[] Encyclopedia of Physical Science and Technology

8/12/2019 [] Encyclopedia of Physical Science and Technology

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Space Plasma PhysLarry LyonsUniversity of California, Los Angeles

I. IntroductionII. Basic Concepts

III. Solar Wind and Interplanetary Magnetic FieldIV. Solar Windand Interplanetary Field Interactions

with the Geomagnetic FieldV. Particle Access to, and Transport within,

the MagnetosphereVI. Auroras and Auroral Currents

VII. Geomagnetic DisturbancesVIII. Conclusions

GLOSSARY

Aurora Emissions from the upper atmosphere by con-stituents that have been excited by the impact of ener-getic particles from the magnetosphere.

Auroral oval The prime region of visible auroral emis-sions, which consists of approximately circular zonessurrounding each geomagnetic pole that are a few de-grees in latitude wide and centered near 70 geomag-netic latitude.

Convection Flow of plasma throughout the magneto-sphere that is driven by the solar wind.

Geomagneticlatitude Latitudebased on theearths mag-netic axis.

Gyroradius Radiusof thecircularmotion of charged par-ticles about a magnetic eld.

Interplanetary magnetic eld Magnetic eld from the

sun that is carried throughout interplanetary space bythe solar wind.

Ionosphere Region of enhanced ionization that sur-rounds the earth at altitudes between 75 and 500 kmaltitude.

Magnetopause Current layer that to a large extent sep-arates the interplanetary magnetic eld from the geo-magnetic eld.

Magnetosphere Region of space within the magne-topause that is dominated by the geomagnetic eld.

Plasma An ionized gas in which electric forces main-tain approximate charge neutrality (the excess of neg-atively or positively charged particles is everywheremuch smaller than the total ion density).

Plasma sheet Energetic plasma region that occupies theouter portions of the magnetosphere.

Precipitation Loss of magnetospheric particles to the

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578 Space Plasma Physics

atmosphere by collisions at the low-altitude ends of magnetic eld lines.

Radiation belts Region of high uxes of very energeticelectrons and ions that encircles the earth in the innerportion of the magnetosphere.

Solar wind Plasma that ows outward from the sun andlls interplanetary space.

SPACE PLASMA PHYSICS is the study of the plas-mas that originate from the sun and from the planets andmoons within the solar system. These plasmas occupyinterplanetary space and the magnetospheres of planets.This article gives an overall description of the plasma pro-cesses which control the large-scale structure and dynam-ics of the near-earth space plasma environment. This in-cludes the formation of the solar wind and interplanetaryplasma disturbances. It also includes the interaction of thesolar wind plasma and magnetic eld with the magneticeld of the earth and how this interaction leads to the in-teresting and dynamic space plasma environment whichexists in the vicinity of the earth. Topics include energytransfer to and within the earth s magnetosphere, forma-tion of magnetospheric structure, and disturbances of themagnetosphere ionosphere system which constitute what

Open-closedfield boundary

Magnetopausecurrent sheet

B

Cross-tail current sheet

Auroral zone( ~ 63-73 )

Plasma sheet

Radiation beltsand ringcurrent

Lobe

Lobe

V

E

E

E

VV

~5 R E

~5-12 R E

V

E

Plasmasheet

Bow shock

~10 R E

~ 4 0 R

E

Radiation beltsand ringcurrent

FIGURE 1 Schematic illustration of the magnetosphere in the noonmidnight meridian plane.

has recently been termed space weather. Space plasmaphysics also includes the interaction of the solar plasmawith other planets, the mixing of solar and planetary plas-mas, and a wide range of wave modes associated withplasma oscillations in space.

I. INTRODUCTION

The sun continuously emits a stream of ionized particles,which is referred to as the solar wind and is the primarycomponent of the plasma which lls interplanetary space.The average speed of this stream in the ecliptic plane is

400 km/sec, so that it takes about 4 days for particles toreach the earth. Solar wind speeds, however, can be quitevariable. Theytypically range from 300to 800 km/sec,with speeds exceeding 1000 km/sec being occasionallyobserved. The earth s internal magnetic eld is approx-imately that of a dipole. However, the interaction of thesolar wind particles with the earth s magnetic eld com-presses the earth s eld on the dayside and draws the eldout into a long tail on the nightside. This interaction alsoconnes most of the magnetic eld of the earth to a re-gion referred to as the magnetosphere (see Fig. 1 , whichis a sketch of the magnetosphere in the noon midnight


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Space Plasma Physics 579

meridian plane). The outer boundary of the magneto-sphere is called the magnetopause, which typically lies

10 RE (earth radii) above the noon equator and 15 REawayfrom theearth withinthe dawn duskmeridianplane.On the nightside, the magnetosphere ares outward withincreasing distance away from the earth, eventually be-coming approximately cylindrical with a diameter of 4050 RE. Solar wind speeds are supersonic, so that ashock (called the bow shock ) lies several RE upstreamof the dayside magnetopause.

Plasma particles move in circles around magnetic eldlines and thus can become trapped within the magneto-sphere. Major regions of trapped energeticparticles withinthe magnetosphere are the plasma sheet and the radia-tion belts. As illustrated in Fig. 1 , the plasma sheet onthe nightside is displaced from the high-latitude magne-topause by what arereferred to as thetaillobesand extendsalong the entire magnetospheric tail inward to an equato-rial radial distance from the center of the earth r 512 RE. The plasma sheet also extends around the earth toother local times and has an outer boundary that lies adja-cent to the magnetopause on the dayside. Typical energiesof plasma sheet particles are 150 keV for ions and

0.210 keV forelectrons. Earthward of theplasma sheetlies a population of more energetic electrons and ionswhich encircle the earth and are referred to as the ra-diation belts. These particles form a current encirclingthe earth which is referred to as the ring current.

Particles from themagnetosphere can move along mag-netic eld lines and strike the upper atmosphere. Thosethat reach an altitude of 100200 km undergo colli-sions with the neutral atmosphere resulting in a loss of

their energy to the neutral atmosphere and their loss fromthemagnetosphere. Suchlossofenergetic magnetosphericparticles is referred to as precipitation. The energy fromprecipitating particles excites constituents of the upperatmosphere, and the relaxation of the upper atmosphericconstituentsback to their groundstate givesoff emissions,which when suf ciently intense are referred to as the au-rora. Such precipitation is most intense from the plasmasheet, leading to an approximately circular region of emis-sions surrounding each magnetic pole that is referred toas the auroral oval. The oval is typically a few to severaldegrees in latitude wide and is centered near 70 geomag-netic latitude.

II. BASIC CONCEPTS

Space plasma physics often requires that dynamics be an-alyzed in terms of both the motion of individual particleandin terms of macroscopic moments such as temperatureT , density n , and pressure P . Individual particle motion

FIGURE 2 The motion of electrons and positive ions in uniformand constant electric and magnetic elds.

is based on considering the force F = q (E + v B) actingon a particle of charge q , mass m , and moving with a ve-locity v in an electric eld E and magnetic eld B. Particlemotion is generally separated into components v parallelto B and v perpendicular to B. With E = 0 and a uniform,time-independent magnetic eld, v is a constant and v iscircular motion about B with a frequency | q B / m | , whichis referred to as the gyrofrequency, and radius mv / |q B | ,

which is referred to as the gyroradius. The direction of gy-ration is right (left)-handed with respect to the directionof B for electrons (positive ions) as illustrated in Fig. 2 .Except very near current sheets, particle gyroradii are gen-erally very much less than the scale length for eld andplasma variations in space plasmas. Also, particle gyrope-riods are generally very much less than space plasma timescales for transport and for changes in plasma and eldproperties.

Figure 2 shows the motion of electrons and positiveions in uniform and constant electric and magnetic elds.The acceleration by the perpendicular component of theelectric eld E alternatively increases and decreases the

particle gyroradius once each gyration, so that, in additionto the gyromotion about B , particles move with an aver-age velocity V E = (E B)/ B2, which isreferred to astheelectric eld drift speed. This relation can be rewritten as

E = V E B. (1)

When | V E | | v| , as is the case throughout most of space,we can separate the particle motion into its gyration aboutB anda drift of thegyratingparticlewith velocity V E .Anyelectric eld parallel to B simply gives constant particleacceleration along B .

As shown in Fig. 2 , electric elds perpendicular to B

cause all charged particles to drift with the same veloc-ity, which does not lead to currents. Spatial variations inmagnetic eld also give particle drifts. However, the driftsfrom magnetic eld variations are oppositely directed fornegatively and positively charged particles, so that a cur-rent is formed. This current is azimuthal in the region of the radiation belts, giving rise to the ring current in thisregion. Such a current also ows within the tail plasma


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sheet and is directed across the tail from the dawn side tothe dusk side.

The current formed by an individual charged parti-cle gyrating about B can be represented as a magneticdipole with magnetic moment = K / B , where the per-pendicular energy K = (mv2 )/ 2. As long as magneticeld changes experienced by a particle are small duringthe course of one gyration about the magnetic eld, isconserved for particles undergoing electric and magneticdrifts perpendicular to B and motion parallel to B. This isimportant because itgenerallymeans thatparticleenergiesincrease (decrease) when particles undergo a drift acrossmagnetic eld lines into regions of increasing (decreas-ing) B . On the other hand, motion along magnetic eldlines results in a conversion of parallel energy to (from)perpendicular energy as B increases (decreases) with thetotal particle energy being conserved.

When we think of the plasma as whole, we deal withmacroscopic variables thatare de nedperunit volume.Weconsider the forces acting on the plasma per unit volume,which we write as

d V/ dt = P + J B, (2)

where is the total plasma mass per unit volume, V isthe mass-averaged velocity for all particles within a unitvolume, P is theplasma pressure, and J is thecurrent den-sity (current per unit area normal to the current). Equation(2) assumes charge neutrality (essentially equal numbersof positive and negative charges), an assumption which isnearly always valid for space plasmas, and neglects grav-ity, an assumption which is valid for most space plasmas(neglect of gravity is not valid, for example, near the sun).

When plasma and eld changes are small in the direc-tion of B, (2) can be rewritten using the Maxwell equation

J = B/ 0 0E / t (3)

to obtain

d V/ dt = (P + B2/ 2 0). (4)

Here the constants are 0 = 4 10 7 H/m and 0 =8.85 10 12 F/m, and the term 0E / t in (3) was ne-glected in (4) because it is small for the large-scale phe-nomena discussed here. Assuming steady state and nochanges in the direction of V , we obtain for (4)

P + B2/ 2 0 = const . (5)

Equation (5) is referred to as pressure balance and isusually applied to regions, such as the geomagnetic tail,where changes in the direction of B are small. The quan-tity B2 / 2 0 can be thought of as magnetic pressure, sothat (5) states that the total pressure (plasma+ magnetic)is constant. This tells us, for example, that the magneticpressure in the lobes, where plasma pressure is low, is

greater than the magnetic pressure in the plasma sheet,where the plasma pressure is high.

Equation (3), with 0E / t neglected, relates currentsand magnetic eld structure. For example, it tells us that achange in magnetic eld strength B across a plane per-pendicular to B must be associated with a current withinthe plane across which B changes. Such a planar cur-rent is referred to as a current sheet and has a magnitudeper unit distance normal to the current direction of I = B / 0 [A/m]. For the magnetospheric tail, this cur-rent is directed in the dawn-to-dusk direction across thetail and is referred to as the cross-tail current sheet (seeFig. 1 ).

III. SOLAR WIND AND INTERPLANETARYMAGNETIC FIELD

The sun is a large ball of gas held together by its owngravity. The gases are about 90% hydrogen and 10% he-lium with minor amounts of other constituents. Due to thehigh temperature of the sun, the solar gases are mostlyionized. The sun appears to have a visible surface becausethesteep radialgradient in solar density gives a sharp tran-sition between lower regions, where photons are absorbedand reemitted by solar gases without traveling very far,and higher regions, where most photons move away fromthe sun along straight trajectories without collisions. So-lar radiation appears to arise from this narrow transitionregion (only a few hundred kilometers thick), which isreferred to as the photosphere.

Solar gases extend outward well beyond the photo-

sphere with very high temperatures, forming the solarcorona. Thesolar coronais suf ciently hotthatmanycoro-nal particles have outward-directed velocities with a mag-nitudethat exceeds thespeedforgravitationalescape fromthe sun. Such particles streamoutward from the sun form-ing the solar wind. The solar wind escapes toward the nearvacuum of interstellar space at supersonic speeds, llingthe entire solar system with coronal plasma.

A. General Structure

If it were not for the solar magnetic eld, the escapingplasma from the solar corona would form an approxi-

mately spherically symmetric solar wind owing radiallyoutward from the sun at 750 km/sec. However, the es-caping plasma is strongly affected by the magnetic eldof the sun because of the tendency for particles to movemore easily along magnetic eld lines than across them.The solar magnetic eld is highly variable, which makesthe solar wind and the magnetic eld it carries with it intointerplanetary space highly variable in space and in time.


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FIGURE 3 Sketch of coronal magnetic eld and plasma structure during solar minimum (upper panel) and solarmaximum (lower panel).

To a rst approximation, the magnetic eld near thevisible solar surface can be regarded as a dipole like thatof the earth. This eld is carried outward into interplane-tary space from the sun by the solar wind, giving a solarmagnetic eld con guration (sketched in a plane perpen-dicular to the ecliptic plane in the upper panel of Fig. 3)which is like a dipole near the sun, but is highly stretchedaway from the sun. At radial distances of more than afew solar radii, the stretched solar magnetic eld reversesdirection across a narrow region near the ecliptic planeforming a current sheet surrounding thesun. In theregionswhere the magnetic eld lines are approximately dipolarand do not extend well away from the sun, plasma accu-mulates giving regions of high-density coronal plasma asillustrated in Fig. 3 . Such regions are clearly visible inimages of the solar corona. For the magnetic eld con-

guration shown in the upper panel of Fig. 3 , a region of high-density corona extends around the sun in the vicinityof the equator. Free escape of plasma only occurs wellwithin the regions where magnetic eld lines extend largedistances into interplanetary space, where the solar windspeed reaches 750 km/sec. Near theboundaries betweentheapproximatelydipolar eldlinesand the eldlinesthatextent out large distances, the solar wind escapes, but with

a loweraveragespeedof 350km/sec. Theearth, which isnear the ecliptic plane, is exposed more often to this slowsolar wind than to the fast solar wind that covers most of the region away from the ecliptic plane.

The magnetic eld and solar wind ow con gurationillustrated in the upper panel of Fig. 3 corresponds to pe-riods when the solar magnetic eld is more dipolar thanat other times. During such periods, which are referredto as solar minima, magnetic and sunspot activity on thesun is low. Solar minima occur every 11 years. After so-lar minimum, the dipolar magnetic eld structure of thesun gradually is destroyed. This process takes a few years,leaving the solar magnetic eld in a much more disorga-nized state, as illustrated in a plane perpendicular to theecliptic plane in the bottom panel of Fig. 3 . Magnetic andsunspot activity on the sun is high during these periods,

which are referred as solar maxima. At solar maximum,localized regions of magnetic eld lines that return to thesolar surface without extending far into space and containhigh coronal densities can occur over almost any portionof thesun. After solarmaximum, thedipole eld ofthe sunreturns with thedirection of the dipole reversed from whatis was during the previous solar minimum. This gives an11-year solar cycle from one solar minimum to the next,


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with the direction of the magnetic eld reversing everycycle. While the solar cycle is 11 years, the total periodfor this magnetic eld variation of the sun is 22 years.

B. Solar Wind Disturbances and Their Relationto Solar Magnetic Structure

Both the dynamic pressure of the solar wind and the inter-planetary magnetic eld (IMF) are important for the inter-action of the solar wind with the earth s magnetosphere,andbothof theseare generallyquite variable. Inaddition toa variety of wave phenomena, there are two types of large-scale disturbancesof thesolarwind plasmathat areknownto have large effects on the magnetosphere. The rst typeis related to the shape of the interplanetary current sheet.Ratherthanbeingpreciselya disc withinthe ecliptic plane,the current sheet is generally tilted somewhat with respectto the ecliptic plane and also has a wavy structure as func-tion of azimuthal angle around the sun. Within azimuthalregions where the tilt and/or wavy structure displaces thecurrent sheet suf ciently far from the ecliptic plane, fastsolar wind can be emitted near the ecliptic plane. Due tothe rotation of the sun (with an 27-day period) locationsnear the ecliptic plane can thus be exposed to periods of slow solar wind followed by fast solar wind. This is illus-trated in the ecliptic plane in the upper panel of Fig. 4 . Inthis plane, the solar rotation also imparts a spiral shapeto magnetic eld lines. Within azimuthal regions wherefast solar wind follows slow wind, the fast solar wind willcatch up with the slow solar wind. The interaction of thefast solar wind with the slow solar wind (referred to asstream streaminteractions ) causesa compression of the

solar wind plasma and magnetic eld within the interfaceregion between the fast and slow streams. Such compres-sionsgive regionsof greatly enhancedsolar winddensitiesand magnetic eldstrengthswhich cansigni cantly affectthe magnetosphere. These stream stream interactions areparticularly important during the period after solar maxi-mum, but before the next solar minimum, when the solardipolar magnetic eld is reforming.

The second large-scale disturbance of the solar windplasma is associated with the localized high coronal den-sity regions that form during solar maximum. These re-gions can become buoyant and break away from the sun,carrying the high-density coronal plasma and associated

magnetic elds radially away from the sun as illustratedin the bottom panel of Fig. 4 . These ejections of coronalmaterial, referred to as coronal mass ejections, can havedramatic affects on the earth s magnetosphere.

As discussed later, the component of the IMF directedparallel to the earth s magnetic dipole (which is directedfrom the northern polar cap to the southern polar cap),rather than the total interplanetary magnetic eld mag-

nitude, is most important for activity within the earth smagnetosphere. This component of the magnetic eld isreferred to as the southward component. Thus the mag-netic eld enhancements associated with stream streaminteractions and coronal mass ejections most strongly af-fect the magnetosphere when the enhanced magnetic eldhappens to be directed southward.

IV. SOLAR WIND AND INTERPLANETARYFIELD INTERACTIONS WITH THEGEOMAGNETIC FIELD

A. The Magnetopause

Thesolar wind canbe generallyviewed as highlyconduct-ing, so that to a rst approximation the interplanetary andgeomagnetic elds do not mix. This requires that the solarwind be diverted around a cavity that has an outer bound-ary which approximately separates the geomagnetic andinterplanetary elds. This boundary is referred as themag-netopause,whichis a current sheet of appropriate intensityto separate the interplanetary and geomagnetic elds.

The location of the magnetopause can be estimated bybalancingthe dynamic pressureof theincomingsolar wind(n swmpV 2sw , where n sw is the solar wind density, mp is theproton mass, and V sw is the solar wind speed) with thepressure of the geomagnetic eld, giving

n swmp V 2sw cos2 = B 2in / 2 0. (6)

This neglects the interplanetary magnetic pressure, whichis generally a reasonable assumption. In (6), Bin is the

magnetic eld just inside the magnetopause, is the an-gle between the solar wind velocity vector and the normalto the magnetopause, and the pressure of the IMF and of themagnetosphericplasma areneglected. Fortypical solarwind parameters ( n sw = 5 106m 3; V sw = 400 km/sec),and a dipole geomagnetic eld, (6) places the noon, equa-torial magnetopause (a location referred to as the noseof the magnetosphere) at a distance r = 10 RE from thecenter of the earth, which agrees very well with its aver-age observed position. [The earth s dipole eld strengthis 3.1 10 5/ r 3 T. However, twice this value is typicallyused for Bin in Eq. (6) in order to include contributionsfrom the magnetopause current.] Equation (6) also shows

that the location of the magnetopause moves further fromthe earth with increasing distance from the nose. This isbecause cos 2 decreases away from the nose so that B inmust also decrease.

If only the earth s dipole eld and the magnetic eldsof the magnetopause current sheet were included, themagnetopause would not extend signi cantly tailward of the earth, and there would not be a magnetospheric tail.


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FIGURE 4 Sketch of two important large-scale disturbances of the solar wind plasma, stream stream interactions(upper panel) and coronal mass ejections (lower panel).

However, the large plasma pressures of the tail plasmasheet form the cross-tail current sheet which is identi edin Fig. 1 , and the magnetic eld of this current allowsthe tail magnetopause to extend up to several hundred RE

away from the earth in the anti-sunward direction.On the dayside, B in varies as r 3. With this variation,Eq. (6) shows that the distance to the dayside magne-topause is proportional to ( n sw)1/ 6 . Solar wind densitiescan be quite variable, and a large solar wind disturbancecan increase n sw to 50 106 m 3. A disturbance of thismagnitude compresses the magnetosphere signi cantly,and brings the nose of the magnetosphere to r < 7 RE,

which is well earthward of its average position. Such anearthward displacement of the magnetopause correspondsto more than a factor of three increase in the magnitude of the magnetopause current. This illustrates one important

way in which the solar wind disturbances mentioned inthe previous section can cause large dynamic changes tothe earth s magnetosphere.

B. Closed and Open Field Lines

The above pressure calculation, with the inclusion of theearth s dipole magnetic eld and of the magnetic elds


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fromthe magnetopause and cross-tail current sheets, givesan accurate description of theshapeof themagnetosphere,which is illustrated in Fig. 1 . Because the calculation as-sumes that the interplanetary and geomagnetic elds donot mix, the calculation gives geomagnetic and interplan-etary magnetic elds that are parallel to the magnetopauseat all locations directly adjacent to the magnetopause.However, this is not strictly valid because the magne-topause current sheet has large, but nite, conductivity,which allows a small portion ( 1020%) of the IMF tocross the magnetopauseand connectwiththe geomagneticeld. Such penetration of the IMF into the magnetosphereconnects the interplanetary and geomagnetic elds and iscritical to magnetospheric dynamics, though it does notsignicantly affect the shape of the magnetosphere.

The connection of the interplanetary and geomagneticelds is illustrated in Fig. 1 f or an IMF that is directed pri-marily southward (i.e., nearly parallel to the earth s mag-netic dipole). The gure shows how the penetration of a small portion of the interplanetary eld into the mag-netosphere modi es the geometry of magnetic eld linesemanating from the polar regions of the earth. Without apenetrating eld, all magnetic eld lines would leave theearth and return to the earth after crossing the equatorialplane. Such eld lines are referred to as closed. With apenetrating eld, closed magnetic eld lines do not extentall the way to the magnetic pole. Instead there is an ap-proximately circular region centered near each magneticpolewhere eldlines cross themagnetopause andenter in-terplanetary space. Such polar-cap eld lines are referredto as open. For the earth, the boundary between openand closed eld lines is at 73 magnetic latitude. Open

eld lines allow for a tapping of energy directly from theowing solar wind plasma, and such energy drives a widevariety of phenomena within the magnetosphere.

C. Mapping of Interplanetary Electric Fieldinto the Magnetosphere

The solar wind ows radially outward from the sun car-rying the IMF with it. In general the magnetic eld is notparallel to the solar wind, so that there is an electric eldin interplanetary space that is related to the solar wind andIMF by

E = Vsw B. (7)

Since particles canmove easily along magnetic eld lines,it is generally appropriate to assume that magnetic eldlines are so highly conducting that there can be no electricelds parallel to the magnetic eld lines. This assump-tion implies that magnetic eld lines are equipotentialsso that the interplanetary electric eld given by (7) mapsalong open polar-cap eld lines through the magneto-

spheredownto theionosphere.(The ionosphere is a regionof ionized upper-atmospheric constituents that surroundsthe earth at altitudes between 75 and 500 km. For thepurposes here, theionosphere is at thelow-altitudeends of the magnetic eld lines shown in Fig. 1 and marks the low-est altitude to which the interplanetary electric eld hassignicant effects.) For the orientation of the IMF shownin Fig. 1 , the mapping of the interplanetary electric eldinto the magnetosphere gives an electric eld through-out the open eld line region of the magnetosphere thatpoints from the dawn side of the magnetosphere towardthe dusk. For other orientations of the IMF, the mappinginto themagnetosphere is similar,but theorientationof theelectric eld can have some differences from that shownin the gure.

Figure 5 shows the mapping of the interplanetary elec-tric eld into the magnetosphere along open eld linesin the dawn dusk meridian plane, where the coordinatesystem used has x directed from the earth to the sun, ydirected from the dawn to the dusk side of the earth, and z directed from the south to the north magnetic pole. Thismapping gives an anti-sunward ow of plasma all alongthe open eld region of the polar caps. At the boundarybetween open and close magnetic eld lines, the mappedinterplanetary electric eld and the anti-sunward ow ter-minate. This boundary thus becomes charged as indicatedin Fig.5, giving anelectric eldthatextendsintothe closedeld line region of the magnetosphere. This electric eldis oriented so as to give sunward ow on closed eld lines.

FIGURE 5 Schematic illustration of the magnetosphere in thedawn dusk meridian plane. Plus and minus signs indicatecharges along the boundary between open and closed magneticeld lines, and shading identi es the region of open, polar-capeld lines.


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FIGURE 6 Electric elds and plasma ows driven by the mapping of the interplanetary electric eld into the magne-tosphere as seen looking down onto the ionosphere from above one of the polar caps.

The total electric eld pattern drives a three-dimen-sional circulation of plasma, which is illustrated in thenoonmidnight meridian plane in Fig. 1 . This ow is re-ferred to as magnetospheric convection. The x componentof the ow is anti-sunward across open, polar-cap eldlines and the ow returns in the sunward direction withinthe closed eld line region. The ow also moves polewardon the dayside and equatorward within the tail, complet-

ing the convective circulation. This magnetospheric con-vection pattern is often viewed by looking at the electriceld, or equivalently the plasma ow, since the two arerelated by Eq. (1), as mapped to the ionosphere. Such amapping, illustrated in Fig. 6 , gives a complete picture of magnetospheric convection because magnetic eld linesare approximately equipotentials. Figure 6 shows electricelds and plasma ow streamlines as seen looking downonto the ionosphere from above one of the polar caps. Thegure shows how the ow moves in the anti-sunward di-rection over the polar caps, crosses the boundary betweenopen and closed eld lines, and returns to the daysidewithin the closed eld line region.

The strength of magnetospheric electric elds and theresulting convection depends upon the magnitude of theinterplanetary electric eld, which varies with the mag-nitude of the y and z , components of the IMF and withthe solar wind speed. Generally, variations in the IMF aremuch greater than are variations of solar wind speed, sothat variations in the IMF are generally more important inmodifying thestrengthofconvection.The ef ciency of the

mapping of the interplanetary electric eld into the mag-netosphere also depends signi cantly on the orientationof the IMF, the ef ciency increasing as the orientation be-comes increasingly southward (i.e., increasing toward thenegative- z direction). Thus variations in the z componentof the IMF when this component is negative (and thusantiparallel to the equatorial magnetospheric eld) havethe largest effects on the strength of convection, though

variations in the magnitude of the y component are alsoimportant.

V. PARTICLE ACCESS TO, ANDTRANSPORT WITHIN, THEMAGNETOSPHERE

A. Access

Particles within the magnetosphere come from both thesolar wind and the ionosphere. While ionospheric parti-cles make important contributions, the solar wind sourcegenerally dominates throughout most regions of the mag-

netosphere.The entry of solar wind particles and their transport toand within the tail plasma sheet is illustrated in Fig. 7 . Be-cause the geomagnetic and interplanetary magnetic eldsare connected, particles with a nite v are able to owacross the magnetopause. This is most effective acrossthe dayside magnetopause. There some of the solar windparticles, which have been heated after crossing the bow


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particles are able to move closer to the earth before beingdeected around the earth by magnetic drift. This leadsto signi cant temporal variations in the location of theinner edge of the plasma sheet, variations which are veryimportant components of geomagnetic activity. Occasion-ally, when there isa very largenegative- z componentof theIMF, convection becomes so strong that particles convectinto the r 25 RE region of the magnetosphere beforebeing de ected around the earth. Particles that reach thisregion of high magnetic elds gain signi cantly more en-ergy than normally occurs and cause signi cant increasesin particle intensities in the region labeled radiation beltsand ring current in Fig. 1 . When the strength of con-vection reduces back to normal, particles left behind inthe r 25 RE region begin to move in complete circlesaround the earth and become part of the radiation belts.The current carried by these particles as they circle theearth, ions in one direction and electrons in the other, in-creases with the number of energetic particles within thisregion. Periods when this ring current is suf ciently strongare referred to as magnetic storms. The ring current dur-ing storms causes signi cant magnetic eld changes onthe surface of the earth at low and mid-latitudes, and thesechanges are the primary means by which storms are iden-tied and monitored.

Particles also have access to the region of the ring cur-rent during periods of weaker convection as a result of uctuations of the convection electric eld. Resonant in-teractions between these uctuations and the azimuthaldrift of particles around the earth give small perturbationsin the radial position of individual particles. The sum of many of these perturbations can viewed as diffusion in the

radialposition, and the balance between this radial diffu-sion and particle losses (precipitation to the upper atmo-sphere and, forpositive ions,charge exchangewithneutralhydrogen which extends from the upper atmosphere intothe region of the radiation belts) forms a permanent dis-tribution of energetic particles within the radiation belts.The discovery of the radiation belts by James Van Allenand colleagues in 1958 using instrumentation on-boardthe rst two successfully launched U.S. satellites receivedwidespread national and international attention, and theradiation belts became popularly known as the Van Allenradiation belts.

VI. AURORAS AND AURORAL CURRENTS

Most visible auroras are formed by the precipitation of magnetospheric electrons into the atmosphere. Such au-roras can be divided into two general classes. The rstis diffuse auroras, which are formed primarily by the di-rect loss of electrons by precipitation into the atmosphere.

Diffuse auroras tend to be broad in latitudinal extend andto not have strong spatial structure. Such auroras are thusgenerally visually unimpressive. Discrete aurora, on theother hand, result from the precipitation into the atmo-sphere of electrons which have been energized as theymoved toward the ionosphere by electric elds alignedparallel to the magnetic eld. The eld-aligned elec-tric elds responsible for this energization are associatedwith currents owing upward from the ionosphere to themagnetosphere. Discrete auroral displays can be intenseand dynamic and are generally the most dramatic type of aurora.

Discrete auroras occur because the magnetosphericelectric eld driven by the solar wind maps to the iono-sphere, and the ionosphere is a good conductor of current.The relation between E and V given by (1), which wouldnot allow for differential motion between electrons andions within the horizontal plane of the ionosphere, onlyholds in the absence of collisions. In the lower regions of the ionosphere, between about 100 and 150 km in alti-tude, collisions with atmospheric neutral constituents dis-rupt the electric eld drift of ions but do not signi cantlydisrupt the electric eld drift of electrons. As a result,the mapping of magnetospheric electric elds to the iono-sphere gives rise to currents in the horizontal plane of theionosphere. These horizontal currents have componentsparallel and perpendicular to the applied electric eld,which are referred to a Pedersen and Hall currents, re-spectively. Hall currents generally ow along closed pathswithin the ionosphere and are responsible for signi cantmagnetic perturbations on the ground that are observablefrom within the auroral oval and the polar caps. Peder-

sen currents, on the other hand, generally have regionsof strong convergence and divergence. Because of the re-quirement for current continuity, regions of convergence(divergence) of horizontal ionospheric currents are con-nected to currents that ow along magnetic eld linesto (from) the magnetosphere from (to) the ionosphere.These eld-aligned currents are an important aspect of coupling that occurs between the magnetosphere and theionosphere, and they are important for the formation of the auroral arcs.

Large-scale coupling between the magnetosphere andionosphere that leads to signi cant eld-aligned currentsis illustrated by the heavy lled arrows in Fig. 5. The

arrows parallel to the earth s surface indicate ionosphericPedersen currents owing parallel to the direction of theionospheric mapping of the magnetospheric electric eld.These currents converge on the dusk side of the polar capregions of open eld lines and diverge on the dawn sideof these regions. This gives a large-scale eld-alignedcurrent system which is upward on the dusk side anddownward on the dawn side. This current system extends


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along the boundary between open and closed magneticeld lines to all local times, as indicated by the convergingand diverging electric elds along the open closed eldline boundary in Fig. 6 . The eld-aligned currents areupward where the ionospheric electric elds converge andthe open-closed eld line boundary is negatively chargedand downward where the ionospheric electric eldsdiverge and the boundary is positively charged. Anothereld-aligned current system lies near the inner edge of theplasma sheet. This current system is oppositely directedfrom the one near the open closed eld line boundary.There are also a variety of smaller scale eld-alignedcurrents, some of which occur within thenightsideplasmasheet and are an important component of geomagneticactivity.

The eld-aligned electric elds which are responsiblefor discrete auroras occur where the convergence of hori-zontal ionospheric currents gives rise to eld-aligned cur-rents owing upward out of the ionosphere that are toolarge to be carried by the precipitation of electrons thatcause the diffuse aurora. The eld-aligned electric eldsenhance theupward eld-aligned currentby increasing thenumber of downgoing electrons which reach the upper at-mosphere before mirroring. Field-aligned electric eldsare generally less important in regions of downward eld-aligned currents than in regions of upward eld-alignedcurrents because downward currents can readily be car-ried by ionospheric electrons moving from the ionosphereto the magnetosphere. (The ionospheric ion contributionto upward eld-aligned currents is generally not as largebecause the heavy mass of ions limits the rate at whichions can be extracted from the ionosphere.)

Most of the aurora within the auroral oval is dif-fuse aurora. Regions where upward eld-aligned currentswithin the aurora become large enough for the develop-ment of discrete aurora include the large-scale upward-aligned currents that lie on the dusk side of the polarcaps near the boundary between open and closed eldlines. There is nearly always at least some discrete au-roral activity along this boundary. Upward currents alsobecome large enough for the formation of the discrete au-rora within smaller scale regions of the nightside plasmasheet in association with geomagnetic activity. The large-scale eld-aligned current system which lies near theinner edge of the plasma sheet is generally not suf -

ciently intense for the formation of very much discreteaurora.

VII. GEOMAGNETIC DISTURBANCES

Transient enhancements of auroral emissions and iono-spheric currents often occur within the auroral ovals and

are good indicators of geomagnetic activity. These dis-turbances occur along magnetic eld lines that extend tothe plasma sheet, and they are observable at high latitudesvia intense auroral activity and signi cant ground mag-netic eld perturbations associated with enhanced iono-spheric currents. There are different types of such distur-bances, having time scales ranging from a few minutes to1 hr or so, and they occur within the ionospheric exten-sion of the plasma sheet. Magnetic storms are a funda-mentally different phenomenon from these disturbanceswithin the auroral oval. They occur when uxes of ener-getic particleswithin theregion of theradiation beltscausea signi cantly enhanced ring current, leading to magneticeld depressions at the earth s surface at latitudes equa-torward of the auroral oval. Auroral oval disturbancesoften occur during magnetic storms, but they are not di-rectly related to the injection of particles into the radia-tion belts that leads to the formation of the stormtime ringcurrent.

Auroral oval disturbances are related to the energy anddynamics of the plasma sheet, which are highly variableand depend strongly on the solar wind dynamic pressureand the IMF. Solar wind dynamic pressure exerts con-trol by compressing the entire magnetosphere, includingthe tail plasma sheet. The IMF affects the plasma sheetby controlling the strength of convection. The strength of convection strongly affects both the heating of particleswithin the cross-tail current sheet and the earthward pene-tration of the plasma sheet. When convection is enhanced,the inner edge of the plasma sheet moves earthward. Thiscorresponds to an equatorward motion of the equatorwardboundary of theplasma sheet as mappedto theionosphere.

This leads to an increase in the latitudinal width of theionospheric mapping of then plasma sheet, and thus toan increase in the latitudinal width of the auroral oval. Inaddition, signi cant enhancement and earthward penetra-tion of the cross-tail current occurs when convection isenhanced.

Three different types of auroral oval disturbances havebeen identi ed that are related to large-scale distur-bances of the magnetosphere ionosphere system: pole-ward boundary intensi cations (PBIs), substorms, andeffects of solar wind dynamic pressure enhancements re-ferred to here as dynamic pressure disturbances. Each of these types of disturbance has unique characteristics and

reects distinctly different physical processes occurringwithin the magnetosphere. The signatures of each withinthe auroral oval are illustrated in Fig. 8 . In that gure,lightly shaded regions indicate regions of undisturbed au-roral emissions, darkly shaded regions indicate regionswith strong discrete aurora, and regions with mediumshading indicate regions of enhanced diffuseaurora whichmay contain some discrete auroral features.


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FIGURE 8 Illustration of the auroral oval signatures of the three different types of auroral oval disturbance discussedin the text.

A. Poleward Boundary Intensications

The most common type of auroral-zone disturbance is thePBI. PBIs occur repetitively with a period on the order of 10 min. They can occur independently from other typesof disturbances, though their intensity and frequency of occurrence tend to increase with the strength of convec-tion. They have an auroral signature that often can be seento move equatorward from the poleward boundary of theauroral oval, which, on the nightside, lies very near theboundary between open and closed elds. There can beseveralsuch disturbances within the nightsideauroral ovalat one time, disturbances typically occurring from neardusk to 1 2 hr past midnight. They also extend varying

distances through the auroral oval, some staying con nedto very near the polar-cap boundary and others extendingthrough a large portion of the auroral oval and becomingelongated in the north south direction. PBIs are typicallyassociated with ground magnetic perturbations of a fewtens of nanoteslas, but perturbations can be as high as

500 nT during periods of strongly enhanced convection.The time scale for individual intensi cations is typicallya few minutes.

Individual PBIs are longitudinally localized and are as-sociated with longitudinally localized bursts (about a fewminutes in duration) of enhanced plasma ow that are of-tenobserved within the tail plasmasheet. Such ow bursts

transport signi cant mass and energy within the plasmasheet and are thus an important component of the dy-namics of the plasma sheet. The ow bursts extend only asmalldistanceacross thetail.They lead to enhance auroralemissions because they are associated via Eq. (1) with lo-calized enhancements in electric elds across the tail. Themapping of these electric elds to the ionosphere resultsin longitudinally localized regions of enhanced dawn-to-

dusk-directed electric elds, which on their western edge

give rise to converging Pedersen currents. These converg-ing ionospheric currents are connected to upward eld-aligned currents which areoften suf ciently strong to leadto the formation of the discrete auroral forms which areobserved as PBIs. Sometimes individual PBI structuresobserved at low altitudes traverse essentially the entirelatitudinal extent of the plasma sheet, which would cor-respond to ow bursts that extend from the distant tailplasma sheet ( 50100 RE) all the way to the vicinity of synchronous orbit.

B. Substorms

Substorms are a far more dramatic and large-scale, but farless common, disturbance than PBIs. Thesubstorm occur-rence rate is highly variable, but there are typically severalper day. Auroral activity during substorms typically initi-ates within a local time sector of 12 hr near the equa-torward boundary of the nightside auroral oval and thenexpands both poleward and azimuthally. Very intense dis-crete aurora lies along the poleward and westward bound-aries of this expanding region. The poleward expansioncan bring strong aurora well into the region which is nor-mally occupied by the polar cap, forming what is knownas the auroral bulge. The westward-expanding region of strong discrete aurora is referred as the westward travel-

ing surge and can continue for up to 30 min after thesubstormonset. Ground magnetic disturbances associatedwith substorms are typicallya few hundred nanoteslas, butcan range from 50 to 2000 nT.

Substorm onsets are preceded by a 30-min growth-phase period of enhancedconvection thatis typically asso-ciated with a moderate to large southward-directed IMF.The onsets are often associated with the impact on the


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magnetosphere of an IMF change, such as a reductionin the southward component of the IMF, that cause areduction in thestrength of convection. During the growthphase, the plasma sheet moves earthward and particleenergization increases, leading to an increase in the cross-tail current. This increase is particularly strong within theearthward portion of the plasma sheet. In addition to be-ing associated with auroral activity, the expansion phaseis associated with a reduction in strength of the cross-tailcurrent and a displacement of the inner edge of the plasmasheet and the cross-tail current away from the earth, andthus with a large release of energy from the inner portionedge of the plasma sheet.

The reduction of cross-tail current during a substormis initially localized and does not extend across a largedistance of the tail. As with auroras at low altitudes, thecurrent reduction region expands azimuthally within theplasma sheet with time after substorm onset. The edges of the current reduction region are connected to eld-alignedcurrents extending to the ionosphere. These currents areupwardand large on thedusk side of thecurrent-reductionregion. The large upward currents connect along magneticeld lines to thestrongdiscrete aurorathat forms thewest-ward traveling surge, and their azimuthal motion withinthe plasma sheet corresponds to the westward motion of the surge.

While many substormsoccurin response to IMF-drivenreductions in the strength of convection, and thus can beviewed as beingtriggered by appropriate IMFchanges, theextent to which substorms result from such convection re-ductions has not yet been determined. There are variousideas of how substorms might result from a large-scale,

internal instability of the plasma sheet during periods of steady, enhanced convection. It is known that substormsare infrequent during periods of steady enhanced convec-tion. However, it has not yet been determined whetheror not substorms are absent during such periods. If theyare absent, then the idea of substorm onset by internalinstability will have to be discarded. If not, then it willbe necessary to determine why some substorms requireappropriate IMF changes and some do not.

C. Dynamic Pressure Disturbances

It has recently been found that enhancements in solar

wind dynamic pressure increases can cause large auro-ral zone disturbances during periods of strong magne-tospheric convection. Dynamic pressure enhancementsaffect the entire auroral zone simultaneously (unlike sub-storms and PBIs). Within a few minutes of the time anenhancement in dynamic pressure hits the magnetopause,the polewardboundaryof theauroral oval moves polewardand the intensity of auroral emissions increases through-

out essentially the entire auroral oval. The equatorwardboundary of the oval is not signi cantly affected, so thatthe latitudinal width of the auroral oval increases. Mostof the increase in auroral intensity is in the diffuse au-rora, but increases in discrete aurora most likely also oc-cur. The enhancement in diffuse auroral emissions resultsfrom the heating of the plasma sheet plasma as the en-tire magnetosphere is compressed by the increase in solarwind dynamic pressure. The poleward motion of the pole-ward boundary of oval can be as much as 10 in latitude,which corresponds to a large broadening of the auroraloval. It also corresponds to a large reduction in the areaof open, polar-cap magnetic eld lines, since, except nearlocal noon, the poleward boundary of the oval lies at theboundary between open and closed eld lines.

Dynamic pressure enhancements compress the entiremagnetosphere and enhance the entire magnetosphericcurrent system. As discussed in Section IV.A, increases inthe current within the dayside magnetopause can be over afactorof three.It isalso known that theglobal eld-alignedcurrent system that lies along the open closed eld-lineboundary, the ionospheric current system driven by mag-netospheric convection, and the cross-tail current signi -cantly increase in response to enhancements in solar winddynamic pressure. However, the relationship between thefull magnetospheric current systemand the solar wind dy-namic pressure is not well understood. The cause of thelarge reduction in the area of the polar cap driven by in-creases in solar wind dynamic pressure is also not wellunderstood, but it is likely related to the large enhance-ments in magnetospheric currents.

VIII. CONCLUSIONS

The interaction of the interplanetary plasmawith themag-netic eld of the earth has only been studied in detail sincethe beginning of the space age in the late 1950s. With theuse of ground measurements of ionospheric phenomenaand limited point measurements from spacecraft withinthe solar wind and the magnetosphere, much is now un-derstood about how this interaction leads to the interestingfeatures and dynamics of the magnetosphere ionospheresystem. This is a remarkable accomplishment. However,much remains to be learned. We do not yet have a full

observational description of the magnetosphere in the ab-sence of disturbances or of thevarious disturbances whichoccur within the magnetosphere-ionosphere system. Weare also far from being able to make quantitatively ac-curate predictions of how the magnetosphere responds tothe highly variable solar wind and IMF which impactsthe magnetosphere. Only with continuing observationalprograms, extensive analysis of existing and future


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datasets, and innovative theory and modeling studies willa far more quantitative understanding of the space plasmaphysics of the earth s environment become possible.

SEE ALSO THE FOLLOWING ARTICLES

AURORA GEOMAGNETISM IONOSPHERE PARTICLEPHYSICS , ELEMENTARY PLASMA SCIENCE AND ENGI-NEERING RADIATION , ATMOSPHERIC SOLAR SYSTEM ,MAGNETIC AND ELECTRIC FIELDS

BIBLIOGRAPHY

Crooker, N. U. (2000). Solar and heliospheric geoeffective distur-bances, J. Atmos . Solar-Terr. Phys . 62, 1071.

Hultqvist, B., Oieroset, M., Paschmann, G., and Treumann, R. (eds.).(1999). Magnetospheric Plasmas Sources and Losses, Kluwer Aca-demic Publishers, Boston.

Kivelson, M. G.,and Russell, C. T (eds.). (1995). Introduction to SpacePhysics, Cambridge University Press, New York.

Lyons,L. R. (2000). Geomagnetic disturbances: Characteristics of, dis-tinction between types, and relations to interplanetary conditions,

J. Atmos . Solar-Terr. Phys . 62, 1087.

Lyons, L. R., and Williams, D. J. (1984). Quantitative Aspects of Mag-netospheric Physics, Reidel, Dordrecht, Holland.

Richmond, A. D., and Lu, G. (2000). Upper-atmosphere effects of magnetic storms: A brief tutorial, J. Atmos . Solar-Terr. Phys . 62,1115.

Schulz, M., and Lanzerotti, L. J. (1974). Particle Diffusion in the Ra-diation Belts, Springer-Verlag, New York.

Wang, Y.-M., Sheely, Jr., N. R., Socker, D. G., Howard, R. A., andRich, N. B. (2000). The dynamical nature of coronal streamers,

J. Geophys. Res . 105, 25,133.


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Plasma Diagnostic TechniqClifford W. Mendel, Jr.Sandia National Laboratories (Retired)

Edl SchamilogluUniversity of New Mexico

I. IntroductionII. Magnetic Diagnostics

III. Particle Flux MeasurementsIV. Refractive Index MeasurementsV. Scattering of Radiation by Plasma Particles

VI. Optical Diagnostics

GLOSSARY

Bremsstrahlung Radiation resulting from free-electron

transitions which occur when one particle suffers a de-celeration on encountering another particle. It is an im-portant component of continuum radiation.

Cerenkov radiation Radiation that results when acharged particle loses energy while moving througha medium at a speed greater than the wave velocity inthe medium.

Cyclotron radiation Radiation emitted by a charged par-ticle moving in a circular orbit in a magnetic eld. Itoccurs at the cyclotron frequency and its harmonics.Also called synchrotron radiation.

Doppler shift A shifting of a spectral line due to the rela-tive velocities of radiating or light-scattering particles.

Electromagnetic scattering Process of radiation emis-sion due to the acceleration of charged particles byelectromagnetic waves.

Gridded analyzer Device that utilizes biased grids tomeasure the ux of ions as a function of their energy.

Interferometer Device that is arranged to compare the

relative phases of two paths of coherent radiation, oneof which passes through the plasma.

Ion spectrometer Device that can resolve different ion

species and record their currents. Usually these involvedeectionof the ions by electric and/ormagneticelds.

Langmuir probe Relatively small electrode exposed toa plasma where it collects electrons or ions when apotential is applied.

Laser-induced uorescence Excitation of atoms or ionsby a laser tuned to a selected transition of the atomicspecies being detected. The resultant radiation is calleduorescence.

Line broadening Increase in the width of a spectral linedue to some physical process in the plasma.

Rogowski coil Multiturn toroidal inductor that encirclesa distributed current which is to be measured.

Starkshift Shifting of a spectral line due to electric eldsin the vicinity of the radiating particle.

Thompson scattering Classical limit of light scatteringby free charges.

Zeeman effect Splitting of a spectral line in the presenceof a magnetic eld.

391


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392 Plasma Diagnostic Techniques

PLASMA DIAGNOSTIC TECHNIQUES are used toobserve physical processes that reveal parameters thatcharacterize a plasma. These parameters include spatialand temporal distributions of constituent particle densi-ties and temperatures and localized magnitudes of electricand magnetic elds. The techniques used include thosethat have applications in other areas of science and thosethat have been developed for their unique applications toplasmas.

I. INTRODUCTION

Plasma diagnostics is the observation of physical pro-cessesthat allows oneto infer parameters that characterizea plasma. It had its inception in the late nineteenth centurywith the observation of colored glows from gas- lled dis-charge tubes. These plasmas were low in temperature andweakly ionized. By weakly ionized we mean that only asmall fraction of theneutralgasis ionized yetthe plasmais quasi-neutral. The eld grew rapidly in the rst part of the twentiethcentury after the discovery of electrons, ions,and the ionizing effects of X-rays. The methods used fordiagnosing the plasmas relied on electrostatic probes andbasic current and voltage characteristics of the dischargetubes. The advent of quantum mechanics led to the use of spectroscopy.

Interest in plasma diagnostics waned until themid-1950s, when the emerging eld of controlled ther-monuclear fusion spawned new interest in the subject.The high temperatures and densities of fusion plasmas re-quired the development of new nonintrusive diagnostics.The accompanying development of lasers and sensitive

solid-state detectors made possible new diagnostic tech-niquesand theapplication of known techniques to thenewparameter regimes.

The requirements for manufacturing microelectronicand optoelectronic devices and the applications to ma-terials processing in general have caused a resurgence of interest in glow discharge plasmas. These plasmas are lowin temperature and weakly ionized, in contrast with theirfusion counterparts. The materials processing communityis now utilizing many of the plasma diagnostic techniquesthat were advanced by research in controlled fusion.

Recently, the plasma diagnostics community has beenchallenged by the need to characterize the strongly cou-

pledplasmasproducedin laser-driven inertialcon nementfusion experiments and pulsed power-driven Z -pinch ra-diation sources. In this regime the predominant diagnos-tic utilizes X-ray imaging techniques coupled with neu-tron and proton diagnostics to determine the parametersof the target plasma. Advances in X-ray instrumentationand components are leading to greater measurement sen-sitivity and ner spatial resolution.

TABLE I Plasma Diagnostic Techniques

Diagnostic Parameter M or F

Magnetic T e , E , B FParticle ux f e , f i , n e , n i , T e , T i , E , v i MRefractive index n e , B M, FScattering f e , n e , n i , T e , T i F

Optical emission T e , n e , n i M, FLine radiation n e , n i , n 0 , T e , T i , vi , B M, F

The two most common plasmas found in the labora-tory can be categorized as (1) high-temperature highlyionized plasmas generated in magnetic con nement fu-sion research experiments, and (2) weakly ionized low-temperature plasmas utilized in the materials processingand gaseous electronics communities.Although we are re-stricting our discussion of diagnostic techniques to funda-mental techniques applicable to laboratory plasmas, manyof these methods apply to space andastrophysical plasmas

as well.Thediagnostic techniques that we will be describing are

listed in Table I . The parameters indicated are f (particledistribution function), n (particle density), T (particletemperature), v (particle velocity), E (electric eld), and B (magnetic eld). Subscript refers to electrons ( e),ions ( i ), or neutrals (0). The diagnostics are categorizedas being most useful in materials processing plasmas (M)or fusion plasmas (F). Many of the diagnostics are equallyuseful in both types of plasmas.

The diagnostic technique, or combination of tech-niques, chosen for a particular application represents acompromise among the precision to which the measure-ment needs to be made, thespatial and temporal resolutionrequired,and thetimeand expense available toperform themeasurement. Plasmas are very complex, often being tur-bulent andperhapsimpure,and thetheoryof thediagnosticcan be equally complicated. In many instances, diagnosticaccess and extreme plasma parameters limit the availablechoices to a meager few. For this reason, plasma diagnos-tics is often referred to as an art as well as a science.

II. MAGNETIC DIAGNOSTICS

A. External Measurements

Much can be learned from measuring the magnetic eldsoutside of a plasma. Figure 1 shows a toroidal plasmabeing heated ohmically, as is common in magneticallyconnedfusion experiments. In thesedevices theplasmaisthesecondarycircuit ofa transformer. Theprimaryis a coillike those in most transformers. The toroidal electric eldin theplasma is generatedby the owofmagnetic ux intothecore of thetransformer. Theresultingvoltageabout the


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Plasma Diagnostic Techniques 393

FIGURE 1 Schematic of a toroidal plasma being heated ohmi-cally. The plasma acts as the secondary circuit of a transformer.Also shown is a plot of the magnetic pressure and plasma pres-sure across the minor radius of the toroid.

loop ofplasma V loop can be measured by a conducting loopparallel to the plasma loop.

The current in the plasma loop is also easily measured.From Ampere s law the loop current is given by

I =1

0 B d l, (1)where the path of the integral encloses the current tobe measured. By recording the integrated voltage froma Rogowski coil ( Fig. 1 ) about the plasma, the integralof the poloidal magnetic eld around a loop enclosing theplasmais measured, andtherefore thecurrent is measured.

Fromthesemeasurementsthe power intotheplasmaandthe resistance R of the plasma are given by

= IV loop , R =V loop

I . (2)

In some cases the power needs to be corrected for changein the magnetic eld energy.

The resistance of the loop of plasma can, in manycases,be related to the characteristics of the plasma. In the sim-plest case the electron temperature, which is generallydifferent from the ion temperature, is measured. The re-sistance of a fully ionized plasma is proportional to thesquare of the number of electrons removed from each ion

divided by the electron temperature to the 3 / 2 power. It isalmost independentof theplasma electrondensitybecausethe numberof scattering centers (i.e., ions) is proportionalto the number of charge carriers (i.e., electrons).

Measuring electron temperature by measuring theplasma resistance applies when currents are small enoughthat theelectrondriftvelocityis smaller than thevelocitiesof the many waves a plasma can support. In cases where

this is not true the electrons leave a wake of waves notunlike Cerenkov light from particles moving faster thanthe speed of light in a material. These waves make localconcentrations of charge which increase the resistance of the plasma. This is somewhat like raising the number of times each ion is ionized. In these cases extensive andsophisticated theory is needed to interpret the data, butgenerally the conductivity is a function of plasma density.

The toroidal magnetic eld Bt necessary to con ne andstabilize a toroidalplasmaisshown in Fig.1.Itisgeneratedby eld coils not shown. In an actual experiment this canbe taken into account if required.The plasma pressure P iscontained by the magnetic eld, primarily by the toroidalcomponent. The magnetic eld has a pressure

Pmagnetic = B2

2 0(3)

normal to the eld lines. There is also a tension of B2/ 2 0 along eld lines, but this can be neglected if theradius of curvature of eld lines is large. If the curvatureis negligible then

P + Pmagnetic = P + B2

2 0= constant , (4)

and the magnetic pressure and plasma pressure look likethe plot inset in Fig. 1 . Since this is a static situation, thetotal pressureis constant. Because themagneticpressureisusually large compared to the plasma pressure for reasonsof stability, it can be shown that the ux excluded fromthe diagnostic loop about the plasma is given by

= 0 B0 r

loop

02 r P dr , (5)

where r loop is the radius of the diagnostic loop. Since themagnetic eld is B0 everywhere outside the plasma, thechange in ux is actually independent of r loop .

This is therefore a measure of the average plasma pres-sure or, more correctly, a measure of the pressure perpen-dicular to the magnetic eld, which can be different fromthe pressure along the eld lines. Since this pressure issimply the kinetic energy density, the total perpendicularenergy is given by

W = r loop

02 r P dr = B0

0. (6)

This energy includes both the ion and electron perpendic-ular kinetic energies. If the density pro le is known fromother diagnostics thetotal perpendicularenergyreveals thesum of the electron and ion temperatures averaged overthe plasma.


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B. Internal Measurements

If the axial current in the plasma ( I in Fig. 1 ) is largeenough, the poloidal magnetic eld Bp must be taken intoaccount. The measurement of current with the Rogowskicoil is a measure of the poloidal magnetic eld outside theplasma, andif thecurrentpro le is known thepressurecan

still be calculated. If the current pro le is not known, itcan be measured with magnetic probes. These devices aresimple, smallcoils ofwire, with outputvoltageequalto therateof magnetic uxchangethroughthe coils.The numberof turnsandthe size ofeach turn dependon theapplication.Usually theturnshave a radiusof one to a few millimeters.For magnetically con ned fusion plasmas the coils needa large number of turns to get suf cient voltage from theslow changes. For faster elds like those seen in inertiallyconned fusion experiments, the coils usually have onlyone or a few turns. The magnetic eld is proportional tothe integral of the coil voltage.

There are two dif culties with these probes. Like any

physicalprobe placed inside a plasma, these probes disturbthe plasma and can lead to rapid plasma loss. In addition,plasmas are much hotter than the melting points of ma-terials. Probe envelopes are usually glass or ceramic, buta probe still must either be in a plasma for a short timeor have a method of removing heat at a suf cient rate. Aless instrusive method of measuring internal elds is withion probes. These diagnostics look at the de ection of en-ergetic ions by the magnetic elds. These diagnostics aregenerally dif cult to eld and interpret. The orbits of theprobing ions in magnetic fusion plasmas are usually com-plex and are also affected by electric elds at the plasmaedge.

III. PARTICLE FLUX MEASUREMENTS

Particle ux measurements generally involve measure-ments of particle energy distributions or measurementsof ion species fractions. One of the rst plasma diagnos-tics was the Langmuir probe. This device consists of anelectrode placed inside the plasma. The probe is a per-turbative diagnostic since its dimension is usually muchlarger than the electrostatic shielding distance, that is, theDebye length

D = 0k B T ee2n

1/ 2, (7)

where k B = 1.38 10 23 J/K is Boltzmann s constant, T eis the electron temperature and n is the electron den-sity far from the probe. The voltage on the probe is sweptslowly in time and the probe current recorded. Figure 2(a)shows such a probe and the current to the probe plotted

FIGURE 2 (a) Schematic of a Langmuir probe measuring elec-tron and ion current in a plasma. (b) A double probe congurationand the analysis of a double probe I V characteristic.

versus voltage. The current consists of both ion and elec-tron parts. The ion current density to the probe is given by

J i =12

n i q i va , v a =q i k B (T e + T i )

em i

1/ 2

, (8)

where ni is the ion density, q

i is the ion charge, and v

a is

the acoustic velocity in the plasma with T e T i in mostcases. This expression is strictly true for a planar probeand the current is approximately independent of the probevoltage. A more accurate expression can be obtained bysolving for the potential distribution in the vicinity of theprobe, taking into account the actual probe geometry.

The electron current density is similarly

J e =14

n eeve = n ee k B T e2 m e

1/ 2

, (9)

where ve is the mean velocity for an electron distributionwhich is Maxwellian in the direction toward the probe

and zero in the direction away from the probe. The factorof one-quarter comes from a factor of one-half which ac-counts for the fact that particles come from all directionsso that theprobearea appears one-half itsactual area whenaveragedoverall angles, andanother factorof one-halfbe-cause the density near the probe is one-half the value farfrom the probe. The latter is because there are electronsmoving towards theprobe but none comingback from it at


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Plasma Diagnostic Techniques 395

the energies that are being collected. The electron densityat the surface of the probe is given by

n e = n eeV / k B T e (10)

if the electrons are described by a Maxwellian velocitydistribution. The total probe current density is thus

J probe 14

n e 2va ve eeV / k B T e . (11)

Clearly, the electron temperature can be obtained froma current plot like that in Fig. 2(a) . More typically the ioncurrent is substracted off and the data plotted on semilog-arithmic scale, in which case the data lie on a straight lineif the distribution is Maxwellian. The reciprocal of theslope of the line is proportional to electron temperature.The product of plasma density and acoustic velocity canbe obtained from the ion current (i.e., the current at largenegative probe voltage), andthe plasmadensity canbe cal-culated. The probe current at moderate negative voltage isoften above the current expected for a Maxwellian in thecase of active discharges such as those used in semicon-ductor processing plasmas. This excess current is due tohigh-energy electrons that are involved in ionizing back-ground gases.

By measuring the current between two probes held at avoltage difference, but with no net current to the pair, theelectron temperature and density can again be found. Theabove equation for the probe current is applied to bothprobes at their differing voltages. In addition, the sumof the two currents is set to zero. This method, shown inFig. 2(b) , disturbs the plasma less. The diagnostic is called

a double probe. Figure 2(b) also shows a way the data canbe analyzed.Electric probes are very easy to eld and, therefore, are

often one of the rst diagnostics used. It is dif cult to getvery accurate density data with these probes. Theeffectivearea of the probe changes with surface conditions of theprobe and nearby insulators. The theory is in general quitecomplex, particularly if there is a strong magnetic eld ora signi cant plasma drift. Electron temperature measure-ment generally works well, even in magnetic elds. Nev-ertheless, Langmuir probes are quite usefulwhen quick oreasy measurements are required.

A slightly morecomplicated electricparticle diagnostic

is the gridded analyzer shown in Fig. 3(a) . This device isexternal to the plasma. In the case of pulsed plasmas of short output duration, it can be used to measure the frac-tions of ion charge in the plasma. To do this the analyzeris placed at a distance from the plasma so that the timeof ight of the fastest ions is long compared to the lengthof the plasma pulse at the source. In this situation the ve-locity of the ions arriving at time t is given by d / t if d

FIGURE 3 (a) Schematic of a gridded analyzer. (b) Data from agridded analyzer taken 1.2 m downstream from a carbon plasmasource.

is the distance from source to analyzer. The analyzer con-sists of three grids. The rst is at the same potential as theplasma source. The second is at a negative voltage that islarge compared to the electron temperature of the plasma,which is rarely higher than a few electron volts. This sec-ond grid removes the electronsfrom the plasmabut allowsthe ions to pass. The third grid is at a high positive voltage,V stop . Only ions of kinetic energy greater than their chargetimes V stop can pass through the third grid to the collector.Thus, the collector measures the current of those ions thatmeet the criterion

m i d 2

2t 2 > q i V stop V stop t 2 1015 cm 3 , T e 4 eV) plasmas. This effect arisesfrom the in uence of the electric eld of particles inthe vicinity of the radiating atom. The frequency of ra-

diation is shifted because of the perturbing effect of the random electric elds, called the Stark shift. If theplasma parameters are such that the Stark shift is thedominant broadening mechanism, then a measurementof the electron density can be ascertained from the linewidth. In high-temperature fusion plasmas, Stark broad-ening is a negligible effect when compared with Dopplerbroadening.


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A diagnostic that is gaining importance, especially inradio-frequency (RF) plasma reactors used for materi-als processing, is uorescence. This diagnostic method isbased on the active perturbation of the excited state pop-ulations to obtain additional information from the emit-ted line radiation. Laser-induced uorescence (LIF) oc-curs when a small volume of the plasma is irradiatedwith an electromagnetic source that is tuned to a reso-nant line of a constituent atom of the plasma (Fig. 7 ). Theatomic species that are accessible by laser uorescencetechniques are limited by the wavelength tunability andthe power of available sources. Neutral metal atoms are of interestto many plasma processingsystems. These specieshave many allowable transitions between the near ultra-violet and near infrared wavelength regions. A tunablepulsed dye laser is generally used as the radiation sourcefor these investigations. Laser-induced uorescence is avery sensitive technique for obtaining temporal and three-dimensional spatial resolution of number densities.

Tunable infrared lasers are gaining importance as sen-sitive probes of species in plasma processing. The mostcommonly used continuously tunable source is the diodelaser. These lasers are used to identify a number of stablemolecules, freeradicals, and ionsfrom thelaserabsorptionspectra. It is possible to obtain translational temperaturesofatomsfromthe widthof theabsorptionlineand thenum-ber density from a measurement of the absolute infrared

FIGURE 7 Schematic of a laser-induced- uorescence experi-ment in an RF plasma reactor.

absorption cross sections. A disadvantage of this methodas a general plasma diagnostic is that it is very cumber-some to tune over a wide spectral range. This limits thespecies that can be detected. In addition, since the sourcesusedare continuous rather thanpulsed, time-dependent in-formationcannot be obtained in theimportant time regimebelow 100 nsec.

Finally, the presence of a magnetic eld imbedded in aplasma causes the splitting of emission lines. The magni-tude of the eld may be deduced from the magnitude of the splitting due to the Zeeman effect. Splitting from evennatural line radiation can be observed, in principle. Thisdiagnostic is primarily relevant to magnetically con nedplasma experiments in tokamaks and to astrophysics. Themain dif culty is ensuring that the splitting of the linedominates over Doppler broadening. Resonance uores-cence techniques may be used to enhance the observedemission intensity.

SEE ALSO THE FOLLOWING ARTICLES

PLASMA CONFINEMENT PLASMA SCIENCE ANDENGINEERING

BIBLIOGRAPHY

Auciello,O., andFlamm, D.L.,eds. (1989). PlasmaDiagnostics,Vol. 1,Discharge Parameters and Chemistry, Academic Press, San Diego.

Auciello,O., andFlamm, D.L.,eds. (1989). PlasmaDiagnostics,Vol. 2,Surface Analysis and Interactions, Academic Press, San Diego.

Beke, G. (1966). Radiation Processes in Plasmas, Wiley, New York.Griem, H. R. (1997). Principles of Plasma Spectroscopy, Cambridge

University Press, Cambridge, UK.Heald, M. A., and Wharton, C. B. (1978). Plasma Diagnostics with

Microwaves, 2nd ed., Krieger, Malabar, FL.Huddlestone,R. H.,and Leonard, S. L.,eds. (1965). PlasmaDiagnostic

Techniques, Academic Press, New York.Hutchinson, I. H. (1987). Principles of Plasma Diagnostics, Cam-

bridge, New York.Lochte-Holtgreven, W. (1995). Plasma Diagnostics, American Insti-

tute of Physics, Woodbury, NY.Manos, D. M., and Flamm, D. L., eds. (1989). Plasma Etching: An

Introduction, Academic Press, San Diego.Oks,E. (1995). PlasmaSpectroscopy: The In uenceof Microwave and

Laser Fields, Springer-Verlag, Berlin.Salzmann, D. (1998). Atomic Physicsin HotPlasmas, Oxford Univer-

sity Press, New York.

Shef eld, J. (1975). Plasma Scattering of Electromagnetic Radiation, Academic Press, New York.

Silver, E. H., and Kahn, S. M., eds. (1994). UV and X-Ray Spec-troscopy of Astrophysical and Laboratory Plasmas, Cambridge Uni-versity Press, Cambridge, UK.


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Plasma Connement

Allen H. BoozerColumbia University

I. IntroductionII. Basic Plasma Physics

III. Toroidal PlasmasIV. Mirror Confined PlasmasV. Transport

GLOSSARY

Ambipolar Equal loss rate of ions and electrons. If there is more than one particle-loss process, the

individual processes need not be ambipolar. However,quasi-neutrality forces the sum of all the loss processesto be ambipolar.

Anomalous transport The transport of plasmas acrossmagnetic eld lines is generally much more rapid thanwould be expected if the magnetic and electric eldswere smoothon a spatial scale smallcompared to that of the overallplasma equilibrium.The enhanced transportdue to small-scale electric and magnetic elds is saidto be anomalous.

Debye length The Debyelength d is the thermal velocityof the electrons divided by the plasma frequency. It isapproximately the distance that the electrons and ions

can be separated before the electrostatic energy equalsthe thermal energy.

Hamiltonian mechanics The Newtonian equations of motion d p / dt = V (x, t ) are obviously equiva-lent to Hamiltons equations, d p / dt = H / x andd x/ dt = H / p, with the Hamiltonian H( p , x, t ) =12 mv

2 +V (x, t ) and thecanonical momentum p =mv.

Any set of differential equations that can be writtenin the form of Hamiltons equations are said to beHamiltonian with p the canonical momentum and xthe canonical position, regardless of the form of H.

A particle of charge q in an electromagnetic eldwith vector potential A and electric potential V hasa canonical momentum p =mv +q A. The potential inthe Hamiltonian is V =q .Kinetic theory Theory that uses the distribution of elec-trons and ions in both position and velocity is calledkinetic theory. The basic differential equation of thetheory is the FokkerPlanck, or Boltzmann, equation,which is derived under the assumption that the numberof electrons in a sphere with a radius of a Debye lengthis very large compared to unity.

Magnetohydrodynamic (MHD) theory The MHD the-ory of plasmas makes the simplifying assumption that

a plasmacan be viewed as a conducting uid with well-dened conductivities for heat and electrical currents.Individual equations based on MHD theory can oftenbe justied under much more general assumptions thanthose required to obtain the complete MHD theory.

Plasma frequency p The plasma frequency is the nat-ural frequency of the electron oscillation that would

373


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374 Plasma Connement

result from a separation of the electrons and the ionsthat form the plasma.

Quasi-neutrality approximation The density of posi-tive and negative charges is almost equal in most plas-mas. The ratio of the net charge density to the den-sity of electron charge is approximately the squareof the ratio of the Debye length to the size of theplasma. The electric eld in plasma physics is nor-mally determined by equating the electron and the ioncharge densities, which is called the quasi-neutralityapproximation.

A PLASMA is a near ideal gas that consists of ions andelectrons. All substances become plasmas at a suf cientlyhigh temperature temperatures above about 10 4 C. Theconnement of a laboratory plasma for a time long com-pared to the transit time of a thermal ion requires the useof magnetic elds to balance the plasma pressure. Astro-physical plasmas may be con ned by gravitational forces.Gravitationally con ned plasmas are discussed as a partof other subjects such as stellar structure. The equilibrium,stability, and transport properties of plasmas that are con-ned by an embedded magnetic eld are major topics of research and are the subject of this article. The physicsof plasma con nement is closely related to a number of other areas such as uid mechanics, kinetic theory, andHamiltonian mechanics.

I. INTRODUCTION

Matter at temperatures suf ciently high compared toatomic ionization potentials, about10 4 C, forms a plasmaover a broad range of density. The con nement of plasmaby a magnetic eld was originally studied to gain under-standing of space and astrophysical phenomena, partic-ularly phenomena of the solar corona and the magne-tosphere of the earth. Although space and astrophysicalplasmas remain an active area of study, plasma physicsresearch has been dominated since the 1950s by the effortto achieve adequate plasma con nement for thermonu-clear fusion. The thermonuclear fusion application placesrequirements on the plasma temperature, density, and en-ergy con nement time as well as an upper limit on the

magnetic eld strength. These requirements have tendedto dene the plasma regimes of research interest. This isespecially true since astrophysical plasmas are frequentlyin similar dimensionless parameter regimes.

The basic concept of magnetic con nement is simple.A current of electric charge, with density j , interacts witha magnetic eld B to produce a force j B per unit vol-ume. This force can balance the force per unit volume

p that is produced by a gradient in the plasma pressure,or p = j B. Ampere s law, B = 0 j , implies theconning current modi es the magnetic eld. Force bal-ance, Ampere s law, and the condition that the magneticeld be divergence free, B =0, dene a large fractionof the physics of plasma con nement.

A simple result of plasma con nement theory is thata plasma cannot be con ned purely by a self-producedmagnetic eld. Either there must be an externalcurrent-carrying circuit, which produces some part of the magnetic eld, as in laboratory plasmas or in themagnetosphere of the earth, or there must be an addi-tional force, such as gravitation in astrophysical plas-mas. To prove that an externally produced magneticeld is needed to con ne a plasma, write the magneticeld as the sum of a eld produced by plasma cur-rents and an externally produced eld, B =Bpl +Bex. Theequilibrium equation is then p = j pl (Bpl +Bex) with 0 j pl = Bpl . Multiplying this form of the equilibriumequation by the position vector x and integrating overall of space, one nds (using vector identities, such as

x =3) that

3 p + B2pl

2 0d 3 x = x ( j pl Bex) d 3 x . (1)

The left-hand side of this equation is greater than zero, sothe external magnetic eld must be nonzero.

Suppose a plasma is to be con ned in a bounded regionof spaceby a magnetic eld. A numberof questionsshouldbe answered. First, what properties must the magneticeldhaveinordertocon nethe plasma? Second, how higha plasma pressure can be con ned by the magnetic eld?

The relevant dimensionless parameter is called beta, 2 0 p / B2, andis a measureof the ef ciency of the utiliza-tion of the magnetic eld. Third, how long can the plasmabe con ned or, equivalently, what sources of energy andparticles are required to maintain a given plasma con g-uration? A plasma in thermodynamic equilibrium cannotbe con ned by a magnetic eld, because plasma particleswould then have a Maxwellian distribution that carries nocurrent j. Plasma con nement by a magnetic eld impliesentropy production, which is balanced either by the decayof the con guration or by external sources of energy andparticles. Although these questions identify the types of issues that must be addressed, they represent too simple a

view of plasma con nement to be answered de nitively.Important but subtle points constantly arise in the the-oryof plasma con nement. Considera trivialconsequenceof the force balance equation, B p =0. The magneticeld vector must lie in a surface of constant pressure.What are the implications? First, the constant pressuresurfaces must be toroidal. It is a mathematical theoremthat the only surface in three dimensions that can have a


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Plasma Con nement 375

nite vector eld everywhere tangent to it is a topologicaltorus. Second, the magnetic eld line trajectories, whichsatisfy the differential equation d x/ d =B(x), must liein the toroidal surfaces wherever the pressure gradient isnonzero. Toroidal surfaces formed by magnetic eld linesare called magnetic surfaces. (The parameter is justa la-bel for points along a eld line trajectory with d

=dl / B

and dl the differential distance along a eld line.) Asshown in Section III.A, the differential equation for theeld lines of a divergence-free eld is equivalent to a onedegree of freedom, time-dependent, Hamiltonian mechan-icsproblem. The condition that the magnetic eld lines liein nested toroidal surfaces, the surfaces of constant pres-sure, is only satis ed by a magnetic eld in special cases(corresponding to integrable Hamiltonians). An arbitrarymagnetic eldcon guration will notcon neaplasmawitha scalar pressure. The presence of a continuous symmetryguarantee

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