View
3
Download
0
Category
Preview:
Citation preview
!"#
$%&&'(( )
!
*
*+,-.**/+,-.-*0*+,-1
!" # !$#
! ! %
"" &
"' "
&&&!
2"'345 "455!!65
(!!)
)( 78.-!!"9:;'"*+
)$ 78.-!!9#44!":9
) 0<84.-!!0""!++
)$ 78.4""; ,
(-)$ +#.=*>:=!"" ,
Page 1 de 3 Direction de la Recherche
mise à jour le 9 décembre 2007
Liste des personnes Habilitées à Diriger des Recherches en poste à l'Ecole Centrale de Lyon
Nom-Prénom Corps grade
Laboratoire ou à défaut département
ECL Etablissement
AURIOL Philippe professeur AMPERE ECL
BEROUAL Abderrahmane professeur AMPERE ECL
BURET François maître de conférences AMPERE ECL
JAFFREZIC-RENAULT Nicole directeur de recherche AMPERE CNRS/ECL
KRÄHENBÜHL Laurent directeur de recherche AMPERE CNRS/ECL
MARTELET Claude professeur AMPERE ECL
NICOLAS Alain professeur AMPERE ECL
NICOLAS Laurent directeur de recherche AMPERE CNRS/ECL
SIMONET Pascal chargé de recherche AMPERE CNRS/ECL
THOMAS Gérard professeur AMPERE ECL
VOLLAIRE Christian maître de conférences AMPERE ECL
Nbre Ampère 11
HELLOUIN Yves maître de conférences DER EEA ECL
LE HELLEY Michel professeur DER EEA ECL
Nbre DER EEA 2
GUIRALDENQ Pierre professeur émérite DER STMS ECL
VINCENT Léo professeur DER STMS ECL
Nbre DER STMS 2
LOHEAC Jean-Pierre maître de conférences ICJ ECL
MAITRE Jean-François professeur émérite ICJ ECL
MARION Martine professeur ICJ ECL
MOUSSAOUI Mohand professeur ICJ ECL
MUSY François maître de conférences ICJ ECL
ROUY MIRONESCU Elisabeth professeur ICJ ECL
ZINE Abdel-Malek maître de conférences ICJ ECL
Nbre ICJ 7
DAVID Bertrand professeur ICTT ECL
Nbre ICTT 1
CALLARD Anne-Ségolène maître de conférences INL ECL
CLOAREC Jean-Pierre maître de conférences INL ECL
GAFFIOT Frédéric professeur INL ECL
Page 2 de 3 Direction de la Recherche
mise à jour le 9 décembre 2007
GAGNAIRE Alain maître de conférences INL ECL
GARRIGUES Michel directeur de recherche INL CNRS/ECL
GENDRY Michel directeur de recherche INL CNRS/ECL
GRENET Geneviève directeur de recherche INL CNRS/ECL
HOLLINGER Guy directeur de recherche INL CNRS/ECL
JOSEPH Jacques professeur INL ECL
KRAWCZYK Stanislas directeur de recherche INL CNRS/ECL
MARTIN Jean-René professeur émérite INL ECL
O'CONNOR Ian maître de conférences INL ECL
PHANER-GOUTORBE Magali professeur INL ECL
ROBACH Yves professeur INL ECL
SEASSAL Christian chargé de recherche INL CNRS/ECL
SOUTEYRAND Eliane directeur de recherche INL CNRS/ECL
TARDY Jacques directeur de recherche INL CNRS/ECL
VIKTOROVITCH Pierre directeur de recherche INL CNRS/ECL
Nbre INL 18
CHEN Liming professeur LIRIS ECL
Nbre LIRIS 1
BAILLY Christophe professeur LMFA ECL
BERTOGLIO Jean-Pierre directeur de recherche LMFA CNRS/ECL
BLANC-BENON Philippe directeur de recherche LMFA CNRS/ECL
BOGEY Christophe chargé de recherche LMFA CNRS/ECL
CAMBON Claude directeur de recherche LMFA CNRS/ECL
CARRIERE Philippe chargé de recherche LMFA CNRS/ECL
CHAMPOUSSIN J-Claude professeur émérite LMFA ECL
COMTE-BELLOT genevièvre professeur émérite LMFA ECL
FERRAND Pascal directeur de recherche LMFA CNRS/ECL
GALLAND Marie-Annick maître de conférences LMFA ECL
GODEFERD Fabien chargé de recherche LMFA CNRS/ECL
HENRY Daniel directeur de recherche LMFA CNRS/ECL
JEANDEL Denis professeur LMFA ECL
JUVE Daniel professeur LMFA ECL
LE RIBAULT Catherine chargée de recherche LMFA CNRS/ECL
LEBOEUF Francis professeur LMFA ECL
PERKINS Richard professeur LMFA ECL
ROGER Michel professeur LMFA ECL
SCOTT Julian professeur LMFA ECL
SHAO Liang chargé de recherche LMFA CNRS/ECL
SIMOENS Serge chargé de recherche LMFA CNRS/ECL
TREBINJAC Isabelle maître de conférences LMFA ECL
Nbre LMFA 22
BENAYOUN Stéphane professeur LTDS ECL
CAMBOU Bernard professeur LTDS ECL
COQUILLET Bernard maître de conférences LTDS ECL
DANESCU Alexandre maître de conférences LTDS ECL
FOUVRY Siegfrid chargé de recherche LTDS CNRS/ECL
GEORGES Jean-Marie professeur émérite LTDS ECL
GUERRET Chrystelle chargé de recherche LTDS CNRS/ECL
Page 3 de 3 Direction de la Recherche
mise à jour le 9 décembre 2007
HERTZ Dominique past LTDS ECL
ICHCHOU Mohamed maître de conférences LTDS ECL
JEZEQUEL Louis professeur LTDS ECL
JUVE Denyse ingénieur de recherche LTDS ECL
KAPSA Philippe directeur de recherche LTDS CNRS/ECL
LE BOT Alain chargé de recherche LTDS CNRS/ECL
LOUBET Jean-Luc directeur de recherche LTDS CNRS/ECL
MARTIN Jean-Michel professeur LTDS ECL
MATHIA Thomas directeur de recherche LTDS CNRS/ECL
MAZUYER Denis professeur LTDS ECL
PERRET-LIAUDET Joël maître de conférences LTDS ECL
SALVIA Michelle maître de conférences LTDS ECL
SIDOROFF François professeur LTDS ECL
SINOU Jean-Jacques maître de conférences LTDS ECL
STREMSDOERFER Guy professeur LTDS ECL
THOUVEREZ Fabrice professeur LTDS ECL
TREHEUX Daniel professeur LTDS ECL
VANNES André-Bernard professeur émérite LTDS ECL
Nbre LTDS 25
Total HdR ECL 89
En mémoire de mon père Louis etde ma sœur Victorine
! " # $ $ % !%
! % $%%"
& ' ( )*" +, -. ! !
/ ( % ! ! ! '
"
& + 0 0 % $ 0 $ , ' 1 +% (
2 % %// %"
%$ , % & 3 %+4& 50 0 ( ( /$%
6( /5( $7 3 8 ( 6+ 7 ! 94"
# / : :' % # % + ' ( 2 2 / $ ; </
( & $ 2 +4 = 3 * ! &
+2 3 / > 3 2 3 & ! , ' /' * $"
& ! %
% $% % * 9 :; , , % ( ( 4 % % 0 $ $ 0
( % ( ! ' *!1"
2 % 7 4 ?
+% ! * & + "
*
!" 5?" 5 ;5!@ !4!
44!!@ 4A# # 84 !""" 5!?
!4!. " !" #!@. " 4!4! "4!@ @!" "
44!!@A;!@"45?"55!"!885?
"4A#4B@4545"#5!"!".
4A#5 " !4 "#!. ; ""!
44!!@$44!!.!."#.!!56"4)
"!"!C"%"4"4A!"4";
84! "85 " !"!@+"5@"!!!
""! 6 "4. " "#. " ! " 44!!
$!@""8! "585"")!8"4!#!8!4!"
5?"4A##5!"!" ""!4!C
"#5!"!4"4C"!5!!"4A#445"4C"
!44A#7" "! "44A""! !5."
! "45 "!"!. " !45
"8! "@" 545"4!"
""@"44!!44A""!#4"4A#
"!5@""44!!!88
". 4 @! ! #5! ; 4" " 4A#
"!!!4""44A#D!"5%5"
56!5"
.*
*A! EF 5 ;5!4 5" 8 !4! 8 A
4A4!!4 8 !4A# #!# "" !"!# 84 ! !4!
E;. A #; "4. A @!" "4!4 4!4!. A A;!4"
4A4!!4 8 A 4 *A! 5" ""E 5! A ! 5 8 A
!4A# !" A 8"A ; F!# ! 44 A !" #5;. A 4A# 8
!4 !# A #!. A ; 8 ""! ! 4A4!!4
$44!!;.A!4F.E!A.!!45A"4)*A"#"!
AA 8 4 A"# E!A! A 4 ";G 44!# A F! 8
"! "# + ! AE A A "4! 8 A ""! E!A # A
"4. A! E!A. A! A!4F A! 44!!! $EF"; #";
"") A !#!8!4 !8"4 A 5 8 A !4A# *A !4 8
A!4F 8 A""! " A !4 8 A !4 8 A 4 A
4!8 A445"4A# A A48 A4A#!#4
A A A!4F A ""! ";. A A A !5 8"A 8 A !" !
0. A 8"A "# ! "" A 5"" A 8"A !5 ! "# *AA!#A
44!!;8A""!";#A!#A4*AA!#AA! EA
44!!! 8 A! . AA!#A A 4 A 4A# D A! 4
6"! ;A5F "!48A!8A!4A#4A"*A"!8
"4!;8""EA8A4"4!4"4A#
!!
+))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))/
0 " "1! "" %)))))))))2
'+4! (
7!4!65?"!@45 (
'0?" '
0?"5F '
0?""H"G!EF! '
0?"!GF '
I0?""!74A '
J0?"K" 'J
0?"L! 'J
30?""44A5!6 '3
(0?"!@4!4"! '(
'0?"4FM!"F! '(
7!4!65?";5!@ '
'04!5#! '
''7#!!!! '
' 7#!84"4!@
!?#!"4A#
'!?/5
!?/FANJO
!?M!"F!
!?4FN'O I
I!?"!74A I
J!?!A!5 J
!?BFA5!!5A
3!?L"";A
(!?AA !.9"PA " (
('75!4 '
( 6!?54
(*!!?54
0?";5!@
'0?"!GF#;
0?"BFA5!!5A I
0?"2BK J
0?"AA !9" J
=!#!
75?!8"4
'+8"4""!
+8"45?"4
A!" '
*545 '
I78!""!"
J45"!"
4A""!!85 J
3Q5! ?4A
I4"! 3
0 ! ! % %
)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))34
'+4! I'
7!4! 5?" I'
7#!"4A#@!4!4!"4!@@!" I
5?4!4!"4!@@!" II
'+54"44A""! II
''!4 II
'''0?""!! II
'' 0?"M!"F! II
''0?";HA!4A# IJ
' 44! IJ
4!!@"4 I
'4!C"%"4 I
!4"4 I3
;4"4A# I(
=!#!"4A# I(
I*!4 J
J*8#!"4 J'
J'74""!!"!@4"!4"" J'
J 744!A5!@ J'
J7!88!5 !"! J
J7;5 J
I4!!@!45 J
JQ485 JI
4"! J(
0 ' ! !" )))))))))))))))))))))2/
'+4!
4A#!:4
'+"484""!!85
+"484""!!85
'+"""5!?!4!C6
''9""4R"S"45
' 9""4R"S"4/* 3
+";8445! !!!!88 3
4A#5"!4 3
'*4A!@6!5" 3I
"6!56 3
2!5"! (
4"! ((
0 '' '))))))))))))))))))))))))))))))))))))))))))))))))))))/5/
'+4! '
!48!#!""! '
'+"484!855"" '
+"484!855"" '
'+"484456 '
''T" """"4R""4/* '
' T" "5!""4R""4/* ''I
+" "" 5!? !4! 4 84 45 !
'
'+"4" """"4 '
+"45" "5!""4 '
+" 45 84 ! : 5?"
6!5"U 'I
'+8"4"44!!"!!! 'I
+8"4"!"44A""! '
445 '
4"! '3
0'' )))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))/34
'+4! 'I'
0?"44A""!"!5"! 'I'
'7""!!85 'I
''*!545 'I
' 4!!@""!!85 'I
7""!!85 'I
' +" ; 84 "" C 85
""U 'I
+" ; 84 "" C 85
""U 'J
+8"4"!!! 'J
+8"4"44!! ""! 'JI
I+8"4"!"44A"" '
J4A""!C"!44!! 'I
4"! '(
))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))/6/
7*..80*)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))/62
'
+
! 45!@ " ! % "! 8 ! BA!
! "5 4! !""! 4!.
85!"S#!"4!@S"4!4!##!@"!C"!4
2 !!5 4" 6!# "S!""! "!# !
! 5 ""!5! 455 "!# ! @!
4V."!.6"!485565.4!!!4!
4!.5%5@S6?#""S.6C!4!75!4""4!.
" ""! !" N'O 4! " 84 5!? !54 "
@"!"8! !"!#!!"8!45"!5!5
"!"5 "!# "!""# "4!@ 4! 88. "
R""@!4"84!".5"!.#
!5!!4! ""!!!8!4!""4@"4!"
! !" 4! 45 !". 4@!
4@4 #. " 5! A !4 " "!# 4!4 #
""!4!44!!" "!! "4!"!
"!"5#!""!!5!4 "5"!"!
!88 4 % C "!#! 4 ""! "". !!""
5!6
""!""%!#!5!!@""!
R5 . "!?A!4"."!U "
#! 8!. " #!# 5A!@ ! 84 " R #"4
445" " !" < " #! ! "4!@ "S!"!
"!#8!"S!!4A#4!454
8 "!. 8!"5 4! "! 65! C " " 4A<
!" " 4" !" 55 " B5! 8!5 !". 4
A5? < " 45 " 4A< !"D "
45"!
4!!!!""!!54"!""!"4!@
55 " !" "!# #!""!44
! 85 4 C 6!5! 88!! 4A? "!?.
4!5!. 45"6 !#!@. 4A!5!@ 5%5 4" A5!@
7"#!6585.4""!%!#!5!@
6!"4A88#"" "A !!. "A!4"5 !"UD""
! ! #! #!4" !" 4 !? 8! "5
44!4.5! ?A;#4!@4"" 4C "A5!!"!
" 4!! 8 A5!! 455 " !"". " "!. " 4!
5!"U."!"!"44!?@"85!
44A "4";!@ #G " 85 4 44A
"4";!@ #5 4 " 44!! " 5%5 5!? @ "
""! 5!. 4 8! 4!4" " " 44A 8!4!"" "
45!N JO
""!5!6"""45 !!"!""!
4! 85 ""! " " ? "6"!! #
"4!@ N. O 7 4@. @"" @ ! " 4 ""!. "
85! 44A "4";!@ C "A5!!8!4! R "! 445"
#!5 C " 84 !" +" !5 5@@ !
"#!!@R""!.!?!"5!"#
6"!!. W""! "!5! X C 4A@ ! @!
"!!"""!5A!@."A4!?."8@4"
"!.U NIO " 44!!@ # 45! ? !
K"5.!"@#!"!#!!!"4!@"@!"
4. "A5!!8!4! R "! 445" #!5 C " 84
!".@""@ ! . @ " 85!44A"4";!@
44!!@A5?""!
4!4#$!)""!4!!!! "
!5!4 "5 "!"!6!+"4!5 !@!8!
"!""!!8!!48!""45!!
4! "! "" !5C!
#"5 44! "!! 4!!! !! @ " 44!!
R""!4!"6!5 5"!!@!"
88. 8! 4 C 4A@ !. 5! !!8855 C ""!
""!!""."!"!@!"!#"58!!C
! " 44!! 8!4!"" 44A "" NO 2" " !6
""!. !!#@ 4" !NO ""! 8! " $4" '). ""!
5;$4" ).8""!5!!!""$4")""!64!"
$4" ) 4A@ 4" 4! ! R " @!" $2)
56!5"4C""!!"!4A"!5$") .I
#&". '#&". 3#&" 'J#&" 4!5 +" 6! !885A5 "
!""!.4A4""#!4!
@#!%4!G"".!"4!@"5!""8!!!
"!"5 5! " "!! @!" !
6!5!! "#@! "45%5!!. !" !! "
! W4 !X !4!6 ! "" 8! % 5
8!!5!#544"!"54!
8!""!"."A"!!!$!4".A!G"!4"!)
4A< !" " " ! @! ; "!@ !8"4
85"!!"44A""!"#S4"!"44A
""!"!".!!@"44!!8!4!"""44A
""! 445". 5! " 5? " " !5 884 " !
!"#". " 44A""! 44 " "5 "
4A<!" !4R44A ! "! "5!6
# 4 " 84 ;# $ 8. 8 "!) 7 4@. "
!! """! " "#4A<!"!85N3OD4
!85! ! " 44 "@ " "# 4A< #5!
4R""#5"@"!"!@644#5
!4!64!?!45""44!!"A
! "! ! $!"! 6!) " 455 " 84 4
45 !4 8 #! !"5 84 44A
#?44!4<4@4!5
445"! 44A "" C " 84 !" #
44!!"4!@8!4!""!!!"""#""!#8!
!! 5!8! 2! " 4!! 5A!@ 455 " "! 8!. "
!""U."!!"4!@"!%!6!
" 84 !" @ !! "5V# 4 "4!@@!. " ! 4
4!4!!""!#8!
*!!!""4!6@""5!"!"
N . . I. (. 'O. "!""! 8! " 8!# ' $) "!! "4 "4!@
"4"!@! ! !5! 54 C ! !! ! +";
" !! 4 8! < 8! " #!. #"5
""!""!D$ )"4"4!@58!6"84!"@
4 4!. ! 54 5%5 ! " 4 4
"!84<.88 A5!@.#! !"
""5 8!""D $4) " 45 $) "!"$) " " 4!4"!
4"4!@C " 84 "!". #!! !5
!4 " "!#. "" B@ 44!4! " "!# 45
4"4AA !""5"4!$!B4)4! C"#!
!"
5!?#". "45 !"""4 "!!
48!445#"85! ?4A4!"-4
#84B@45""!"
Q!#'44!4544A""
!5!5 "!#"4!@! 88!
4 "5 " 4! "4!@ 6"!! "@ #! R
""! !5 " 84 !" +" 44! !4R
8!4!""@!"!#6@"4A!@"4"""!
4""5 4 $#!#. "#. 6 ; !". %5
A;A ).5!BA!"!4!C""
"?5""!4"6"!6
Étape 1 Étape 3 Étape 2
(c) (a) (b)
I
"! 4 " !@ 5V# 5! !@ 4
!.4Y#%"6"!!.@"@""4!
4!4 4 8! "!"5 "! " 5
5!!4 2" #!548!!!
" !.4A!!85"#!"! "!
!6!5"48!"""#!!!!".
"#""!$6!5F#&5.Z25#&45 ) "5%548!
"5%5!"5!C"5%5!!%5!" !5
" !45 4 =4&=E $!45 &
!!4)!%#"488!4!4!4!455!8!
"!#! N O 2! 4 " 4. " "# "!" ! % 5!8!
4@4. !"! " "! !"! "# !" !
45
!88!4"44BA!!C 5<!"
""! !"5@885!? 4A4A
!! "
5!!5?""8544!""
";8!4A;!@@!4!45;5!@
"5 "445. !!R"" C " 84
!".4A5!!8!4!"44A""!
45"6!A5? "#5 5?@! "44!
"@"R""N3.'''O. "!85!R""!N'.
'IO. " 44!! 8!4!"" N'O " 8!" "!" N'. 'JO. "
45A!"5<!54!545 !!88!4!""
4 4A4A5!5! "!5?" "44!!@
4A##"84!"4B@45"
5?"5!!@5!5!!@.8!!"8@6"
4!5?"";!@N'.'3O
5 66.! ! A!@@6!56!
45!.8!5!644A5?455!!"
5"!!"!!!!.5"#"!%
J
"5 !@. 5! ! 45!@ @ " 4A# "
44A !" "" 5!? !4!. "" 5! 45. 45
65"!"644C!! !4!"""!
4 !". ! 6 4A# 84!@ 44A
!" "" 5!? !4!. # !88 85 !
$!5"!""."!4!)+"#!"!4"!?5"" !
5?" ;5!@ !"! " 4!4! "4!@ @!" 5 ! "
44!!@4A##84!"4R
45! ! 8V !4! 54A 4! C ";
"!544!5?@!!!"A5?4A#!4
$C4"!@)5"!484!4!455"44!!"
44A ""!. !. 5"45. U C "!
6!5"545?"54!454!@4A!
" 5! 4A!. !4 " !4!6 5?"
45 !@ ;5!@ " "! !4 "
!4"!?5!884!?#!4A#!!@5?
!8"4 455 " "! " !. " 8!" !" " !!
44A""!
5?" " 4A! ++ !! @ " !88
54!"#!#55!5"!4!#"5!4"!
65?""!8644A""!!8526#"5
" !88 6! 5A5!@ " !4!" 44!!@
4A# 5?" ;5!@ 5 ! " !88 44!!@ "
4A# 84!@ "" @ "! " 5 $"# !
#!)."4"4A#@!"!4!.";4"4A#
84!"#5!"!""!! ""!!!@
"85"!
!!?5 4A! 44 " "!! 4 5?" !
!5"!"""!!6!5"#"5!4
"@!?54!@!?54A!.!4 " "
!5"!!"!4!4!5
Chapitre I
PRINCIPAUX MODELES DE
PROPAGATION DE L’ARC ELECTRIQUE
(
/ +
!4!@!."! 6545
"54!5 4! 45 !" "" 5! !"
5 "!4! 4A5? "45"!" 5!
"! 5?" " 44!!@ 4A# " " 84
!"""B@45*8!.!"84!@""4
5?" 5!!@ 5!5!!@ N'I : 'O B. 5?"
";!@N'3.'(O
5 66.A!@@6!5644B.
5! !C"" !5?"!45!5"5
"5?"44!!@A5?""!+"#!55
"85!"."!!44A""$4!!4!)
" !!!. 4A# A5!@. " !85! 5!""#
"!! 4 !!# " 84 !" !!. " 5!! "
!45!"""4A!!5@.5%5
@"4!!44R"
4A#%#@!"4A5"4!@!"4
$ 4 " ! "!@) 4! " ! W !"X $!
5V#)4A#"@!4!4!!!
7 "; #A!@. Q"G! N'O 5 @ " 4!! 4!!@
"#! "4A# !884!!4!!@45D "
5!?5! "!84!4!?#!B "
4A#."4"8!"!84!4!?"#"#!
9",+:***+
@4A<!"8!"".65"!"!#
A !. "" 5"! 8!5 R" 54!@ . " 4
4A# < 84 4 " "# "5 " "" @ " 4A5
"4!@4A@!!!#5!8!C"!#!!!"4!@
"5A?5 !+"!!@"!"4
'
0"A5. !5 ". R !#! !
$!?. 85. !.U) 445" 8V A5#? " 84
!" @ 44!! "4!@ 8!4!"" @! 5!8! " !!
!" " "# " "!# 8! A#! 4A5 "4!@ "
!88!"!"4%44"A5!!8!4!"5!
#"44A""!!"4!445A!@$"!. !"".
5 .U) 4 4!! 6 ! " ! !". " !
!"4!@"!%!.<"5V#4A#"4!@
@!44!4!!""!#8!
7"!""5"!"#C"!""!
! !"" " @"! "!"5 4 ! ""
8!""4. !" !5!8!5?"5!"45
!"4!@."!5?"8"8! "!"
4!? "!5 "4 4!. ! % 4 !
"!
9)/!+:+.*
N3.'. O@!!"!!.C"!#!5!?
";@!!A5?4!84!"".
444A"".!4!88.5?";
4!4!"4!@@!"4!4"#[!4!4
$8!#+').!"!"!4
= $+')
T+"48!."4"44!!@!@"4
Q!#+'!4!"4!@@!"5?" N3OD""#8!
[
[
4
[
[
4
''
88."!@""!A5C44!4!.4!
( ) ⋅++= $+ )
T="!"!@=."4A!"6 "4D4
!?4!!6!5"$[)"!4"44A""
=4."!4""@
$ )= ⋅ $+)
4 " !4 4 ! "#. [" "# 4 +. " 4 @!
"44A""
4A#44!"44A5"4!@"#!!"
−⋅== $+)
T"@!
−⋅⋅= $+I)
!!. !"@!"!""!@;?5
( )
⋅+⋅⋅+= − $+J)
"5?5!"! "@" Y" "4A#""
!""N'. OD8V#"
'. ≤≤ I ≤≤
!56!5"4""4";.KAA N . 3O
" !88 " 4 44!
"@!"4A#""""4";!"!""5
" "+'
'
* "+'="4N O
;
" J .I(" J' . Q" .JJ2 I .(
9)9!+:+<
6 . 5F N (O ; B "A;A?
44A ""! !4 !85 ! "# 8! +"
"6!!"!4""!
( ) ( ) −= $+)
T4!5""#8!""!45;
!"#
!!46!"5?" ."!=6
"!"
( ) ⋅−+= $+3)
4
( )
−++ $+()
!!.5F!"4""#44!!@
'
'
+
=
$+')
'+=
$+'')
T"6!"!4!!@45
''
'
++= $+' )
'
9)=!+:+*>+?@*<
45 "A;A? 5F ! "!4!
@"@ F!"". " H"G!EF! N O 5! " 4!!
5!!"4"4!@"4!"4;"!!@"#$8!#+ )
( )( ) ''
'
'+
+
−+=
$+')
4["#4
Q!#+ 0?"4;"!!@!"!"H"G!EF!N'O
9)3!+:+?<
!";A!@.!GFN'O4!"A5?!"4
"54!5 " !"4!@ +"5!!4 "6! " !#!!
!"4!@"4!" "!"!"!5!!5"=4$!
455!!5")4!C"!"4."!4""!"!!@
""#8!"85
.
= $+')
9)A!+:+B"0
7"! 5?" 6!56 " 4 !
"!""44"!"!74AN J. O!"!
5?" " 4! "@ 4"!!. 5! 6 "4
4!.444A""!$Q!#+)+"44"
!@
"!45!84!"44!!"44A"".
@!"6!!"#44!!@.!444!!
[[
+
[[
+
'
Q!#+0#6!5""5?""!74A5?"!"!"!!4A5"4!@"8!#+
Q!#+24A5@!"
4
=!""4.
+48!$).
!4""4.
["#"4$45).
$[)!4!4"46!584![
@!4!4!"!
$ ) = + $+'I)
"44!
!"
"44!
!"
[
=
=4
$[)
+
[
=
=4
$[)
+
'I
54"!85! "!"!4!""
'= $+'J)
T
'$ )
= + ⋅ $+')
8! @ " ! "!8. " 4 !5 C 4A@ "4 !
<@ " ! 88!@ " 5V# "4.4@!
5!!"@4!4!!$44!!.A5?
4A# A5!@) 4!! 5V# "! "! 74A
""!
⋅≤ $+'3)
88."5 $ ) ⋅ !88D #"!# ""5V#
"4"4!@44!5#"C3.I
T"!5!!5"!"4
3
= $+'()
8!."!74A "!4"!"48!"!
45-#5!"!""!!!5!!
"!!!""4";D"548!!!@4"""!
4!?45"!! @"!!!!5!.
4!B@C"4!!@ "@"""45!
3 = ⋅ $+ )
'J
J'
⋅= $+ ')
%4""!"8C6!5!
9)C!+:+
?K"NO. "@! " !;
= " "
@ 4A# ; !5!! " "5!44 "4 N'(OD 4 ;
@! % 4 "@ " 4A# 54 !!@5 !!. 4
; 6"!@ " 4 " !4! 5?" " "
5 " 45. !! "" @! 6!5 "
4A5"4""4A#
( )
"−
++=δ
υβα $+ )
\.]. _4@!""4 "@""
""4A#@! "!C!5?"2K" NO
"" 6!5 " 44!!@ -$+.[) 4 8! " !! #
"5A?
9)2!+:+() *
8!!44A!5!"!C4"" "!"""
"4!!"".L!N''O!"!5?"85#5!@!5"
$"@ 4;"!) " G ?4A $8!# +I) G
?4A!"5!?"!$8!#+I )"!!!4!".
"85"554!484""$8!#+I4)
!!"!845!"88!74@."
455 544!@ 4 4 4A!@ !
454! ""!84!!! !
'
- !5"! 5!@ ! 6!5". !"!
A#A!C#!$!5#&4).!"!5!4
!
4!@ " !4 " 44A"" "!!. "@!@! #! 4
5?"
( )!
−+= − $+ )
4 I.≤ ≤≤ D"!4"!!@
#4!!@!""6!
'
'
+
=
! $+ )
( )
!! −+ == '
'
$+ I)
) 44 )85!44)46!4
Q!#+I0?"L!N''O
H"" HH"" H
'3
9)6!+:+0,
744A""!5!6."4!"C"#8Y.
9A5N O4!@4""4!@!"C644A!!.
!4"!!@' .44!5C"!#6!"455
!!@ " 8!# +J 45 " !4 " 8! 6 !4
!""' 4!5"!@"4!?/5N O.!"!"
"! 4! " #! 45 4!!@ $ 8! 4!
A;A?4A!!"6 ')
'3. !
= $+ J)
T"4F 3=&45
Q!#+J0?"!"C"#8Y!! !"!4""!"
9A5 N O
"!@"4!?/FAN'O."6!4!
( )
3.= $+ )
T"!4"!!@"#!""8!'
' ''
'
'
' ''
'
'
'(
9)4!+:++*
M04";N O;!.8V!"."84
!"!"!48!#!#5!@4!4"!
Q!#+0?"!@4!4"!"@!M04";
7 "SA;A?@ " !48!4!"" "44A""!A5!
S6!5 84! ; "S"4 6 " !!! 8!4!""
"".M04";4!N O
( ) ( )
−=γ
$+ 3)
T " ; ""4 6. " "# !!!" "4. a " 44!!
8!4!"" 4 5! 6!5"5 !4
""!$[) '.J' b54D '.
5?" " !8! " !5 C "
!85!"!!!8!4!"""!"
9)/5!+:+<D <*
4FM!"F!N I..O4!@"!C" "4
855!44"6"!5! ?4A$Q!#+3)!!"!4
""!456 5 !4 !! $[)665!
44"!46$[)"
9?4A
4A#
"4! "46
!
"4! "46
!
9""
7"# ! ( )π& & ≥"
( )πγ'= $+ ()
( )
+=
"
ππγ
$+)
T
" &= "!4"!!@"""!
[""#"44A""$5!"")"4!!4!!@
""#"84"!"
";" "4
7 "# !" C !" !@. " !4 6
( )
+=
"J3.
πγ $+')
7!"C!"5"!"
( )
+=
".
πγ $+ )
!!."!4""!"
( ) ( ) ( ) += $+)
7"5%548!#! $Q!#J3 )."4 !.M!"F!
N IO
( ) ( )
+−=
"
ππγ "
' $+)
"#
( )
−
=
πππγ
"
"'
$+I)
'
T[""#4"!4"8!"!"
446!"!C44!46C4"!8"
5!!!8444!!
9?4A9?4A 9""! [ 9?4A R""!$[)& [$[)& 4!4$c ) $) $ )
Q!#+3!4A5!@"84!"! "4
!"!"4"4""!4""!"$)4FN.O$ )M!"F!N IO
=",+:*+;*
" @ "! 5? " " 5. " A5?
45 884 !"! 5?" !@ 8!
4A""! """!C4A!4.65?".
45"!!"54!5?.!!."!
A;!@!"! "!4!?#!"4A#!
";5!@44A#
=)/!*+8
" A5? #! "4 "4!@. !" 6! 6 5
!4!6"#!!!!"#!84"4!@
=)/)/"8*
M!"F! 9#A! NIO 54!5 "#!
"!!! " "45 !4! " % " 4A# 2"M!"F!N IO. "
!"!!!!"#!4"%"4A##.
@"5!!@"!""4#!
2! "!!! 88!. " !" ; 4!4"! 4 "4!@
44!!B#544"!4!.!@4""B4
""4"; 4 $8!# +() 7 4@. " 4 " 4A#
#!5B.<!!"#!_"4A#
M!"F!"!!!.#4"6!44A5C"%"
4A#@ "4"@# "!2 "5!!!. !"4!?"!
!"4!@#!
Q!#+(04!5#!!!!M!"F!
=)/)9"87*
! ! 8! 4" "4";. A" N 'O ;
5 !4 "6!4 84 "4!@ 6V " 4A#.
" "45 "4 +" 5 @ ! "4!@
544!@.484!C "!;5!!! !!".""5%5
4"#4" "!@!4 "84!"84
@ " 4 " 4A# ""4 5 $8!# +') - 8! "
4!!4!!@!8!."4A#"4"""45
?"."6!4484!5"!@88.@"4!?"4A#
455 "5 4!4! 4! 4!4 544!@
4! "!8V"5!"!@".A"4"6!4
"4";
"4";+
_
+
4A# "4";
+
484"4!@@""@!"!"!@5!."54!5
5!44!@"4!484B@C5!5"4
"; 4!!@ !8854!5 #! " 4A#
""!.Q"G!N'O.!!8!A5?"5!
!"4!@ !"" #G6 " B 45. "
A;!@"4A#.CY5C4A"#" "A5?.C!
" 54!5 " #! !!! #! !!. !" ! @
"#5!#!!!C"!!"4A#"5#4
!!!4""4!."84 """"#54A#5
@ !"4A#.4;5!@
Q!#+' "4A#"!4!"4"545
!4"6!484N 'O
=)9:*+8++08
!"@!5 "!#!4#!5
44A ""! 44A "@"" A5!!8! ! 44!4
"!48!@!#4A885!85.T
85! ?4A"#!C"8!4@"!
?4A 85 5%5 5. ?@"@ 4. 4
5!4A!6 " ?4A#"C"!@!
"!@ !!!"5 6 "4 "!" @! 4! C
#5! 4A5 ! " ?4A. C 5V# 4
45"!"""
"4/*
4
4A#"4
*
"4";
"46!""!!
!4!64!?#!4""!. "!
" 4!! 8! !! ! " 4A5 "4!@. ! " 4. ! "
!4.!"#!8!"44"!54
=)9)/:+
6!4./5N O5"4"""!!4"4
B"4"44C"84"74."45
"! "@ " #! ! "4 !8! #! !
""4!""".!"44"@"45"!"@"
#!"4!8!#!"44A""!5."
45 ! @ " 4A5 " 4" " 4A5 C
"!!"4
d $+J)
=)9)9:+*<0ECF
@ "4 ! 4 " 44A ""!5!"" 5!8!
8VC56!5""4@!"!"4"!5!./FA "!
4!?#!"4.6!5""!
≥
$+)
+"44
=)9)=:+D <*
4!? "!5?"!!4!"4!@;?5
"4"48!#!@!"!5!!"56!55#!.M!"F!N IO
#"! " 4!! 4 /FA "! 4!? #! !"! "
!478!"4D"45"!"@
≥
$+3)
I
7"!48!"4[""#"4
7M!"F!."55"4A#!"@"!47#54
"#!@"!"!@;?54."4!?M!"F!
!C"4!! "!/FA
=)9)3:+<E/2F
4!? "! #!5 4! "!@ " !4!
55 !" 4 4! 4. !" 6!5 "44!5
!"-;?5@!"!!!!""#485
!88!""
+
= $+()
4=4 ! 4. !4 ""!. [ "# 4 [ "# "
44A""!
74."4"4! #$$! !"!54!@)
=)9)A:+B"0
746."45"!"!="@"4
8!+""4!!@+4""!
3= $+)
T[4""#44!!@"""@!
( )[ ]
=
$+')
4 @!$[) " 84! !! " 44A ""-
5!?"5!!@NIO
J
=)9)C:+*0
!A54!?56!5"@!5!"!
5V#4"# "!454!NJO+"6!5
"!6 !"""455"55!5"!
#!4=."!4!@="4A!"""!=
"@
" = $+ )
++= .
J. $+)
( ) = $+)
!
( )"
++++= .
J. $+I)
4 .4.4$ )"!4"44A""!!44
"# +"@"88"5#"!# ""#!
"S4 '@!"48!!
( ) ( ) ( ) ( )( )"
"
++−−−+−−
=
...
$+J)
7 ! 4 +$ ) ". !" 8 @ " 5 " !4" ! !!8 +"
4A4A4""56!5"=
( )( ) " +++= . . $+)
45!$"#""!#8!")!5!"4"C"
"!5!!5"45
=)9)2:+G<*0*0
!5!" "4 C 4" #G @!"! A5;5!@. B
FA5!!5ANO "!4!!4!C"#!"4.
"4!!#!@"#!"8!M"!%!#"C
"#!MA4!5!!"4C5
M"eMA $+3)
=)9)6:+(;0
4!? L""; A N3O " 4"4" 4 " !
4!!@4!455?" $4A54
!4!4$Q!#'')4!"@!"4!@4C4
4A5
( )
% +−+= − $+()
4
=:"4A!45"6"4$4).
$[)+:"4A!"!4.
[+:"4A!"4
4 6!. + " 4 8!. " !4 !
"#"44A""!.4"!5
! #A!@ = 84! + !88 " [
5@ " 4 =$+) ! 455 4 +4 =4
""!
'
'
+
=
% $+I)
% += ++ '
'
' $+I')
3
"C4"!4!!@. "45! "4!4!C
=4455""!45
2!"!45"!4""?"C"4@"""5%5
!!!@""44A.!C
( )
% ++= ++ '
'
'' $+I )
L";A""!458!!!
""A!"!!"!N3O""!"
"4A5"4!@N=&45O4+NOC"!4N45O!""
4A"4C"84
J .
I.−
=
$+I)
!4"!""!$3)$()4!.!" !
% I.3..3 −−= $+I)
45"!4""?""4.""!!
% I.3.' −−= $+II)
4 "!4! "# "44A""!7 "". !"
!"! .'45
K" N(O 884 " 6!4 "@ 4#"!
"# "# "5?" !" !"! "@!!
6!5"4A!"4"#6N(O
( )
"−
++=δ
νβα $+IJ)
(
8! !! " ; ! "4. " ! " 6
"!"""
( )
"
"
"
+
−+
−+=
"
'ππ
$+I)
!4!!@454!!4!4 =
84!+!88"64\.]._f5!"!
! 5! "4D g " 44!! 84!@ " 44A
""!
=)9)4:+) 00.H)$)#0.
!564!?4$5!!@5!5!!@).AA !
N'3O 4!? ";!@ #! " 4A# 8! !!
"!54 @!" 4!4! "4!@ !5" !" "" "@"
4A#!78!.!"4!?!"""#8!
"@" 4!" "#[ !44455 "5 "
8!#+''4A!64!6!5!B!8!"8!@"
A5? 45 !""5 44!!@ 84!@ "
44A ""! 44A ""! C % 5"!
!4 ""?" 4 44! !!. " 4A5 "4!@ @!"
5?"455!!@"8!#+'
Q!#+''24A5!"""Q!#+' !4!"4!@@!"T!4"44.!!"6454!44!!
"4"44A""!
!
!
!44
[
-
-7=4[
7"4!""
( )
&ρ
−= $+I3)
&
ε=
− $+I()
Tρ .ε . .
& 4!5"!!!."5!!!.""#8!"
4! " 44A "" 6! @ "
6!5!!"!" !"4545?"N'I.'.
. I O7!""4!@"44"4;"!!@4! & .
"# !!! ρ .!4
&ρ= $+J)
T"6!"!54@!""4!!h"
'
'
( ω= +
+ $+J')
4
( )( )'
'
& & (
ρ ρωρ ε−
= ++
$+J )
4ω ""!
7 "! 4!? #!. 4 4!? " 5"
"!544!4!@!"C"!"""
!!."4"5""!54H@.
( )( ) ( )
'
' & & & & &
ρ ρ ω ε ρ = + − + − $+J)
T ' ω ρ ε= + $+J)
'
( ) & & &α ρ ρ ω ε ρ= − + $+JI)
"45""!544!
( )( )
'
' & & & & & &
α α ρ ρ ρ ρ = − + − +
$+JJ)
!C[
( )( )
'
' & & &
& &α α ρ ρ ρ = − + −
$+J)
- 4!! 4! C " #! "4 @ "!! "!54 !
4!
'
≤ $+J3)
4@!4!C
( )'
& & &
ρρ ρ
α
< + −
$+J()
4"!!4!"85
( )'
& & &
ρρ ρ
α− < − $+)
";46!4!C!!#!4
=)9)4)/"*
( )
& & &
ρρ ρ
α− ≥ $+')
455 " 5 & ρα
B !!8. !" ; B #! "4
4!!$+')!"
( ) & & ρ ρ− > $+ )
5"4!"4!@4.4!5"4A5"4
"44A""!%6!5"5!?!
&
ρ= $+)
!"44
)
&
ρ= $+)
T ) "48!4!4""44A""!"444A
""!4!.!"#!!444!
2""5?"4!4!$8!#+ ).
) = $+I)
"!."4!!$+'I)4!C
< $+J)
24A@"44! ' = .4!
< $+)
@"4!?"!544!C4!?#!!!@C4"!
"!/5N O
=)9)4)9 ,:*
( ) '
& & &
ρρ ρ
α− < − $+3)
-8!".44!!4!C
& &
ρ ρ< $+()
44."4#@!4"!!@!C4""
"44A""!
=)9)4)=*:*
( )'
& & &
ρρ ρ
α− < − < $+3)
";46!8!<"4T"4""#B@C!4[.
!!!4[8!!
( ) '
& & &
ρ ρ ρα
= + −
$+3')
4! 4 4 T " 4!4"! 4 8! <
4A885 " 44A "4";!@ 88 L" ! "!!
?4A G " 84" 44!4D " A5? 54
!5";?5!!"
45"!#"!$+3)4!C4!!"4!"4!@
> $+3 )
"44!T ' = ."!#"!$+3)!
> $+3)
55 "4 ""#5%5! > . "4!?/54C
4!!88!C "#!"4. !"!@"4!
!"4"4
=)=!+:*+;*
+" 6! "! 5?" 44! " ;5!@ "4 ""
""!55!464!
=)=)/!+:+?<8;
744!";5!@"4"44!.!GF#;NO
4!!44@!!""@!0;N'O
ττ
' +
−= $+3)
4i 'Z.45"4
.3 J
5""4";4"4"C! !"#!@!45
#!C"!."44!"4!
( )( ) ( ) *
++
,
,
&
+ −
+−−= δδδ
$+3I)
TA "! " 44A " ""!. _ "5"5!@ ""4";./
"A"! $ J L&#). /4 " 488!4! 8 " 4A" 44! $ I
ZE&45 &). "4A"4!8!@!4.* " 55 !
2$[)"84""4";4
4 5?". !5"! 4 !8! C ' .
"#5! "! ""4";A5!!8!4!$AE)#"!# "
!5!!!$A)!?%4"4"5*
'C!"@!
( ) ( )( )[ ]
−+−−
=
++,
++,&
δ&
$+3J)
7 4"4" " ! #!. !GF #; NO "6!
5!!@ "! " 9#A! NIO @ !GF B!8! ";
!5!"" N O " 6!56 5 @ 4 5?". !
445 "!8"4 " !4 4! "4 ! 4 ""4 A
!
I
=)=)9!+:+G<*0*0
BFA5!!5ANO 5?" ;5!@
"@! 0;N'O " 5?" !@ N3. O +" @
"!" !! 4!5 85 6 ;5!@
C "6 "!" @ "4 4" #G @!"!
A5;5!@"#!
!+-.
= $+3)
T*"5"4.0"5 !4""4F"4
9"G5
7"#!"4.BFA5!!5ANO5?".
""@""4"4@!#!"M!#"C"#!
MA4!5!!"4C5M"6!!
( ) . ∆−= $+33)
4 " #! "4. 7 " ! "# 4! 455
4D4"84!44!;5
5 "4 " 5 5 ! 4 #"
4!5CPP
2! " 4!! #! !8!. " ! !45 j= "
#55 !! " 7 4. ! "4!! !8!. "!
#!"44"4"
µυ = $+3()
TZ"5 !"!"4
Kk45j.!"!!""#4[$[ j)
2! " "" " " "# 4 [ l [ ! " !? . !" ;
45.!"5!45j"4"4"!!"
J
=)=)=!+:++G
2B K NO 5?" ;5!@ @! 5 "
5?" 4 8 @!" 455 4!? #!. 4"! /5
$4d)"44!
4@! 44 "#! ! " 44A""!. 4 !"!
"6!
''
'
++=
$+()
T"!4""!"!!@. J .I@""
!"!2BK8!"4!4!!@
''
'
++=
$+(')
""4! "!5FN (O
7"4"!8.2BKNO!"!"5%55?";5"V"
4!? #! "4 " 4!! ""5# "! !GF N'O $=
.)
=)=)3!+:+) 00.)$
45?".AA !9"NO4!?@"4A#%
4A5"4!@@!"455!!@"8!#+'!.!.!
=! 4!5 " !4. " 44!. "!44 " ! 4 C
4A@4"""""54"45!" "4
!4"!4"44A""!
!!
+ +! + +
- =!=! =
Q!#+'24A5"4!@@!"
4!"@!"4!@4C44!4!855!4!""
!"! " 4!? !54 N'3. IO 455 4!? #!H 4 5?"
5 4"4" " ! 45 4!!@. " 5 45 "
! #!. ! ""! 5? 44!!@ "4
$44.!#!.4A!"4.!C"%"4
4A# !B4 "!"" ! "4). !
!""58!6C"4!45?""4A!!
=)3'**+8
5 6 54!5 6"!@ " #! "
4A# " 84 !" "". 5! !" 6! "! 5
""!#!"4A#
8! "A;A? @ """#5 " 4A# "! C " !4 7
!! "C"!4"4A#C"#!4!" !.H"G!EF!
NI.IJO "!""!!
( ) /
−=
σ $+( )
Tg!#"444"4A#.,"!#!"!!@"4A#.[
""#"4"!4"!!@""!
0 NJO 8V !4 " "!! "!
#! !"! 8! !@ "4 " 4A5! " 4A# C
!4"5"!""5"!#6
"5!64"8! !@.!"!"!5;#!
"4A#
"! 45 " !. " 9#A! NIO "! "!
5!!@"!
( )I. 'I.' 0 −⋅= − N45&O $+()
T!4"44!!@"!4"!!@""!b&45
3
!GFN'O @ 4 85" 44 4 ";!5!""N O "
!"!"5?";5!@NO
A"NO!@""45"4A##"!@!
6!@"!5;4!!""4A56!C
" 4! "4 ". 84 " " 4" " 4A#.
644!4A5"6V"!"#"C"!884
4."!6!
( )
0 −== µ $+()
TZ!#"5 !"!"4"4
?A"."4A5%6!5
+
= '
π
πρ
$+(I)
T..+.m4!5"8"44A"4";.""#
4"4"44A""!."4"4A#."!!!""4";
";"4A#
6! "!#! "4@! 5 ""
? 4444""56!5"54""9"N3O
""4!. "! C "!#! " 5 " !"4!@ "!@!
444?64A#5!"!66!84!"4!@""
"8!@"#!"4."#!".!88
85 N3. (O. @ 84! $β) 4 #! 8 4" 4
85#!4!!@."!5!!""#!4
. .β= $+(J)
(
β ""@ 'β< <
75
'
. 0ρπ= $+()
";"4.0 "!#!ρ"5"5!@#G
24A@
0= $+(3)
"
( ) ( )'
0 . ρπ β= $+(()
74@
( ) ( ) '&
. 0
βρπ
= ⋅
$+')
4
( ) ( )
0
βρπ
= $+'')
( ) "!4!B4"!""
!"! 4 6!. AA ! 9" NIO. ! " "
!? 4444""5!45?"
!C4""!""$ Z4).5%55 !"!"!5
#$"'45 &=)."#5!"!#!
4""#"4"4A#45?"48!5!
" ! " "!N'. '. . I'O. 4@! " 4 4
"6! " ! 84! " 5 !"! $ Z4) T 4""4! !5! 4
"#5! " "# " 4A# @ " 4A5 4 !5! "@ "
4#5
3":*+7
3)/ 7+
5?" 4"!@ 45 ! 4!. 8 "
!884 " "! 4 8!. 4 5?" 6"!@ " "
6!564!5 4A4AN.I .IO.""@""
! 4!!@ "! #! ! & ! 4!!@ "!
!!
M!"F! "9#A! NIO 5@ @ " #
!4."!#!44!!@"#?5!8!C46
!!!4!%6"!@"A!""#!!!!
"4 !#!.#!" ! " % "4A#
" !5 Y C " 4A# 4. 8! " "!!!. 4 4
4!!@!8!C4"!!!!"!@
".;HA!4A#NIO5@"!8"4"
"! "!8!" "!"2! " B ;5!@. !";4!884
""!74.!"!5""!.4#!8" "
@4!!8!#"!A "84 "!" !!
84!"5
5%5. 6"!@ " " " 8! " "! #!.
4!N.I .IO@"R""W"!!4A!@X"!
!!."!!#""4""4A#!"!
5!8! !! " #! ! 4""4! "5A? "@""
""4A#"!#!.""!!;"!."4A#
#"!4
3)9 7+*:*+*
!"!5"!6!4.!GFNO5@4A
! 56!5" 6 "4 !4 " 6"!@ " " "
! 4!!@ 6 5? " 4 +" 5@ " 5 "
! 4!!@ 6 5? " 4 % 5!
!5!"64A#."44!"44!!"4"
"!""!""!
'
6 "! @! % 6!5 5
!5!""4A#!".!"4!"4!?!5!5
"44!"44R"
!"4!@.7!"NI O";"!8"4"45
@4!?BR"!5"#!"4A#
3)=0+
Kk4C56!5".M!"F!NIO "!@"554A
!C"4AC".4 "!"4"4";!@!
3=
-5?"A!@4"4""4A!"4A!@A
NIIO5?" "! "44A# "5!4 4!84
5""!@ "@!7!"54!5"4A*E
" 5!@ 44 4 " 5 6!5"D 4 @!
5! 6 44" @ " " 3 = " 4A !"
! "
?!GFN'O.A4!!T"!!"6%55
" T 45"!" Y" !. !4! #"!# " 4A
!"6"4
3)3*+
* 4 45 55. 4 ! 44! "
5@!4" "!5V# "4A# "!T!!
""4 ! " 4 ! "!. 4 5 4
5 " #@ 5! ! "@" " 4A# ! ""5
"! 8!4 "84 "!" 5 " 5
D !" 4 C " "@"" " 5!"! T Y" " 4A#.
!!"6!5"54A5"4!@"4
84!5.2E!8NIJO "45454"
5!""#"!"
KAAABN . 3O5@"5454<4
"#5! " !"!@ "4A!5!@"" +"
@4A@"4";.!";"!4"!?"!"!@
"@""45! '5@#5!"!
885@ ""545
0F NIO5#"5@"545
"4A!5!@""+"!5!"A;A?"5@!"6!
4"! " !! 5"" 44!!@ " !4 "
""!"545
! "!8"4 " ! "!@ " 5 45
4""4";!4!.7""NI3O @C!!!"4";
4. " 5 45 5; " " @ "
4A " " " ! 4!!@ 45 +" ! 4 @
"! #!. " 5 45 ! C 46 "!
!!. C !!! #" C! ! #" 4 #"5
7;?NIO
3)A"7+*
784!."8!""!"!!8!"4!!!
"#8!56!55
5 !55 $ !"" "!")@! 5
!!45""
#5!"!"5";#"4!"
""!
!5? "!" !88 45!!!85
4!45""
7!4565!?4!!.ANI(O8!!5?
n@!44! "88!44! " "#8! +"5@ "4
;5!4;"!!@.45?#"584!""#"!E.
A"!4@!"!"6;5!"!"$Q!#+')
Q!#+'65""8!"!"
!56!5".!"!"!5!!@"85
−−=
!*6'ξ $+' )
T F !@5 ! 45!! "# 8! 884!
4
)) ξ= $+')
7!8885!"."!74AN J. O4
!! &m84! " "# "!"!84!Q$[)
""@
( )1 ρ= $+')
Q$[) " 84! !! " 44A ""!D m
4!5"!4"!!!"44A""
""!!8!4!"".8!5"!84!
"# ! 85 !". ; H!4A# NIO 5 @ " 85
"!" " !8"4 " 854 "!" 4!@ "!8
!8"48!""!""!45!"!#
2BKNJO
E
E& E&
3)C***
! 5 @ " #! "4. 4A#
#"5 54 7 4@. " 4 ! 8! " 4
5!!44!!"64!!4!!@D"!!%!#@
4""4!#"!
!GFNO 4!?@!" 6!5 4 ! 5 ?4A . " 5
4#"5 ?4A8C5@"44"
4A5!8!. "5 !#""5""8V@45. !"
;@"4"4#!.!GF@4
!4j6."5 4!j5!""5C5Cj6D8!
"@!!88!""".!" !""!!
&'−= $+'I)
5 5 ?4A#"C !@!"5 4
! " 4"4" " 4A ! " 4"4" " !
#!NO5?" 4"! N3O!!."!6
"!"
( ) ++= $+'J)
T="4A!445"C""4A
"?5 ! ! A NI(O @!" 6! 5
4A# !5"5?" . !" 4!?@ " 4@!
4!4" " 44A ""! " 55 4 4A@ 4A#
4A4A 4!! 4!!@ " $4SC! " 4A# " "
4). " 4! C " " 4A 5@ 46 5?"
"A;A?45"!"
4A55?"5"!4"8!#+'I@!@!4!"5?"
4!4!@!"44NI(O
( )
!
!
+−+= =
−
'
$+')
I
Q!#+'I0?"5"!4
5?"5?"!@@!4!.6!"!"
44!!@M!"F!.64!!4!!@45."@""!!
=
$+'3)
=
$+'()
5?" 5"!4 A NI(O H5BF!4 NI'O. @!
!4! " #! " 4A# 5V# 5!8!4!
44! " 4" !4!" " 4A#. @ " 5!8!4! "
4A# " " 4 ""4 5 !88 4"" @!
4? 4A# 4 4! "@! ! NJ'O $5?"
K"). "@ "4 4! "@!; $5?"A
)NI(O
74A#55!8!4!."@!5?""!
( ) ( ) =
−
+−+
++=
!
!
'
"δ
γβα $+'')
T+F"4" 4AF[5""#" 4A5
[5
[
[
['
+5++ +'+
=
J
6! $+'') " 4A ! " !? 4A "
4A#"!"!? 4A5"!? 4A$5')4!
455!
( ) ( ) −
=−−
−−
−
−+=
++'
''''
"
!
!
δ
γβα $+''')
" 4A4!"@!
( ) =
+−
+−+ −+=
(
!
!(((
((
( '
''' $+'' )
TB'. U5
3)20+7
44A " ""! @! "!" "! % !85
.!#"85"4"!!44A5??
"! " 6 884 !5. 5 @ " 4
""! !85 5 " % " 4!!@ T " B!8!4! "A;A?
""! !85 !5"!8! " 4"4" "?5 ! "!
4A4A @! #"5 ! !!! !88 C 4A@ G
"!"
7 ! 45 "!85! " 44A""! "5?".
2B K N'JO # " 8!" "!" "! G
! 2 $R ! " @!") !88 4A@G +"
@ " ! 45 4 4 "#?5 ! C 4""
4 C ""! !85 "2 "5%5 " 84
"!"
!"! " 5%5 !4!. B FA5!!5A NO ! 6 5%5
44"!
!6!4""!!8!4!"".0F NJ O@"
#!85!44A""!5"!644!!@"
!484!@C"!!84!5
3)6&+*.+**:0*
"?5 " 85! ?4A !!884A4A
NJJIOK""5NJIO5"!"85! ?4A"5
8!!4! ""! 85! " . " ! "!! ! "
5 " 44A""! "! %4! ! @!
6!!""4"
( ) )+2
−+∆∆=∂∂
$+'')
"!! !" .
( ) =∆∆ σ $+'')
"!! !"!.
( ) ( ) σρ +3
+ ∆+∆∆=
∂∂
$+''I)
"!! !"5.T
N#&45O"@! !"5R"".
N45 &O"488!4!!88!.
=N#&45O"!5!""#.
8N#&45O"84!!.
gN'&b45O"44!!.
NL&#O"4A"4!8!@C!4
mN#&45O"!.
PNM45O"488!4!844!.
"5
@!$+''):$+''I) "!4!@
! ""5"5C 8!!88!
"!8"4"#!!#"!#."5!""#"!"!"84
5!C"44A$44 ""@"44A8!)D
3
"!"!@"44!!5!"48!D
4445"!4A#! "D
" ! ! % 84 "! " 44! 6 !!#
#"!#D
"4A""!!@"5"4""44A""!
""!"84"!"
!"!"4!!6 "!5! !8!!.K"" 5NJIO
444@"!!4""6!56. 4
!"C8!6"!45?"
A*
A5? 45 8! !! "! 5? @! "
" 57 !"". " 4 A5? "! "
5?"!@"!4;5!@64"5?"AA !
9". 45?" 4 6"!4! "54!5A;!@ "
#!"4A#.445?"!"48!#!
"" 44A ""! @! 8! !4! 8! " #5!
"4."!!!$!4"!!)#;#"$"!.U)
" 4A! !. 5?" ;5!@ 5
5! " !88 44!!@ " 4A# # !"
444A""!!! 8V!4!
(
Chapitre II
MODELISATION DYNAMIQUE DE L’ARC
ELECTRIQUE SUR DES COUCHES
DISCONTINUES
- 4
I'
/ +
5B!5?"""!.5?"!@
4! 8V 5!!@ 4 ;5!@ 5?" 5
!"!454!!@!45""!5""
!885?"4!@.A5!@.#5!@.U!5"!@"A5?
45 4 4A!. 5?" ;5!@ 5
5!45"!!"5!885?"!4!
!5!"!.4A.C4"!AA !9"N'3O " !"
!855""!884!"8!@4!44A
""! !4! 7 4@. " 4"4" 4! 5? 884 "
5%5 5!? @ " 6 ! # @ "
4A##84 "
9"*+.*++:
5?" 4! C "!" "" 4 !88 !!
@"4A##C844!4!"4!@@!"8!#++'
65"""48!#!"8!#++ ."4A5"4!@
4" 4A# # ""! 4" " 4A#
!5!"C4;"!44@"4""" $.
4!5 " !4. "!44 " 44! 5! C ! "!
A;!@. " A! 4A# " #G 4"4" 4A5
"45#!@)
Q!#++'8!#!84!"4!6 $"")
0
$+
.+8+
<+.+
)
$+
70
+
$+
"
0
$+
.+8+
<+.+
$+
70
+
$+
"
- 4
I
Q!#++ 0?"4!4!"4!@@!"4"4A#!4"44A
""! ""!"84"!"
4.44 4!5 " !4. "!44 "44! "
4"4)"!4"44!"44A""!"
4!="!"4="!"!@6
"4
@"6AA !9"5@"!8"4"!44!
#"!# "NIO
="8++08*+B
7 !!! "4A#. !" 8@" !"!@!88!55"
5!?C!8!"4!?!!!!4A#;42!" "4.
4A# 4 "# 6 !4 2! " 4" 4A#
88!55 "!5 " 4 4A# 4. " 4A# "
""4!."4"8!!!<.8!"44!!@
" ! "!@ 8! 4!! 4" 7 "; " A5?
#!.!"!4554!?#! "4A# "4"4"!
"!54"!!@"4A!4N'3O
A@8!@"4!?#!!8!."4A#4$ )
C 4A@ "45 !" 4 "" 4""" @! !
44C"4!!."#!"4A#4!4"""
!455!!@"8!#++ "!"!@6 "
' '
' '
- 4
I
""!4!D.4!5"!4."!44"
44!"4"""5""54 "5 "4A#
"!4"84" 84A!@"4A#44!4!
"#!!!.""4!#!"
5%5 5!?. " ! D " 5? " 4A# ! " "
44!!@ " "" ". @ " 4A# "#
!!!"$!4$!4!44$44!$""?"
"$!"!"4A4A'o""#8!"N'J..O
4@! !. @ "! " 84 "!" $ )
!55!?C#"!#"8844!!8"!"
Q!#++0?"4!4!"4!@@!"4!"#!"4A#
""!"84"!"
!!.4!"@!"!"4"4!4!.
'$ ) $ )− − = +
$++')
( ) $ )$ )
)
= + $++ )
( )$ )
)
'= $++)
' "!54@!""44A""!$ ""?"4 )
$6)
!$6)
!$6)!$6.)
=$) =!$)=$)
$6.)
$6) =$)
!$6) +8$)
- 4
I
!"!"!.4!"@!4!85
;?5@!!88!""5!
( ) ( )$ )
% 5
= + $++)
( ) ( )$ )6 2 = + $++I)
T % . 5 . . 2 5!444!5C";5!@
;?5.4R".C" !C"5!!!4
( ) ( )6 4!5"5!4!
"! 4 @! $@!!88!""5!)5
4"4" "!8844!!@ "4A# $"4 "4A#"4!@. "
! #! !. " ; 4" " 4A#U) 84! "
#5! " 84. " "#. "!. " !!! !88
""!"84"!"!!."4""!
( ) ( )'
− −= $++J)
4A#!B4"554A#"5!
( ) ( )' '
/ = =
= = $++)
" 5 "4. " 44! C " % "4 "
!C"%"4
4A!"4""6!4!
( ) ( ) ( ) = − $++3)
- 4
II
7 4"4" " ; 4" " 4A#. !"! " 85"
M!"F! NO 7 4 @! " !. "" 4"4" " "!
9"N(O
3*:*+B
3)/ ++0+
3)/)/**
8! " 45"6! " #5! !" " "4
45. !" ? !88!4!" 6!5 " !4 ""! !5"
@!.!6!4!4
5?"!5"
3)/)/)/!+:
5?""!!""!"!N'I'. ..O"!4!4!C6!5
"!4"44A""45584!"!!""#8!
( ) = − $++()
"!4"!!@
3)/)/)9!+:+D <*
*45"4!4!"!#4!!85"
"4.M!"F!N IO@4!855!44"6"!5!
?4A!"! "5A84!4B# "?5
4A5"4!6!5!.M!"F! 4556! "
4 !
( )'"#
ππσ π
− = +
$++')
- 4
IJ
"4 "#. 6!N IO
' "# "#
ππσ π
= −
$++'')
4σ . . . 4!5"44!!8!4!""""!.""#
8!".""#"4.";"4""#"
3)/)/)=!+:+;>008
HA!4A# ;NIO 5@ 5 4 45"6 C
5?""$8!#++).4!"!4 "85
'"
πσ−= $++' )
σ "44!!"44A""! ";C"%"4
Q!#++0?";HA!4A#
!"!46!"!4!"
3)/)9
44! 4 C " 44A ""! 4"4" 8!
"6!5!"!!!
[
4 4
[
- 4
I
&
ε=
− $++')
ε . & "5!!!"4!"44A""!
7"4!"4;"!!@."4!6!5
( ) & π= + $++')
";@!""!" "!"44A""!
7"484". & "6!
& = ⋅ $++'I)
""#"44A""!
3)9**+
3)9)/IJ+
44! C " % "4 4"" " % "4
""484D""% 8!6!5!A?"NJJO
[ ] '
'
$ ) $ )
πε α α∞
−
=
= ⋅ $++'J)
4
( )4A
α −= $++')
5!!!"G!!?!88!4!"C".4."4"4"884
55!!!#"C ε "
- 4
I3
3)9)9**+
74!"455;5!@"4."@!0;
NJO "! @ "4 !5!" " C 4;"! ; 4 @
"4! "#! ! 88 L". !@5 C " 44!!
A5!@ @ " !4 "4 "!! ". ! " 44!!
A5!@ "4 " 5 ! 4. " !4
4 "4"44!!"4!@!"!6!""!
C!"@!4A"445""4A#
−=
'
''"
τ $++'3)
T "!"4"4. !4τ "4
5"484!"!!A5!@5!"!
@ " 5?" 0; " " @ !"" 5 !
8!!D ""4 τ ? "#G4
!!@4@!!.""!"!!""N'J..
O.!
' τ µ= $++'()
= $++ )
2!"5?"";!@@" ."4A5"46!5
'−= % $++ ')
!!!C"47
%= $++ )
- 4
I(
4"5%5"τ #4G
@C 4 !. "4 ! 45"?5. @ " 5!"!
!!"4!@!!!"@"A5?5""4!
4"5%54!!!!!"@5!4R"!"
3)9)=;+++08
5!5?4"4?"!44"!"5!
845 !!@ C " ! @! " 44!! C " ! "@""
!"4A#4.455"8!?"48!!
8V ? 55 5 C !"! !5? @!" 7 8!.
!"!"5?"M!"F!8!!"@!$++ )"!"4";4
"4
πI.'
= $45) $++ )
3)9)3'**+8++08
!#!"4A#4"4"C!""!9"
N3O
&'
)$ )$
=
.
0
ρπβ
$++ )
&'
)$
)$
=
0
ρπβ
$++ I)
4β"84!"#!"!"45"4A# 'β< <
";"4.0 "!#!ρ"5"5!@#G
( ) .78"!4"#!!B4"!""
$ ) = ⋅ $++ J)
- 4
J
3)9)A*+
6! " ! 4 5! 4 4!!@ "!8
4!?#!$4!?!54).AA ! N'3O88.?
"6!$+).
( )
& & &
ρρ ρ
α− = $++ )
T
& & ρ ρ= $++ 3)
4
= $++ ()
T"!4
&
ρ= $++)
@!$++ )$++ (). !""!"!4
&
ρ= $++')
"!48!"44A""! )9 "
)
9 σ ω ε
ρ= + = $++ )
σ "44!!"4!@
455
= = $++)
- 4
J'
"
)
= $++)
3)9)C*7+8+*EC6F
44"!"4"884A5"4!@4!C4""!!
4"!4""<!!"5"!"!4!4A#
"#5!4!!4A5"4!@"4!!@"4
42! $)"4 $=5')"!!4A5"4!@
"4."#!8!4!"#6"4#"C
= $++I)
!4"!!@!""4!8885
3)9)C)/"**-B**+*-
$ )
! + + )
= − $++J)
. . + + "5"5"4!4"".
" ! "!!@ "4 ! " 4 9"G5 ) " 8@4
4""!!
3)9)C)9"+0
@!4A"5!""!Q!NJ(O4
A!@."V"A;A?"@!"! A5;5!@"4"$*)
+/ %
λ ∂= =
∂ $++)
- 4
J
λ . % . + 4!5 " 44!! A5!@. ""5 84. "
5" " !4! #! " 5 " 5 "4 /
"@!4A""!!@"4
3)9)C)="+77*.
I '
% %
. !+ 2
∂∂ = + ∂ ∂ $++3)
. "#! !!! !4" " " 5I
. !+ +
"#!""4D4"55"A"!#G"4"#!
@!"8"8!@!"!""!C"5
3)9)C)3";
#!4;5"5!64""!!!"!@
""#"!# "68! "" ."!5445#5
4"5"4!@<!!"#5!4""!!!"!@.
"44!!A5!@."4!@"!88!
"V "A;A? *. " !! 8! " " !4
"!!@ !@5!!"444!A5!@N'I.IJO4
4!!
/
= = = $++()
/ "@!4A"!"#"4
@"84!A5!@4"4A5!A?
@"@!#!"5!!5!"".!"!
0 +πλ= $++)
- 4
J
+ " 5 6!" 4! C "!!! A5!@. 0λ " 44!!
A5!@"!"""%5!""!NO
( )''
0
0
% 0
0
λλ=
=−
+ $++')
λ . 0 % 4!5 " 44!! A5!@. " 84! "5!@ "
488!4!4!!@#G4A@4!5"#D"!6 0 "!
4!5C"!C"
!4%!45 !"@!$++).$++)$++')
( )''
0
+
% 0
0
λπ=
=
− +
$++ )
' = ( )''
0
+% 0
0
λπ=
=
− +
= $++)
6! ";!@5 "" 4"" 5!!@ 5! 5!!@
4 " "! "! C ! " 6!56 !"!
!884A4A44!"!4N'I.'. . I O"
!884%""!765" '+ = P.
" 44!! "! .J ( λ = M&5P N'O 4"" " .(0λ =
M&5PN O
- 4
J
4!4!@!".4!
'
)$ −+= $++)
' "!54"44A""!
744A""!C5!4!!."@!$++)!
)$ −+= $++I)
A*+
"4!!@4 8! " !45
5? 856 @! 5. ! !@. !5! "
!" !!. " 4 4!!@ % ! "@! $++)
C
'
'
+ =
$++J)
!"@!$++I)C .
'
''
−
+
+
$++)
T""#44!!@
'
=
+ $++3)
- 4
JI
!4!!@45" 4!"
''
'
++=
$++()
"48!!"44!!@!@"4.
"5!"!T Y""4A#D""!""$ "++')
" 5?" ";!@ NIO. "@! " 44!!@ !@ "!
4! @ " 4A# "! 5"# !
44!!@ ( ) ) = 4!885?"5!!@N'.
. I. O? 444"5?"";!@88."
!4 "!!@ "" B@C ' b&45. " 44!!@ " 5?"
";!@ 4"" ! 5?" 5!!@ "" < 455
4 5;C4"""5?"5!!@44!!@
4A54!!@ ( )& 84! ."5?"";!@!
4444"" "5?"5!!@N'. . . I. O
* "++'="4!"
*
' ."!74A ' .I
M .3M!"F! J .JL""; 3 .J
!4
/5 I . A"/6 I .
=
!%5?"@@!" "!";!@5C!
4!!A;!@+"5!"#44!!@A5?
45"!4"!?5"!"44!!@
C&+7
745"#5!"!".!!"8485)
"@!$++3)N'J.....IO
- 4
JJ
'
$ )
)
2 π= $++I)
T ( )2 "!5?"!"C""# D ""#""!"
8!!"!5?884!8""!
))
2
)π= $++I')
4
'
S))2)π
= $++I )
4
S
))
= $++I)
7!"4;"!!@."!4"!!@""!
'
))
2σπ
= $++I)
σ"44!!84!@
!!"8485."6!"!4!!@!
)
''
' S ++
=σ
$++II)
"!@!!%!!"#!#55"8!#
++I!4!"#5!"!"$"#8! .;884!8 "# )
"44!!8!4!""""!σ "?5#55
54"4""!454!!@;5!@!@!"
45"!!"54!5?."545"
! #!D ! ""! 4! 5?
44!!@"4"@4.!#!.4A!."
!C%"4A#!B4"!""!"4!
!""58!6C"4
- 4
J
"#!#55"8!#++I.B5"
C4A@;!"!@!5"!640*9
!5"5 " 4!! !!!" "!" "" @ #5!. "#.
"! " 44!! 4A@ . " !! ! $4C! "
48!#!)"!.4"4" "!885?4!4!
! 884 " 4 " 4!? #! " "# 4A@
@"4!?@!"!4"!"!54 "!#N'3O
- 4
J3
Q!#++I#!#555?";5!@
5
+!!"!!. F.6. F.m F.'.'.'.5
.
"4"!.!.!.!.+!
"4"p Fl'$ !)
"4"p F$ 4)
7#!
l
βρπ
=
6! 6!l!
6!d8
!q!
6!d F
! !l!
!
!
!
7#!
#5"!
- 4
J(
" "# !"4. 6 " "# !!!" "4. F. F. m F
""#."!"44!! .'.'.'"
!4."!44"44!"4!!!"!.!.!.!.!.+!4!5"
!4""!."!4"4."!44."44!"4"4
4"""!$@"4@).6!""#4"4B@C!
!@p Fp Fl' 4!5 " !4""! "
48.8!=!"!"4C"!!
2*
5?"";!@ "@!"! #!@."4!4!"4!@
@!" " 44!!@ A;!@ "4 +" ! 45 " #5!
"!" "#k4C "!4! 84 855?"54"4" "
!45!"4!";5!@"445
4A#5 " !4 " #!. ; $"
44!!@).8!""!"."4!4!"!#4!"
4A#. " !! ; "4 "! 4 B@
45 " ! ! #! " 4A# +" 5
#"5!""!"!C"%"4"4A!"4
"4A!!."""!@45?"5! "!88
44!!@ " 4A# # 84 !" 4
44A!4!5!C!88;!
'
Chapitre III
VALIDATION DU MODELE EN TENSION
IMPULSIONNELLE
/ +
!8!"!"."S!!"!4!""!.
4A88#"4"@!#"4A#4!G"84!"."
44A""!#"5!85!#"!"!! !
"""! !8"4!45 "#!4A# 84!@ " !
45$S4)!"5 884"!
S4 " 4 8! 84! " 44!! R ""!. "
#5!""#8!!"548!4!
!"!4!65S4!"!"""!.""
5?"!4!8""! "!5?"!""
7!"4!"4;"!!@.4!4A4A!!84
85. "5?"6! 4A#!5!"C4"
4;"!!@!@
4A!44C "5!!44!!@4A##
84 !" "" 8V !4! 4 !
!5"!""D!"456!5!?!""!!
5?" " 4 4A# 5 4 $ 5 4") 7 8!.
4! " 4 84 !" 4 44A ""!
!85. !5" 6!5"5 44A "! "4";!@
"@"" ! " 5 NJJO. ! !5"!"" ;
5 - 8! " 5?" "! " 44A !85.
! " " !5"! 44A !4! 8! !
! 5? " 6!?5 ! 4 4A!. ! C "
5A"#! 4A# 5"! 4 6 4 4!. !
!5"!"";8$'. &Ir)-";5?455""!
"5"! " ! "!@. "! " 44A ""! " #
44!! 4 44A "" #"5 884 @ "
!5"!884!"!"44"4"0*9
9*++08K
9)/ *B*7+7
!!!86!5"4!5 " "C4"!0 NJJO+"4!
!"""@"4!'45"#.'45A 45
"#. 5"! "! "4";!@ !!! 3 Ω45$Q!# +++') "4
A!!!!#"4"84""4";$44!4)D
""4""!C"5"#'45A"#?5!C'45
!@!"!"!@!5"!""'&3r""4%'.I
F=!"!"5%54!!!@0 .64"S!R""
@"#"C55!5"!$"!'45"5?"6!5").
44!!@!5""85""! 4444""
6!5"5"4!$8!#+++ )@"8!55455
!C8!B!8!@"4A##??"848!#+++
+++"S"!;4""4"!!"4A#
! !5"! ! 5%5 @ 4"" 5 6!5"5
$@"@4!5&)NI.JJO7!!!."4#54"S!
R""$8!#+++I)+"#5#"54"44!!R"
8!6"!R$8!#+++J) 44""5?"
46 6!5"5.4!C4!@5?""!@
""!@ C R ""! ! 8V !4! " 84
"!"
Q!#+++'!!!86!5"!"!0 NJJO
3
:$
:
;$
I
Q!#+++ 5!45?"$)4"!5
0 $------)"4!!6!5"!!@"84NJJO
Q!#+++;"4A#4" "4!!"8!#+++
Temps (µs)20 40 60 80 100 120 140 1600
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
Ray
on (m
)
Temps (µs)
Cou
rant
(A)
0 20 40 60 80 100 120 140 160 180 2000
5
10
15
20
25
J
Q!#+++=!!5""4A#"4"5
"5%54!!@"Q!#+++
Q!#+++I"4A#!5"!88!44A""!
!!!3IΩ45D!'&3r"4% 'IF=D
"#8!"8 '45
0 20 40 60 80 100 120 140 1600
100
200
300
400
500
600
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
20 40 60 80 100 120 140 160
Temps (µs)
00
10
20
30
40
50
60
70
80
Cou
rant
(A)
épaisseur 2 mm épaisseur 6 mmépaisseur 10 mm
Q!#+++J"4A#!5"!88!!!44A""!
55!D!'&3r"4% 'IF=D8 '45
9)9 *B*7+7
9)9)/ *+:+*I+,.+*
7 "; " 44!!@ 4A#. 4! !" "
" 84 45 6 !!! !88 @ "
5!? " 4 "" "# 8! $!4 !
"4)!#"C'45455"4464C4!
$') " ""! 4R " 5 $ ) " "" 4R
""4A!
9)9)/)/$++L+M++**
8!#++++++3"S"!4!5";4"
"4A#!88!!!" ""!$ ρ = 3Ib45.Jb45
b45) ! 55 "# #" C "5!! " "#
" "!" S @ " 4 #"!# " "
$5!?!"!")!#5"@!3Ir
Temps (µs)
0 20 40 60 80 100 120 140 160
0
5
10
15
20
25
Cou
rant
(A)
résistivité 1000 .cm résistivité 2000 .cm résistivité 3000 .cm
3
#5!"!5!!!8! " "5%5!!
4";4"4A#
S.!!!!" ""!."4
5 4 $#"!# ") " A #! " !
!"#5!$8!#+++)#5!"!5"@"
""!5!!!5%5!!" ""4;
"4A#$8!#+++3)8!#+++(+++'5"S"!4
; " 4A# @ 8! ! "! R ""! 4
$4!5";)"4A#!@54" D4"!
4!4!!5@"44A""7""!"
""! #. " " 4 " 4A# !5 4! 48!5 "
! 6!5" !! "! ! 4"" " 4A# !B4 7
4@."!#5@"S!""!!5!
Q!#+++"4A#!5"!88!!!S44A""55
!D!'&3r"4% 'IF=D8 '45
0 20 40 60 80 100 120 140 160 0
10
20
30
40
50
60
70
80
Cou
rant
(A)
Temps (µs)
résistivité 85 .cm
résistivité 600 .cm résistivité 3000 .cm
(
Q!#+++3;"4A#!5"!88!!!S44A""55
!D!'&3r"4% 'IF=D8 '45
Q!#+++("4A#!5"!88!S44A""
!!!3Ib45D!'&3r"4% 'IF=D8 '45
0 20 40 60 80 100 120 140 1600
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
Ray
on d
e la
déc
harg
e (m
)
Temps (µs)
résistivité 85 .cm résistivité 600 .cm résistivité 3000 .cm
0 20 40 60 80 100 120 140 1600
10
20
30
40
50
60
70
80
Temps (µs)
Cou
rant
(A)
épaisseur 2 mm
épaisseur 6 mm
épaisseur 10 mm
3
Q!#+++';"4A#!5"!88!S44A""
!!!3Ib45D!'&3r"4% 'IF=D8 '45
9)9)/)9$++L+M++
!5! "4T " ""4R "S"4/*
!!44!!@4A#?!884"" 4
""?""45$8!#+++''+++' )
0.045
0 20 40 60 80 100 120 140 1600
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
épaisseur 2 mm
épaisseur 6 mmépaisseur 10 mm
Ray
on d
e la
déc
harg
e (m
)
Temps (µs)
3'
Q!#+++''"4A#!88!S44A""$ .J'55)
!!!3Ib45.!'&3r"4% 'IF=D8 '45
Q!#+++' ;"4A#!88!S44A""$ .J'55)
!!!3Ib45.!'&3r"4% 'IF=D8 '45
7
0 20 40 60 80 100 120 140 160 1800
1
2
3
4
5
6
Temps (µs)
Cou
rant
(A)
0 20 40 60 80 100 120 140 160 1800
0.002
0.004
0.006
0.008
0.01
0.012
0.014
Ray
on d
e la
déc
harg
e (m
)
Temps (µs)
3
4 !@5 4 ? 8! " " ' 5!?
5!44$3Ir"44)!#58V "
@4455!!@"!88!""!4A!!
" !5"!4@! 44 " ; "4A#. 5@@S?
#5! ! " 5!?5!44. !" !5!B@SC ! (r
#5#5!4C "#! "4A#
" "" +" 4 " !5"!@ " 44!!@ "
4A#"!! 6"4.48!5!!"
"6!56 #!"!NJO
9)9)9 *;*7*.+*+**B*+77*
2!48!#!4! "84!""
"# ' 45 "# ' 45. 5! C 85 !5"!"" ;
5'&3r$8!#+++')"#4A@ 4!"
"#""!"!'&454A@
Q!#+++'0?"!"!"S";"5"4A##
84!"45! $""&&"")
8!# +++' +++'I5 "S!8"4 " !!! " 4 "
4A# !88 ! 6 "" 4 4
$!#"!# ")B@SC!''r.4@!4C"4A#@!"
65!? $""&?4A)7"!.<#5!!@
"4A#"!? $"")55"44.!
!@"4"!5@"44A""!"!S
.45%54#"5!5@"44!!#5$8!#+++'J)
+
$+
"+
.+
"+
.+$+
$+
$+
)
3
Q!#+++'"4A#!5"!88!S ""!
!!!3Ib45D!'&3r"4% 'IF=D8 '45
Q!#+++'I"4A#!5"!88!S ""!
!!!Jb45D!'&3r"4% 'IF=D8 '45
0 20 40 60 80 100 120 140 0
10
20
30
40
50
60
70
80
Temps (µs)
épaisseur 2 mm
épaisseur 6 mm
épaisseur 10 mm
Cou
rant
(A)
16040200 60 80 100 120 140 180 0
10
20
30
40
50
60
70
80
Temps (µs)
épaisseur 2 mm
épaisseur 6 mm
épaisseur 10 mm
Cou
rant
(A)
3
Q!#+++'J"4A#!5"!88!!!S44A""
55!.!'&3r"4% 'IF=D8 '45
+"4@!4?@"4 ""?""4
5#?445 4"!55@#"5
@""!!!"44A""!8! ".""4!5"
5#!"4A#47!"".!5!!"!4
5%544A""!#5"5#!4!45
=*++08-*
4!.!C"6!5""5A"#!
4A#44! !!5"!"";
8$'. &Ir)";!4"!"!8"44!5?455"
"! "5"! " ! "!@. "! " 44A ""! "
# 44!! 4 44A 884 " ! !5"!
"!" !6!5"
0 20 40 60 80 100 120 140 160 180 0
10
20
30
40
50
60
70
80
Cou
rant
(A)
résistivité 85 .cm résistivité 600 .cm
résistivité 3000 .cm
Temps (µs)
3I
=)/0*,*
!!!8 6!5" 4! 4""" ! 45 "!"
!! @ ;?5 "4 ! " +" 45 #"5 4
!4!C!!.;?5!"!!4A#5
!#6"4!@!@@! "445# 8!# +++'5 " 4A5
"5 "!!!86!5"!"!
4"""!$8!#+++'3)4"!"4!44
"!7=55! 554R$4R!!)'55
A""5!!#8!"$')"@""4"!7=$ )
"@"8!6""4!$)44C"A!"5$)#
#"#5"!!"!4""4!"!"+"8
@6@!"4"""5!$"6!#")$I)
5"4R"!"44""4!4"!"2" "
4"""8!6"@4!4"!4!$3)'55!5?!'
554!""45!C"5"4A!!'
r5 ; 4 "" "! #? A! C o!"!!
#? 5 884 ? # 5 ! " % "
!!4A5"4"#!4A#4D"!8!
#?J
84 !" ! 4! 4A!"" "! ! A"
$9F"!)!"6"4C"!"! !""!!"!
44!4"!!5?!!88.4546$4")@
" 5"! "! "4";!@ $/ l") !88 !!! !5"
!! "44A""! !" !5!6$";4A"!;"
$7=)."6!#"";8"A;"?$7*Q)4554!"!"5@*8")
#"5
4 @! ! @ " " "!8 C !"
4!4"! F"!'J(55!5?'55S!45
4" !88 "# '55 8 $8!# +++'( $ ))
4" ! 5"! S"4"; $/ l ") !88 44!!
!5"" ""!$8!#+++'()
! 884 ! !5"!"" '. &I r 8!
#06 F=
3J
!!@4A# "!5# !#!
#k4 C 45 44 C 4 4@!!! ! 85 $0
++&0"!A") 45 ; 2=K W21 [/I3X A
"!$JsI3!6")4!5#4R"!#k4C"4
4@!!!C!I!5#&4
Q!#+++'24A5!!!86!5"
':*!#8!""6!:"4!#?:+" :2$5 !")"4I7!"6!#"3"4":4#"#J:Ak!7=
Q!#+++'324A5"4"""!
45
7
K/*
24 4!""4
!
"""!
"4!!
"4"
+"
$ )
$')
$3)$)
$J)$I)
$)
$)
3
Q!#+++'(24A55?""!"$)"4!"5"
!5!4A4 $ )
544!64A#884C!4$
!4!)Ib44!4"4""".#k4C4!""4C55!.
A "! 5"" ;*F!62J' $!#!!G!#2!#"";G)
4A# "4!@ !#! 4 5!@5
"4!""4
=)9**,,
854A#"5#!"48!#!
"!""44!!4A@ 2!!5"!""."4A#
# !"5 46 4A# 4! !4! " "
44!! ""7 "4"; 44!! ". " 46
4A# !4! 8!# +++ 5 "5A"#! "" 4A#
44!!S"4";'r2"6"!"!#5
!4! 46 4A# $4 C !. " ! !! " 46
4A#) 44 " 4" 5"! S"4"; 7 " 4A# #!
.+.+
(a)
'55 'I55 ' .55
'55
'.55
'.J55 ' .I55'55
"" ?4A
'55
'.I55$ ?4A)
(b)
33
$ 4 "4 ! "! #!). 4 #5 " 5!
! " @ "! !!. 4 #5 6 ""
45 455 "4 8" S . " 5 4A "
!5"!!!@"!#!!.""#
4A# " !5 "! !! "# 8!" " 4A#
#54"!$8!#+++ '+++ )
Q!#+++ 7A#A!4A##"!#!$)!!$ )44!!
""4";g 'r2.!8"4%-4% .F=
Q!#+++ '+8"4"5"!"!""!"4A##!
44!!""4";σ 'µ2.!8
"4%-4% 3F=$)-4% 3F=$ )
NO N.O
N.ONO
3(
Q!#+++ +8"4"5"!4A#!!!
44A"4";44!!σ 'µ2.!8
"4%-4% 3F=$)-4% 3F=$ )
4 #! 4! !5"! ? ? 5"!
!5!"S#5!"!$8"!).
4"6"!$8!#+++ )
NO N.O
(
Q!#+++ 464A#"8!#+++
=)=
7"!5?".4! "5?" "!"!"! "
!6!56$8!#+++'()5"!!"4A#5"!4884
45 "!#"! R " 84 "!". "#
Temps (µs)
0 50 100 150-25
-20
-15
-10
-5
0
Cou
rant
(mA
)
$)
0 50 100 1500
5
10
15
20
25
N.O
Cou
rant
(mA
)
Temps (µs)
$ )
('
""#."!"44!!4A@
@"!4A#$4)!!@.4C!@S!"#S
8V;5!@D"!""#!!!@C!
4 8!. " 4 " +4A 4! C " 4A# $4) " 55 4
4 C 4A@ ! 4A# A@ ! 4A# #
4 "!" 4!4"!S #" #" C 1π $ 1 "5 !
4A#) !!. " 5"!! " 4A# N'3. O 8 455 4! "
#A++
7 4"4" " ; . 1 4A@ ! 4A#. !"! " "!
M!"F!N IO;!!"5 !4A#"@
.
$ )
'I
1
1
π= $+++')
"5%55!?."!!4A@!"4A#N.O
'
. .
. )$
)$
=
0 1
1
11 ρπ
β $+++ )
T1 1 .. =
< <14!5"!4!""4A#"!4
!S!4A# ρ "!"! 1β "84!"#!"
4!"454A@!4A# 1 1β β= β "84!!""
"S#!"4!""45"4A#45"?$≤β #:=
!!"4A#0"
1 00 .= $+++)
!! " 44!!@ "4!@ #5!@ "!" 4A@
!!@"85S"!"!@.4"4"S "!88
5?4!4!!"!#"5"4!?!54 "#!
. 455 " 4 4 8 $'. &I µ) ?
8! ". @ " " !5"! 4
5t'&3r2I&r
(
8!# +++ C +++ 3 4! 44!!@ !5" " 4A#
# " 5?" 6!5" "!" D " 44!! 84!@ "
!?4A" F"!!"!"!5"!!#"C'r2
Q!#+++ 4A#!"4!4"!45 ""
! . 55. 44!! g ' r2. "# " 8! 8 3.I 45. !
!5"!""'&3r-4% F=
Q!#+++ I=!"4A#"45"!"5!6
4!!"8!#+++
0 10 20 30 40 50 60 70 80 900
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Temps (µs)
Cou
rant
(A)
0 10 20 30 40 50 60 70 80 900
200
400
600
800
1000
1200
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
(
Q!#+++ J!44" "4A#!! !"4!4"!45
""!.55.44!!g 'r2D"#8!"
8 3.I45.!'&3r4"4%-4% F=
Q!#+++ ;"4A#4"!"4!4"!45
""!.55.44!!g 'r2."#8!"8 3.I45.
!'&3r4"4%-4% F=
0 10 20 30 40 50 60 70 80 900
2
4
6
8
10
12x 10
6
Temps (µs)
Rés
ista
nce
de la
déc
harg
e (
/m)
0 10 20 30 40 50 60 70 80 900
0.5
1
1.5
2
2.5
3x 10
-3
Temps (µs)
Ray
on d
e la
déc
harg
e (m
m)
(
Q!# +++ 3*! " % "4 4A ! "4A# "45
!"4!4"!45 ""!.55.44!!
g 'r2. "#8! "8 3.I45. !'&3r4"4%
-4% F=
@ " 4 !5"! 4< "! "
4"!5@"46!5"4!4"!
65"!"4A#544!!# C"
"4C"44!!"84?4A"!"$ F"!).@!
'r274A"""!.4C!5"!
8!6"""44!!C.'r2*8!.!"84!@"!"!!
"" 44!! "!# C #5 " ! "!@ 8! ! "
45 "!" 8!# +++ ( +++5 " "" !88
!4#!"45@!!!'3F=
8!# +++'5 " "5 " 4A#@! #5 8V "!! C
!IrB@45@!<5"4@"4
4 8!# +++ "!! "!D 4""4! #5 5!?
4! " 6 4!! !5"!T!#! " 45
"!"F=
0 10 20 30 40 50 60 70 80 900
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
4
Temps (µs)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de la décharge
(I
Q!#+++ (*!4A#!"4!4"!45 ""
!.55.44!!g 'r2."#8!"8 3.I45.!
'&3r.!45-4 '3F=
Q!#+++4A#!"4!4"!45 ""
!.55.44!!g 'r2."#8!"8 3.I45.!
'&3r.!45-4 '3F=
0 10 20 30 40 50 600
2
4
6
8
10
12
14
16
18x 10
4
Temps (µs)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de la décharge
0 10 20 30 40 50 602
3
4
5
6
7
8x 10
-3
Temps (µs)
Cou
rant
(A)
(J
Q!#+++'#"4A#"45"!"4!4"!45
""!.55.44!!g 'r2."#"8!8
3.I45.!'&3r.!45-4 '3F=
Q!#+++ "!"!"4A#"45"!"4!4"!
45 ""!.55.44!!g 'r2."#"
8!8 3.I45.!'&3r.!45-4 '3F=
0 10 20 30 40 50 600
200
400
600
800
1000
1200
1400
1600
1800
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
0 10 20 30 40 50 600
1
2
3
4
5
6
7
8
9
Temps (µs)
Lon
gueu
r de
la d
écha
rge
(cm
)
(
8!# +++ +++J " !4!" 44!!@ !5" " 4A#
84!@!I&r."5?!4A#
Q!# +++ " 4A# !" 4!4"! 45
""!.55.44!!g 'r2."#8!"8 3.I45.
!I&r4"4%-4% 'IF=
Q!#+++!"4A#!"4!4"!45 ""
!.55.44!!g 'r2."#8!"8 3.I45.!
I&r4"4%-4% 'IF=
0 10 20 30 40 50 60 70 800
0.00
0.00
0.00
0.00
0.0
0.01
Temps (µs)
Cou
rant
(A)
0 10 20 30 4 50 60 70 800
200
400
600
800
1000
1200
1400
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
(3
Q!# +++I "! " "# " 4A# " 4 45
!"4!4"!45 ""!.55.44!!g '
r2."#"8!8 3.I45.!I&r!45
-4 'IF=
Q!# +++J "! " 4A# " 4 45 !" 4!4"!
45 ""!.55.44!!g 'r2."#"
8!8 3.I45.!I&r!45-4 'IF=
0 10 20 30 40 50 60 70 800
1
2
3
4
5
6
7
8
9
Temps (µs)
Lon
gueu
r de
la d
écha
rge
(cm
)
0 10 20 30 40 50 60 70 800
1
2
3
4
5
6
7
8
9x 10
-9
Temps (µs)
Cha
rge
(C)
((
3*
44A!.!""" !8"5"!!;5!@
4A# " A!4!4!"4!@@!"5A4!
!"!4!44!!@4A##84!"
""5!?!4!!5"!5!5!"!88
5?"4A#$"4. "4A#!B4. ";"4A#. "!
!)4544!!@"!"$#5!.!! !
!!!R"")"!! 6"4
''
Chapitre IV
VALIDATION EN TENSION ALTERNATIVE
0
'
/ +
! "! 44! # G 4!!. "
854 !" 4! "!5! 4!!@. "4A#
! ? 85! ?4A 5! 54 7
4@. " ! 45 " 5%5 4!! ! "
!5"!8@4!45!"5!C!
"!!!?"5!?"4!4!4!!!
45 % !55! ! " !!! " 44A ""! @!5
4@ " !"!@88! "44!. "45
!! "@ " !!! " 44A ""! !5! " @ " !
"!@!88!
4 4A!. ! " !4"!?5 A5?
45 4 45 8! < 4A# "4" C "
84!"#"5
9+++B**78*+
8! ! ""! 5"" !88 44!!@ 4A#.
4! !" 85 4;"!!@ "# 8! $8) '3 45
;'I4546;!!"44A""!84!85
!857 " 4!85. ! ! ; 48!#! $')
!"4844!6 .$ )!"4844!!
. $) !" 4 84 4! 5?"
48!#!C $8!#+++'()4"!@!#"5!"!"!
6!56
9)/ *B*77
4!?!""#8!" ) ."@"#4
"4!@ "# " 4!?5 $ ') ) * " "#
$ ) − ) 4 !#"5 44A ""! !85 44!!
! 2! " 4!! 4! C " #! 4 4 !.
0
'
"4 " " " 44A ""! 8!# +=' C +=
"S"! 5"" " 4A !. " ! C " % " 4A#
4 84! 56"44!! " 44A""!
4!5 Ir2 Ir2 ! 45 ;5!@ 4
4!5 I((I F= '33 F= @ " 4 #5
S "!!5 " 5!? 5!""!4 ! 8V 6!""
B@C!"45"64."45!"
5!?"4!!S. " "" " 44!! "44A
""! #. " " 4 " S5"! 4 " 5%5
#55@4"" 6!5"5S4A4ANO,C"!
#!. "" !5! @ " " " 44!! " 44A ""
#5 $8!# +=I +=J)! !5"!5%5
@4""56!5"5$@"@4!5&)N I.(O
Q!#+='"!5""!"4A#84!"""
5!?!85D44!!Ir2!55*!45
;5!@ I(.(IF=
4
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
1
2
3
4
5
6x 10
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0
'I
Q!# += "! 5"" 4 " 4A# 84 !"
"" 5!? !85D 44!! Ir2 ! 55 *!
45;5!@ I(.(IF=
Q!#+="!5""!"4A#84!"""
5!?!85D44!!Ir2!.55*!45
;5!@ '3.3 F=
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Temps (ms)
Cou
rant
(A)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
4
Tension appliquéeChute de tensionTension à la tête de l'arc
Tens
ion
(V)
Temps (ms)
0
'J
Q!# += "! 5"" 4 " 4A# 84 !"
"" 5!? !85D 44!! I r2 ! . 55 *!
45;5!@ '3.3 F=
7 8 Q!#+=I=!!"4A#44!!Ir2.!
""!.55*!45;5!@ I(.(IF=
Temps (ms)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
Cou
rant
(A)
Temps (ms)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
200
400
600
800
1200
Vite
sse
de la
déc
harg
e (m
/s)
1000
0
'
Q!#+=J=!!"4A#44!!Ir2.!
""!.55*!45;5!@ '3.3 F=
9)9 *B*77
9)9)/ *B*7+,.+*
9)9)/)/*P.+**+L++)
4 4. 4!? !" " 84 45 6
44!!g'g 5!? 44!!σ'4""4R
""4A!D"##"6!@$&)""#8!
" "!" 6!?5 44!!σ . "# #" @
$'&)" "#"$g'qg )5@@"4!8V
!4!$8!#+= C+=' )!4!!"5@@"
"44!!6 !5"!48!
! 5!? 5@ "#? #5! "!! !!
T44"5!48!!?T "4
#5?!5!54?8! ".!4""
4! 4< 4;4" 8"4! 8! ""@ " 4!? #!
!8! $8!# +='' +=' )*8!. " 45. ""
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
100
200
300
400
500
600
700
800
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
'3
"?#"#"4A#!""!"!$8!#+=')D
"" 4< 8! "# ! 4554 4!4. 4
556"!@" 4#!"4A#D4@!4@
"""""#"4A#!#C4"!
$)
$ ) Q!# +=u"! 5"" " ! $) 4 $ ) "4A# "
!"854;"!!@"#8 '345.!""!55.g' Ir2
g 'r2!45;5!@ 'I J'F=
0 0.5 1 1.5 2 2.5 3 3.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Temps (ms)
Cou
rant
(A)
0 0.5 1 1.5 2 2.5 3 3.50
2
4
6
8
10
12
14x 10
4
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0
'(
$)
$ )Q!# +=3u"! 5"" " ! $) 4 $ ) "4A# "
!"854;"!!@"#8 '345.!""!55.g' Ir2
g .'r2!45;5!@ I.('F=
5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
1
2
3
4
5
6x 10
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
Temps (ms)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Temps (ms)
Cou
rant
(A)
0
''
$)
$ )Q!# +=(u"! 5"" " ! $) 4 $ ) "4A# "
!"854;"!!@"#8 '345.!""!.55.g' Ir2
g 'r2!45;5!@ 'J(.3F=
0 1 2 3 4 5 60
2
4
6
8
10
12
14
16
18x 10
4
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Temps (ms)
Cou
rant
(A)
0
'''
$)
$ ) Q!#+='u"!5"" " !$)4$ ) "4A#"
!"854;"!!@"#8 '345.!""!.55.g' Ir2
g .'r2!45;5!@ I3F=
5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
1
2
3
4
5
6x 10
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Temps (ms)
Cou
rant
(A)
0
''
$)
$ )Q!#+=''u"!5"""!!"4A#!"85
4;"!!@ "#8 '345.!""! 55 $)g' Ir2g 'r2
! 45 ;5!@ 'I J' F=D $ )D g' I r2 g .' r2 !
45;5!@ I.('F=
0 0.5 1 1.5 2 2.5 3 3.50
200
400
600
800
1000
1200
1400
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
''
$)
$ )Q!#+=' u"!5"""!!"4A#!"85
4;"!!@"#8 '345.!""!.55$)g' Ir2g 'r2
! 45 ;5!@ 'J(.3 F=D $ ) g' I r2 g .' r2 !
45;5!@ I3F=$ )
0 1 2 3 4 5 60
200
400
600
800
1000
1200
1400
1600
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
500
1000
1500
2000
2500
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
''
$)
$ )Q!#+='#"4A#!"854;"!!@"#8 '3
45.!""!55$)g' Ir2g 'r2!45;5!@
'I J'F=D$ )g' Ir2g .'r2!45;5!@ I.('F=$ )
0 0.5 1 1.5 2 2.5 3 3.50
20
40
60
80
100
120
140
160
180
200
Temps (ms)
Lon
gueu
r de
la d
écha
rge
(cm
)
Temps (ms)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
20
40
60
80
100
120
140
160
180
200
Lon
gueu
r de
la d
écha
rge
(cm
)
0
''I
9)9)/)9*P.+**+L++)
74448!#!. "5!? 44!!g'"4
4R ""4 A ! 4 " ! @ $&) " "# "
"!"D"@$'&)""#"8!$8)4"6!?5
44!!g g'dg @"45@!54
"!@5@!4?"45.!"5"@"
" 4A#4 " 84 "!"@! @!5 ?4A $8!# +=' C ')
!.#5!!"!@5.4@!4
#"4A#" 85""4"!5
@ " " 44!! " "! ! ! 4""
44A#$8!#+='3'()D!"5%5"56!5"
8!# += ' !"" ""! " 4A# ; "4
!"854;"!!@; !45"@"B
" 4 ""! !4! ! 6 4g' d g 5!?
44!!g'.4""4R""4A!D""
"#'. I45"@"4 44!!g 5J.I45
@ " 4A# " !5 g &g' " !5. 4 @!
!#"5#5!;"4A#
4A# 5 @!5 4 B@C ! . 5 ! 5 C
4<!"" $8!#+= )"6!?54."4A#
45544!4 .5!3'CI.5$8!#+= )
; "4A#!@5!5" "g &g'I8!
"#
0
''J
$)
$ )Q!#+='u"!5"" " !$)4$ ) "4A#"
!"854;"!!@"#8 '345.!""!55.g' 'r2
g Ir2!45;5!@ ' .(F=
0 0.5 1 1.5 2 2.5 3 3.5 40
2
4
6
8
10
12x 10
4
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0 0.5 1 1.5 2 2.5 3 3.5 40
0.2
0.4
0.6
0.8
1
1.2
1.4
Temps (ms)
Cou
rant
(A)
0
''
$)
$ )
Q!#+='Iu"!5"" " !$)4$ ) "4A#"
!"854;"!!@"#8 '345.!""!.55.g' .'r2
g Ir2!45;5!@ J. 3F=
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
3.5x 10
5
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
3.5
4
Temps (ms)
Cou
rant
(A)
0
''3
$)
$ )
Q!#+='Ju"!5"""!4"4A#"!"
854;"!!@"#8 '345.!""!.55.g' 'r2g I
r2!45;5!@ '' .IJF=
0 0.5 1 1.5 2 2.5 3 3.5 40
2
4
6
8
10
12
14
16
Temps (ms)
Cou
rant
(A)
4
0 0.5 1 1.5 2 2.5 3 3.5 40
2
4
6
8
10
12x 10
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0
''(
$)
$ )
Q!#+='u"!5"""!4"4A#"!"
854;"!!@"#8 '345.!""!.55.g' .'r2g I
r2!45;5!@ I .(F=
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
2.5
3
3.5x 10
5
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0 0.5 1 1.5 2 2.5 3 3.5 40
10
20
30
40
50
60
70
80
Temps (ms)
Cou
rant
(A)
0
'
$)
$ )
Q!#+='3u"!5""!!4A#46
48!#+='$)+='I$ )
0 0.5 1 1.5 2 2.5 3 3.5 40
200
400
600
800
1000
1200
1400
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
200
400
600
800
1000
1200
1400
1600
1800
2000
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
' '
$)
$ )
Q!#+='(u"!5""!!4A#46
48!#+='J$)+='$ )
0 0.5 1 1.5 2 2.5 3 3.5 40
500
1000
1500
2000
2500
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.5 40
200
400
600
800
1000
1200
1400
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
'
$)
$ )
Q!# += u"! 5"" " 4A# " 45 !" 85
4;"!!@"#8 '345.!""!.55$)g' 'r2g Ir2D$ )
g' .'r2.g Ir2
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
2.5x 10
-7
Temps (ms)
Cha
rge
(C)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
1
2
3
4
5
6
7
8
9x 10
-7
Temps (ms)
Cha
rge
(C)
0
'
7
$)
$ )
Q!#+= 'u"!5"";"4A#"45!"
854;"!!@"#8 '345.!""!.55$)g' 'r2g I
r2D$ )g' .'r2.g Ir2
0 0.5 1 1.5 2 2.5 3 3.5 40
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-3
Temps (ms)
Ray
on d
e la
déc
harg
e (m
m)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
1
2
3
4
5
6
7
8
9x 10-3
Temps (ms)
Ray
on d
e la
déc
harg
e (m
m)
0
'
9)9)9 *+:+*B*7*.+*
4"5%5!"@455!4"!
!4! 4@ !" 45 ! ! ! 6 48!#!
!8884"!"!!!85! "4
8V"!"44!!"5!?48!#!.@"
?""4"@"48!#!." 4"
4"" "44!! "" 8! " "# !88
""4 A ! ""4 5. I 45 "
5!? .'45"6!?5 'I45"!!?5
9)9)9)/ *B.+*
O!"4T"! "##"$!8&)@"
6 6%55%544!!.!'r2."@" 4"C
44!! r2 8!# += C I ""! 44!!@ "
4A# 4 4!! 5@@ " 4 #5 "?#?5
4A4" 4"""44!45C4<
"!54#5! ""!? 4A#4554
C#5!"!4A" ""44!4
#5!"!!6" !54" "#
!56!5"!5%5@4""5"48!#!C
6 5! " !! 45"?5 !88 #! "
4A#884" 4"""44!4D?G
"#. #5! ".C'J5&
0
' I
Q!# += " 4A# "!" 4;"!!@ "#8 '3 45
;'I45.!""!.55D"#44!! I.''I45."
!45'(. IF=
Q!#+= A#"45"!"4;"!!@"#8 '345
;'I45.!""!.55D"#44!! I.''I45.
!45'(. IF=
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.2
0.4
0.6
0.8
1
1.2
1.4
Temps (ms)
Cou
rant
(A)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
-7
Temps (ms)
Cha
rge
(C)
0
' J
Q!# += =! " 4A# !" 4;"!!@ "#8 '3 45
;'I45.!""!.55D"#44!! I.''I45."
!45'(. IF=
Q!# += I u"! " !4 " 4A# " 45 "!"
4;"!!@ "# 8 '3 45 ; 'I 45. ! ""! .55D "#
44!! I.''I45
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
200
400
600
800
1000
1200
1400
1600
1800
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 107
Temps (ms)
Rés
ista
nce
de la
déc
harg
e (
/m)
0
'
.O4!?48!4!44!! 4" !5
@ 455 " 6%5 @!5 ?4A 4SC! 4
44!!.'r2!@" 4"?""444!!
Ir2 "# !!@ $8&) 8!# += J@"@
44!!@ 4 4 5@ @ " 5"! 4
! 4""@"44$)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
2
4
6
8
10
12
14
16
18x 10
6
Temps (ms)
Tens
ion
(V)
tension appliquéechute de tensiontension à la tête de l'arc
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Temps (ms)
Cou
rant
(A)
0
' 3
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
500
1000
1500
2000
2500
3000
3500
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.2
0.4
0.6
0.8
1
1.2x 10
-3
Temps (ms)
Ray
on d
e la
déc
harg
e (m
m)
0
' (
Q!# += J 5 " 44!!@ !. 4. ; " 4A#. ! "
4A#.!4"4"#"4A#"!"4;"!!@"#8 '3
45;'I45.!""!.55D"#44!! I.'
'I45."!45'.(0=
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
20
40
60
80
100
120
140
160
180
200
Temps (ms)
Lon
gueu
r de
la d
écha
rge
(cm
)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
9
Temps (ms)
Rés
ista
nce
de la
déc
harg
e (
/m)
0
'
O # " 5%5 48!#! 5! 4A# " "#
"# " 4"@! """"#" " " "#
6%5.!8& .44!!Ir2 ""44
4A4 " @ " "# 8! " 44!! ' r2
!44A.55" ?"".'55"
"""44"!."4"4A#."!4
" 4A# "! #! "4. 4 4!!. "
8!#+= += 35@@"!!! "!"
!4"!?5 " "# " 44!! $! " 44!!
") #! 8V !#!8!4! $! 4A# !4"5) "
44!!@"4A#
$)
0 0.5 1 1.5 2 2.50
2
4
6
8
10
12
14
16x 10
4
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0
''
$ )Q!#+= u"!"!$)4$ )"4A#"45
"!"4;"!!@"#8 '345;'I45.!"44A?""
.55"".'55D"#44!! I.''I45
$)
0 0.5 1 1.5 2 2.50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Temps (ms)
Cou
rant
(A)
0 0.5 1 1.5 2 2.50
0.5
1
1.5
2
2.5x 10
7
Temps (ms)
Rés
ista
nce
de la
déc
harg
e (
/m)
0
'
$ )Q!# += 3 u"! " !4 4A# $) " ! "4 $ ) "
45"!"4;"!!@"#8 '345;'I45.!"
44A?"".554"""".'55D"#44!! I.'
'I45
9)9)9)9 *.+*
4" 4"" @! C " " " 44!! " 5! "
"444'r2"@"6 6%5"5%544!!C!r2
! "5%5"#!"!""#"8!
0 0.5 1 1.5 2 2.50
200
400
600
800
1000
1200
1400
1600
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
'
Q!# += ( " 4A# "!" 4;"!!@ "#8 '3 45
;'I 45. ! ""! .55 " 6%5 .'55 "
4" D "#44! ! I.''I45. " !45
'3.IJF=
Q!#+=A#"45"!"4;"!!@"#8 '345
; 'I 45. ! ""! .55 " 6%5 .'55 "
4"D "#44!! I.''I45.!45
'3.IJF=
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
1
2
3
4
5
6
7
8
9
10
Temps (ms)
Cou
rant
(A)
-7
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
Temps (ms)
Cha
rge
(C)
0
'
Q!# +='=! " 4A# !" 4;"!!@ "#8 '3 45
;'I 45. ! ""! .55 " 6%5 .'55 "
4" D "#44! ! I.''I45. " !45
'3.IJF=
Q!# += "! " !4 " 4A# " 45 "!"
4;"!!@"#8 '345.;'I45.!""!.55"
6%5.'55" 4"D"#44!! I.''I45
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
200
400
600
800
1000
1200
1400
1600
1800
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
0.5
1
1.5
2
2.5
3x 10
7
Temps (ms)
Rés
ista
nce
de la
déc
harg
e (
/m)
0
'I
9)9)= **7*.+*K+:,
!5"! 5?" "!" !!@ " 8!# +++'(. 5
5 !4 "!8"4 " 44!! " 44A ""!
!"""R"@B"!45%544A
9)9)=)/ 7++B++**+*.+*
8!# +=. += +=I " !4!" 44!!@ @!
4""4!!4A#@"44!! 8! "5""
!#"C'r2"@4"" 85""'r28!#
+=J. += +=35 " 455 !88 44!!@ "@ "
44!!"44A""!8! ".'r2"@"""!8
44!!'r2"#8!45?"3.I45!."
!5!!!@"8!#+++'(
55 " 4 " ! !5"!"". " 4 #5 @ "
!!!"44A""!!5!D"45!!?5
#!"#D4!. I544!!.'r2
I5'r244!!
"# " 4A# 4 ! 4< "!@ "
5#!" 5D""4<4!4!C"4A
45 5 5 ""! " "# 4
""!"!$8!#+=I+=3)+"!46"!4
!!4!!"5!5 "#"444AC
"5!!4!?#!@!!8!C!
0
'J
$)
$ )Q!#+=u"!"!$)4"4A#$ )"45
"!"45 8! "5""C'r2.'55! 85
""C'r2.55!!45J. JF=
0 1 2 3 4 5 60
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
Temps (ms)
Cou
rant
(A)
0 1 2 3 4 5 60
0.5
1
1.5
2
2.5
3
3.5
4x 10
4
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tension Tension à la tête de l’arc
0
'
$)
$ )Q!#+=u"!;"4A#"45"!"45
8! "5""C'r2.'55!85""C'r2.
55!!45J. JF=
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2x 10
-3
Temps (ms)
Ray
on d
e la
déc
harg
e (m
m)
0 1 2 3 4 5 60
0.2
0.4
0.6
0.8
1
1.2
1.4x 10
-8
Temps (ms)
Cha
rge
(C)
0
'3
$)
$ )Q!# +=Iu"! "! " "# " 4A# " 45
"!"45 8! "5""C'r2.'55! 85
""C'r2.55!!45J. JF=
0 1 2 3 4 5 60
100
200
300
400
500
600
700
800
900
1000
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 1 2 3 4 5 60
1
2
3
4
5
6
7
8
9
Temps (ms)
Long
ueur
de
la d
écha
rge
(cm
)
0
'(
$)
$ )
Q!#+=Ju"!"!$)4"4A#$ )"45
"!"45 8! "5""C.'r2.'55!85
""C'r2.55!!45''.I'F=
0 0.5 1 1.5 2 2.5 3 3.50
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
Temps (ms)
Cou
rant
(A)
Temps (ms)
0 0.5 1 1.5 2 2.5 3 3.50
1
2
3
4
5
6
7
8
9
10x 10
4
Tens
ion
(V)
Tension appliqué Chute de tension Tension à la tête de l’arc
0
'
$)
$ )
Q!#+=u"!;"4A#"45"!"45
8! "5""C.'r2.'55!85""C'r2
.55!!45''.I'F=
0 0.5 1 1.5 2 2.5 3 3.50
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 10
-8
Temps (ms)
Cha
rge
(C)
-4
0 0.5 1 1.5 2 2.5 3 3.50
1
2
3
4
5
6x 10
Temps (ms)
Ray
on d
e la
déc
harg
e (m
m)
0
''
$)
$ )Q!# +=3u"! "! " "# " 4A# " 45
"!"45 8! "5""C.'r2.'55!85
""C'r2.55!!45''.I'F=
0 0.5 1 1.5 2 2.5 3 3.50
200
400
600
800
1000
1200
1400
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 3 3.50
1
2
3
4
5
6
7
8
9
Temps (ms)
Lon
gueu
r de
la d
écha
rge
(cm
)
0
'
9)9)=)9 7+**+0+
7""!8"4"!"44A""!"#!
" 4A#. "! !5"! " 5?" !" 4;"!!@ 4
84 !85""444!!'r2
6!!88!'5555"45!84
!"8!#+=(+=#5!"!
" 44A ""! @ 45 ! "!" 7 55
!" ""."5#!$ 5)!5%5"@
"5!"4!!"@4"!4!!C5'55!
I5!.55$8!# +=)""!4!44!!@
@!B!8!"44!?#!C4!55
""! "4. ! " " 5@ "@ ! "! "
44A "" " 5%5 4!! !5"! 4! 5
#! C #5! "! " 44A "" !
4@4" !""8!""!45$8!#+=)7
44A!55."!8!"I5&"@4!?
!C'5&@"!444A'55
9)=.*+
4!C"5%5!"4;"!!@"#8 '345
;'I45 84 "!" 45 ! "# !!@
$8&). " ! 4 44!! Ir2 "# ' 45
6%5?4A$.'r2)7!"!@ .0=6
4 !". 4@!" ; 45 $8!# +=') 4
!"6"!@"#8!@!G!55!
" 8! @!" @!5 55 6 65! 0%5 ! " "
4 8! " 44A "" 4 4 !". " ! "!@
44! 45*8!. #! "4"
!""#"8!4!"$8!#+= )
55" .!";454A#4@
45""#8!"'3456!4!"48!4A"!C
""";!@"4!!5V#"4!
0
'
"! ; "4 ! 4"" 4 455 " 48!#!
$8!#+=)
7 8
$)
$ )
Q!#+=(4A#84!5$)44A""!
'55$ )44A""!55
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
0.01
0.02
0.03
0.04
0.05
0.06
Temps (ms)
Cou
rant
(A)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
0.005
0.01
0.015
0.02
0.025
0.03
0.035
Temps (ms)
Cou
rant
(A)
0
'
$)
$ )Q!#+==!4A#84!5$)44A""!'
55$ )44A""!55
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
100
200
300
400
500
600
700
800
900
1000
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80
100
200
300
400
500
600
700
800
900
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
'I
$)
$ )
Q!#+='u"!5"""!$)4$ )"4A#
5!"4
0 2 4 6 8 10 12-0.5
0
0.5
1
1.5
2
2.5x 10
6
Temps (ms)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l'arc
0 2 4 6 8 10 120
0.2
0.4
0.6
0.8
1
1.2
1.4x 10
-3
Temps (ms)
Cou
rant
(A)
0
'J
$)
$ )
Q!#+= u"!5""""#$)"!"4A#$ )
5!"4
0 2 4 6 8 10 120
5
10
15
20
25
30
Temps (ms)
Long
ueur
de
la d
écha
rge
(cm
)
0 2 4 6 8 10 120
500
1000
1500
2000
2500
3000
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0
'
$)
$ )
Q!#+="!5"""4A#;"4A#!
0 5 10 15 20 250
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8x 10
-4
Temps (ms)
Ray
on d
e la
déc
harg
e (m
m)
0 5 10 15 20 25-3
-2
-1
0
1
2
3
4x 10
-7
Temps (ms)
Cha
rge
(C)
0
'3
=*
#!"4A#8!B8V"!!D""4
! 4! 4 ! T " 4!?
#!!8!.4SC!@"!4"4!C4"""
44A""!74 5.4!@ "4A# !
#""#@""4B@C4@"4!?!C!8!A@
8!@"4!?#!!8!.@"!#!
"4A#""!!!R""!!8"4"455
"4A#!!! !@""8! "585""
6"4!54#"!# ""5?"4A#-
48!#!C"! 4" "44!!"""4R
""45"448!#!C6 .6 "
" 44!4 $" " "") 4A "4 " 4
48!#!C! ".#4"!5@"4
!!@!5"5%54!!!!@!5"!
!@ "#?#5!"4T"65!"!"
4 "5!""!?4A!4"484!
4! 5 @ " 4!? #! !8! " "# B
45
'(
Chapitre V
VALIDATION EN TENSION CONTINUE
'I'
/ +
"4!@"S!"!44!4!!""!
5!.5 64."!5!"85!"4""5"
! " " " ;?5 C 4 4! 6"!! "
@"@4!F!""NIO
4""5. !" B !5" 5! " 455 !4
!"C!"!""!!8!4!"".55"!
"!!8!4!"@S!5!"854
!"4!!!4! ""!!8!4!"" #"
! 4 45 C " ! !" !" !4 7
4@. !" ! 455 ! !!""!5 7 !
!!84!58! ".!"4!!"""68!
" !!!4
44A!. "44!!@!5"4A##
" 84 !" "" !88 48!#! ";
"!8"4!5?44!"44A""!
9!+:*+0+**+*
5!? . 4! 44A ""! !85
45 " !5"! C 46 6!5"5
4A4A5?"4!4"!!"4;"!!@'345"#
8! 'I 45 ; ! " "# " 44A ""! !
#"C.55 .II454!56;""!!$')
""!!"#?4C44!!'r2D$ )""!!8
4C44!!'r24.";"4
44A ""! !85 4 85 "" 'r2
44!! 8! "5""'r244!!.455 "4
! !5"!"" "! $A! +++ +=) !5"!
#"58844!88;48!#!@! !
!!! ""!!8"444!! !4
""!"44!!@#!"4A#45
'I
#"5 ! 8!. 4 C 45! !
45 4!"!8"!
9)/"7
9)/)/**+
8!#='"44!!@"!"545
!"4;"!!@.84!"44!!"44A""!
44!! "" r2 ! 45 !5
!"" C " 44!! $8!# =' ) " @ " 5 45
#5 4 " 44!! $8!# =' ) 5?" "
45 "#?5 ! C 4"" " 5?" ;5!@
2B N'JO " 8! " 44!! $8!#= )4 "
644!!@"44!!"4!!@
9)/)9**7
!88 # 44!!@ 8!#= 5
45 " 88""! "#?'r2""! 8'r2
4#5 "5B@C!6!$ &)""#8!
"#!"! "4C "8!".4SC! "
45 " ! " 4 " " @ "
44!!"44A""!!5$8!#= )!4"4
@! 4"#"4""! "#?C
""!8$8!#=4).!!68!"4. @C"" !
84!4!5D4@!8!444"#!"4
" 4 B@ 45 ! " 4A# !5! !
#5 ? @ " ! " 5!! " "# 8! "
"!"!!5 "!4""4A5$5?"A?)@!#"5
5!!55 C ! 5! C 6 ! $'& C &) "!"" !"4
NJO2! " 4 ""! "#?. "! " 4A# " '5&
$8!#=).4""4!!5&""!8$8!#=8)
'I
!? !<4!C""#!@884!#
" A5? #! 4A# 4 "#5! " 44!! "
44A ""! < #5! " !. 8 @ 4 A!
" "@"@"!"!@545"!""5%5
"!88"44!!4A!!
$)
$ )
Q!#='*!54584!"44!!
0 5 10 15 20 25 30 35 40 451.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
Conductivité surfacique (µS)
Tem
ps d
e co
ntou
rnem
ent (
ms)
0 5 10 15 20 25 30 35 40 4520
30
40
50
60
70
80
Conductivité surfacique (µS)
Tens
ion
de c
onto
urne
men
t (kV
)
'I
Q!#= *!4584!"44!!5?"
4"!2B N'JO
$)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.2
0.4
0.6
0.8
1
1.2
1.4
Temps (ms)
Cou
rant
(A)
0 5 10 15 20 25 30 35 40 45 500
10
20
30
40
50
60
70
80Te
nsio
n de
con
tour
nem
ent (
kV)
Notre modèle dynamiqueModèle dynamique de Sundararajan et al
Conductivité surfacique (µS)
'II
$ )
$4)
78
$)
0 0.5 1 1.5 2 2.5 30
1
2
3
4
5
6
7
Temps (ms)
Cou
rant
(A)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
0.5
1
1.5
2
2.5x 10
5
Temps (ms)
Rés
ista
nce
de l'
arc
(/m
)
0 0.5 1 1.5 2 2.5 30
0.5
1
1.5
2
2.5
3x 10
4
Temps (ms)
Rés
ista
nce
de l'
arc
(/m
)
'IJ
$)
$8)
Q!#=4!!@""!!85"#?$.4.)8$ ..8)
! 45 C 4A@ 44!! !!
#!IF="4"""!"#?'IF="4"""!8
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20
200
400
600
800
1000
1200
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
0 0.5 1 1.5 2 2.5 30
100
200
300
400
500
600
700
800
Temps (ms)
Vite
sse
de la
déc
harg
e (m
/s)
'I
9)9"7
9)9)/ *;*7I2.+*+=.+*7*
!5"!"!"5%54!!@"4"!
!5"!""!4!"48445
! 85 "" ! . 55 4A4 @ 8! "5
"" ! .'55 8!# = ""! " ! "!@. "
4A!"!C"%"484!58!#= .4.
5"!!4.""#"!"4A#84!
54!55@@"45!!C 'F= ''
r. " 4 " 4A# @ C "!. 4< "! ! II 5D 4 !
#55!?!#!8!4!@"5#!!C3r.4C!
? @ " 4A# 4 " & " "# 8! " $4 @! 4
5!!554A5"4!@)!#58V "?""!4!"
!!35&D"""#?!4!!$!5!!)C35
"#"4A#@C""4<"!8!5"!!
8!# =I 5 ""! " ! 45 84! "
44!! 55 " !. "#5! " 44!! <
!5!!"!45""4!4<"!5B@C4@"
44!!!#r2D"C. "!5!! " !45"
"@"44!!"44A""!#55!?!5
"!"!45!""C"!"4A#"
A5?45D"44!!@ @!"!!$8!#=I )
7 !"". " ! 45 " 8! " @ " 5
45"$8!#=I4)
'I3
$)
$ )
$4)
0 20 40 60 80 100 1200.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
0.055
0.06
Temps (µs)
Cou
rant
(A)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5x 10
4
Temps (µs)
Tens
ion
(V)
Tension appliquéeChute de tensionTension à la tête de l’arc
0 20 40 60 80 1000
1
2
3
4
5
6
7
8
9
Temps (µs)
Long
ueur
de
la d
écha
rge
(cm
)
'I(
$)
Q!#=4!!@""!!8544!!'r2"44A
""'r2"44A?""."!45 'F=
$)
$ )
0 10 20 30 40 50 60 70 80 90 100
20.4
20.6
20.8
21
21.2
21.4
21.6
21.8
22
Conductivité surfacique (µS)
Tens
ion
de c
onto
urne
men
t (kV
)
735 740 745 750 755 760 765
20.4
20.6
20.8
21
21.2
21.4
21.6
21.8
22
Vitesse de la décharge (m/s)
Tens
ion
de c
onto
urne
men
t (kV
)
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
800
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
'J
$4)
Q!#=I4!!@4584!"44!!""!$)."
!#!$ )545$4)
8!! " 44!! I 'r2 4 48!#! C !
85 "". 5@ "6!4 ! A !!4 4 5
45@!4A4'r5!?A54!4 "!!
!."4B"!!5!!8!"!?B"!!
45!!@"65!?A
9)9)9 *;*7I2.+*+3.+*7*
44.4!48!#!45 ! @!5
?4A4@?""!44A""!"5%5
@ " 4 4 " !4! ! " 45 "!"
#"5" "
44!!@"!"!@."4A!"!C"%"4
84!5.!!@"4"4A#.""#4!?
!"8!#=J
111.5 112 112.5 113 113.5 114
20.4
20.6
20.8
21
21.2
21.4
21.6
21.8
22
Tens
ion
de c
onto
urne
men
t (kV
)
Temps de contournement (µs)
'J'
$)
$ )
$4)
0 20 40 60 80 100 1200
2000
4000
6000
8000
10000
12000
14000
16000
18000
Temps (µs)
Tens
ion
(V)
Tension appliquée
Chute de tensionTension à la tête de l’arc
0 20 40 60 80 100 1200
2
4
6
8
10
12
14
16
18
Temps (µs)
Cou
rant
(A)
0 20 40 60 80 100 1200
1
2
3
4
5
6
7
8
9
Temps (µs)
Long
ueur
de
la d
écha
rge
(cm
)
'J
$)
Q!#=J4!!@""!!8544!!'r2"44A
""'r2"44A?""."!45'3F=
45 !!C !'3F= ''(r4 "
4A#4!5C"48!#!!4555@!54
8! " " ! #! @! " " ' r
4<#5!"@6!""@!'
"# " 4A# " "!!5 B@ 45 ! "
4A# " #! "#?5 5! " @ " 5!?
48!#!5%5! "64.4!#"C "8!45.
!!I5&
9)9)= 7++**+*.+*
!! "84"!"BR"#"!# "
" 4 #! 4A# 44!!@ 8!# =
"!!"648!#!";"#A '
44 " ! 45 84! " 44!! 84!@
1200 20 40 60 80 1000
100
200
300
400
500
600
700
800
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
'J
$8!# = ). " ! " 4A# $8!# = ) 5 45
$8!#=4)44!!@5#"545"!8"4
" !! 6 "4 55 " 4 " !
!5"!"" "!. " 8! ! " "" 4A "4
#?44A#"!5$8!#==J)4@!5
4 " ! @ $&) 5 #!. 4 @! 4
!"" 5%5 5 " 5!? 48!#! 4<
4!4 ""A45444A@?4A
665!@!!84"?4A"!"!C"84
" "" " 4 " 8! " #! " 4A#
B!8!44!!@"#"!!5 !"#"!4
4! 45 ! @"@ !88 "
#!5!8!!"6I5&
65! " 8!# = . 5@@ " 5%5 44!!. " !
45 5! !5 " 48!#! 45 6 ?
""665!"84"!"4SC!."48!#!4!
@ ""! @!5?4A+"<#"5@"4
" 48!#! ; ? "" 4A "4. "!! "
44!!IC'r2#?!!!45$4"
"5!!5"56!5""!45)"!5@
"48!#!44!6 ?4A665!"84.4C
!4""@!45@ ?4A! ""5%5 !
8!"8!#= 5!48!4!"!45"!
452!"5!?48!#!"!45!
5&CJ 5&. "448!#!"".!!I5&35&
!!. " 5%5 5@ 5 " " " 44!!@ " !
45 5 4! 445"! 45 "
"!"$8!#=4)
8! ";#"44!!"!""I'r2."5 "
4@."545" ""48!#!45
" ""
'J
$)
$ )
$4)
Q!#=4!!@4584!"44!!""!$)."
!#!$ )545$4)
0 10 20 30 40 50 60 70 80 90 10017
17.5
18
18.5
19
19.5
20
20.5
21
21.5
22
Conductivité surfacique (µS)
Tens
ion
de c
onto
urne
men
t (kV
)
Bandes extrêmes sèches Bandes extêmes polluées
735 740 745 750 755 760 765 770 775 78017
17.5
18
18.5
19
19.5
20
20.5
21
21.5
22
Tens
ion
de c
onto
urne
men
t (kV
)
Bandes extêmes sèches
Bandes extrêmes polluées
Vitesse de la décharge (m/s)
111 112 113 114 115 116 117 118 11917
17.5
18
18.5
19
19.5
20
20.5
21
21.5
22
Temps de contournement (µs)
Tens
ion
de c
onto
urne
men
t (kV
) Bandes extêmes sèchesBandes extrêmes polluées
'JI
9)9)3 7++B+*.+*+
7 "; "!8"4 " 44!! " 44A ""! "
44!!@ "4A#84!@4!45 !".
884!5"!"5?"C@ ""! ?4A
@ " 44A 8! "5 "" $@!5 ?4A) 44!!
4'r274."44A""."!5"!64
44!!'r2Ir28!#=35"4554
" 6 44!! "" 5@ @ @ " !4 "
""!!C"!4"4.4@!44C
" !84! 4!? #!. " 4A# " "@ "4
4@8! " !?@"4!!"#!!
446.""5"4445#"4!5
4!"""@"44!!#;"
4A#.4"4"C!5?"M!"F!N IO.!"854$8!#
=();!@54""5!!""#"8!.
! 44A "#?5 $44A# 4 " !! " " 4 8! "
44!!)!@48!!4#5! "
8!#!744!!""!'r24;.Ir5D!"
!' r544!!"8Ir24"4A#445".""
""5%58V"64$8!#=')D"" 4"!5
" 44!! Iµ2@ 'µ2 5 45@ C "!
B" !5 "@ " 44!! #5! 5%5
"644!!$8!#='')
'JJ
$)
$ )
Q!#=3"4A#44!!'r2$)Ir2$ )
0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Temps (µs)
Cou
rant
(A)
0 20 40 60 80 100 1200
1
2
3
4
5
6
7
Temps (µs)
Cou
rant
(A)
'J
$)
$ )
Q!#=(;"4A#44!!'r2$)Ir2$ )
0 20 40 60 80 100 1200.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
-3
Temps (µs)
Ray
on d
e la
déc
harg
e (m
m)
0 20 40 60 80 100 1200
0.002
0.004
0.006
0.008
0.01
0.012
Temps (µs)
Ray
on d
e la
déc
harg
e (m
m)
'J3
$)
$ )
Q!#='"!"4A#44!!'r2$)Ir2$ )
0 20 40 60 80 100 1200
1
2
3
4
5
6
7x 10
-8
Temps (µs)
Cha
rge
(C)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3
3.5
4
4.5x 10
-7
Temps (µs)
Cha
rge
(C)
'J(
$)
$ )
Q!#=''=!#!44!!'r2$)Ir2$ )
4!?5! "5%548!#!4@ "" !
@!?4A5!444!!D"G""44!!
Ir2"@" ?4A44!!.'r24?
Temps (µs)
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
800V
itess
e de
la d
écha
rge
(m/s
)
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
800
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
'
7 !"454!".!"8"!@!JF=
$8!#=' )4"4A#!!@"4A#4!!@5
" ! µ #5 ! 8V ? " $8!#='
4) ! 4!5 " ! C ' r 4!5
"44T"44!!!'r2."4!@J
4A#.Ir!"4A#I5&C''5&74@."
5 4! 45 444! ! @ $'&)
5"!44!!'r2.!!r545
5?" ? !8! C 46 AA !NIO
44A ""! !85 @! 6 ! BC !8! C 465 A"
7!" N. I O 44A !85 ? 8! "5 "" 7 #55
44!!"!4"!!@45!'' Fb&5."5
45#54 "44!!? " !7!"N O.
"! !! 8! " !4 "!!@ $ ' Fb&5). " 5
45"!54$@"@5!""!4)D"8!4
$ ' Fb&5)@""@ ! " "!. 4 5 45 "!5
"#
9!@5?"5!@ 8!!4! "6"!.
4! @ " 4 6 4 !4 "!!@ ?
8! "
$)
Temps (µs)0 10 20 30 40 50 60 70 80
0
1
2
3
4
5
6x 10
5
Tens
ion
(V)
Tension appliquée
Chute de tensionTension à la tête de l’arc
''
$ )
$4)
$)
Q!#=' "!!$).4"4A#$ )."4A#$4)"!
#!$)544!!.'r244A?4A
Ir2"44A""D!45JF=
0 10 20 30 40 50 60 70 800
5
10
15
20
25
30
35
40
45
Temps (µs)
Cou
rant
(A)
0 10 20 30 40 50 60 70 800
200
400
600
800
1000
1200
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
x 10-5
0 10 20 30 40 50 60 70 800
0.5
1
1.5
Temps (µs)
Cha
rge
(C)
'
9)9)A 7+**+0+*.+*
";"!4!4"!"!C"!!!5"!
5?"!" ; 6 65! 84. ""!
85 "" ' r2 884 C R" 6 44A ""!
"!55!'55#5!"!""!4
!4A# " 5?5@ " !4 "4 #5 $8!#=' 4)
!@"4A#445"!5!$8!#=' ).4@!@" !4
4A# $8!# =' ) 55 " 4 ! 455. " 4 5
@!5 4 ? 8! " " #! 4< 4!4
""@!G!?5!44@!"A45
$)
$ )
0 20 40 60 80 100 1200
2
4
6
8
10
12
14
16
18
Temps (µs)
Cou
rant
(A)
0 20 40 60 80 100 1200
5
10
15
Temps (µs)
Cou
rant
(A)
'
$4)
$)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
-7
Temps (µs)
Cha
rge
(C)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3x 10
-7
Temps (µs)
Cha
rge
(C)
'
78
$)
$8)
Q!#='"4A#.4A#!4"4A#84!5
6!!88"44A""!55$.4.)'55$ ..8)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
6
Temps (µs)
Rés
ista
nce
de la
déc
harg
e (
/m)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5x 10
6
Temps (µs)
Rés
ista
nce
de l’
arc
(/m
)
'I
9)9)C0+I**+B*
! 5! " 4 ""! 5!6 T " ""!
85 " 84 "!" 45 !88" 44!!
!!"8!#='44A'4R""4A!
" @ " 44A 4R ""4 ! ! 45!8.
65! 6 48!#! $ " =') " 5!?. 4!
44!! ""!4! ""4A !
""4 5 " 4. " 4! $* " =') "
44!!5";"!5"!4""5!" "='
Q!#='!!! "84"!"
* "='="44!! "648!#!
78/
N+BO
789
N+BO
4A' 'r2 'r2
4A 'r2 'r2
4A r2 r2
4A 'r2 'r2
4AI r2 r2
4AJ 'r2 'r2
4A 'r2 'r2
44A'
44A
44A
44A
44AI
44AJ
44A
'J
" 648!#!""!5!6 5 " C
46 " 48!#! """!!8546 ?""
665!T" ""!"5%544!!
""!5!6 5 " "!54 " " !?
$""?4A)T!"45!@"4
"".""4"4A#!5"45$8!#='I
)+"8#"54!@"88"" T5"#!
!5!! #"!# "D "" 4! C " 5!!
4 8!". "! #! 4 5 45 4A#
445" " !5 455 " 4 " 45 " 4 T "
!? 44!!"$8!#='I4)74."!
#!@4""4!"5!4."4"""4
T " 44!! 44A ""! 8! " $8!# ='I) "
#! " 8!45 44! "5%5! "6
48!#!$8!#='8)
$)
0 20 40 60 80 100 1200
2
4
6
8
10
12
14
16
Temps (µs)
Cou
rant
(A)
'
$ )
$4)
$)
0 20 40 60 80 100 1200
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Temps (µs)
Cou
rant
(A)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5x 10
-7
Temps (µs)
Cha
rge
(C)
0 20 40 60 80 100 1200
0.5
1
1.5
2
2.5x 10
-8
Temps (µs)
Cha
rge
(C)
'3
$)
$8)Q!#='I.4A#!"4A#84!5!"4
44A""!5!6!! 8V!85
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
800
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
0 20 40 60 80 100 1200
100
200
300
400
500
600
700
800
Temps (µs)
Vite
sse
de la
déc
harg
e (m
/s)
'(
=*
4 4A# " 45 !" "" !
4!#54"!44!! ""!5!4""
" !? G "@"" !! " A 45 !5 C
4! 4 4 "!8. ! 4! " "# #! "
B5!?@!"!!
!45!4!5"8! "@!
"! . " 4 "!8. ! " 45 !! "
5!?"4. !"4!@"4!!5V#! 5"! +"
!"" !5 @ " 4 "!8. !" #! " ! 4%2" "
!""!"85!".!"!@"!"!88!44
45!" 8! "@ " !4!4.
" 4. " ! "! 4% 45 " "@ " !
4!45
2!4!.!"!54"4"!5!G8! ".!";
"!4!@!C"445"!5458!4"!4!
4"4A
'3'
CONCLUSION GENERALE
'3
4!".5?"!4!";!@;5!@.
"@!"! #!@. " 4!4! "4!@ @!" " 44!!@
A;!@ "4 5 "!"! " A! 4!4! "4!@
@!" " 5"!! ;5!@ 4A# # 84
!"""5!?!4!"!4!"44!!@!!.4
5?"5!5!"!885?"4A#45
" #5! "!" " #k4 C "!4! 84 85 +" 5
4"4" " ! 45 !" 4! " ;5!@ "4
454A#5"!4"#!.;
44!!@$44!!.!."#.!!56"4).
8!""!"."4!4!"!#4!"4A#."
!!;"4"!4B@45."!
!#! "4A# +"5#"5"; ""! "
!C"%"4"4A!"484!"85"!
"!@$!5"!""."!4!)
+"!88!5"!@.!!5"!""."#!
"4A#884#" ! 4A@
. ! T " 4!? #! !8!. 4SC! @ "
!4 "4 ! C 4"" " 44A ""! 4 . "
4A#C"%"4A#4!5!?C4@"4A5!!
"5C"4A#4
!!! ""!6"4.""#."
!"44!!$!@""8! "585"")
!8"4!#!8!4! "5? "4A#-48!#!C"!
4" "44!!"""4R""45
"448!#!C6 .4"6 ""44!4
$"""")4A"4 "448!#!C !
". #? 4 " !5 @ " 4 ! . " "
44!!"44A""!".""4!5"5
#! "4A#47!"".!5!! "!45%5
44A""!#5"5#!4!45
'3
7 !" 4!4"!. " 854A# 6!5"5
"5#!"48!#!"!""44!!
4A@ 2!!5"!"". "4A##!"546
4A#4!!4!""44!! ""7
"4"; 44!! ". " 464A# !4!S . "
5 4A" !5 "!!!@"!#!
! . " "# 4A# " !5 "! !!
"#8!""4A##54"!
."4 !5"!4<"!" 4
" !5 @ " 4 6!5" 4!4 "! 6
5"!"4A#544!!# C
2 ! "!. ! " 45 !! " 5!?
"4. !" 4!@ " 4!! 5V# ! 5"! +" !""
!5@"!8.!"#!"!4%!45
!4!5"8! "@!"!55"
4 " ! !5"!""."!8 "4#5@ " !!! "
44A""!!5!45. "44A# !"
"" ! 4! #5 4 " 44!! ""! 5!
4"" " !? G "@"" !! " A 45
!5 C 4! 4 4 "!8. " "##! !
4!."B5!?@!"!!
#5!"!" ""!4!C"#5!"
!4"4C"!5!!"4A#445"4C" !4
4A#.""!"44A""!!5."!
"45"!"4!5#!4@4"
! "! " 8!" !. " ! 45 "
8! "@"545"
,C"!8"4"44!!44A""!.@"4
!""@444!!#4 "4A#
" !5@ " " 44!! !88
". 4 @! ! #5! ; 4" " 4A#
'3I
"!!!4""44A#D!"5%5"
56!5"
!."!45!"""!
!5"!""@!"!"""""!8@4!
'3
REFERENCES BIBLIOGRAPHIQUES
7*..80*
N'O 2 Q"G!. Q+ + +* ** *
"*H : +8 + 08 ; + 0:Q.
2 >& 0 & " <+<1 <:?@A=
N O !5. 0 B. 7 /8!"". 0 0. Q!0+* +
* +* ** + 8* * 8* "*Q.
B< CC>$D<:?A@=
NO 0FA"!. Q+ + B + * * 7*
** * " *Q. + - < <
%<9:??$=
NO /6 0 A". Q +* ** *
0I++!+:+.Q.B<+@D<=E<=D;F>D;?<
9:?AF=
NIO 7 "! 1 74A. Q* "0:* + " +* **
*+*B8*8*"*Q.B<+@;< = C< =:EE>
:?D<- :?AC=
NJO 09"PA!;."2AF!.00E./0HG.00PA"!8
!.Q"7+0R*+ *****I
"+ *Q.B< CC>$?< :?@;=
NO 7 "!4! + '' . Q * +H +Q. &
<:?AE=
N3O Q . Q&+*00.*08 + #0@8S8Q. 2
!<=D<=:CF>:CE<:?F@=
'33
N(O 7L 5 A. / 6". 07 =5. Q!0++!*+ B+
"+* 7* +* **I
*Q. <=;$<9 0:?A;=
N'O M/!.07=5./!F"A./!F./24A! .KQ6.Q:*+
"*** *
L+ *Q.B< CC>$?< :?A@=
N''O L!.Q*0*"&*0B!+Q.D &4
, < DE>:;<%<F>?&":?@C=
N' O / HA#. /4F5. Q 7 **H ;+0.; +
77*"0"'Q.+ ===<=E<=:<=AC>
@C<1" 4:???=
N'O /0.*QB!A!5P/.Q.@<8 ++
B * *; *+@;Q.
+ ===<=E<=:<=::A>:;:<1" 4:???=
N'O !52=!.Q"+* **Q.21>< =;A<
9:??$=
N'IO ". 2 H"G!EF!. Q@0 7 *08* "+ **Q.
+ =%&<=::$<=A<=:;E$>:;EE<94:???
N'JO 2B2K.Q ;!+87"&*0B
**+ '8Q.+ ===<=;@<=;<=
;$?>;:?<%:??C=
N'O Q!GF.Q!0!+*7"&*0BQ. <=A@<=A:>
:$C<:?@:=
'3(
N'3O AA !:0#!4A.9"PA A".Q@"*!+7
"+ **&*0BQ.9 )42G%=4=7C$8<= F<=
@@?>@?D<- :??A=
N'(O 0 0A!. Q ; + 8 * 7 &.
++ 087Q.+
>& 0 & " <+<1 <:?@E=
N O / 95 Q . Q" &*0B ** + **
.; + ;** + !+ 7 8 "0 &*0BQ.
B<:D@F=::< =D$E<9:?EE=
N 'O 0A"/6.Q&*0B!0*780'8 **Q.
+ = * % &4< = >?@< = E< = ;;;C>;;C:<
:?A?=
N O 9Q/5.Q&*0B!0*7"+ *Q.=<=:::<
=F<=?@F>??$<- 4:?ED=
N O 72 KAA. 2 A4! AB. Q*7 &*0B
0**7+;7**8@<Q.
+ =2= ==<=;<=E<=:$ED>:$AE<2":??F=
N O "2H"G!EF!.Q@07 *08*"+ **Q.
+ =%&&<=::$<=A<=:;E$>:;EE<94:?EC=
N IO M!"F!.Q&*0B'8780'8H **@077
"*&*Q.=<=::E<=C<=DFA>DEF<- :?E?=
N JO 7 "!. Q"+ 7 0 $0B 7 "+ **Q.
+ =%&<=?$<=D<=:?$;>:?$@<94:?A:=
N O 7 "! 1 74A. Q@ 0* ** 7 "+ *Q.
+ =%&<=?;<=C<=::;:>::C:<:?AC=
'(
N 3O 72KAA AB.Q"++ *&*0B!+7)
'8Q.+ =2= ==<=;<=:<=:;@>:CE<1" 4
:??F=
N (O K 5vF. Q'*0?8*?*+ + #0@8Q. - " 2= 2=
%! <.=<=:<=CF;>CF?<5:?F?=
NO 2 K" 1 ; . Q 0 &*0B !0** 7 "+
**Q.&&2<+=<-%2%&<=:>E<:?@C=
N'O 2/FA.Q70"+7"&*0BQ.=
<=::D<=D<=FC:>FC;<%:?EA=
N O //ML04";.Q **@0+7H"
H !+87 *08!0**Q. < + = %&&< = @?< = @< =
:@F@>:@EA<0>2:?A$=
NO / 4F. Q0.8 &*8< + #0* &*8< ' *
77Q.2 04)5> ,":?E;=
NO / 4F. Q. + &+*00+8 + 0 +*
&+*00.*08*Q.+'H%<=:E<=FAA>F@F<:?EE=
NIO M!"F! L "9#A!. Q "8 8 ;
7Q.=<=::@<=:;<=:@@E>:@?;<2":?A:=
NJO 2!A5.QB7&*0B0**7"+ **Q.F
=&=,===<=F;>:EI:>D<5 *;D>;@%:?@A=
NO 2 B 2 FA5!5A. Q+ 7 &*0B '8* 7
"+ ***8 ;!+Q. E &4
, < C$>$?<*J < &%<:?@?=
'('
N3O L""; 2* A. Q7 $<+@ ,+ +
***Q.9=%=4=F$7:$8<=E:?E>E:??<J":?A?=
N(O 2 K" 1 . Q&*0B "0 7 "+ **Q. =
=<=:C:<=<=D<=:D$>:DC<94:?@D=
NO Q0!GF/#;.Q 87 *
' "**Q.<+ =*204<=D$F>D:$<:?@@=
N'O 0;. Q$8 > 0 + *0 + + ;*00
0.8*Q.%=1=!<=CA<=FF@>E$@<:?DC=
N O Q0!GF.Q7 *;**&*0B0**7
"+ **Q.=<=::A<=;;FA>;;E$<:?A$=
NO 2B2K.Q++ *87" **
+"++*Q.+ =2= ==<=;<=:<=
:;:>:;A<1" 4:??F=
NO AA !0#!4A 9". QB + "+ **
&*0B '8 7 77 D B7* *8 B
@<!+Q.:: &4, <<
3:???=
NIO AA !:0#!4A9".Q ;!+7 *08"8
"+7*+ *'8Q..=>B=+ =2"=<
=:DA<=F<=;A?>;@D<&";$$$=
NJO *F4A!. * 15A!. PP !A!. * QB!A!5 / 0.
Q"80**7 *08;7Q.(
&4, < C;>:D<B K<% <
:??F=
'(
NO /0 A". Q * !** "0;** + +*
** *Q. + & 4< 0 & " <
+<1 <:?A?=
N3O +Q89".Q@"*770+';
.*+8;*+*Q.9 4=2=G%=4=<=;?<=E?:>
E?E<:??E=
N(O 9".Q+**"***0$<+@"07
+*Q.9 )%4AC7?8<=DF;@>DFCC<- 4<:??C=
NIO AA !.Q!+* ;+* 08***7*+ **
"*** 77*&*+**.+:;
+"8Q.+ 4<1 <:??@=
NI'O 7 H5BF!4. Q!+* + '+
,+!**,*+ 08Q.+
0 & " <+<1 <:??E=
NI O L 7!" Q!"A. Q;* + + 7 &.
+ 08Q.+
&4< 0 & " <+<1 <:?@E=
NIO K7;?.0A" /6.Q&*0B7++8&H
")9&*0B-!0**Q.+ ===<=:A<=
:<=:$>:?<:?@;=
NIO H ; K H!4A#. Q +; 0 77 .@ 0 &*0B
'8*7+ **++ '8*Q.+ =<
=CC;>CCD<:?@F=
NIIO * A. /+0 1 M. Q 7 $<+@
+;7*Q. + == =<=:?<=E<
=FCE>FD;<2":?@D=
'(
NIJO 2E!8. Q&*0B 7 "+ ** &+ 0 Q. E
&4, < C$>:$<*J <
&%<&":?@?=
NIO 0F. P P. P ! 0 +A!!. Q 7 7 .
*0&*0B'877;+ **Q.
+ =*204<=::<=:<9 4<:??E=
NI3O 0!4A"7"".Q*+*!+:*+.++
+* ** "*Q. + 0
& " <+<1 <:??E=
NI(O *A/+0.Q+;0"77' **Q.
+ ===<=;D<=:<=::C>::A<1" 4:?@?=
NJO 2B 2 K. Q 7 . * 0
&*0B '8 7 " **Q. + = 2= =
=<=C<=:<1" 4:??E=
NJ'O M!.Q"*+0.8Q.* <=:;@>:C;<5 *<
:?EA=
NJ O 0F. / 2A!F . P P. 1 0!G. P !. * QB!5 *
*.Q****7$*D 0*+'80**
7"; **Q. + = *204<=::<= D<=:@?F>
:?$$<J":??E=
NJO K"0A;.Q&*7780 ;$+&7
8?+ "+ **Q. I &4 ,
< F;>$@<5 *<B 4:?@A=
NJO 2 K" 1 . Q + @0 7 ; $+ "+
** 7*Q. I &4 , <
F;>$A<5 *<B 4:?@A=
'(
NJIO 9 K"". LP 5 . Q& !+8 7 ; >
&"++' **Q. J &4
, < ;D>>$A<*J < &%<:?@?=
NJJO /0. *15A!. *QB!A!5 *F4A!.T"8B;
+0***;7+*08;*7U.
+ =2= ==<=C<=DDD>DD?<:??E=
NJO 0FA"!. 5. 2 9G ! 9". w&*0B 7
** " ; 80 '8 **U. + =
2 <=E<=?$$>?$E<:???=
NJ3O 2=4@!.QQ. *4A!@ "+#!.= 2; < L2
;@A$<:?@E=
NJ(O M/ 045. Q*** + 0Q. 6!?5 !! 7!.
'(J'
NO M 04"A 04#A"!. Q +B; 7 *
&+!,*Q.74!#8AQA+!"84*A5"
4!!;! ;7KP"5*P".'(I=
N'O L7/"5.Q*7Q.+!"2!!.QA!!.'(J=
N O M ". Q+.< 0*; + "0;**Q. !! JJ.
7.!4.94.Q"!.'(3I:'(3J
NO 9" AA !0#!4A.w ;!+7 *08"8
** " ;* + '8* + ,
'+U< % < ;$$; 2< < / < -<
=CC:>CCD<J";$>;D<;$$;=
'(I
NO 9".TB*+;+7+*0888H+*H
*+V+7*++U.:C &4,
<2)<+ <%;F>;?<;$$C=
NIO *4A!@:*; .T***+7***0
*+**,*,IU. H :;DF< :??C>:$=
NJO 9" * G.T".<+@"0+ *U.
<+ ===<;:<=D<=E:C>E;A<:?@E=
'(
!" # !$#'34 *A? 24!"!K!"4!@
! ! % "" &
"' " &&&!
* !"5?"5;5!@!4!44!!@4A# # 84 !" "" 5!? !4!. " !" #!@. "4!4! "4!@ @!" " 44!!@A;!@ "45?"55! "!88 5? " 4A# 4 B@ 45 45 " #5! "!". 4A#5 " !4 " #!. ; ""! 44!!@$44!!.!. "#.!!56"4)"!"!C " %"4 "4A!"4";84!"85" !"!@ +" 5@ " !!! ""! 6 "4. " "#."!"44!!$!@""8! "585"")!8"4!#!8!4!"5?"4A##5!"!" ""!4!C"#5!"!4"4C"!5!!"4A#445"4C" !4 4A# 7" "! " 44A ""! !5. " ! " 45 "!"!."!45"8! "@"545"4!"""@"44!!44A""!#4"4A#"!5@""44!!!88 ".4@!!#5!;4""4A#"!!!4""44A#!**!".""!!85.4A#"4!@.5"!!.45 ! ! & "" ' "
& D " $! && '
"
.* *A!EF5;5!45"8!4!8A4A4!!48!4A##!#""!"!#84!!4!E;. A#; "4.A@!""4!4 4!4!. A A;!4" 4A4!!4 8 A 4 *A! 5" ""E 5! A !5 8 A !4A# !" A 8"A ; F!# ! 44 A !" #5;. A 4A# 8!4 !# A #!. A ; 8 ""! ! 4A4!!4 $44!!;. A!4F.E!A.!!45A"4)*A"#"!AA84A"#E!A!A4";G44!#AF!8"!"#+!AEAA"4!8A""! E!A # A "4. A! E!A. A! A!4F A! 44!!! $EF"; #";"")A!#!8!4!8"4A58A!4A#*A!48A!4F8A""! "A!48A!48A4A4!8A445"4A#AA48A4A#!#4AAA!4FA""!";.AAA!58"A8A !" ! 0. A 8"A "# ! "" A 5"" A 8"A !5 ! "# *A A!#A44!!;8 A""!";#A!#A4*AA!#AA! EA44!!!8A! .AA!#AA4A4A#DA!4 6"! ;A5F "!48A!8A!4A#4A"*A"!8"4!;8""EA8A4"4!4"4A##;@+*!".!85""!."4!4"!4A#.5""!#.8"A
0! A59-.78!! $ !07.4"";. k/(.JK;""#.J(':4"";6.Q
Recommended