Adv. Space Res. Vol. 11, No.9. pp. (9)11 l.(9)115, 1991 02734177/91$O.~+ .50Printed in Great Britain. All rights reserved. Copyright (~)1991COSPAR

ON THE STRUCTUREOFROTATIONALDISCONTINUITIESWITH LARGE PHASEANGLES

PeterRichterandManfredScholer

Max-Planck-!nsriturfür extrarerrestrischePhysik,8046Garching,F. R.G.

ABSTRACT

Using hybrid simulations(particle ions and electronfluid) we haveinvestigatedthestability of rotational

discontinuities.A densityincreasebuildsup at thepositionof therotationaldiscontinuity. Thefinal density

structureof the rotationaldiscontinuity developsindependentlyof the initial phaseangle~ andof thehalf

width D. Only minor differencesoccurfor different sensesof rotation, i.e. for a rotationaldiscontinuity

exhibiting an ion senseor anelectronsenseof rotation, respectively.Howeverthestructureof themagnetic

field, B, stronglydependson thephaseasshownby simulationsof rotationaldiscontinuitieswith 2700phase

angle. Rotationaldiscontinuitjeswith 2700 phasedevelopindependentlyof the initial senseof rotation into

structureswith 90°-rotation.

INTRODUCTION

Rotationaldicontinuities(RDs) areimportant structuresin spaceplasmas.During times of reconnectionthe

magnetopauseis thoughtto bearotationaldiscontinuity(e.g., /1/). Rotationaldiscontinitiesarestructures

of ideal magnetohydrodynamics(MHD). It has recentlybeenshownthat in dissipativeMHD rotational

discontinuitiesare unstableanddecayinto intermediateshocks(/2/). This has renewedinterest in the

structureandstability of rotational discontinuities. The structureof rotational discontinuitieshasbccn

investigatedanalyticallyby steadystatesolutionsof the Vlasovequation(/3-5/), by numericalsolutionsof

the dissipativeMHD equations(/2/), andby onedimensionalhybrid simulations(/6-10/). We will analyze

in this paperthestructureof RDs within the frameworkof a hybrid plasmamodel (ion macroparticles

andinertialesselectronfluid). The magneticfield, B, canrotatethrougha rotationaldiscontinuityby an

arbitrary phaseangle ~. By comparinga rotationaldiscontinuity of phase~ = 180°with a rotational

discontinuity of phase270°we will show that the evolution of the density profile of a RD is relatively

independentof thephaseangleandthesenseof rotation. We then analyzethebehaviorof themagnetic

field of 270°-RDsandshowthat they evolveindependentlyof their phaseangleinto 90°structureswith

reversedsenseof rotation. The evolution strongly dependson the phaseanglebut not on the senseof

rotation.

SIMULATION MODEL

We useda hybrid code, in whichthe ions aretreatedas particlesandtheelectronsas a massless,charge-

neutralizingfluid (/11/). We restrictourselvesto onespatialdimension,whichis in thedirectionnormalto

the discontinuity(B~= Br). Thereforeonly wavevectorsk parallel to B~arepossible.

(9)111

(9)112 P.RichterandM. Scholer

~ ~

o sc;..,,) 201)0 zIc,~_,) 200

Fig. 1. Stackedprofiles of theB9 component(left) andthedensityn (right) of aRD with ~ = 180°,left

handsenseof rotation.

2tfl)~~

O x(c/~..’,~) 200 (I rlr/~,,1l 200

Fig. 2. Sameas Figure 1 but with aphaseangleof ~ = 270°.

Initially, thesimulation regioncontainstwo RDs. The system is long enough(L~= 1000~ so that

interactionsbetweenthe two RIDs during the time of the simulation are unlikely. The two rotational

discontinuitieshaveoppositesenses,i.e., one rotational discontinuity hasan ion senseof rotation (left

handed)and thesecondrotationaldiscontinuity has an electronsenseof rotation (right handed). The

simulationis performedin thede Hoffmann-Tellerframe, in which thebulk ion velocity, v, is parallel to B,

so that at time i = 0 theelectricfield E = v x B = 0. Becauseinitially thereis no jump in thepressureand

the densityfrom upstreamto downstream,onecan implementperiodic boundaryconditions.This method

hasfirst beenintroducedby Wu andHada(/10/). In thesimulationsthe time is expressedin units of the

inverseof theiongyrofrequency~ = eB0/mc,wherecis thespeedoflight, e is themagnitudeof theelectron

chargeandm is theionmass.Distancesareexpressedin unitsof theion inertial length A = C/Wpj, where

is the ion plasmafrequency. The anglebetweenB andthediscontinuitynormal,®Bn, is 60°throughout,

the half width D of theRD is 2c/w~~,the resistivity of thesystemis ij = 106(4ir/wp~),wpj/fZci= 1, the

plasmabeta(ratio of thermalto magneticpressure)/3 = /3~+ 13e = 0.01+ 0.01.

COMPARISON BETWEEN 2 PHASES

The simulation was run in caseof the 180°RD up to t = 100f1~and in caseof the 270°RD up to

i = 200cl;1. Figure 1 showsstackedprofilesof B9 on the left handsideandof thedensityn (normalized

RotationajDiscontinuities (9)113

to 1) on theright handsidefor aleft handpolarizedrotationaldiscontinuity (ion senseof rotation)with an

initial 180°phaseangle.Figure 2 showsthesamequantitiesfor arotationaldiscontinuitywith 270°phase

angle. Timeruns from top to bottom. A low passfilter hasbeenappliedin orderto suppresshighfrequency

fluctuations. After initialization a numberof wavespropagateupstreamand downstreamawayfrom the

discontinuity. This wasalreadyshownfor the180°-RDby Wu and Hada(/10/). From thedensityprofiles

it can be seenthat thewaveswhich areexcitedin theB9-componenthavealsocompressionalcomponents.

Thesamewavescan be seenindependentlyof thephaseq~.Thesewavescanbeidentified accordingto their

phasevelocity as afast rarefactionwave(FR), a contactwave(C), anda slow shock(SS), respectively,as

indicatedin Figure 1. Note that thewholesystemis moving with Alfvén velocity v~,i.e. a wavestanding

in the simulationsystemmoves with VA downstream(to the right). The two simulationshavebeenrun

up to different times. Therefore,in thesimulationrun of the270°RD somewaveshavealreadyleft the

region shownin the figure. Only a part of thecompletesimulation box is plotted, this part startswith

= 0 at the left handside. Figure 3 showsthat thesituation doesnot changedrastically if the

oppositesenseof rotation(electronsense)is obtained.

0 ,(rj~1,,) 2(1(1 II 200

Fig. 3. Sameas Figure 2 but with right handsenseof rotation.

Themainfeatureis adensityenhancementat thepositionof therotationaldiscontinuity.This enhancement

developsrelatively independentof thephase~ andthesenseof rotationof the rotationaldiscontinuity as

can be seenfrom Figures1 to 3. Howeverthefinal structureof themagneticfield dependssignificantly on

the phaseangleaswill beshownin thefollowing section.

EVOLUTION OF THE HODOGRAMS

It is alreadyknown that themagneticfield of rotationaldiscontinuitieswith a phaseangleof 180°(and

~3Bn= 60°)is relatively stationary(/6-8/). In this section we will presentresults on theevolution of

hodogramsof rotationaldiscontinuitieswith 270°phaseangle. In ahodogramthe two tangentialcomponents

of B areplotted againsteachother. Thereforethehodogramvisualizesthe rotationof themagneticfield

throughthediscontinuity. Figure4 showshodogramsfor the right handsenseof rotationat varioustimes.

The left panel representsthestateat thebeginning, andthe right panelthe stateat t = 200cl1. The

parametersof thesimulationarethesameas in therun describedin theprevioussectionfor therespective

phase.The senseof rotation is indicatedby an arrow. The initially 270°-rotationevolves at later times

into a 90°-rotation.At theendof thesimulationtheoriginally right handedsenseis left handed.Swift and

Lee /6/ havesimulatedalsorotationaldiscontinuitieswith suchaphaseangle.For the initially right hand

(electron)senseof rotation theyobtaineda similar evolutioninto a90°-rotationwith an ion sense,whereas

for theinitially left hand(ion) senseof rotationno conversionto a90°-rotationdid occur. In order

(9)114 P.RichterandM. Scholer

B.,

3

t=O t=100 t=2001

Fig. 4. Hodogramsof a 270°-RDwith right handsenseof rotationat varioustimes.

___ B~ ___ v ___ ___

*1 __ ____

= 0 = so tc2~= 100

tcl~= 110 = 130 tcled= 150

Fig. 5. Hodogamsof a270°-RDwith left handsenseof rotationat varioustimes.

to investigatethelatter resultfurther we simulateda 270°-RDwith similar parametersas Swift andLee

(~3= 0.1). Figure 5 presentshodogramsof this simulationrun at varioustimes. Swift andLee endedtheir

simulationat tcl~2= 110. The resultSwift andLeeobtainedat theendof their simulationis quite similar

to what we observedat that time. However, thedramaticchangein the shapeof thehodogramoccurs

later. At tcl~~= 150 the RD hasdevelopedalso into a structurewith a 90°-rotationandreversed(now

right handed)senseof rotation. We havesimulateda numberof rotationaldiscontinuitieswith various

valuesof /3. The hodograrnsevolvedall in thesamemanner. Thus, thehodogramof a270°-RDdevelops

independentlyof the initial senseof rotation into ahodogramwith 90°-rotation.Thetime constantfor the

senseof rotationto invert dependson the initial halfwidth, D, andon the temperature(or /3). If /3 1 (as

in thepresentsimulation),this time constantis largecomparedto cl~.The time constantdecreaseswith

increasing/3j//3e. When thehalf width is lower thanaboutoneion inertial length (c/wpj), theevolution of

the90°-hodogramoccurswith atime constant

RotationalDiscontinuities (9)115

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