Plasma (physics)

For other uses, see Plasma.

Plasma (from Greek , anything formed[1]) isone of the four fundamental states of matter, the oth-ers being solid, liquid, and gas. A plasma has propertieswhich are unlike those of the other states.A plasma can be created by heating a gas or subjectingit to a strong electromagnetic eld applied with a laseror microwave generator. This reduces or increases thenumber of electrons, creating positive or negative chargedparticles called ions,[2] and is accompanied by the disso-ciation of molecular bonds, if present.[3]

The presence of a non-negligible number of charge car-riers makes the plasma electrically conductive so that itresponds strongly to electromagnetic elds. Like gas,plasma does not have a denite shape or a denite vol-ume unless enclosed in a container; unlike gas, under theinuence of a magnetic eld, it may form structures suchas laments, beams and double layers.Plasma is the most abundant form of ordinary matter inthe Universe, most of which is in the rareed intergalacticregions, particularly the intracluster medium, and in stars,including the Sun.[4][5] A common form of plasmas onEarth is seen in neon signs.Much of the understanding of plasmas has come from thepursuit of controlled nuclear fusion and fusion power, forwhich plasma physics provides the scientic basis.

1 Properties and parameters

1.1 Denition

Plasma is loosely described as an electrically neutralmedium of positive and negative particles (i.e. the over-all charge of a plasma is roughly zero). It is importantto note that although they are unbound, these particlesare not free in the sense of not experiencing forces.When the charges move, they generate electrical currentswith magnetic elds, and as a result, they are aected byeach others elds. This governs their collective behav-ior with many degrees of freedom.[3][7] A denition canhave three criteria:[8][9]

1. The plasma approximation: Charged particlesmust be close enough together that each particleinuences many nearby charged particles, rather

Artists rendition of the Earths plasma fountain, showing oxygen,helium, and hydrogen ions that gush into space from regions nearthe Earths poles. The faint yellow area shown above the northpole represents gas lost from Earth into space; the green area isthe aurora borealis, where plasma energy pours back into theatmosphere.[6]

than just interacting with the closest particle (thesecollective eects are a distinguishing feature of aplasma). The plasma approximation is valid whenthe number of charge carriers within the sphere ofinuence (called the Debye sphere whose radius isthe Debye screening length) of a particular particleis higher than unity to provide collective behavior ofthe charged particles. The average number of parti-cles in the Debye sphere is given by the plasma pa-rameter, "" (the Greek letter Lambda).

2. Bulk interactions: The Debye screening length(dened above) is short compared to the physicalsize of the plasma. This criterion means that inter-actions in the bulk of the plasma are more impor-tant than those at its edges, where boundary eectsmay take place. When this criterion is satised, theplasma is quasineutral.

3. Plasma frequency: The electron plasma frequency

1

2 1 PROPERTIES AND PARAMETERS

(measuring plasma oscillations of the electrons) islarge compared to the electron-neutral collision fre-quency (measuring frequency of collisions betweenelectrons and neutral particles). When this conditionis valid, electrostatic interactions dominate over theprocesses of ordinary gas kinetics.

1.2 Ranges of parameters

Plasma parameters can take on values varying by manyorders of magnitude, but the properties of plasmas withapparently disparate parameters may be very similar (seeplasma scaling). The following chart considers only con-ventional atomic plasmas and not exotic phenomena likequark gluon plasmas:

10-2 10-1 100 101 102 103 104 105 eV10-5

100

105

1010

1020

1025

1015

ELEC

TRO

N D

ENSI

TYEl

ectr

ons

per

cubi

c ce

ntim

etre

RANGES OF PLASMAS

TEMPERATURE102 103 104 105 106 107 108 109 K

Photosphere

Flames

Metals

Magnetosphere

Solar wind

Ionosphere

Interstellar

Interplanetary

Galactic

Solar corona

Chromosphere

LasersCentre of Sun

Fusion

e-/cm3

Range of plasmas. Density increases upwards, temperature in-creases towards the right. The free electrons in a metal may beconsidered an electron plasma.[10]

1.3 Degree of ionization

For plasma to exist, ionization is necessary. The termplasma density by itself usually refers to the electrondensity, that is, the number of free electrons per unitvolume. The degree of ionization of a plasma is the pro-portion of atoms that have lost or gained electrons, andis controlled mostly by the temperature. Even a par-tially ionized gas in which as little as 1% of the parti-cles are ionized can have the characteristics of a plasma(i.e., response to magnetic elds and high electrical con-ductivity). The degree of ionization, , is dened as = nini+nn , where ni is the number density of ions andnn is the number density of neutral atoms. The electrondensity is related to this by the average charge state hZiof the ions through ne = hZini , where ne is the numberdensity of electrons.

1.4 TemperaturesSee also: Nonthermal plasma

Plasma temperature is commonly measured in Kelvins orelectronvolts and is, informally, a measure of the ther-mal kinetic energy per particle. Very high temperaturesare usually needed to sustain ionization, which is a den-ing feature of a plasma. The degree of plasma ioniza-tion is determined by the electron temperature relativeto the ionization energy (and more weakly by the den-sity), in a relationship called the Saha equation. At lowtemperatures, ions and electrons tend to recombine intobound statesatoms[12]and the plasma will eventuallybecome a gas.In most cases the electrons are close enough to thermalequilibrium that their temperature is relatively well-dened, even when there is a signicant deviation froma Maxwellian energy distribution function, for example,due to UV radiation, energetic particles, or strong electricelds. Because of the large dierence in mass, theelectrons come to thermodynamic equilibrium amongstthemselves much faster than they come into equilibriumwith the ions or neutral atoms. For this reason, the iontemperature may be very dierent from (usually lowerthan) the "electron temperature". This is especially com-mon in weakly ionized technological plasmas, where theions are often near the ambient temperature.

1.4.1 Thermal vs. non-thermal plasmas

Based on the relative temperatures of the electrons, ionsand neutrals, plasmas are classied as thermal or non-thermal. Thermal plasmas have electrons and the heavyparticles at the same temperature, i.e., they are in ther-mal equilibrium with each other. Non-thermal plas-mas on the other hand have the ions and neutrals at amuch lower temperature (sometimes room temperature),whereas electrons are much hotter ( Te Tn ).A plasma is sometimes referred to as being hot if it isnearly fully ionized, or cold if only a small fraction (forexample 1%) of the gas molecules are ionized, but otherdenitions of the terms hot plasma and cold plasmaare common. Even in a cold plasma, the electron tem-perature is still typically several thousand degrees Celsius.Plasmas utilized in plasma technology (technologicalplasmas) are usually cold plasmas in the sense that onlya small fraction of the gas molecules are ionized.

1.5 Plasma PotentialSince plasmas are very good electrical conductors, elec-tric potentials play an important role. The potential as itexists on average in the space between charged particles,independent of the question of how it can be measured,is called the plasma potential, or the space potential.

1.6 Magnetization 3

Lightning is an example of plasma present at Earths surface.Typically, lightning discharges 30,000 amperes at up to 100 mil-lion volts, and emits light, radio waves, X-rays and even gammarays.[13] Plasma temperatures in lightning can approach 28,000Kelvin (27,726.85 C) (49,940.33 F) and electron densities mayexceed 1024 m3.

If an electrode is inserted into a plasma, its potential willgenerally lie considerably below the plasma potential dueto what is termed a Debye sheath. The good electricalconductivity of plasmas makes their electric elds verysmall. This results in the important concept of quasineu-trality, which says the density of negative charges is ap-proximately equal to the density of positive charges overlarge volumes of the plasma ( ne = hZini ), but onthe scale of the Debye length there can be charge imbal-ance. In the special case that double layers are formed, thecharge separation can extend some tens of Debye lengths.The magnitude of the potentials and electric elds mustbe determined by means other than simply nding the netcharge density. A common example is to assume that theelectrons satisfy the Boltzmann relation:

ne / ee/kBTe :

Dierentiating this relation provides a means to calculatethe electric eld from the density:

~E = (kBTe/e)(rne/ne):

It is possible to produce a plasma that is not quasineutral.An electron beam, for example, has only negative charges.The density of a non-neutral plasma must generally bevery low, or it must be very small, otherwise it will bedissipated by the repulsive electrostatic force.In astrophysical plasmas, Debye screening preventselectric elds from directly aecting the plasma overlarge distances, i.e., greater than the Debye length. How-ever, the existence of charged particles causes the plasmato generate, and be aected by, magnetic elds. Thiscan and does cause extremely complex behavior, suchas the generation of plasma double layers, an object thatseparates charge over a few tens of Debye lengths. Thedynamics of plasmas interacting with external and self-generated magnetic elds are studied in the academic dis-cipline of magnetohydrodynamics.

1.6 Magnetization

Plasma with a magnetic eld strong enough to inuencethe motion of the charged particles is said to be magne-tized. A common quantitative criterion is that a parti-cle on average completes at least one gyration around themagnetic eld before making a collision, i.e., !ce/vcoll >1 , where !ce is the electron gyrofrequency and vcoll isthe electron collision rate. It is often the case that theelectrons are magnetized while the ions are not. Mag-netized plasmas are anisotropic, meaning that their prop-erties in the direction parallel to the magnetic eld aredierent from those perpendicular to it. While electricelds in plasmas are usually small due to the high conduc-tivity, the electric eld associated with a plasma movingin a magnetic eld is given by E = v B (where E isthe electric eld, v is the velocity, and B is the magneticeld), and is not aected by Debye shielding.[14]

1.7 Comparison of plasma and gas phases

Plasma is often called the fourth state of matter aftersolid, liquids and gases.[15][16] It is distinct from these andother lower-energy states of matter. Although it is closelyrelated to the gas phase in that it also has no denite formor volume, it diers in a number of ways, including thefollowing:

2 Common plasmasFurther information: Astrophysical plasma, Interstellarmedium and Intergalactic space

4 3 COMPLEX PLASMA PHENOMENA

Plasmas are by far the most common phase of ordinarymatter in the universe, both by mass and by volume.[18]Essentially, all of the visible light from space comes fromstars, which are plasmas with a temperature such that theyradiate strongly at visible wavelengths. Most of the or-dinary (or baryonic) matter in the universe, however, isfound in the intergalactic medium, which is also a plasma,but much hotter, so that it radiates primarily as X-rays.In 1937, Hannes Alfvn argued that if plasma pervadedthe universe, it could then carry electric currents capableof generating a galactic magnetic eld.[19] After winningthe Nobel Prize, he emphasized that:

In order to understand the phenomena ina certain plasma region, it is necessary to mapnot only the magnetic but also the electric eldand the electric currents. Space is lled witha network of currents which transfer energyand momentum over large or very large dis-tances. The currents often pinch to lamen-tary or surface currents. The latter are likely togive space, as also interstellar and intergalacticspace, a cellular structure.[20]

By contrast the current scientic consensus is that about96% of the total energy density in the universe is notplasma or any other form of ordinary matter, but a com-bination of cold dark matter and dark energy. Our Sun,and all stars, are made of plasma, much of interstellarspace is lled with a plasma, albeit a very sparse one, andintergalactic space too. Even black holes, which are notdirectly visible, are thought to be fuelled by accreting ion-ising matter (i.e. plasma),[21] and they are associated withastrophysical jets of luminous ejected plasma,[22] such asM87s jet that extends 5,000 light-years.[23]

In our solar system, interplanetary space is lled with theplasma of the SolarWind that extends from the Sun out tothe heliopause. However, the density of ordinary matteris much higher than average and much higher than thatof either dark matter or dark energy. The planet Jupiteraccounts for most of the non-plasma, only about 0.1% ofthe mass and 1015% of the volume within the orbit ofPluto.Dust and small grains within a plasma will also pick upa net negative charge, so that they in turn may act likea very heavy negative ion component of the plasma (seedusty plasmas).

3 Complex plasma phenomenaAlthough the underlying equations governing plasmas arerelatively simple, plasma behavior is extraordinarily var-ied and subtle: the emergence of unexpected behaviorfrom a simple model is a typical feature of a complexsystem. Such systems lie in some sense on the boundary

between ordered and disordered behavior and cannot typ-ically be described either by simple, smooth, mathemat-ical functions, or by pure randomness. The spontaneousformation of interesting spatial features on a wide rangeof length scales is one manifestation of plasma complex-ity. The features are interesting, for example, becausethey are very sharp, spatially intermittent (the distancebetween features is much larger than the features them-selves), or have a fractal form. Many of these featureswere rst studied in the laboratory, and have subsequentlybeen recognized throughout the universe. Examples ofcomplexity and complex structures in plasmas include:

3.1 Filamentation

Striations or string-like structures,[27] also known asbirkeland currents, are seen in many plasmas, likethe plasma ball, the aurora,[28] lightning,[29] electricarcs, solar ares,[30] and supernova remnants.[31] Theyare sometimes associated with larger current densities,and the interaction with the magnetic eld can forma magnetic rope structure.[32] High power microwavebreakdown at atmospheric pressure also leads to the for-mation of lamentary structures.[33] (See also Plasmapinch)Filamentation also refers to the self-focusing of a highpower laser pulse. At high powers, the nonlinear part ofthe index of refraction becomes important and causes ahigher index of refraction in the center of the laser beam,where the laser is brighter than at the edges, causing afeedback that focuses the laser even more. The tighterfocused laser has a higher peak brightness (irradiance)that forms a plasma. The plasma has an index of refrac-tion lower than one, and causes a defocusing of the laserbeam. The interplay of the focusing index of refraction,and the defocusing plasma makes the formation of a longlament of plasma that can be micrometers to kilometersin length.[34] One interesting aspect of the lamentationgenerated plasma is the relatively low ion density due todefocusing eects of the ionized electrons.[35] (See alsoFilament propagation)

3.2 Shocks or double layers

Plasma properties change rapidly (within a few Debyelengths) across a two-dimensional sheet in the presenceof a (moving) shock or (stationary) double layer. Doublelayers involve localized charge separation, which causesa large potential dierence across the layer, but does notgenerate an electric eld outside the layer. Double layersseparate adjacent plasma regions with dierent physicalcharacteristics, and are often found in current carryingplasmas. They accelerate both ions and electrons.

3.7 Non-neutral plasma 5

3.3 Electric elds and circuits

Quasineutrality of a plasma requires that plasma currentsclose on themselves in electric circuits. Such circuits fol-low Kirchhos circuit laws and possess a resistance andinductance. These circuits must generally be treated as astrongly coupled system, with the behavior in each plasmaregion dependent on the entire circuit. It is this strongcoupling between system elements, together with non-linearity, which may lead to complex behavior. Elec-trical circuits in plasmas store inductive (magnetic) en-ergy, and should the circuit be disrupted, for example,by a plasma instability, the inductive energy will be re-leased as plasma heating and acceleration. This is acommon explanation for the heating that takes place inthe solar corona. Electric currents, and in particular,magnetic-eld-aligned electric currents (which are some-times generically referred to as "Birkeland currents"), arealso observed in the Earths aurora, and in plasma la-ments.

3.4 Cellular structure

Narrow sheets with sharp gradients may separate regionswith dierent properties such as magnetization, densityand temperature, resulting in cell-like regions. Examplesinclude the magnetosphere, heliosphere, and heliosphericcurrent sheet. Hannes Alfvn wrote: From the cos-mological point of view, the most important new spaceresearch discovery is probably the cellular structure ofspace. As has been seen in every region of space ac-cessible to in situ measurements, there are a number of'cell walls, sheets of electric currents, which divide spaceinto compartments with dierent magnetization, temper-ature, density, etc.[36]

3.5 Critical ionization velocity

The critical ionization velocity is the relative velocity be-tween an ionized plasma and a neutral gas, above which arunaway ionization process takes place. The critical ion-ization process is a quite general mechanism for the con-version of the kinetic energy of a rapidly streaming gasinto ionization and plasma thermal energy. Critical phe-nomena in general are typical of complex systems, andmay lead to sharp spatial or temporal features.

3.6 Ultracold plasma

Ultracold plasmas are created in a magneto-optical trap(MOT) by trapping and cooling neutral atoms, to temper-atures of 1 mK or lower, and then using another laser toionize the atoms by giving each of the outermost electronsjust enough energy to escape the electrical attraction ofits parent ion.

One advantage of ultracold plasmas are their well charac-terized and tunable initial conditions, including their sizeand electron temperature. By adjusting the wavelengthof the ionizing laser, the kinetic energy of the liberatedelectrons can be tuned as low as 0.1 K, a limit set by thefrequency bandwidth of the laser pulse. The ions inheritthe millikelvin temperatures of the neutral atoms, but arequickly heated through a process known as disorder in-duced heating (DIH). This type of non-equilibrium ul-tracold plasma evolves rapidly, and displays many otherinteresting phenomena.[37]

One of the metastable states of a strongly nonideal plasmais Rydberg matter, which forms upon condensation of ex-cited atoms.

3.7 Non-neutral plasma

The strength and range of the electric force and the goodconductivity of plasmas usually ensure that the densitiesof positive and negative charges in any sizeable regionare equal (quasineutrality). A plasma with a signicantexcess of charge density, or, in the extreme case, is com-posed of a single species, is called a non-neutral plasma.In such a plasma, electric elds play a dominant role. Ex-amples are charged particle beams, an electron cloud in aPenning trap and positron plasmas.[38]

3.8 Dusty plasma and grain plasma

A dusty plasma contains tiny charged particles of dust(typically found in space). The dust particles acquire highcharges and interact with each other. A plasma that con-tains larger particles is called grain plasma. Under labo-ratory conditions, dusty plasmas are also called complexplasmas.[39]

3.9 Impermeable plasma

Impermeable plasma is a type of thermal plasma whichacts like an impermeable solid with respect to gas or coldplasma and can be physically pushed. Interaction of coldgas and thermal plasma was briey studied by a groupled by Hannes Alfvn in 1960s and 1970s for its possibleapplications in insulation of fusion plasma from the reac-tor walls.[40] However later it was found that the externalmagnetic elds in this conguration could induce kink in-stabilities in the plasma and subsequently lead to an unex-pectedly high heat loss to the walls.[41] In 2013, a group ofmaterials scientists reported that they have successfullygenerated stable impermeable plasma with no magneticconnement using only an ultrahigh-pressure blanket ofcold gas. While spectroscopic data on the characteristicsof plasma were claimed to be dicult to obtain due to thehigh-pressure, the passive eect of plasma on synthesisof dierent nanostructures clearly suggested the eective

6 5 ARTIFICIAL PLASMAS

connement. They also showed that uponmaintaining theimpermeability for a few tens of seconds, screening ofions at the plasma-gas interface could give rise to a strongsecondary mode of heating (known as viscous heating)leading to dierent kinetics of reactions and formationof complex nanomaterials.[42]

4 Mathematical descriptions

The complex self-constricting magnetic eld lines and currentpaths in a eld-aligned Birkeland current that can develop in aplasma.[43]

Main article: Plasma modeling

To completely describe the state of a plasma, we wouldneed to write down all the particle locations and veloci-ties and describe the electromagnetic eld in the plasmaregion. However, it is generally not practical or neces-sary to keep track of all the particles in a plasma. There-fore, plasma physicists commonly use less detailed de-scriptions, of which there are two main types:

4.1 Fluid modelFluid models describe plasmas in terms of smoothedquantities, like density and averaged velocity around eachposition (see Plasma parameters). One simple uidmodel, magnetohydrodynamics, treats the plasma as asingle uid governed by a combination of Maxwellsequations and the NavierStokes equations. A more gen-eral description is the two-uid plasma picture, where theions and electrons are described separately. Fluid mod-els are often accurate when collisionality is sucientlyhigh to keep the plasma velocity distribution close to aMaxwellBoltzmann distribution. Because uid modelsusually describe the plasma in terms of a single ow ata certain temperature at each spatial location, they canneither capture velocity space structures like beams ordouble layers, nor resolve wave-particle eects.

4.2 Kinetic modelKinetic models describe the particle velocity distributionfunction at each point in the plasma and therefore do notneed to assume aMaxwellBoltzmann distribution. A ki-netic description is often necessary for collisionless plas-mas. There are two common approaches to kinetic de-scription of a plasma. One is based on representing thesmoothed distribution function on a grid in velocity andposition. The other, known as the particle-in-cell (PIC)technique, includes kinetic information by following thetrajectories of a large number of individual particles. Ki-netic models are generally more computationally inten-sive than uid models. The Vlasov equation may be usedto describe the dynamics of a system of charged particlesinteracting with an electromagnetic eld. In magnetizedplasmas, a gyrokinetic approach can substantially reducethe computational expense of a fully kinetic simulation.

5 Articial plasmasMost articial plasmas are generated by the applicationof electric and/or magnetic elds. Plasma generated in alaboratory setting and for industrial use can be generallycategorized by:

The type of power source used to generate theplasmaDC, RF and microwave

The pressure they operate atvacuum pressure (