Direct axisymmetric Vlasov simulations of space charge dominated beams

HAL Id: hal-00129677

https://hal.archives-ouvertes.fr/hal-00129677

Preprint submitted on 8 Feb 2007

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Direct axisymmetric Vlasov simulations of space charge dominated beams

Francis Filbet, Jean-Louis Lemaire, Eric Sonnendrücker

To cite this version:

Francis Filbet, Jean-Louis Lemaire, Eric Sonnendrücker. Direct axisymmetric Vlasov simulations of space charge dominated beams. 2002. �hal-00129677�

0/'1*32$45%' 67298:;<

=?>@=ACBCD@EFHGIKJL>MON>PNQERTSUACVWE!XI@Y.>@Z\[^]_]_E]P`LVUa

bPced EVgf

h&ikjlnmo^pqsrutwvWxzy{ru|U}v~@!€^ruy?ƒ‚yO|zve€^xHo\„†…ˆ‡w‰Š‹Œ*Ž|{x‚y{L!€‘xz’;“vH”‘vg•_o

–U—!˜™Uš!›wœH\ž›!ŸQ ¢¡‘£Ž¤›!¥UžŽ¤¦™Ž§ƒ ˆ–w¥

¨ “6©mosª?«K«u¬¦­UoL„†…k®U¬H‡‹!Šª-xz€‘¯_°vWxzveyO…¢±²vW…O“³†´‚|zve±µoL¶

˜!šH\žw—¥Žšwœ™w¥!¡Ž·Žš!¥wšU¤† {¸šwžK ˆ–w¥

¹ºikjlnmo^pqsrutwvWxzy{ru|U}v~@!€^ruy?ƒ‚yO|zve€^xHo\„†…ˆ‡w‰Š‹Œ*Ž|{x‚y{L!€‘xz’;“vH”‘vg•_o

¤»¼w¼Uš¼ŽœH\ž›!ŸQ ¢¡‘£Ž¤›!¥UžŽ¤¦™Ž§ƒ ˆ–w¥

½;¾ƒ¿eÀeÁ¦Â\ÃÀ!Ä

m:qU€^ÅvgxzruÆH‚±^Åvg|z³sU”ÇÈx-|z³sv0”^rÉxzveÆg|-y{ruŀ^±Ê‚¦|zru!qÇ_|z³^v?‚¦•‘r²yO¯‘Å˅

Åvg|{xzruÆ̱²‚y{¦tTvH͎€\‚¦|zr²qruy.ruqŽ|{xzU”^€sÆgvH”P«_i¢|7r²y.s‚y{vH”º!q΂4ÅU”‘ruÏsvH”ÐÇCxzŀ^…

±²‚|zruq'Ç6|z³^vË̱²‚y{tTvH͎€s‚|zru!q΀sy{ruqs’&|z³^vËruqUt!‚¦xzrʂqsÆevÇ6|z³^vËÆH‚q^!q^r²Æe‚±-‚q^…

’€s±²‚xÅÅveqŽ|z€sÅn«!Ñ6³sruy±uvH‚!”‘yr²q*Ò\‚¦x{|zruÆe€s±²‚x|z‚yO|{x‚ru’!³Ž|{ÇCx{ӂx”Ђq\”;twvgx{¯

vgÔËÆeruveqŽ|Òs‚x‚±u±uve±Q‚±²’xzrÉ|z³sÅn«\Ñ6³sveqÐrÉ|?ruy‚ÒsÒs±uruvH”&|zy{ruŀ^±²‚|zru!q^yǂjlЍU…

Å;‚¦|zÆW³^vH”4y{veÅrɅkՂ€^y{y{r²‚qnLvH‚Åւqs”&‚ÒLvgx{|z€‘xzLvH”*|z³^vgxzÅ;‚±_vH͎€^r²±uru^xzru€^Ån«

× Ø^Ù?Ú\ÛPÜ.ÝÞ߆ÚLàzÜÙ

Y b

BCEVgAµSU]`LACVWE

c

FƒáBµS‘âW[ŽãâWACR

b

BµSUFWAC[‘].[‘äLâWåPS

c E ceæ

S‘VWç^E6`_[‘RÐAC]PSŽFgE`D@E!SURTâ

æ

S^âƒå_Vg[Žã‘E]Fg[

[email protected]]&E¦è

c

AÈE]sF6S‘BÊFgEVg]PSŽFgACã‘E6FW[é0êWë:RÐE¦F

æ

[L`_â6S‘âAÈF6Aµâ

c

[^RÐå_BCE¦FWEBCì`LEã‘[^AC`;[Uä@]

b

RÐEVWA

c

SUB

]_[‘AµâWEU>\êOFE]PSUD_BCE!âAC]ºåPS‘VFgA

c¦b

BµSUV6Fg[4ç^E¦F.S*D†E¦FWFWEVAC]PâWACç

æ

F0AC]sFW[;å

æ

E]_[^RÐE]PS

æ

SUåPå@E]_AC]_ç

SŽF&F

æ

EE`Lç^Eº[‘ä7F

æ

ED†ESURîí

æ

EVgEºF

æ

E`_ACâFWVgACD

b

FgAÈ[^]:ä

b ] c

FgAC[‘]ïAµâ4ã‘EVgìðâRTS‘BCBˆ>ñ

æ

EâWE

VWEç‘AC[‘]PâSUVgEËç‘E]_EVeSUBCBCì&`_Eâ

c

VgAÈD†E`ºD\ìÐFW[\[näòEíóåPS‘VFgA

c

BCEâAC]'éêWëôâACR

b

BµSŽFWAC[^]Pâ¦>

õ:Eâ

æ

S‘BCB‘`LEâ

c

VgACD@E?SF

æ

VgEEMO`_AÈRÐE]PâWAÈ[^]PSUBwösIw÷UøŽIw÷Uù?SUú\AµâWì\RÐRÐE¦FWVgA

c

FgVgS‘]Pâã^EVeâEâW[‘BCã^EV

AÈ]\ã^[‘BCã\AÈ]PçäòEíEV7`LACRÐE]PâAC[^]PâF

æ

SU]ûS

c

[^RÐåPSUVeSUDPBÈE

c

SUVWFWE!âAµS‘]ÎâW[‘BCã‘EVI\í

æ A ceæ

í[

b

BC`ÎD†E

äò[

b

V`LACRÐE]PâWAC[‘]PS‘B?AC]üå

æ

S^âEûâWåPS

c

EUIE]PS‘D_BCAC]_ç

b

âÐFg[

b

âWEýSþBµSUVgç‘EVÐ]

b

R&D†EVT[‘äËç^VWAµ`

å@[^AÈ]sFeâ¦>

ñ æ ERÐE¦F

æ

[\`&AµâDPS‘âWE`&[^]*F

æ E b âWE.[Uä†F

æ E c SU]_[^]_A

c

SUB\SU]Pç

b

BµSUVRÐ[‘RÐE]sF

b

Rÿí

æ A ceæ

Aµâ

AÈ]\ãŽSUVgAµSU]sFIUS‘]P`nF

æ\b

â0[‘]_BCì&SUå_å†ES‘VgâS^â0Så@SUVeSURÐE¦FgEVAC]nF

æ

EE

b

SUFWAC[‘]@â¦>‘ñ

æ

S‘]

d

âFg[;F

æ E

b

âEË[‘ä-F

æ

AµâAÈ]\ãŽSUVgAµSU]sFI\SÐâzFgVgS‘ACç

æ

Fäò[^VWíSUVe`&ã‘EVgìTEè

c

ACE]sFå@SUVeSUBCBCEBCASŽFgAC[U]4Aµâ.S

ceæ ACEã‘E!`K>

ñ æ E c [\`_EAµâF

æ

E]ÎãŽSUBCAµ`_SŽFgE`n[‘]TFzí?[*FWEâFM

c

S^âE!âAC]\ã‘[^BÈã\AC]_ç

æ

ESwã\ìnAC[‘]PâI‘F

æ

EEã‘[^B

b M

FWAC[‘]'[UäSnFgVgS‘]PâWã‘EVeâWEËâWåPS

c

E¦M

ceæ

S‘VWç^EíSwã‘EËAC]ûSýZsMORTSŽF

ceæ

E`'âWERÐAÈM ËS

b

âgâAµS‘]TD@E!SUR

SU]P` F æ

Enäò[‘VgRTSŽFWAC[^]û[UäS

æ

SUBC[AÈ]þSD@E!SUR í æ

EVgEÐSÎå†EVWF

b

VWDPSUFWAC[‘]ýäòVW[^R SûSUú\íEBCBÈM

?[^BÈFRTS‘]_]ÐF

æ

EVgRTSUBKE

b

ACBCACD_VgA

b R AµâAC]sFWVg[\`

bPc E!`K>

ñ æ E[

b

FWBCAC]_E7[‘äQF

æ

EåPS‘å@EV?Aµâ0S^âäò[^BCBÈ[Ží7âsõþEËâ

æ

S‘BCBPVeâzFVWE

c

S‘BÈBPF

æ

EËSŽúLAµâWìsRÐRÐEFWVgA

c

áBµS‘âW[Žã$E

b

SUFWAC[‘]þSU]P`þAÈFeâËå_VW[^å@EVFgACEâ>ñ

æ

E]ƒIí?EÐåPVWE!âE]^FF

æ

Eº`LAµâ

c

VgE¦FgA!SŽFgAÈ[^]$[UäF

æ E

SŽúLAµâì\RÐRÐE¦FgVWA

c

áBCS^â[ŽãÐE

b

SŽFgAÈ[^]ƒ>7]@`@]PSUBCBCìÐí?EåPVWE!âE]^F.]

b

RÐEVWA

c

S‘BKVWE!â

b

BÈFeâ0äò[^V.F

æ E

S‘âWEâ[‘äSnâWERÐAÈMËS âgâAµSU]nD†ES‘R SU]@`S&å†EVWF VgD†E`ÎF EVWRTS‘BKE ACBCAÈDPVWA R'>

õ:E

c

[‘]@âAµ`LEVTSU]+SUú\AµâWì\RÐRÐE¦FWVgA

c

D†ESUR

b

]PAÊäò[^VWR AC] F æ E BÈ[^]_ç‘AÈF

b

`LAC]PSUB.`LACVgE

c

FWAC[‘]ƒ>?êOF

c

SU]ðD†ETVgEå_VgEâWE]sFgE`:D\ìýF

æ

EÎSUú\AµâWì\RÐRÐE¦FWVgA

c

áBµS^â[Žã$E

b

SŽFWAC[^]ƒIí

æ A ceæ

`LEâ

c

VgACD@E!âËF

æ E

Eã‘[^B

b

FWAC[‘]Ë[‘äPSâWå@E

c

ACEâ[Uä

ceæ

S‘VWç^E`ËåPS‘VFgA

c

BCEâ

b

]@`LEVSUåPå_BCAÈE!`ËSU]P`;âWEBÈäµM

c

[^]PâAµâFWE]^F @EBµ`_âI

SU]P`ÎVWE!S‘`_â

!

÷ ø

"

ö

#%$

&')(+* (-,/.

$ 0+1

& ÷ ù ÷ Xù ö32

÷Uø!4

#$ 051

& ÷ ø

÷UùQ÷Uø

ö62

÷Uù87:9<;

'=>.

í æ EVgEûF

æ E `LAµâFWVgACD

b

FWAC[^] äb ] c FWAC[^]

AµâºSþä

b ] c

FWAC[^]ô[Uä;VeS‘`LAµS‘B7å@[sâAÈFgAÈ[^] ö^I.ã^EBC[

c

AÈFzì

'

÷Uø@?g÷Uù

.

SU]@`$FWACRÐE

>†õþEnS‘âgâ

b

RÐE

æ

EVgE*F

æ

SŽFF

æ

E&S‘å_å_BCACE`'RTSUç^]_E¦FgA

c

PEBµ`$AµâBC[‘]_ç^AÊF

b M

`LAC]PSUBSU]@`

b

]_AÈäò[^VWR'I†Aˆ>EU>

0 7 '9 ? 9 ? 051

.

IQí

æ

EVgE 0+1

' .

[^]_BCì'`_Eå†E]P`_âË[^]ûFgAÈRÐE‘>Kñ

æ E

S‘âgâ[

c

AµSUFWE`ïã‘E

c

FW[^V4å†[UFgE]sFWAµSUBF

æ

E]

æ

S^â4[^]_BCìðS ]P[‘] ãwS‘]_Aµâ

æ

AÈ]PçBAù

c

[‘RÐå†[‘]_E]^F&F

æ E

ãwS‘B

b

E4[‘ä0í

æ A ceæ

AµâCAù

7 øX 051

>ñ

æ

EnâEBÊäµM

c

[^]PâWACâFWE]sFEBCE

c

FWVgA

c

PEBC`

( * '

?Wö

.

I-`_EVgAÈã\AC]_ç

äòVW[^R Snâ

c

SUBµSUVå@[‘FWE]^FgAµSUBED

*

Aµâç‘ACã^E]TD\ìTF

æ

ESŽúLAµâì\RÐRÐEFWVgA

c

é6[^AµâWâW[‘]ÐE

b

SŽFWAC[^]ºí

æ A ceæ

VWE!S‘`_â

=

ö ö ( *

ö 78F

' ?gö .HGJI@K

? F ' ?Wö

. 7

$MLNO

' ?gö>?W÷Uø@?g÷Uù

.P

÷Uø

P

÷Uù

;

'RQ.

ñ æ E

ceæ SUVeS

c

FWEVWAµâFWA

ccb

VWã^Eâ[‘äF

æ

E;SŽúLAµâWìsRÐRÐEFWVgA

c

áBµS‘âW[ŽãÐE

b

SUFWAC[‘]'SUVgEËF

æ

E*â[^B

b M

FWAC[‘]Pâ[‘ä-F

æ

EËäò[‘BCBC[Ží.AC]_ç*`LATSKEVgE]sFWAµSUBKâWì\âFWER

UVV

WV

VXZY ö 7

÷Uø

Y

÷Uø

7

÷sX

ù

ö $

&

÷Uù 051

$

& ( *

Y

÷ ù

7[4

÷ ù ÷ ø

ö 4 $

& ÷ ø 0 1 ;

')\].

ë?BCS^âWâWA

c

S‘B@AC]\ãŽSUVgACS‘]sFgâ?[Uä6F

æ

E4SŽúLAµâì\RÐRÐE¦FgVWA

c

áBµS‘âW[ŽãTE

b

SUFWAC[‘]

'=>.

SUVgEËF

æ

E_^SURÐACBÈM

FW[‘]PACS‘] ` '

ö>?g÷Uø@?W÷Uù

. 7 =

Q & ÷ X

ø =

Q & '&

÷Uù

4 $ öQ 0+1

.X $ D * 'bac.

SU]P`ºF

æ E c SU]_[^]_A

c

S‘BKS‘]_ç

b

BCS‘V?RÐ[^RÐE]sF

b R

d ' ö>?W÷Uù

. 7 &

öw÷Uù ö X

Q

$@051

;

'Re.

NQE¦F

b

âRTS

d E b âWE4[‘äF

æ

AµâBCS^âzFAC]sãŽS‘VWAµSU]sFIPS‘ââ

b

ç^ç‘E!âzFgE`$AC]gf

\@h

I@Fg[ÎâWACRÐå_BCAÊäòìÎE

b

SUFWAC[‘]

'=J.

>]iE]_[‘FWAC]_çD\ì_j

7:kl

SU]P`&RTS

d

AC]_çF

æ E ceæ

S‘]_ç‘E[UäƒãŽSUVgAµSUD_BCE

'

ö>?g÷ ø ?W÷ ù

.nmo' ö>?W÷ ø ?pj

.

í.AÊF

æ

÷Uù

7 jö 4 =

Q

$q0 1

&

ö>?

í?EËç‘EF

"

÷Uø

"

ö sr

$

& ( * '

?Wö

.

jsX

ö f 4 =

a

#n$q0 1

& 2 X ö>t

÷Uø 79

?su"jMvxw

;

')y].

ñ æ

Aµâ]PEíÿäò[^VWR

b

BµSŽFgAÈ[^]'[Uä0F

æ

EÐSŽúLAµâì\RÐRÐEFWVgA

c

áBµS^â[Žã'E

b

SUFWAC[‘]ýACâåPS‘VFgA

cb

BµSUVgBCìTí?EBCB

S‘`_S‘åLFWE!`TFg[ÐåPSUVeSUBCBCEBCASUFWAÈ[‘]nS‘âF EãwS‘VWAµS‘D_BCEjÐ[‘]PBÈìÐåPBCSwìLâ?F EVW[^BÈE[UäS&åPSUVeSURÐEFWEV>

õ:E

b

âWES;ç^VWAµ`&AC]Tå

æ

S^âEâWåPS

c E ' ö>?W÷ ø ?pj

.

>E¦FAÊFAµâ]_E

c

EâgâgSUVgì;FW[*FgS

d

E7åPS‘VFgA

c¦b BµSUV

c

SUVgE

[Uä6F

æ

E_jº`LACVgE

c

FgAC[‘]ƒ>Lê{]P`LEE`KI†í

æ

E]'F

æ

E*âWEBÈä

c

[‘]@âAµâFWE]sF.EBCE

c

FWVgA

c

@EBµ`ACâ7BÈAC]_E!SUVI_S‘âäò[^V

F æ

E Mká `_ACâFWVgACD

b

FgAÈ[^]ýä

b ] c FgAÈ[^]ƒIF

æ E ceæ

SUVeS

c

FWEVgAµâzFgA

c*c¦b

VWã^Eâ*S^âWâW[

c

AµSŽFgE`ýFW[:Y @>

'Ry.

I

SUBC[‘]_ç4í

æ A ceæ

F æ

E;`LAµâFWVgAÈD

b

FWAC[‘]Tä

b ] c FgAC[‘]ACâ

c

[‘]PâFgS‘]^FIPSUVgEË[UäF

æ

EËäò[‘VgR

X

Q ö X ÷ X

ø

jsX

ö X

7 ;

^7E]

c

EnAÈFAµâ]_E

c

EâgâWS‘VWìÎFW[

c

[‘]sFWVg[‘B-F

æ

EnVeSŽFgAÈ[ j G ösIƒF

æ

EVWEäò[‘VgE4íE&`_ACâ

c

VgE¦FgAEF

æ

E3j$`LAÈM

VWE

c

FWAC[^]ÎâW[4F

æ

SŽF

j

7 ö X ;

õ:E F æ E]

b

âWE F æ E c

[^]PâEVWãŽSUFWAC[‘] [Uä*F

æ

Eþ`LAµâzFgVWACD

b

FWAC[‘] äb ] c

FWAC[‘] SUBC[‘]_çïF

æ E ceæ

SUVeS

c M

FWEVgAµâzFgA

c

â4FW[ `_Eã\AµâE'F

æ

Eû]

b

RÐEVgA

c

S‘BS‘BCç‘[‘VgAÈF

æ

Rí

æ A ceæ

í.ACBCB.D@EûD@S‘âWE` [‘] F æ

EýâWERÐAÈM

NSUç^VgS‘]_ç‘AµS‘]4RÐEF

æ

[L`L[^BÈ[^ç‘ì%f

e>h

>Lñ

æ

E]_EíüãŽSUB

b

Eâ?SUVgE

c

[^RÐå

b

FgE`TSUF0F

æ

Eç‘VgAµ`nå@[^AC]^FeâAC]

Fzí?[âzFgEåPâ 'A. c [‘RÐå

b

FWE;F

æ

E&[‘VgAÈç^AC][‘äF

æ E ceæ

S‘VgS

c

FgEVgACâFWA

c

E]@`LAC]_çÎSUFF

æ

E&ç^VWAµ`'å†[‘AC]sF

[‘]_EËFgAÈRÐEâFWEåD@S

ced I '

ACA

.

AC]^FgEVgå@[^BµSŽFWEF

æ

EãwS‘B

b

E[UäF

æ

E4`LAµâzFgVWACD

b

FgAC[‘]Ðä

b ] c FWAC[^]ÎF

æ

EVgEUI

í æ A

ceæ

Aµâ;S‘Bµâ[F

æ

ET]_Eí ãŽSUB

b

ETSUF;F

æ

ETç‘VgAµ` å†[‘AC]sFIäòVW[^R F æ

ET[‘Bµ`:ãŽSUB

b

E!â;SŽFF

æ

EÎâ

b

VWM

VW[

b

]P`LAC]_ç4ç‘VgAC`nå†[‘AC]sFgâ>_ñ

æ

Aµâ0RÐEF

æ

[L`ºACâ]_[‘Fâ

b

DzE

c

FFW[nSÐë?[

b

VeSU]sF

c

[‘]P`_AÊFgAC[‘]Ð[‘]ÎF

æ E

FWACRÐEâFWEå'í

æ A ceæ

í[

b

Bµ`ÎD@Eã^EVgìÐVWE!âzFgVWA

c

FgACã‘E7]_E!SUVF

æ

E;SŽúLAµâö

79

>

ê{] F æ

ETSŽúLAµâWìsRÐRÐEFWVgA

c

áBµS‘âW[Žã'E

b

SUFWAC[‘] F æ E jsX

G

öŽf&ä¢S

c

FW[‘V4S

c

FeâËBCA

d

E&S'VgEå

b

BµâAC[‘]

å@[‘FWE]sFgACS‘BLí.AÈF

æ

VWE!âå†E

c

FFg[F

æ

EFg[UFgS‘BLEBCE

c

FWVgA

c

PEBµ`K>Uñ

æ

Aµâ6å@[‘FWE]sFgACS‘B\ACâ6BµS‘VWç^EâF-]_E!SUV6F

æ E

SŽúLAµâ¦I†í

æ

EVgE;F

æ

E4EBCE

c

FgVWA

c

@EBµ`$Aµâ7]_Eç‘BCACç‘ACD_BCEU>â

b â b

S‘Bäò[‘VËSŽúLAµâì\RÐRÐE¦FgVWA

c

å_Vg[‘D_BCERTâI

F æ

EÎRTSz[‘V4`LAÈè

cb BÈFzìýAC]þF

æ

EÎ`LAµâ

c

VgE¦FWA!SŽFWAC[^]ý[UäF

æ

EºáBCS^â[Žã E

b

SUFWAC[‘]þAC]

c

ì\BCAC]P`LVgA

c

SUB

c

[\[‘Ve`LAC]PSŽFgEâBÈACE!â.AC]$F

æ E æ

S‘]P`LBCAC]_çÐ[Uä0F

æ

E&E

b

SUFWAC[‘]û]PESUVF

æ

E&SUú\Aµâö

7 9

>Ė

æ

E&RÐ[^âF

]PSŽF

b

VgS‘B_RÐE¦F

æ

[L`&í?[

b

Bµ`

c

[‘]PâWAµâzF6AC]nâWEå@SUVeSŽFWAC]_çF

æ

E.äòVWEEFWVeSU]PâWå†[‘VWF6å@SUVWFí

æ A ceænc

SU]nD†E

â[^BÈã^E`ÎE¦úLå_BCA

c

AÈFWBCì4äòVW[^R F æ E*âWEBÈäµM

c

[‘]@âAµâFWE]sFåPSUVWF>^7[ŽíEã‘EVIL]

b

RÐEVWA

c

S‘BKEVgVW[^Vgâí[

b

Bµ`

D@E.ç^E]_EVgSUFWE`*]_ES‘V6F

æ

E.SUú\Aµâ6SU]@`*å_Vg[‘å@SUç^SUFWEAC]PâAµ`LE0F

æ

E7`_[‘RTSUAC]ƒIŽSU]@`*[

b

Vç‘[sSUB

æ

EVgEAµâ

FW[4`_Eã\AµâE7Sã^EVgì4åPVWE

c

AµâE]

b

RÐEVWA

c

S‘BLRÐE¦F

æ

[L`&äò[‘Ví

æ A ceæ

F æ AµâAµâ

b

]PS

cc

Eå_FgSUDPBÈE‘>sZ\[PI^íE

âæ

S‘BCB†ç^[ní.AÊF

æ S c BCS^âWâWA

c

S‘BP[‘å†EVeSŽFg[‘V.âWå_BCAÊFWFWAC]_ç;RÐEF

æ

[L`KIPS‘]P`'âåPBÈAÈFD@EFzí?EE]'S‘`Lã^E

c

FWAC[‘]

AÈ]ö4S‘]P`'S‘`Lã^E

c

FWAC[‘]TAC]÷ ø >

]F

æ

E?FWACRÐEAC]sFWEVWãŽS‘B f

?

G h í?E?å_VW[

c

EE`*S‘âƒäò[^BCBÈ[Ží7â ¦F

æ

E`_ACâFWVgACD

b

FgAÈ[^]ä

b ] c FgAÈ[^]

SŽF.FWACRÐE

Aµâç‘ACã^E]ºD\ì

'

ö>?W÷Uø ?pj

.

IPíE PVgâF

c

[^RÐå

b

FgE

â

bPceæ F æ

SUF

UV

WVX

"

÷Uø

"

ö 789

?

'9

?Wö>?g÷Uø>?pj

. 7

'

ö>?W÷Uø ?pj

. ;

'! /.

õ:EF

æ

E]

c

[‘RÐå

b

FWEËF

æ

E*âEBÈäµM

c

[‘]PâWAµâzFgE]sFEBCE

c

FgVWA

c

PEBµ`

( * äòVg[‘R(F

æ

E;AC]sFWEVWRÐE!`LAµSŽFWEËSUå_M

å_VW[wúLACRTSŽFgAC[‘]

'!"

?Wö>?W÷Uø ?pj

.

>@ñ

æ

E] # â

bPceæ F æ

SŽFI

UVVV

WVVVX

"$

r

$

& ( * ' ?gö

.

jsX

ö f 4 =

a

#n$q0 1

& 2 X öJt

"#

÷Uø 79

?

#

9

?Wö>?g÷ ø ?pj

7

?gö>?W÷ ø ?pj

;

'&%].

' . 7

'!" .

ñ æ E;`LAµâ

c

VWEFWASUFWAC[‘]º[UäE

b

SUFWAC[‘]

'! /.

VWE

b

ACVWE!â0Fg[ºSUåPå_BCìºSUVWFWA

c

ACS‘BKD@[

b

]P`_S‘VWì

c

[‘]_M

`LAÈFWAC[‘]Pâ> c Fb

S‘BCBÈì‘Iƒäò[‘VF

æ

AµâE

b

SUFWAC[‘]QISŽF*ö

7 9

S‘]P` äò[‘V;÷Uø

9

I-F

æ

EºåPSUVWFWA

c

BCE

b ú

ACâAC]

c

[‘RÐAC]_çPIsí

æ

EVWE!S‘âåPS‘VFgA

c

BCEâ?í.AÈF

æ

ã‘EBÈ[

c

AÊFzìn÷ ø

9

BCESwã^EF

æ E c [^RÐå

b

FeSŽFWAC[^]PSUBƒ`L[‘M

RTSUAC]ƒ>@ñ

æ\b

âI@íE;]_EE`FW[ÎRÐ[L`LEB

æ

[Ží F æ E*å@SUVWFWA

c

BCEâ

c

VW[sâWâ.F

æ

E&SŽúLAµâö

79

>Kñ

æ

Aµâ

c

S‘]

D@E;`L[^]_EËD\ìºACRÐå@[sâAC]_ç4âå†E

cb

BµSUVVWEPE

c

FWAC[‘]

c

[^]P`LAÈFWAC[‘]@â

'9

?W÷Uø>? j . 7 '9 ? 4

÷Uø>? j .

?6u$÷Uø

9<;

ñ æ En]

b

RÐEVgA

c

SUBQVgEâW[‘B

b

FgAC[‘]'[Uä?FWVeSU]PâWå@[^VFE

b

SUFWAC[‘]Pâ

'! /.

S‘]P`

'&%.

AµâF

æ

E]ýå†EVWäò[‘VgRÐE`

b

âAC]_çÎSTâERÐAÈMON-SUç‘VeSU]Pç‘AµSU]ÐRÐEF

æ

[L`$í.AÈF

æ S c¦b

DPA

c

^7EVgRÐAÈFWEAC]sFWEVWå†[‘BµSŽFgAC[‘]ƒI

b

âWAC]_çÐF

æ E

ãwS‘B

b

Eâ?[UäƒF

æ

Eä

b ] c

FgAC[‘]ºS‘]P`TAÈFgâ`LEVWACãŽSŽFgAÈã^E7SŽFF

æ

EE]@`Tå†[‘AC]sFgâ?[UäQF

æ

EËAÈ]sFgEVgãwS‘Bk>^NQEF

b â

`LEâ

c

VgACD@EAÈF7AC]û`LE¦FeSUACBµâäò[‘V7E

b

SŽFgAÈ[^]

'! . > ]ûS‘]$AÈ]sFgEVgãwS‘BnföH?Wö G h

I†í?E4SUå_å_Vg[wúLACRTSŽFWE

F æ

En`LEVgACãŽSŽFWACã^E[UäF

æ

E&`_ACâFWVgACD

b

FgAÈ[^]ä

b ] c

FgAC[‘]ýSUFE!S

ceæ

ç^VWAµ`'å†[‘AC]sFD\ì$STäò[

b

VF

æ

[‘Ve`LEV

P]_AÈFWE`LATSKEVgE]

c

EËâ

ceæ ERÐE

ø

7 =

=JQ "

ö

% f

G 4

G h 4 f

X 4

X

h

;

ñ æ

EÎå†[‘BCì\]_[^RÐACS‘BVWE

c

[^]PâzFgV

b@c

FWAC[^]:Aµâ*F

æ

E] ç^AÈã^E]ð[^] ES

ceæ

AC]sFWEVgãŽSUB5fö ?gö G h D\ìþF

æ E

c¦b D_A

c

å†[‘BCì\]_[‘RÐAµSUBAÈ]sFgEVgå@[^BCSUFWAC]_çÐF

æ

ET`LAµâFWVgAÈD

b

FWAC[‘]'ä

b ] c

FgAÈ[^]:S‘]P` AÊFeâ`LEVgACãŽSŽFWACã^Eâ7[^]

F æ Eç^VWAµ`

'ö . 7

'ö 4

ö

. ø

'ö 4

ö

. X \ f

G 4

h 4 "

öf

Q

]

G

h

'ö 4 ö

.f

"

f ø

G

h 4 Q f

G 4

h

;

ñ æ Aµâäò[‘VgR

b

BµS;S‘BCBÈ[Ží7âFW[ÐEãwS‘B

b

SŽFgEF

æ

E;`LAµâzFgVWACD

b

FWAC[‘]nä

b ] c

FWAC[^]S‘]sì\í

æ

EVWEË[^]ºF

æ

Eç‘VgAµ`K>

êOF0[‘]_BCì;VgERTS‘AC]Pâ-FW[

b

âWE.F

æ E ceæ

SUVeS

c

FWEVWAµâFWA

cc¦b VWã^Eâ6í

æ A ceæÐc

S‘]&D†EâW[‘BCã‘E!`*EúLå_BCA

c

AÈFWBCì[^]

ES

ceæ

âåPBÈAÈFâFWEåýFg[

c

[‘RÐå

b

FWE;F

æ

EÐ`LAµâzFgVWACD

b

FWAC[‘]ä

b ] c

FWAC[‘]:SŽFF

æ

Enç^VWAµ`'å†[‘AC]sFgâSŽFFWACRÐE

G >

ރÛPàßq&Û sÞ+{Ú

"!$#&%('*))+%(,.-/%(

õ:E&íS‘]sFFW['âF

b

`Lì

æ

EVgE;F

æ

E4Eã‘[‘B

b

FgAC[‘]'[Uä?S‘] SUú\AµâWì\RÐRÐE¦FWVgA

c

âWERÐAÈM ËS

b

âgâAµS‘]ÎD†ES‘R'>

ñ æ

EVgE¦äò[^VWEÎí?Eâ[^BÈã^EÐF

æ

EÎáBCS^â[ŽãsM{é6[‘Aµâgâ[^]ûAC]

c

ì\BCAC]P`LVgA

c

SUB

c

[s[^Vg`_AÈ]@SŽFWE!â¦Ií.AÈF

æ

S‘] SUå_M

å_BCAÈE!`

b

]PAÊäò[^VWR SU]P`

c

[^]PâFgSU]sFBC[‘]_ç^AÈF

b

`LAC]PS‘B-RTS‘ç‘]_EFWA

c

@EBµ`

051

>-ñ

æ

E] F æ

ET`LAµâFWVgAÈD

b M

FWAC[‘]'âWSUFWAµâ PEâF

æ

E;áBµS^â[ŽãÐE

b

SŽFWAC[^]

y

>Pñ

æ

E;AC]_AÈFWAµSUBK`LAµâFWVgAÈD

b

FWAC[‘]ºä

b ] c

FWAC[‘]$`LE!â

c

VWACD_AC]_ç

S&âWERÐAÈM ËS

b

âgâWACS‘]nD@E!SUR AC]Aµâ?ç^ACã‘E]ÎD\ì

K

'+

?10?W÷

?g÷32

. 7 K

'Q54

÷ X

6+7

.E'498 X .

EúLå

r 4 '÷

4;:=<?>X l 0 .X '÷ 2

:@<?>X l . X

Q ÷ X 6+7

t ?

äò[‘V

X 0LXBA

8

XTSU]@`

K'C

?D0?g÷ ?W÷ 2 . 7 9 I-AÈä

X 0LX

8

XŽ>6ñ

æ

ETRTS‘ç‘]_EFWA

c

PEBµ`

0+1

SU]P`ÐF

æ

EF

æ

EVWRTS‘BPã‘EBC[

c

AÈFzì;÷

6+7 S‘VWE

c

[‘RÐå

b

FWE!`&äòVW[^R Z b

SU]sFgAÊFgACEâI‘â[F

æ

SŽFF

æ E

D@E!SUR AµâE ACãŽSUBCE]^FFW[ÐS&RTSŽF E` MOáóD†ES‘R'>

æ c b

'

7 = & 7 \ ;

=8

&

.

ñ æ

Eº`LE]PâAÈFzì

K ACâ

c

[‘RÐå

b

FWE` äòVg[‘R F æ E

cb VgVWE]^F j

759

>Q

A(SU]@`ýF

æ

ETD†ES‘R ã^EBC[

c

AÈFzì

SUBC[‘]_ç*F

æ

E‘M{SŽúLAµâ

÷ 1 7 X 4 =

X ? 7 = $

&

X

?

í æ

EVgE Aµâ.F

æ

E*D†ES‘R

d

AC]_EFWA

c

E]PEVgç‘ì

7 % ; = 9

Eá*>K=AC]PS‘BÈBCìnF

æ

E*D†ES‘RVeS‘`_A

b

â.Aµâ

8

759

>9 Q &

S‘]P`ÎF

æ

EËF

b

]_E;`LEå_VgEâgâAC[‘]ºACâ

G K 7

=>G>a

>

õ:E&[‘DPâWEVgã‘E&SÎâWåPS

c E ceæ

SUVgç‘E*íSwã‘E4âzFeSUVWFWAC]_çÐäòVg[‘R F æ

EnE`Lç^E4[‘äF

æ

EnD†ES‘R'I†å_Vg[‘å_M

SUç^SUFWAC]_çAC]síSUVe`_âËSU]@` @]PSUBCBCì$D@EAC]_ç'VWEPE

c

FWE`:[^] F æ

EºSUú\Aµâö

7 9

>-ñ

æ

ETAC]_AÈFWAµSUB6âEBÈäµM

c

[‘]@âAµâFWE]sF PEBC` AµânBCAC]_ES‘V&í.AÈF

æ

AC] F æ

EûD†ES‘R'>0ñ

æ

EûãŽSUVgAµSŽFWAC[^]Pâ4S‘VWE$VgEBµSUFWACã‘EBÈì:íES

d

D b F;â

b è c

ACE]sFFg[âFWVg[‘]Pç‘BCì'å@EVF

b

VWDýF

æ

EÐ`LE]PâWAÊFzì

'

=AÈçP>

=>.

>-Z\[^BCãsAC]_çTF

æ

EÐSŽúLAµâWìsRÐRÐEFM

VWA

c

E

b

SUFWAC[‘]:SUBCBC[Ží7â

b

âFW[$EBCACRÐAC]PSŽFgE;[‘]PET`LACVWE

c

FWAC[^] SU]@`ûF

æsb âFW[

b

âEÐS P]_EV;RÐEâ

æ

F æ S‘]ºAC]ÐF

æ E c

SUVWFWE!âAµSU]

c

S‘âWESU]@`º`LE!â

c

VWACD†E7F

æ

E`LAµâFWVgACD

b

FWAC[^]4ä

b ] c

FgAÈ[^]ºRÐ[^VWE7åPVWE

c

AµâEBCìU>

$[‘VgE[Žã^EV[

b

V4]_Eí äò[‘VgR

b

BCSUFWAC[‘] [Uä.F

æ

EºáBCS^â[Žã E

b

SUFWAC[‘]

c

[‘]PâWEVgã‘E!âËF

æ

EÎAC]sãŽS‘VWAµSU]sF

j 7 ö÷Uù

:< >

X l öwX‘>

ñ æ AµâQRÐE¦F

æ

[L`;ç^AÈã^Eâƒã^EVgìâWSUFWAµâzäòì\AC]_ç.VgEâ

b

BÈFgâäò[‘V-F

æ

Eå_VgEâWE]sFFgEâF

c

S‘âWEU>Žñ

æ

EVWE!â

b

BÊFeâ

SUVgE

c

[‘RÐåPS‘VgS‘D_BCE7Fg[nF

æ

[sâE[^DLFgS‘AÈ]PE`Îí.AÊF

æ S c SUVWFWE!âAµSU]

c

[L`LE‘I@S‘â.åPVWE!âE]^FgE`ÎAC] f

y@h I_äò[^V

F æ

EËâWS‘RÐE.VWE!â[^B

b

FWAC[‘]ÐS‘]P`nF

æ E c [L`LEAµâ0R

bPceæ

ä¢S‘âFWEV> $[‘VgE[Žã^EVAÈFACâ0å@[sâWâWACD_BCEFW[4ç‘[Fg[

R

bPceæ

P]_EV7VWE!â[^B

b

FWAC[‘]@â0SU]@`TF

æ

E]û`LACRÐAC]_Aµâ

æ F æ E]

b

RÐEVWA

c

S‘B@`_S‘RÐå_AC]_ç_>

€^ŐLvgxÇQÒ^xzŽÆevgy{y{xzy ­ô“6‚¦x{|zvey{r²‚qÐy{!±utwvWx„K“ m•^ruyO¯‘ÅÅvg|{xzruƍ‘!±utwvWx

ŒËÒ^xzŽÆevgy{y{xzy ¬¦‰‹Åruq ®År²q

‹Ò^xzŽÆevgy{y{xzy ‹!®År²q ­!‰År²q

Âs¾sÄ !#"$!%&'"$()!%+*-,./0"+12+3412657"/8!9*.:7%#"&;"&'<="?>@%:7AB+*C!/D%#5B:D$(E*./D:8F

9G H JI$K'-I -/'LMK@N OI %QP -/%(

õ:EâzFeSUVWF]_[ŽíþäòVg[‘R S7`LACRÐE]PâWAC[‘]_BCE!âWâ ûSŽúLíEBCBÈM[^BÊF RTS‘]_]`LAµâFWVgAÈD

b

FWAC[‘]

'$ 7 & 7

=>.

K]' ö>?g÷Uø ?g÷Uù

.

7SR

Q 4 E¦úLå

'4 ` . ? ' .

í æ EVgE

`

AµâF

æ

E4`LACRÐE]PâWAC[‘]_BCEâgâ ^SURÐACBÈFW[^]_AµSU]T[^DLFgS‘AÈ]PE`ºäòVW[^R

')a].

I c [ b

å_BCE`Îí.AÈF

æ F æ E

é6[‘AµâWâW[‘]ºE

b

SŽFgAC[‘]

4 =

ö

ö # ö D *

ö 2 7 R

Eú\å

' 4 D * 4 öŽX

a . ;

'=

9 .

õ æ E]

R

Aµâ7`LATSKEVgE]sF7äòVg[‘R EVW[º[‘V[^]_EUI@F

æ

EVWE&SUVgE;]_[ºS‘]PSUBCìsFWA

c

SUBQâW[‘B

b

FWAC[^]Pâ[Uä0é6[^ACâM

â[^]Tâ;E

b

SŽFgAC[‘]

9

>-ñ

æ

EVWEäò[‘VgEUIQíETSUå_åPVW[wúLACRTSŽFgE;F

æ

EÐå@[‘FWE]sFgACS‘B D b

âAC]_ç$S P]_AÈFgE

0 5e+14 1e+15 1.5e+15 2e+15 2.5e+15

0.005 0.01 0.015 0.02 0.025 0.03 N at z=0.00

-1.5e+19 -1e+19 -5e+18 0 5e+18 1e+19 1.5e+19

0.005 0.01 0.015 0.02 0.025 0.03 Jr at z=0.00

-5e+18 -4e+18 -3e+18 -2e+18 -1e+18 0 1e+18

0.005 0.01 0.015 0.02 0.025 0.03 Jo at z=0.00

-1e+11 -8e+10 -6e+10 -4e+10 -2e+10 0 2e+10 4e+10

0.005 0.01 0.015 0.02 0.025

Etot at z=0.00

0 5e+14 1e+15 1.5e+15 2e+15 2.5e+15

0.005 0.01 0.015 0.02 0.025 0.03 N at z=0.32

-1.5e+19 -1e+19 -5e+18 0 5e+18 1e+19 1.5e+19

0.005 0.01 0.015 0.02 0.025 0.03 Jr at z=0.32

-5e+18 -4e+18 -3e+18 -2e+18 -1e+18 0 1e+18

0.005 0.01 0.015 0.02 0.025 0.03 Jo at z=0.32

-1e+11 -8e+10 -6e+10 -4e+10 -2e+10 0 2e+10 4e+10

0.005 0.01 0.015 0.02 0.025

Etot at z=0.32

0 5e+14 1e+15 1.5e+15 2e+15 2.5e+15

0.005 0.01 0.015 0.02 0.025 0.03 N at z=0.48

-1.5e+19 -1e+19 -5e+18 0 5e+18 1e+19 1.5e+19

0.005 0.01 0.015 0.02 0.025 0.03 Jr at z=0.48

-5e+18 -4e+18 -3e+18 -2e+18 -1e+18 0 1e+18

0.005 0.01 0.015 0.02 0.025 0.03 Jo at z=0.48

-1e+11 -8e+10 -6e+10 -4e+10 -2e+10 0 2e+10 4e+10

0.005 0.01 0.015 0.02 0.025

Etot at z=0.48

0 5e+14 1e+15 1.5e+15 2e+15 2.5e+15

0.005 0.01 0.015 0.02 0.025 0.03 N at z=0.64

-1.5e+19 -1e+19 -5e+18 0 5e+18 1e+19 1.5e+19

0.005 0.01 0.015 0.02 0.025 0.03 Jr at z=0.64

-5e+18 -4e+18 -3e+18 -2e+18 -1e+18 0 1e+18

0.005 0.01 0.015 0.02 0.025 0.03 Jo at z=0.64

-1e+11 -8e+10 -6e+10 -4e+10 -2e+10 0 2e+10 4e+10

0.005 0.01 0.015 0.02 0.025

Etot at z=0.64

0 5e+14 1e+15 1.5e+15 2e+15 2.5e+15

0.005 0.01 0.015 0.02 0.025 0.03 N at z=0.96

-1.5e+19 -1e+19 -5e+18 0 5e+18 1e+19 1.5e+19

0.005 0.01 0.015 0.02 0.025 0.03 Jr at z=0.96

-5e+18 -4e+18 -3e+18 -2e+18 -1e+18 0 1e+18

0.005 0.01 0.015 0.02 0.025 0.03 Jo at z=0.96

-1e+11 -8e+10 -6e+10 -4e+10 -2e+10 0 2e+10 4e+10

0.005 0.01 0.015 0.02 0.025

Etot at z=0.96

¬ ­

Œ

Ä\Ä'*.B%" :7:7%#"&7*"+FO&'"D :$!: , :D(%#5D*.:B,=< *.&O:7%#!A

!#"$

&%

1('/8:D!

*.&'! %&*),+

%

.- '-/D:D! *.&'! %&/)0

%

1=!#!#"$( ,./5D*2' *C(<43(5

!#"&$

7698;:=<

>

¨?>A@

¨ $

%&O:7%#<$* !BJ*

7*" "$! !%+*.:C;DFE

%

EFG-1

%

E$FH1JI

%

EFK1

%

E$FLKNMF