Dynamo Process and the Magnetic Field of the...

;t; 5fi .;t, (200:1) ~I I ~2S J't

ltnllilk'J:I;s:F~Jil1L\liJf~t ;_, 7 -* lUI fF R tJ 'J 7 ""lo-"--riffk'l'** David J_ Stevenson

Dynamo Process and the Magnetic Field of the Earth and Planets

~asaru KONO

Institute for StCJdy of the Earth's Interior, Oh.ayarna Cniversilv, Yamada 827, :VIisasa, Toltori-ken 6f\2 01 ~:~. J;wan

David J STEVENSON

Ctliiornia Institute of Tcchno:ogy, I :10 21 PaS<Jdena. Ci\G 1125, USA

: r:ectt vee: J utce 12, 2003; AcTepted October 1 0, 2 00:~)

Th!-f'~-(ii~n ... ,r, <(Hl~J. , lu11~- r~onlinl'~Jr d~ namo n to(.k'Lj were ~ ir~t presented in lt)93 ~J~· \\\"U gn_lllP~ 1:1

,l ap:tr: " nd l ' S_\ Since then. ahoul. •en group~ lli~\'E ~eported similm simulation results. a nrl ~onw

1r:ipona·;: J)rOpl..'rt!t·s n f :he dYr.an1o~ bccan1c known from these ~tudie~. Also iu recer1t. ~--cars. nc\' obser-vational results <:ccuruulaled for the raai{netic fields of planets (inc!Ltcling satellitesl, and indicate ver)- diverse rlynarno Dnd inrluc t ion effect~ in these bodies. In this review, we first go thro ugh the

'net hoc' r: mploycd fur cltt' gcodyi':lmo :>imulatior!s, a:td ~how how the magnelic field is genera tell and :naintained by che convection system in t he rota t ing sphere~ and spherical shells through a process similar to rl-cllcct studicc.l by kinematic models We then review the observation of the planetary magnetic fieltis in the solar system, and investigate the conditions required for maintaining the dvnamo process. Lsing these results, we examirce the magnetic fields of the individual planets and consider how these C1elds are produced: hv d.ynarno. induction, or remanent field.

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** 130-21 Pasadena, CA91125, USA

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Table 1. Groupi n)( of the :JD D;muuo Simulat ion Rt'su l ts

Group Publications included in the group - ----

K S9.'i

G R90 GR96

Kagcyama el ul. (1990>), Kageyama and Sa to (1 997a. h c). Ochi el al. \ 1999)

Glalzrnaicr and Roberts (199.)a, b) G lalzmai er a nd l~oberts { 199fla .h 1997). Coc <'l at. :.2000). 1-lu'uens and Glat zma ier 1.20001 ,

G latzmaicu•t al. ( 1999) KB97 K AK97

Kuang and Bloxham ( 1997, l \l9H, 1 !:J99 ), lJio xham :2000a. b) K irl·a et al. ( 19971, Kida an d K itauchi (1998a. b ). I< ila uchi an ti Kid a ( UJ98:1, Ishihara and K i!la

(2000) COG98 SK99 GBT99 K MH99

Christensen el ai. ( 1998, 199!:!, 200 I i. Olson et al. ( 1999). K utzner and Chri~tensen (:!OOOJ Sakuraba and Kono (199!:J i, Konu el al. (2000 1 Grote et a/. ( 1999. 2000a, bi Katayama el al. (1 999)

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l 9fJOSf~f,, :, 1980 41~ i : /J'n-.:-:.~ . <" :.~ :'5 J:f.;..l:.J;:

Bullard a nfl Gell wan ;J 054.' ~:i .-j:.J;.-L c( . ; · i / · ? •

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~!!V'> f.!i~C'i Kagcyama eta/. (1 995i t;J'_ c..~ Glal7.maie r

and Robc:rts (1995) :: o':. ., ·na~ ~ ~l. f. ~LJ:..!-~U Wrfl -c 10 ;J .C:.'v.l :'l' lv - 7' f.·> ,~ .f s,;; /;; ·"£- 7' •> -a: ft~ 1.. -r •. • ;;, (Table I J. -~ :.'J~;';.J:ll: . 71 7' .o:.- fHJ.lc.i)~J:t! (f.J t.; .~ 1; -"-

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::.. c/)J!ili:<:: :: ~iH 1 ·c:J:, Kun o and Ro hP.r ls ·:2002; :F.;J: ')

Sttvenson (2008) :: J: 6&iLfO'J?;£;l#.Jii\)(i: t, >.: -·i c '"l ,

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i'i 2. 171 7 'E <DM~'¥$

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rnaier and ]{oberts J J -;t ,-_. - 7't;> 2 ·.:> i: 7j i:t 'C !.·) 9 o)

it. GR95 ·c;; Boussinesq j~fU-'!2L-I:i r, 'i: <7>i: i -J ~ . ·c ~~y)i#:v!~ -T 'v <Gl<9f:i) Ti:;:;ll -iljif::i[f;:J.;: .,; ·o T ~ ' ;;,r .. ,

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:~ J -1 i~ !l!i 1*' • Davic.l J. SLHenson

101~

101 111

1017

1018

1015

101 4

1013

rn , Q12 a:

~ 1011

E ~ 1010

~ C) 109 ·a; >. <tl 10" a:

107

10•

10'

10<

10"

10' Pr = 10 2

-{::( Earth

~; KSS5

e GR95

• GR96

• KB97

., KAK97

'7 COGQB

'I' SK99

0 GBT99

.1 KMH99

(> Benchmark

10' ~----~--r---------------------~--------~ 10"10 ro11 10"' 10 7 10..., 1o<· w·~ 10·3 to-2 10-1

Ekman Number E

Fig. I Relation I.JeLwef'n the Ekman nu:nhcr E ar;d the Rayleigh numher N.a in various MH D d~· umno

mudc!s. T h ick l:ncs inuical t: Lhf' t hcorclical crit:cal Rayleign numbc:·s c.lderm inecl by Jones 1'1 al. ~:woo:. Thin lines ,;iluw v.1 1cLCs of lhe m odified Ray iP-igh IEimbe r Ra~. 1 - !-; · Ra. Afler Knn o ' tnd RohP.rts (2002).

to-" i;;c t,;. ~J . td~+- -T :vcl'JlW'-''l1!rr;~t,.:: v)i/~;v· ui:;

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1 :;:J:?.1:fGR95 c GR9fi r :t !t~ <l.l:C -T';v ! :: rc '-::'(~-7

< :..-~tJl~~t~· _., -r 'i'~ ~ 'IJ i, c. t.t ; OJ ·r 5' Jvc;·;j:~ ~ •.ti'.l t6tt.~IR;t Vet; •:J, i" OJ :: !: ~;J:ltft:&J~I : 1·5)- :i5 r;:~~~ ~ ,f?J;! f.l<i.F)7.> . J:.I.T !.:~.; l , ·c:.t, KS95. "-/·r <- ~,

SK~9. GR9fi 0) ~ -1:c 'f' ;t.- :;:: ;::f. f; i... ·c ~~ 1 7 ->:: f'l· 4-J !.: ·:; I,. ·r~-~-9 0. ..: c:j -) r, KS90.!: ~< / + "?-. '7 ·e -i-' ·•

1:1., [ii]fr;.>?>}!I < ..r. ;(. Jv-1"- Un: t •t~A-0 Wil, SK99 :;J:[!!J

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:J cartri dge bell L YP~' convection ~ I")'A-t~· ). GR95,

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31() ;:O;!V(· :R • lla v it! J. S Leve nson

(b) SK99

L g. :1 Snnpshot~ of tbc r<td ial compon(•:1h of the vc>rLici ty : W.: ill. r= O.!J8 [~.:- anc th t> magm:lic iie lcJ (H,) at the C\:!B for (a:· the hncr,ma:·k ar:d -: lJ' SK99 mo<il'l,, T he conc inuvus i.J as lwcll li nes inc ica\c uutwa~d :inwnrrl) nelr:1s. T he maguetk !lu x is concen tra ted in the cyclones ilV, >O) in both models. Orthogonill projection ceutered a\ the north pole. After Kuno and Rohfrtli (2002).

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:.11 7

(b) SK99

F i:.<; . 4. Snaps:;o \s o: tile ax:al cumpoJJt'llh or ti:c \"or·.ic:n· '1-t·, , and the :nag nctJC ficla :A, : in li1P

cc,ua:orial plant'. for UL the bt!ncLrr:ah ;md tb.l SK99 ruode: o. The cur:tiii;JOU~ !clashccl: lines

indic"tc ·Jpwarct •aow nward:t nclds. anrJ rl onerl l inf S:ww, \.J·.e zero cor:lour. T l:e ::wguetic (ll.;,

concer:trate, in tLc anticyclo;lcs t il'_, < 01 in both models. A ftc'r Kono ar. ri Roherts (2002).

::)> :.;, a vJ V 1 -J· '!': :,; 'B :3 •! · ;.; . ·b . ., J: L Olson (;/ a/.

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OJ {) :L --::: ~~;-1t~.:. 7( /i ··) -c l-' 6 . Fig. 7 ~i Fig. 5 ~~ l:lj ~~- .1

--~ t:::.tfi [ni;,Jvl 'f'.:-:-J ?: ;), L t..: L u ::.' J, ¢> 11:. iJ iJ.'·.J -·cc tJ;~7111J ~il1 .h ~b ;:) t (l n~·cn t cv\i!1dcr r*r L::: 1f·+ r_ --:-- l- 1 ~-;

n L ,JI,"K::kdili: ::~Lj.J I, -c: \ '0 .

Glatzmaicr a n d Roberto (l !.lV7i ;.: ; ~L!;L C. ~ t ,:, :7)

l1•f•~ (ti); u;.L-'; :.: L, ·c cil?Aih <" ~ -5 ;Fig. ilL @l-'dtllL: Ti] .;~ kr·mif.~Jl •iHg 4' 0 6\E(:f·:: (;:, :;r;tr}JpV<i~:h''<'fJ

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3 LR ito!!!!' k · David J. S tevcn~on

B,

l'lg . . i. Snapsho1:; o~ <·tr,irTturlnl <l l'l' r&gc·~ of merictional <tnd at i :n11 1h<rl c:ompolleJJI ~ <lf q•locity ( V.t;, V~.: ;mil ma~nct ic !ide! iR:.1• 11~1

~or t he t.Jenchrr.ark :tup ro w). SK\19 :rni ddk row), a7HI (;R96 (bott<Jm roW.' m<xicb. T l11:'

I)Dsit i vc !:1cga tivei lXIll t.our!' iudicalP coun· terclockw i:,e (ciockwi~c.; raeriritonal fi eld lines ( v,,. and R.1:1, ami eastward (west ward) a~inmlha l fields i.l·,, and B.). After Kono and l<oberts (20021

'· · <S: ," J.: .~f.l ::!:J·t 7.> . -::. oy,'t,t;u; ~~-g· ;.: ® < ~!\ t I -Jh¥ .;;·t : n;::. , tangent cyl inder J:. >) :$'1- ::. (:j: i:! .!: k}.:'}JIJ!;f)fJi

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1',!. t ' ·

anticyclone (a)

cyclone

l·'ig. li. Th~ <iyn;;mo mcchall:~rn a5 texpla iucd b v KagP-ya ma and ::ialo i 19'l7l'). ;.:) Cyclo

nic nnd anl t<:y<.:!onic convection cell~ ior :11 a pair. and are associa tec~ with counter· clock wise or clock wise ro t.a tion (as seen f r om \:ort.h Pole, shown by lar).(e cmve d arrowsi as well as cquatorwarrl or pok· ward flow :l arge straight. arrows). T he toroidal magnetic fie ld l ine~ an• deforme:1 il <; l ~ 2 -~· 3. (hi Deformed fie ld lines in two hemisphere:; reconnect ncar a and for m t.he poloitlal field.

§·t. ~~11.)m~

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Temperature

Differential Rotation

\ )

Helicity

M~ridional Circulation

Fig. 7. 1\ snapshot of the longitudinally avP-rageC: temperature perturb~tion, l":clicity,

differential rota tion, i\lld meridional c :rctt

lation in the Cl.{\!5 mode L ~ote the ;;t.rongly concentrated activit y within the 1<1ngent. cylinder. Repmduce<l from Glatzmaicr and

l~obcrts ( l ~EJ5a: .

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!: ~~u)[R~r :t-4>:'8 IJ':rc ii: tJ: <, ~ ::. -c iii ,':: Y) -n~

").

1-tl!I:f.~~~ i7f<.t;l. #Q-. l1t!};t'. ~- ·J:Y. 17·-, i±

l-:!:Ai;;A -ct~Wi'i t {J tllr'l'l (~'!i .': -< .7 :f. '-' -~· ;.. ..r; '-' '.I 'r 1 ~-\"'~iHt~. i:::J:cr~.~jJJ tJ .. _;t.;6. j.:t3-T::i:v 11;·

1 I· ~JH\<'Vco&;gUJ>A:~ < fi$.6.fJi{L\Y':J;-c. -~'J:i:};l,;

319

s l'ig. 8. A »ketch of lhe flow pCJll ern in lh e GR

models. The rrwridiona' circttlation.' rw;; r

nort h a n rl snut>1 poles ctt-r y heat truw t he lCl\ ·.u tile CMB, ll"iticlt induce a slroctg wral thurr:ll winrl in tl~c' rl t rPcti C> ns inrJ i.

c a tcd bccJ.uf;.C' of : h e rotati o tl. T h e d as hcc: .i n c· <·tovr·:'i t:·:c t. a n,,~cn t c .. -:J nth.· r· l<t ·pro

d uced (:·orr: GLt:zn~ aier a::d Ro bcrh J_ l 0~j 7~--

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.~: . ..t.:~ ·,}:U; ·c _,, ( i(;'j.;;c-'J 1l0% < _,_. c ·:< <:' H,O. CH,

J;:;.;>.~=- ., -::- ', ""' · :k~fJ:j_j(jlj~bJ<~~ ~ )j" ::.;,;' -) · .

1) 1; 7, ~-, ;( 1' :/ /, I·') ~ / ~]=_tp; :r. 0:,• [J n' :Jj'#),IJ

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:. tl .; oJ'[_<;.'t,t.i :·· -cJt;f.iX.t./f; -Hi i:i!tf'.;?>:;;. .., t;;. f_,'i!/.:::--c

Table 2. Observed Planetary l'vlagnctic l'ie!ds

Planet :salellile)

cvlercur~

Venus

Earth

\foon

Mars

Jupiter fo Europa

Ganymede Callisto Saturn Tit au Ura nus

Observed surface 1ielrl

tin T, approxim<ltct

2 10 ' < 10-"(globa!)

5 X I o-5

Patchv no·" 10-';

4.2 X lU 1

< 10_, '! 10-7

2/ 10 .; 4/ ro-r-2>: ro-.. <.I o-' 2/ 10 ; 2 !0-"

· ;t·;~cht:. 'L -Jl<+!(JJ!'',t~ ,-cL, i ,,_,,t,CH" :'r-(*./~1!tf

·kt.t:J.s~·;: -·,:;s_ t\i!tr1\'l~<Pc:;. ':>(H#•:,,rJ\~ ··:-.nh;

i"f!'c 1: i;?;J l -c ' 6.

1.2 il!iliJ c ttt::~~lilt~ ;..· :.- -7 u . '-' :.-· 7i1H:: _:: t; ~~~..-~;~~-:>:-:Lo. f<'i':>!-' l:,f"'

L . .7-~.tJ ,., r~u~::tflf)};"' ;•,r:r~lt~:= ~: -· -::- ii'I~W.~iPIJ c- ;f':

t:. itli~_,j(: (j);'ijii'lff{ :.: J:. 0 b J) -~ fl yby :: .l 0 t u 7)• h

M~•. hto01vi'i8·o·)J;t;":~L'r-'J{:'j.;t,;;,_ Table

2 :::;:: •i"c .:o0il!V~.ilVi:~H~·:t ~ s'd: \Russell. 1993: Con

nerney. 1992: Showman am! ;vlalhu tra, 1999: Acuna

et at .. 2001). flA~.,VI!or.t:'XUt>Jcj.J:.: .J.) 0~~~c>)f~tl:#il.: -:,

> ,-c li :?l-tl!Hi£:±;\oc ~'iJm: {\:-'f: L~ I\ ,-z- /.'; -:S. ~:: !ji'f; L --c c't;,t,-!J<, *l11~'-';tf_!L)h:'(;J.~x@(-O)(t{l;Ht lO':I',.'f[, +

::t T I!..JJ11 L ·c f,J"Zffi:·h' $.PL. -n ' <S. ·777\-=f.!;jj hf.i ±.li'.TI;i:J~~'f-.':[Jll./<li!'f:;IG]f.£.~cD:*:c'i t<T!f: <·) , :t t:

~:i:Jo:'E-(<I)fll'\ ~(i40° 60'2*5''·

4.3 ~rx1imt.J~~::: ·Mkllf 1£Jb)ilJ..:~- ~ ,i ~ ~Ll1~j!f.)Jf±i\ (3} ;:_ J~ ~~· ·c·:z~L.~ At

Q. 15) ::t~.WJ/J;f;_',IJ-li;\CJ:.:t;t~Jtt1Jf2.c\:.!: f:;_ •J, ~J.~flii

il:!f!Et!z r--L2 i:r"r; -c;~(f:nt 0 ~L lt%'-':lt7'4~tYJt~ft::~ J. :_. t=M-, -r, lr£:;£.f.~f~t4-~!, l~ lb :.: L;. r5) J:\J) -bill~.{\~

Comments and inLer!Jretatioi:

Not well characterized or umltrstoocl

No dynamo, ~mal\ n~rnanence No useful constraint on loc<Jl 1ielcts

Cure dynamo Ancie:t l dynamo'? Impact. genPralecP \"o global iield

Ancient dynamo Locally s trong remanent magnet ic linea t io n Dynamo (extencls to ne;;r surface)

Comple x \dccrlv imbcdcterl in Jovian fi (~ ldl

Induction response l;;alty w a ter occan_t

llynamo likr-ly lncluc:tiun re;;pnnse (,;ally waLer o cean·l

Dynamo iJccp dowu:

l\eed more daLa llymimo (·:l nculilin rli'pl :1)

llvna:no ;uncertain dcntJll

:c:: .. J~~ · . .rtl::.-t_---< 7~·-:·· <· J)"'t::~ ·. , · :.:J> ._~-~-~:.1'·;;~, . -

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kit Uu:L<' ..P'JJ'Jtl'lf:! tt !WJ:l;l<l ;;, -: t :.·.<I ;;:, . :1 T t;:

·1$:/.:. r~H:-a ;;:, t 'W:E-cJ 0 ,t-_, ;i>ll.i: 1+.-: 'l'lt r t.AY<: ! ~ I

:. -c (i ) ~~;frl ~: ~i~

F:ut~t l ----:- -pC('r(d'f./dl)_/3 (22:

::. ::_ -:: t i i ·l;fH H. c._. : :J:J:l~: c J::, .;s . i:~li 4> :-1 T LjJ ;::- en~

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•2:1,

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F \V!;!) 2 Fj;~·I•O. ~ld t! ~ -, "i"' -11 t: r :;::ltf~rJL. -c l ' ~(I) ~c' ~~-;n

ilft&"J~';t$ f.S(-;__'.')\.!tct.') )(~ .',\;- 'i>'t)",'f,(O)~C 6 ;:t/i .;" ! .:. .l ::,

C. fJ' ·c ~ 0IJi, :c- i!J/iH !ik!!;j(O) :J T T !:J. 100 K/Ga !.'r ro.:. -'2 i ·, J: !J ;J,"' '•:iJ!fS1.n~~~ (!i'J;t ~-f ti =-; cr') -c ~ i

300-400 Kil~a f',rt-cJ:s 0. rt~J;J(0tf';{;-, :. ~)i~:!;IJ.:!i!.t

/, .~

IWl-.AMO

~LlilU~

, _ .'Il.'h

{_'fJ:"\-VECTICl'!'ll hLH ~()[IY!-JA\-10

r.-.. _,rr~ .. ; p :':m f }

L__ ___ • ... - -·· ·----·-· I

tk~trk•l (illd thermal) con.:Ju.(t!.\"ity

F1g . >)_ A schematic diagram tihuwrng the clcpendence or dynamo opcra Lin g region on pi<"HW' si7.e a nd electrical conductivitv. At ,;ullicic:J\ly low couductivil v. Lhc~c is a size ckpcnrlPnl ctJI·of hasect on tlw n~Prl to c xcc-crl a criti ca l n1agne1ic Rcvn•)lds num·

l)(·r l'i·Ic- !'\: i !-i al~u a!l appco;.;irlli;;tc~\ s :zc·

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~. I .Trl::~t r·i .. JI !•l.::.d ·~· -. .-... lie· Jl l'~ ~ : ·.:Jc :·i.<ill ; i ~I Jtd

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ct.Hn:·t.)rtablv rcnHJVcd :ru:n ci:~~t'!' buunc

o.rv. A t11o:-e t;(Jtfl plicatel~ ·~jut s irn :Jar dit:,~· ;~:·: ) n' \vi:l ~:pply if ·here is cornpo:-;!J io:·wl

convect1on or lAte"t hrilt releil:;e fro1'1 a in:lcT core. :\ftcr S:cvcr:so1: i.i!OO:-J:

h/aT-2.45/ !()-" W/SK ' 1241

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32 1

3000

2CCC

l OC C

0.5 1 • s 2

l'ig. 10. Var·iation ul mag netic l~cynolds nurn· \)er with heat llow. The horiwnlal coordin!lt.; </J is th~> total hent flux in units of

F .,,., ,,,. Purclv therma l co nvect ion is

assum ed and requires <1> > l. The vertical axis is lhe value of lite functiom labeling

tlw cutTPS. 1<"'·'"1 is ·Jw m agnel ic Reynolds nurnbr: r fur mixing length theory ami

R "· ,.,.,. is the cstirEalc [or Lhc rnay,nc lostr()phic reglnl(' ~sef~ text: " is tht• co re· r,·,diuc in u:1its or Ear;.h'~ co re. :--Jo tc tha : N.,.,_ .,,., t ~ 1~. p~cali~ s tt:allt:r l;y , :.11 u nlcr •: .d

m;:gnil·.rdP. Thi' plo l sr:ow~. lr:at Rm r~1a'

r· i ~,;c r·api(J:\ n nce tht.' t"·ritr·rin·' fnr p"tfiVH.'·

inn t ~ : ~; aiJ ~:.i l c-~ 1. ~;o tll:tt l~ ~ (' critcrl():: rnr· d

d:~· !nm •; Jrti::~ :~ q ; niffer gr(•a i i:.- fro 1:1 I. lie·

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s imilar d i . .:-tgr'i:H11 (:lp)ijc·~ fuc· con1pt .. l:<: ion~tl

cunvedtou but r[J ts the1: :·elated to tlic h .:o\·anl·y il11X ;;nn 1:-:t: l:t: t i~:a l ~ u: ::.:. flqw is

d.illvr·r;l: \. .\Ite r Stc1 ('r·r,;<.w :o!Oi.~:.-: 1 .

'. t·--.. ::<:~i:t; '. ' . u . ...:.: .i.\ltlf.fiirig.'l : :.·j : .:. 1 , -c: ~ ·

0.

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;:. Q {, J; ""C (e.g .. Clayton. 196/:l: Stevenso n, 198/l.

F,,· ·. 0 .. 3iLF" "''·/pH7·J 1' '' (2!\:

.: ~~ :::• V,,, i1Tft2 tc~~i[J:(t. L :i;'1.~i.='l11f Ut:~·:::' 1·

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}] i~' il iJ[ii]fi'lt <': -s· ~ •L IJ.l L' ;y,;:, ~e. g., .To nes. 2000:

Stevenson, 1987:>. ::. :nlii(~;rt!iiiii\t_ili:i~J -c(i,

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:-'l22

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1) 11'- .!: t.;. ~. .: : -c C/> = F,(lr.•l/F<·lr-.d. ~~ -c_; £f.>~ . ...: (i) l¥]{*

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n1ha and Kor:o \19~H1:..- _·: J_ --:; :1'-lff~ViJ.·~;:);;j/>:- ~ : ;: 1• 1

·:::·j;~;: .. · ·~; t.St c\·(~nson. 198:3_1, 1j ; .:.; _;{~i' ·):~;; ) .·( > ~~ ;: ,, \.:

:~.: ... _ -~ i~f.q:. ~ .{ L :·-.-.. .!::. .'d:.:. :t1J. -~ ~;. I-.-- - ~- -r v: v) ';'it:~. · Ut~ ' :.1:;· r7·:rj: ~- "i> . / ;.· ". 7 I· !: ') lh~)rtH<;Ji;i 7' 1 r 17:1 ::J -1: ;z-.~j'J'

~' - ·7' 1 1--t: U,i>:· . .. -.f.~.: l'Ci, , -'C ~ l.t JAJhY/_;;:,.;: .,·c ''~ l'·l ~:-l{~ f...: (I ' H:. :11 t. '·q~ Q .::. ~, -; :hi-17>0 ~ • .;; ·c.t, ·• U 1·

:k~ ::t<J -~ c> < 40 {ffl: ;:. ~J rFiC.:l J' 1 ·J- ~ ~{~ ~~~ L ~ I, •r.·. (,\cuna el al., 200 l; Stnen:;on, 200 I; . • ::. u:,v_,·c

Table Cl. Operating Condi t.ions ior Rcpresenta tivP. Dynamos

Qua n t ity Un it Earth (;anyrncdc J u piter Uranus

Rotati on rate. Q s-1 7/10 ,; I / II) ; ~ ...:Jo-• 1.-1 K I 0 1

i )r;nsity,p i.:g n' l.J< l O' 6 _.A ll)·' I ·10 ' I :<.10·· Siz<.' of dynam o reg ion Ill ;1 X 1 0'' 7 ;v: 10·:, :1 '< l () " l ', 10 T empera ture scale h eigh t. Hr rn l / Hf 4 :< 10' 1 / 10'" I >, I 07

Conct uc:tivc hea t flow along ad ia ba t Wm _ •;

L5 X 10-' i :.r 10 ., < 10- 1 <J O ' :\om inal convective heat flow Wm I .,. 10··J ] X j Q

., :"l -.. 1 / 10 " 1

Ele<:Lr ica1 concluct ivity, o S m 2 " 1 o• I -'~ 1 06 l X 105 5 / 104

Surfnr:f' !'icld ;;trc:lgth tEar!h - J; ().0.1 b 0.-l R, ba$cd on V,u 3 x. Jo:' 70 Cl X ] () ' 700 R,. based orl l~!llo.l" 30 3 ,H){) ') C .::.. .)

Elsasser numher .t1 at top of rlynamo 0.1 0.1 0 .25 .. 000 1

(2! ·k -~:.:·J:th/·t~·)~_r\1/ sta~nant lid it~_~ ,:: ~-ft Lt.:, ·::3i kt;!u) .J T :i; :·ii~i:DfJ ;.ig.;:,ifJ$:11"i::i .7 / + ·t:-2:: {1: ; !, _,~

b~ -; <: \' ~ 2: .rt,;t .Hi 6 . .-:, --;-7] X_~-~. :; ~1/;·~ VYf~t[~ .!_: ~~~!l .8~

;, -~~tr.?.dJi -:7 ,2: ~.

4 ;;t ~: ·J l·~ --c· IJ. :~t:Jf; iJ"~ 1~ "CJ · ~ .. :_ C : .. t~,4_j~~_fi tt~-:;

: . .::: .;: .. , -c-~1:-tr ~-) ll--:: ~~ · g r; -~ L~-r.~}t;,~ :~ .f·) f: -~· t ;-~~"1: J l. -c ~ \ /f; ::: (i -.s- ~- f~) ~l i:1,- ;~ , .

9-1' 9 ;.; : : U.,f'5 '4i£U!i·'~i':<:,')'~:· ) li;:l~~>.t, 6'r·L :_it:;

·= I[ i ~ IJ , / -'-h'tJ:>l~ C: !J;' [j ;/'1_~'#;~\ ~~ 0 .•. :)•\..

.::, -l.: J.~: ~,._ ;~t~0 ( .r.? r: -"'. h 1.: 7 .. r· _) ,;]~ () ~~lF~IJ~Jtlf'·.:· j tl';J!.- .- -::: ~'- __ :

;;<;.I:!IL:i!IJ:E~LH/Il J.:;,, ~i.i.>~.;·:·:·/·<.r.!: :f;/• ·.,'. <f .. <:'·. ,-;: _ f,; f-F ··· :?)7_\!:J:. --:. "C .J{'/f1i ·~-;~;Jfi·~x;_rrtiJ \ .i~ ~:) /l. ~t _.->

JJiiHt t. J;. ;;, .

t--!.1 t--;.;c:~:E~:;~.k. 7 :.--t,.::. {':;;iii;~·t rc •. ~ ~:

I' 5. ~:tBJ:.Uta~~

;-·1 .'- <.c f- -; ·.•vo'J > 2 _, v - :..- ,, > \t , (' I W~u) i!i")J

-:J) 7\:tQ ~;. ;5--J\. C . ..: 1~- A: ?:' 1: :~~ ~ J): f.-; ~l t:.. Flf.~~R~t; .'&

~~~+-:-;· ~~ L -c. ~~i1i CJ#.:~'P- .'1~!;:_~~0~ti 'k. .II~~,j)Sif ·c

i:. t;._ ~ 'l 7 J' "-'9 :!) .), -{, ;;: \ ' 1:,1,\j< ,:_; ::. .:: ;6>, ?: < J){iff)Y,;ii:

.1 . , -c r- '?f:f' '·J :: tlti.t 2: :J1 ·c '· · 0 . r: t~· - {o -; · .. ~ :: ~w · :~, f c 'C L · 0 ,. 7 J- 'J Ulti!I;;<:'.J :J 7 ;:_;. ~; ~ ) .__ \ •{[1fZ, .. ; il

I.:~ <. 11~ :+ ~F::h ·c ~· ' :;S . :i .)- t.:. , cW-70:.::: /1 \ t.>- fi. _L -~· -~~ > :t~(

:..··;l.: tf, i.:i#W iej )_;r"ft~ ~J ~~~~~ :..: {~-< t; ;) \)t!f:j;: t:~) ~1 7U>

'-~~,(1, <~ 1 rn\ /~;-it:11 · Wr~:(t) ~f~ JJ f) \ 't~~L~:i~ ;;Jf'/ 1·[ ·c

i ;: . Jf!~fl~rJ·,· 7;- 'J! .: ·-)L·-c,;~~t\}i/ '.,i:: r~ ·.f -0~ ··'

_-;, ... :;. i =~ :~· /v ._J-~· /:; 1• • . -: .. tJ·~ L fhl !+ J ·c 1)) Y -: _-:. !/ - -> ::: .:..

· .. r • ~ • .-·. j ~- _ .. ·, j.:jJ•

, .··. : ~ l .. :Y ;; ..

. ,,- .; I·.!.; .•

·-; J i. ·_:i . ~ :_·,-·t_~ ~ ·{ ·:; · ::_.1.1 -_ ,:.= ~ _tl_L;· 1.. .~~-··.:-:t_)(·

t" ;:. _ .. ~~ (;-- t J_, ::) ~ Ct)(: c.' al., 2ft00 ;. t:J{ j j(;:: ~; ~i ·c-, .:_ ,_,:) --~:

<- ~~ -~ r;.-t ·:.t .. t .: ... -i~ :.Ll:( · .. l> f /;/.~ · -:. t~ ~4: L ~ .;; h..u 1 ~o

:mel Robl'rts t2u02) -~·{;!.':8~'. •t: '. ··.

~:; --:: ! .:::. --; t .. ·r-~ t?) i Jt_-'J- r~ r: -·-_r.tJ.t""L ~t~l .. , .:: ·g;~~ -: r~{,·.:;

!:. 7; .~- :: .;; '· '· .. :n .c:: -c e:ri7i'f:; 4~i: · - :. FH:c: '' ;;,;:!.' '·' L!<'=H'·f :•.' lf: f.t;:[:"}Jc) HT\•1' 4; < :~!~" ~o; ':1 . {- :tl/;<.;J; . ' ·-.

tJ >7- -~ ~{)·-.:if1i}J~:.7< ~..t- -=.:- ' l~htl:~ . _.-cfp t; i;5"1;(~

:~r:. . .L ~ ·. {.. (.') --:- (V: 6 ,=-_ ~'" ;<~ ~- UJJ ... _:, /) ·.;: .~.;, -~> t:_ 4-: -) -:f" ~ ,:: ,

1"TH N: • Dnvid J. Stcvcn~on

Y1 J- ·E-o~-:4\~>iDJ,~. :iJI] >t:fii&~JiUt;t.;:~; !J;~'i34J.O):#.

. ~j:..: f~ ., <: ~ • ~ !;· ti ~ oJirHII :i . -c v.: .T.~t,!(•W'J;\f>l/l)iti<:>

.ieL~.JII!i'ki:~·x_ .;, 1·.-.c•i~l •;!;1WJ:~ '4 1-'JJ..~.::: .!:M~

JW~~-d. -j _

.'5/i! :;(:"fti ~<im.;_, _ ltJ;J:~<;xv~ o"'-><:! 1 ! '~" l!tiifi (j) ili~t¥.(T.J m+

C: U ts;io') 'C~ ft :.:·l:ii· .-\, t.'. f~tt~o) {-j' f:-: t;i.:fl ;> ;J.;: t>- ~l. 111!

BRf~J:I,\ ,.::: :i1;>t.: t; ,~ ·· t: .'l 1 7- -t ~~~~b:(~i~','I) !L-'1 ' -;f.;:l;~

1 ·r ·-f. t~.'IJ~~):i!ii:t)i ..: -; t ·-ct. ~tl!ff '"j;B ;:) C: f_,J : ~ J:. ·! u -t-7' IV( ,; ~~H):j<:; ~ -:0 :l i -c j';- •1' L~:i;;,.l)ltfiH';(;" 'j'cU~Jf.,( u: tr. f=l·.~\·ltif:;r~~·;:::;;.:.;) ·=J . •, \ -g"·~-L~;:: . __ -c ~), -LRU:c.t f~~hii .

lmiRJ c ~-, J!i.i.'t;{~Y) T 1 1~- < • .: ttfi• ; , tii.J-:: 11' ~' i<r<· ,:, ~ ·-r· ~, ., (-: ttf<l,ti t.;H~~f;iJ!'~.: lirtzttt;<l:';',t '· A:1t'~ ~

:\cu na. :VI. H .. .J. r:. P. Conncr,leY. Jl. Wa>Ci le"~J..:. el a!.. :!IJO l. Magnc-ti<.: iielu of :VIa rs: Su:nn::uT oi ...-,ul t s rrun: : :".C ~H~robral<i ng :·Jllci Tllappi n?, ' ... ~)i t s. J_ Gt..•n

p :; 1 s. I( c.; .. 106. 21. •lW{-2:~. -11 7

B!n 'l:!:•.m . .l.. :;!IJOOa, T lw <-:'kci ,r r!· ···rn· ·J! ''"'-'·:tt<,:t:k inl fl r:lcr.in n!-i nnd !.t1c· l :~ll .:.tL'OSt'cuh r \",:j;·i.:Jtion. Phil Tr·;; l ~-~- 1~. Soc. I ~nnd .. :\ a:1R 1_ 1 7 1 1 1'/'l.

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Jll'ag in,;ky, S. 1.. 19114, Kinemat ic ·w1ccls r.{ the Ear ·

til's h yrl rnmngncr ic dy r:amo. Gcu11 1agn. Ae:·on., 4 ,

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Dynamo Process and the Magnetic Field of the...

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