydrogen, helium, and oxygen ions, while higher-mass molecules, such as carbon dioxide, are more likely to be retained.

During the Soviet Venera program, the Venera 11 and Venera 12 probes detected a constant stream of lightning, and Venera 12 recorded a powerful clap of thunder soon after it landed. The European Space Agency's Venus Express recorded abundant lightning in the high atmosphere.

"During a rare period of very low density solar outflow, the ionosphere of Venus was observed to become elongated downstream, rather like a long-tailed comet. ... Under normal conditions, the solar wind has a density of 5 - 10 particles per cubic cm at Earth's orbit, but occasionally the solar wind almost disappears, as happened in May 1999. ... A rare opportunity to examine what happens when a tenuous solar wind arrives at Venus came 3 - 4 August 2010, following a series of large coronal mass ejections on the Sun. NASA's STEREO-B spacecraft, orbiting downstream from Venus, observed that the solar wind density at Earth's orbit dropped to the remarkably low figure of 0.1 particles per cubic cm and persisted at this value for an entire day."

"The observations show that the night side ionosphere moved outward to at least 15 000 km from Venus' centre over a period of only a few hours," said Markus Fraenz, also from the Max Planck Institute for Solar System Research, who was the team leader and a co-author of the paper. "It may possibly have extended for millions of kilometres, like an enormous tail."

"Although we cannot determine the full length of the night-side ionosphere, since the orbit of Venus Express provides limited coverage, our results suggest that Venus' ionosphere resembled the teardrop-shaped ionosphere found around comets, rather than the more symmetrical, spherical shape which usually exists."

"The side of Venus' ionosphere that faces away from the sun can billow outward like the tail of a comet, while the side facing the star remains tightly compacted, researchers said. ... "As this significantly reduced solar wind hit Venus, Venus Express saw the planet’s ionosphere balloon outwards on the planet’s ‘downwind’ nightside, much like the shape of the ion tail seen streaming from a comet under similar conditions," ESA officials said in a statement today (Jan. 29). It only takes 30 to 60 minutes for the planet's comet-like tail to form after the solar wind dies down. Researchers observed the ionosphere stretch to at least 7,521 miles (12,104 kilometers) from the planet, said Yong Wei, a scientist at the Max Planck Institute in Katlenburg, Germany who worked on this research."

## Earth The International Space Station is featured in this image photographed by an STS-134 crew member on the space shuttle Endeavour after the station and shuttle began their post-undocking relative separation. Credit: NASA.

Between the surface and various altitudes there is an electric field. It changes with altitude from about 150 volts per meter to lower values at higher altitude. In fair weather, it is relatively constant, in turbulent weather it is accompanied by ions. At greater altitude these chemical species continue to increase in concentration.

The air pressure is lowering as is the ambient temperature.

Upon reaching the top of the mesosphere, the temperature starts to rise, but air pressure continues to fall. This is the beginning of the ionosphere, a region dominated by chemical ions. Many of them are the same chemicals such as nitrogen and oxygen in the atmosphere below, but an ever increasing number are hydrogen ions (protons) and helium ions. These can be detected by an ion spectrometer. The process of ionization removes one or more electrons from a neutral atom to yield a variety of ions depending on the chemical element species and incidence of sufficient energy to remove the electrons.

From the ground below, or with spectrometers on platforms at higher altitude, including satellites, ion species and concentrations are measured. Into the exosphere or outer space, temperature rises from around 1,500°C (centigrade) to upwards of 100,000 K (kelvin).

## Birkeland currents This is a schematic of the Birkeland currents and their connection to Earth's ionospheric current systems. Credit: Le, G., J. A. Slavin, and R. J. Strangeway. Auroral-like Birkeland currents were created by scientist Kristian Birkeland in his terrella, featuring a magnetised anode globe in an evacuated chamber. Credit: Kristian Birkeland. The complex self-constricting magnetic field lines and current paths in a Birkeland current that may develop in a plasma (Figure 15.3.2, Alfvén and Arrhenius, 1976) Credit: .

The schematic at right describes the Birkeland or field-aligned currents and the ionospheric current systems they connect to.

A Birkeland current is a set of currents which flow along geomagnetic field lines connecting the Earth’s magnetosphere to the Earth's high latitude ionosphere. Lately, the term Birkeland currents has been expanded by some authors to include magnetic field aligned currents in space plasmas in general. In the Earth’s magnetosphere, the currents are driven by the solar wind and interplanetary magnetic field and by bulk motions of plasma through the magnetosphere (convection which is indirectly driven by the interplanetary environment). The strength of the Birkeland currents changes with activity in the magnetosphere (e.g. during substorms). Small scale variations in the upward current sheets (downward flowing electrons) accelerate magnetospheric electrons which, when they reach the upper atmosphere, create the Aurora Borealis and Australis. In the high latitude ionosphere (or auroral zones), the Birkeland currents close through the region of the auroral electrojet, which flows perpendicular to the local magnetic field in the ionosphere. The Birkeland currents occur in two pairs of field-aligned current sheets. One pair extends from noon through the dusk sector to the midnight sector. The other pair extends from noon through the dawn sector to the midnight sector. The sheet on the high latitude side of the auroral zone is referred to as the Region 1 current sheet and the sheet on the low latitude side is referred to as the Region 2 current sheet.

"A reason why Birkeland currents are particularly interesting is that, in the plasma forced to carry them, they cause a number of plasma physical processes to occur (waves, instabilities, fine structure formation). These in turn lead to consequences such as acceleration of charged particles, both positive and negative, and element separation (such as preferential ejection of oxygen ions). Both of these classes of phenomena should have a general astrophysical interest far beyond that of understanding the space environment of our own Earth."

Auroral Birkeland currents carry about 100,000 amperes during quiet times and more than 1 million amperes during geomagnetically disturbed times. Birkeland had estimated currents "at heights of several hundred kilometres, and strengths of up to a million amperes" in 1908. The ionospheric currents which connect the field-aligned currents heat up the upper atmosphere due to the finite conductivity of the ionosphere. The heat (also known as Joule heat) is transferred from the ionospheric plasma to the gas of the upper atmosphere which rises and increases drag on low-altitude satellites.

Birkeland currents can also be created in the laboratory with multi-terawatt pulsed power generators. The resulting cross-section pattern indicates a hollow beam of electrons in the form of a circle of vortices, a formation called the diocotron instability (similar to, but different from, the Kelvin-Helmholtz instability), that subsequently leads to filamentation. Such vortices can be seen in aurora as "auroral curls".

Birkeland currents are also one of a class of plasma phenomena called a z-pinch, so named because the azimuthal magnetic fields produced by the current pinches the current into a filamentary cable. This can also twist, producing a helical pinch that spirals like a twisted or braided rope, and this most closely corresponds to a Birkeland current. Pairs of parallel Birkeland currents will also interact due to Ampère's force law: parallel Birkeland currents moving in the same direction will attract each other with an electromagnetic force inversely proportional to their distance apart whilst parallel Birkeland currents moving in opposite directions will repel each other. There is also a short-range circular component to the force between two Birkeland currents that is opposite to the longer-range parallel forces.

Electrons moving along a Birkeland current may be accelerated by a plasma double layer. If the resulting electrons approach relativistic velocities (i.e. if they approach the speed of light) they may subsequently produce a Bennett pinch, which in a magnetic field causes the electrons to spiral and emit synchrotron radiation that may include radio, optical (i.e. visible light), x-rays, and gamma rays.

"[T]he currents there are imagined as having come into existence mainly as a secondary effect of the electric corpuscles from the sun drawn in out of space, and thus far come under the second of the possibilities mentioned above". And p. 105, "Fig. 50a represents those in which the current-directions at the storm-centre are directed westwards, and 50b those in which the currents move eastwards".

"[C]urrents there [in the aurora] are imagined as having come into existence mainly as a secondary effect of the electric corpuscles from the sun drawn in out of space,"

## Interplanetary medium

"[F]luxes of ions should be measurable from a detector in a 100 km lunar orbit."

## Electrohydrodynamics

Electrohydrodynamics (EHD), also known as electro-fluid-dynamics (EFD) or electrokinetics, is the study of the dynamics of electrically charged fluids. It is the study of the motions of ionised particles or molecules and their interactions with electric fields and the surrounding fluid. The term may be considered to be synonymous with the rather elaborate electrostrictive hydrodynamics. EHD covers the following types of particle and fluid transport mechanisms: Electrophoresis, electrokinesis, dielectrophoresis, electro-osmosis, and electrorotation. In general, the phenomena relate to the direct conversion of electrical energy into kinetic energy, and vice versa.

In the first instance, shaped electrostatic fields create hydrostatic pressure (or motion) in dielectric media. When such media are fluids, a flow is produced. If the dielectric is a vacuum or a solid, no flow is produced. Such flow can be directed against the electrodes, generally to move the electrodes. In such case, the moving structure acts as an electric motor.

## Waves

Waves in plasmas are an interconnected set of particles and fields which propagates in a periodically repeating fashion. A plasma is a quasineutral, electrically conductive fluid. In the simplest case, it is composed of electrons and a single species of positive ions, but it may also contain multiple ion species including negative ions as well as neutral particles. Due to its electrical conductivity, a plasma couples to electric and magnetic fields. This complex of particles and fields supports a wide variety of waves.

Waves in plasmas can be classified as electromagnetic or electrostatic according to whether or not there is an oscillating magnetic field. Applying Faraday's law of induction to plane waves, we find $\mathbf {k} \times {\tilde {\mathbf {E} }}=\omega {\tilde {\mathbf {B} }}$ , implying that an electrostatic wave must be purely longitudinal. An electromagnetic wave, in contrast, must have a transverse component, but may also be partially longitudinal.

Waves can be further classified by the oscillating species. In most plasmas of interest, the electron temperature is comparable to or larger than the ion temperature. This fact, coupled with the much smaller mass of the electron, implies that the electrons are much faster than the ions. An electron mode depends on the mass of the electrons, but the ions may be assumed to be infinitely massive, i.e. stationary. An ion mode depends on the ion mass, but the electrons are assumed to be massless and to redistribute themselves instantaneously according to the Boltzmann relation. Only rarely, e.g. in the lower hybrid oscillation, will a mode depend on both the electron and the ion mass.

The various modes can also be classified according to whether they propagate in an unmagnetized plasma or parallel, perpendicular, or oblique to the stationary magnetic field. Finally, for perpendicular electromagnetic electron waves, the perturbed electric field can be parallel or perpendicular to the stationary magnetic field.

Summary of elementary plasma waves
EM character oscillating species conditions dispersion relation name
electrostatic electrons ${\vec {B}}_{0}=0\ {\rm {or}}\ {\vec {k}}\|{\vec {B}}_{0}$ $\omega ^{2}=\omega _{p}^{2}+3k^{2}v_{th}^{2}$ plasma oscillation (or Langmuir wave)
${\vec {k}}\perp {\vec {B}}_{0}$ $\omega ^{2}=\omega _{p}^{2}+\omega _{c}^{2}=\omega _{h}^{2}$ upper hybrid oscillation
ions ${\vec {B}}_{0}=0\ {\rm {or}}\ {\vec {k}}\|{\vec {B}}_{0}$ $\omega ^{2}=k^{2}v_{s}^{2}=k^{2}{\frac {\gamma _{e}KT_{e}+\gamma _{i}KT_{i}}{M}}$ ion acoustic wave
${\vec {k}}\perp {\vec {B}}_{0}$ (nearly) $\omega ^{2}=\Omega _{c}^{2}+k^{2}v_{s}^{2}$ electrostatic ion cyclotron wave
${\vec {k}}\perp {\vec {B}}_{0}$ (exactly) $\omega ^{2}=[(\Omega _{c}\omega _{c})^{-1}+\omega _{i}^{-2}]^{-1}$ lower hybrid oscillation
electromagnetic electrons ${\vec {B}}_{0}=0$ $\omega ^{2}=\omega _{p}^{2}+k^{2}c^{2}$ light wave
${\vec {k}}\perp {\vec {B}}_{0},\ {\vec {E}}_{1}\|{\vec {B}}_{0}$ ${\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}$ O wave
${\vec {k}}\perp {\vec {B}}_{0},\ {\vec {E}}_{1}\perp {\vec {B}}_{0}$ ${\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}}{\omega ^{2}}}\,{\frac {\omega ^{2}-\omega _{p}^{2}}{\omega ^{2}-\omega _{h}^{2}}}$ X wave
${\vec {k}}\|{\vec {B}}_{0}$ (right circ. pol.) ${\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}/\omega ^{2}}{1-(\omega _{c}/\omega )}}$ R wave (whistler mode)
${\vec {k}}\|{\vec {B}}_{0}$ (left circ. pol.) ${\frac {c^{2}k^{2}}{\omega ^{2}}}=1-{\frac {\omega _{p}^{2}/\omega ^{2}}{1+(\omega _{c}/\omega )}}$ L wave
ions ${\vec {B}}_{0}=0$ none
${\vec {k}}\|{\vec {B}}_{0}$ $\omega ^{2}=k^{2}v_{A}^{2}$ Alfvén wave
${\vec {k}}\perp {\vec {B}}_{0}$ ${\frac {\omega ^{2}}{k^{2}}}=c^{2}\,{\frac {v_{s}^{2}+v_{A}^{2}}{c^{2}+v_{A}^{2}}}$ magnetosonic wave

$\omega$ - wave frequency, $k$ - wave number, $c$ - speed of light, $\omega _{p}$ - plasma frequency, $\omega _{i}$ - ion plasma frequency, $\omega _{c}$ - electron gyrofrequency, $\Omega _{c}$ - proton gyrofrequency, $\omega _{h}$ - upper hybrid frequency, $v_{s}$ - plasma "sound" speed, $v_{A}$ - plasma Alfven speed

## Hypotheses

1. Ions are as easy to create in a polar liquid like water as they are in a polar medium like the interplanetary medium.