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Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ/ðüóóóó ó ó.ó8ó<ó>êî“ï € 0 ðûÀð4ð“ð( ð ð4ðr ð4 S ð€‘è¿ÿð=Kè·ðà  è ð žðr ð4 S ð€nè¿ÿðàV0ðà è ð žðl² ð4 “ ð6A�ƒ¿ÀÿPPËjJÿ?"ñ¿ ð"0 ðl² ð4 “ ð6A�ƒ¿ÀÿPPËjJÿ?"ñ¿ ðS t A ð—¢ ð4 “ ð6€þý¿�ƒ¿ÀÿPPËjJÿ"ñ¿ ðF t+4 ð#Ÿ¨ïAt constant electric field the heating power goes up with temperature, but also the current is increased. It is the current that is limited by the kink stability limit, and at constant current the heating power decreases with temperature ¡ð 2ðÿþðl² ð4 “ ð6A�ƒ¿ÀÿPPËjJÿ?"ñ¿ ðS pZ ðl² ð4 “ ð6A�ƒ¿ÀÿPPËjJÿ?"ñ¿`ð¤t KðH ð4 ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.ÆbÈÀ!£Èî$ï € 0 ”ðŒàð<ð$ð( ð ð<ðr ð< S ð€ô×è¿ÿð=Kè·ðà  è ð žðr ð< S ð€lÛè¿ÿðàV0ðà è ð žðH ð< ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.ÇbÈÀ·‡„ð ñ 0 Œð„ðð@ðð( ð ð@ðX ð@ C ð¿ÿ ð°Ð ðà  èð„ ð@ S ð€œŠè¿ÿ ð° °0Ððà  è 🪠ðH ð@ ƒ ð0�ƒ“Þ½h”ŽŸ‹¿ÿ ?ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.ÇbÈÀ(Š„r²·; Ê= »ÏçÑõ™Ž·ûÓ>Å1èÆé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©ø¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©ø¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©ø¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ ˆð€ð�@Qo    12 CD L MNO/ðbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹Jð$ÿbð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdÌKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©Ô¢Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðk óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡"AZ�ZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…F/ðüóóóó ó ó.ó8ó<ó>êî˜ï € 0 ðàð<ð˜ð( ð ð<ðr ð< S ð€ô×è¿ÿð=Kè·ðà  è ð žðr ð< S ð€lÛè¿ÿðàV0ðà è ð žðl² ð< “ ð6A�ƒ¿ÀÿPPËjJÿ?"ñ¿`ð¾ ò˜e ðH ð< ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.ÇbÈÀ·‡„rCÔ=ëõ™Ô±í>Å1èÆé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©ø¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©ø¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©ø¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ ˆð€ð�@Qo    12 CD L MNO/ðbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹Jð$ÿbð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdÌKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©Ô¢Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðk óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡"AZ�ZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…F/ðüóóóó ó ó.ó8ó<ó>êrííõ™Éí»>Å1èvé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©ø¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©ø¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©ø¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€  ð˜ð¨LTv    12 CD L MNOPQ/ðbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹Jð$ÿbð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdÌKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©Ô¢Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðç óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡"AZ�ZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ª÷/ðóóóó ó ó.ó8ó<ó>ó@êîžï € 0 ððDðžð( ð ðDðr ðD S ð€ì¿ÿð=Kè·ðà  ì ð žðr ðD S ð€Rè¿ÿðàV“ ðà ì ð žðr ðD S ð€,²úè¿ÿðàó 0ðà è ð ŸðH ðD ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.ÈbÈÐèð ñ 0 Œð„ðHðð( ð ðHðX ðH C ð¿ÿ ð°Ð ðà  ìð„ ðH S ð€˜3ì¿ÿ ð° °0Ððà  ì 🪠ðH ðH ƒ ð0�ƒ“Þ½h”ŽŸ‹¿ÿ ?ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.ÈbÈÐèrï? m!õ™Ë'#@Å1èTé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©ø¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©ø¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©ø¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€  ð˜ð¨LTv    12 CD L MNOPQ/ðbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹Jð$ÿbð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdÌKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©Ô¢Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðÅ óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡"AZ�ZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today /ðóóóó ó ó.ó8ó<ó>ó°ªê°ù²µ#õ™°ä#Ã<@Å1èTé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©ø¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©ø¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©ø¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€  ð˜ð¨LTv    12 CD L MNOPQ/ðbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹Jð$ÿbð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdÌKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©Ô¢Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðÅ óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡"AZ�ZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today /ðóóóó ó ó.ó8ó<ó>ó°ªê°ù÷<õ™Ó<SV@Å1èðé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£�‚ƒ„…†‡ˆ‰Š‹Œ�Ž��‘’“”•–—˜™š›œ�žŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍÎÏÐÑÒÓÔÕÖרÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ      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Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember�‚ƒ„…À‡ˆ‰Š‹Œ�Ž��‘’“”•–—˜™š›œ�žŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÐÁÂÃÄÅÆÇÈÉÊËÌÍÎ}ýÿÿÿÑÒÓÔÕÖרÙÚÛÜÝÞßàáâãäåæçèéêëìíîïðñòóôõö÷øùúûüýþÿ Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. 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by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. 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MNOPQR SVWOðpbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜Ôs ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðdóŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today óAŸ¨Saw-tooth instability Ÿª óCŸ¨A real discharge again /ðPóóóó ó ó.ó8ó<ó>ó@óBóDêî¢ï € 0 ð `ð`ð¢ð( ð ð`ðr ð` S ð€„y·¿ÿð=Kè·ðà  · ð žðð² ð` ³ ð¢A�‚ƒ„†Á¿ÀÿPPÁÂÿÿÿÄÅÁËjJÍÎÒÓÔÕ×ÿ ?ˆ"ñ¿ ðà„ðà ·ðH ð` ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.ccÈPïRð ñ 0 Œð„pðdðð( ð ðdðX ðd C ð¿ÿ ð°Ð ðà  ·ð„ ðd S ð€œÅ·¿ÿ ð° °0Ððà  · 🪠ðH ðd ƒ ð0�ƒ“Þ½h”ŽŸ‹¿ÿ ?ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.ccÈPïRrñ“C ´®^±õ™Í“r³DÅ1è»é(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ 0ð(ðàh[ƒ    12 CD L MNOPQR SVWOðpbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜Ôs ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðdóŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today óAŸ¨Saw-tooth instability Ÿª óCŸ¨A real discharge again /ðPóóóó ó ó.ó8ó<ó>ó@óBóDêr²³õ™޳uÎDÅ1è»é(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ 0ð(ðàh[ƒ    12 CD L MNOPQR SVWOðpbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜Ôs ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðdóŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. 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The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨ÙTemperature profile is peaked Therefore conductivity profile is peaked Since the electric field is roughly constant The current profile will be peaked This means that the safety factor profile will not be constant ªÐ óAŸ¨Saw-tooth instability Ÿª /ðlóóóó ó ó.ó8ó<ó>ó@óBóDóF êîžï €  0 ð°ðtðžð( ð ðtðr ðt S ð€t·¿ÿð=Kè·ðà  · ð žðr ðt S ð€ÔÕ·¿ÿðàV“ ðà · ð žðr ðt S ð€Œð·¿ÿðàó 0ðà · ð ŸðH ðt ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.tcȰSÿdð ñ  0 Œð„Àðxðð( ð ðxðX ðx C ð¿ÿ ð°Ð ðà  ð„ ðx S ð€Xõ·¿ÿ ð° °0Ððà   🪠ðH ðx ƒ ð0�ƒ“Þ½h”ŽŸ‹¿ÿ ?ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.tcȰSÿdrÃE a$'õ ™Ÿ)FÅ1è„é(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ „ð|ð|`Š    12 CD L MNOPQR SVW[\_ðœbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜ÔRð$„Ç…ï»æùÑSIªAÿ†ÂÐ,s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ð½óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. 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The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨7Temperature / conductivity / current profile is peaked óAŸ¨&Saw-tooth instability / Internal kink Ÿª /ðlóóóó ó ó.ó8ó<ó>ó@óBóDóF êîÒï €  0 Bð:°ðtðÒð( ð ðtðr ðt S ð€t·¿ÿð=Kè·ðà  · ð žðr ðt S ð€ÔÕ·¿ÿðàV“ ðà · ð žð¦² ðt à ðf„…AÁ�ÿÿÿƒÿÿÿ¿Àÿ€€€currentprofileðåØ + ðà ðH ðt ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.tcȰSÿdrÅIEÛeõ ™¡IµhFÅ1èé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ °ð¨ð|`Š    12 CD L MNOPQR SVW[\oðÈbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜ÔRð$„Ç…ï»æùÑSIªAÿ†ÂÐ,bð$ÈM¸PõÈÌê%Ú#;b‰Vÿ­Vïs ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðóŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. 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ŠVkRõ빕ä;ZœªW¿ÒP ¬|¿;ä“D rMSíÍÔžÌuˆÞP �â±UŸ€¤ji†Ø ZÇ'\>6s ¤Ô±À²øn�êc�òÆÒ-rûµ] »@v�ìé®ö£@.ßbFIEND®B`‚`!ðT “Ý^!þg£¸¯Iza_IÛ68¼€—"þxÚí�¿oEÇÇq�B Q„”Æ¢@‘Ò':Ñ!ÜE¹ àHAI�:èB�dÑP ¥¥¸ —WÐYVÒ„Ú%®Í{Ïä±w»7·7»³Þû<ékß�™Ý¹Ùï›yóÞ›Ý÷¶s»?üæDîëß{wœûèæ{îý/Ÿîº£¹wïDÿßÔ?{Î}ó‹àOýܹ¯Ýy)xdÞï¾ïÜï×¥ÊgO÷µ´ÖomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ ÜðÔð|`Œ    12 CD L MNOPQR SVW[ \ðôbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜ÔRð$„Ç…ï»æùÑSIªAÿ†ÂÐ,bð$ÈM¸PõÈÌê%Ú#;b‰Vÿ­Vïbð$†aÁ&µÖܰozAÿ s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ð±óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨ÍTemperature / conductivity / current profile is peaked Safety factor is smaller at smaller radius A critical value of 3 at the edge does lead to the stability of the plasma as a whole but not locally óAŸ¨&Saw-tooth instability / Internal kink Ÿª /ðlóóóó ó ó.ó8ó<ó>ó@óBóDóF êî2ï €  0 ¢ðš°ðtð2ð( ð ðtðr ðt S ð€t·¿ÿð=Kè·ðà  · ð žðr ðt S ð€ÔÕ·¿ÿðàV“ ðà · ð žð¦² ðt à ðf„…AÁ�ÿÿÿƒÿÿÿ¿Àÿ€€€currentprofileðåØ + ðà ðX² ðt ƒ ð0A�ƒ¿Àÿ?ðØ¢}  ðH ðt ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.tcȰSÿdîëï € 0 [ðS ð Pðëð( ð ðPðr ðP S ð€ˆ�¿ÿð=Kè·ðà   ð žðð² ðP ³ ð¢A�‚ƒ„†Á¿ÀÿPPÁÂÿÿÿÄÅÁËjJÍÎÒÓÔÕ×ÿ ?ˆ"ñ¿ ð§È «àðà ·ðð² ð P ³ ð¢A�‚ƒ„†Á¿ÀÿPPÁÂÿÿÿÄÅÁËjJÍÎÒÓÔÕ×ÿ ?ˆ"ñ¿ ð/¿š 6 ðà ·ðI¢ ð P “ ð6€=¿�ƒ¿ÀÿPPËjJÿ"ñ¿ ðÎ m À ðÕŸ¨¥Temperature and current increase in the centre -> q drops below 1 An internal kink becomes unstable and throws out particles density and current -> q again above 1 ¡¦ 2¦ðH ðP ƒ ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.bcÈ ]Ë¿r;…AM¥E¢õ™…@ªFÅ1èÐé(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£n�‚ƒ„…†‡ˆ‰Š‹Œ�Ž��‘’“”•–—˜™š›Î�žŸ ¡¢£¤¥¦§¨©ª«¬­®¯°±²³´µ¶·¸¹º»¼½¾¿ÀÁÂÃÄÅÆÇÈÉÊËÌÍæÏÐÑÒÓÔÕÖרÙÚÛÜÝÞßàáâãäåîçèéêëìí<ïðñòóôõö÷øùúûüýþýÿÿÿÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ ÜðÔð|`Œ    12 CD L MNOPQR SVW[ \ðôbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜ÔRð$„Ç…ï»æùÑSIªAÿ†ÂÐ,bð$ÈM¸PõÈÌê%Ú#;b‰Vÿ­Vïbð$†aÁ&µÖܰozAÿ s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ð±óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. 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eð¬bð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜ÔRð$„Ç…ï»æùÑSIªAÿ†ÂÐ,bð$ÈM¸PõÈÌê%Ú#;b‰Vÿ­Vïbð$†aÁ&µÖܰozAÿ 2ð$ “Ý^!þg£¸¯Iza_ÿ\bð$ç~å…I�W—Ä‚-S‰ÿyz2ð$åvÌÊ’†¹\xb\¥Aªÿ| óbð$câšHÉôÄ%]A_¶Ë­÷ÿpo+2ð$µè�.àƒ/޹¦@}U%ÿÇß.2ð${ëÖ=8rö‡IbÔ…2ƒ‰xÿΦ6ð$ÿbð$ ç÷¢ mÉ�×YU­£ÿXtE2ð$ýaÅX`Ì�,ôd³’(‰Œÿ‘ÌL2ð$0¥â] H{Šëõ¹‹² Ïÿå]es ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðóóŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨ÍTemperature / conductivity / current profile is peaked Safety factor is smaller at smaller radius A critical value of 3 at the edge does lead to the stability of the plasma as a whole but not locally óAŸ¨&Saw-tooth instability / Internal kink Ÿª óG!óI"Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨ˆParticles undergo scattering. 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The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨ÍTemperature / conductivity / current profile is peaked Safety factor is smaller at smaller radius A critical value of 3 at the edge does lead to the stability of the plasma as a whole but not locally óAŸ¨&Saw-tooth instability / Internal kink Ÿª óG!óI"Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨ˆParticles undergo scattering. The diffusion coefficient Typical step size is the Larmor radius, typical time the collision frequency ¡‰‰ªS0óJ#Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨MTypical values for a reactor The particles satisfy a diffusion equation ¡NN/ðÀóóóó ó ó.ó8ó<ó>ó@óBóDóF óH!óK"óL#êrâBõ#™¾BµdLÅ1èq"é(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ 4 ð, ðP i¶%    12 CD L MNOPQR SVW[ \^_abdefg?ðbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜ÔRð$„Ç…ï»æùÑSIªAÿ†ÂÐ,bð$ÈM¸PõÈÌê%Ú#;b‰Vÿ­Vïbð$†aÁ&µÖܰozAÿ 2ð$ “Ý^!þg£¸¯Iza_ÿ\bð$ç~å…I�W—Ä‚-S‰ÿyz2ð$åvÌÊ’†¹\xb\¥Aªÿ| óbð$câšHÉôÄ%]A_¶Ë­÷ÿpo+2ð$µè�.àƒ/޹¦@}U%ÿÇß.2ð${ëÖ=8rö‡IbÔ…2ƒ‰xÿΦ62ð$³[ÿsäXÛ7äFÇaˆ%ÿ4 Bubð$ ç÷¢ mÉ�×YU­£ÿXtE2ð$ýaÅX`Ì�,ôd³’(‰Œÿ‘ÌL2ð$0¥â] H{Šëõ¹‹² Ïÿå]eð$ÿbð$8Ùáa³|%È¥AaUb¼Ëÿ´v�s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ðŠóŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨ÍTemperature / conductivity / current profile is peaked Safety factor is smaller at smaller radius A critical value of 3 at the edge does lead to the stability of the plasma as a whole but not locally óAŸ¨&Saw-tooth instability / Internal kink Ÿª óG!óI"Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨ˆParticles undergo scattering. The diffusion coefficient Typical step size is the Larmor radius, typical time the collision frequency ¡‰‰ªS0óJ#Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨MTypical values for a reactor The particles satisfy a diffusion equation ¡NNóM$Ÿ¨Particle motion in a tokamakªŸ/ðÜóóóó ó ó.ó8ó<ó>ó@óBóDóF óH!óK"óL#óN$êî$ï €$ 0 ”ðŒ`ðœð$ð( ð ðœðr ðœ S ð€xIý¿ÿð=Kè·ðà  ý ð žðr ðœ S ð€°Lý¿ÿðàV0ðà ý ð žðH 𜠃 ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.•cÈ€C�,ð ñ$ 0 Œð„pð ðð( ð ð ðX ð  C ð¿ÿ ð°Ð ðà  ýð„ ð  S ð€^ý¿ÿ ð° °0Ððà  ý 🪠ðH ð  ƒ ð0�ƒ“Þ½h”ŽŸ‹¿ÿ ?ð ÿÿÿ€€€»àã33™™™™Ìˆ8Š0º___PPT10‹ë.•cÈ€´Ÿ,rédM b‡މõ$™Åd¢‹NÅ1èm#é(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ  @@``€€ < ð4 ðX¤j·%    12 CD L MNOPQR SVW[ \^_abdefg?ðbð$YVÔÄÚ7’DµuÙ½oèEÿ£/bð$MŒBÄäMb¶§¶çPáVÿN •bð$öié.ð”Ï&:¹…»aÿ•2ð$¶¯s.;±¿(ÕË"çH ÆÿÀã2ð$Æ–2È,Ža­ûhÙvýz¥Gÿk{Ybð$2®]–©8¶3f®ÆÇ�.ÿ/¸B2ð$žñ!@ˆtqŽvÓ–›ÿ”çH2ð$¯­ôïrñ}ãî˜áz‚FPÿÕæq2ð$bœw$Ç–‚Àu””³bKðÿd»�2ð$…Ö/o`$wU½`ƒ9Ìÿ`“2ð$ò…Þ+ä‡wµÛïïkƒÿ‚§2ð$0BYŽ]Œ�veé$ê,ÿP'¸2ð$ŸïÔlXò†ø*Ú˜ÙHœkÿ‚Qß2ð$Kr~ÙüAD˜YZQoáÿwÓï2ð$�Ý©$¡ƒœ#N¿¢y.óÿ‹J2ð$üsdUyG‹pïÔh¦âZ ÿ2-T3bð$ö�è¦t@àyd¨¤œb%´eÿžÕ2ð$Õ.ìQxà茸Hb¸#UTÿás#2ð$aÍUŽ}¹m¨þ-AYÍÿt†`2ð$\M%¿,¬ty´1� ,�ÿ8X˜ÔRð$„Ç…ï»æùÑSIªAÿ†ÂÐ,bð$ÈM¸PõÈÌê%Ú#;b‰Vÿ­Vïbð$†aÁ&µÖܰozAÿ 2ð$ “Ý^!þg£¸¯Iza_ÿ\bð$ç~å…I�W—Ä‚-S‰ÿyz2ð$åvÌÊ’†¹\xb\¥Aªÿ| óbð$câšHÉôÄ%]A_¶Ë­÷ÿpo+2ð$µè�.àƒ/޹¦@}U%ÿÇß.2ð${ëÖ=8rö‡IbÔ…2ƒ‰xÿΦ62ð$³[ÿsäXÛ7äFÇaˆ%ÿ4 Bubð$ ç÷¢ mÉ�×YU­£ÿXtE2ð$ýaÅX`Ì�,ôd³’(‰Œÿ‘ÌL2ð$0¥â] H{Šëõ¹‹² Ïÿå]eð$ÿbð$8Ùáa³|%È¥AaUb¼Ëÿ´v�s ðŠ�‚ƒ„†A¿ÀÿPPÁÂÿÿÿÄÅAËjJÍÎÐÑÒÓÔÕ×ÿ"ñ¿ ñÿPPÿ@ñ÷ð8ó€ó€Ðwº“°öÊš;­”ÇÊš;úgþý4YdYdtrKô–É 0þÿÿ”ÿÿÿpûppû@ <ý4dddd —‘w 0T©à¡Kÿ <ý4BdBd —³x 0T©ˆ8Š0º___PPT10‹ pµpµ?Ù Ú %ð~óŸ¨Physics of fusion power Ÿ¨"Lecture 11: Diagnostics / heating ó+Ÿ¨ContentsŸ¨<Heating Ohmic Neutral beam Transport Classical transport ¡4  =ª /ó6ó Ÿ¨ Collisions Ÿ¨ÏPreviously derived Velocity scaling surprising related to For larger velocity, also a larger change in velocity is necessary to deflect the particle over a given angle The contact time scales as 1/v¡ÐZÐó Ÿ¨Mean velocity Ÿ¨ªThe mean electron velocity can be modelled by the equation This has the solution Such that the velocity decays on a typical time given by 1 / collision frequency ¡«Z«ó Ÿ Ohm s law Ÿ ÈAdding the electric field acceleration The current follows Ohm s law The conductivity scales as ó Ÿ¨Heating power Ÿ¨¥The change in energy (of one particle) follows from The total energy per unit of volume is Therefore the energy put in the plasma due to the electric field is ó;Ÿ¨Ohmic heating ª Ÿ¨1This energy change Is the Ohmic heating power ªó=Ÿ¨Key things to remember Ÿ äCurrent density follows Ohm s law with the conductivity increasing with temperature Ohmic heating power is the product of current and electric field Since it is the current that is limited in a tokamak reactor (kink) at higher temperatures one must use a smaller electric field. The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨ÍTemperature / conductivity / current profile is peaked Safety factor is smaller at smaller radius A critical value of 3 at the edge does lead to the stability of the plasma as a whole but not locally óAŸ¨&Saw-tooth instability / Internal kink Ÿª óG!óI"Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨ˆParticles undergo scattering. The diffusion coefficient Typical step size is the Larmor radius, typical time the collision frequency ¡‰‰ªS0óJ#Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨MTypical values for a reactor The particles satisfy a diffusion equation ¡NNóM$Ÿ¨Particle motion in a tokamakªŸ¨¦Drift moves the particles of the surface Distance can be estimated from the canonical toroidal angular momentum This quantity is conserved due to toroidal symmetry ª>W5 /ðÜóóóó ó ó.ó8ó<ó>ó@óBóDóF óH!óK"óL#óN$êî¤ï €$ 0 ð `ðœð¤ð( ð ðœðr ðœ S ð€xIý¿ÿð=Kè·ðà  ý ð žðx ðœ c ð$€°Lý¿ÿðàV“ ðà ý ð žðr ðœ S ð€´Ný¿ÿðàó 0ðà ý ð ŸðH 𜠃 ð0�ƒ“ŽŸ‹”Þ½h¿ÿ ?ð ÿÿÿ)))€€€Ì™ÌÌ™™™3²²²ˆ8Š0º___PPT10‹ë.•cÈ€C�,râ‹MW¯õ$™¾‹²NÅ1è³#é(€àà€ ò¬/È 0ÒÕä·DArialngsRomanT©T©¢KÜ–É 0Ü–Õ"·DTimes New RomanT©T©¢KÜ–É 0Ü–Õ ·DWingdingsRomanT©T©¢KÜ–É 0Ü–Õ¤€@ÿÿ¥ .©  @£nÿý?" dÿd@ÿÿïÿÿÿÿÿÿ ?¾wüÒüüÏ�›æÛ»K~÷Ågr¹æÑî~ñ÷÷šæ¯î‰OÝÿŠžkþûnóéO5tßþãß'�¿+àǯÿàøÌñ/Ž¿~{ÝÓæZŸ—ç¾{ûý‰ü§Ìë,Þ¼y!„B!„B!„B!„®šíµZ+ðµ_÷çý‚Âñ|þüùƒ%ùùôôt¯vIãý‚ðø¼¾¾n^¿~½ãùùùž�†ç®®®x¿ ¬�j³———¼'VN™Oñ‡!\ïïïÙƒáÂhsP777¼'VN‰c$ÿÄ{aý¹ä€³³³õÔ ¼¤V�www»9PlêÅ‹lLr¿bwSÚ°¬…µ\ùaí‡øÂaŠ­ûûû‘¸S(Ï…xTly¬í†µ±Y'ä1ù=a¬¸½½Ý}Oü a¿ ‰Íнt½NlÇڵ̇%cC°ý¶ëe¬�ßak1ˆ!Ü·!AÊü)væ\ùšc·2§¦ÔVØõÜ%Å¿rÝ4§ÖAl/Ì·9×åŒöµÄ´îÛEnM¡øÉâ'§\“£Ú<1-„m¨$f´1gŠ_m÷û¤Ø ­S&¦…ðÍß³¤v߯§b�C±­EŠ Ú5]øÌ }zj>X+0EN(gÞÌOâñƒÏ²�ýùèœ��7‡æå¸¦#åþöš¾5+·ûŽÉ YÛï›kã½òSÏãn)Ç6þ})c„]×%þ…Ô"ß=°!ñC§°ý®|³ø¶¹9+bZûý㒘Ѯë͇vÏmjí1-„Ýö–ZKÑ7_÷Ūq cØO�ºfLL áýë)k²)6Û«Ú¹6Å­ï]2¦@¸ÆekGcjSlÑÆµ)1´½iÌ +«ø„¾Ç´ñœ½·¡rN=‡}ýмl׋S}o·f·C{tã|’Ø‘Í}¥äƒízRßﲯÐ#ÂöXXìnÈ>Äž‚ßmcèÜúŠ®1"ìß—çB®™øÂöx3Ì›¡”õICŸ(»ç�Sçi¹—Ø¥Püä�/ ½0¸!÷“Ÿ‰!|Ó›[’ùSì6Ô3†ž2ñç­rê&ÅNC_:»&ßCþÎ8€pž}ƒì‡pY6K}Ó°Óvnh j²á¡l–÷#}�,Þ%1BxnÊ~ÕpÝõÊò5·~jiuIµOê«°ó1k_°´V*§/†­�díf\m*ïÌÉõ¦î#è«mÂ÷×K„µ/˜Ã‡…µÕÜ=õèmšñ’zN˜ëç䈭ވňiáqb«œóEÂÜÌY!ÓÅ´¬Á’½Â!-øÄ¹gÁþ˜ÖîÉßÇ®…u#ÞoÛ­Ø£hGÆ[%ωï|9Ñú™>¦•ø$®Ñ5¡¡ž›´¥±ô‹oãú¶Ä¾ú²¹8±Õ³¢´¥å¶÷8쯸¿³¾³óᵷɲÑ5µ¢)ÑÀð‡‰‡l‡°®ø7÷œ¸éúì´¡³æüø—s´³!°Àßš®í³¦À¾±ð믳§Žçæ)°ì7µþ/…C³ô<—R§l{‡L9×¶í>ðàÚë”ã>¸äö!¬;¦-9G B8OL›ÛÙóˆsk›“j®Î 8A7–ÿ¦Æ�6þe¯åqcø”ZU°.›�ãß”:ñ8þÅV�—+OÉ=€åÚl8«¡onH·±Y;§Æcsnükû„¥œÛ!oÅyáÜ5]k³Sõ5 þÂn¿6Î ç®õX›�j]ˆú ÛzØÆ¹&;Ï�—hãYzËA8?C/šØŽÃ¼öÖvÍ¡a/µp‘}^­»V@ìÙλa޵ý¾ÂY†2„¼³\ú™°§Âï…: ™c»úʼn]‡×…óPéO!„B!„B!„Û­ek;œ#á2ê4JÏ‡Õ |M_x¸¾ ¼/2'C§¯«’¯Ä¾BxÜu©o•ñØž-#?Kí9õ¬Öµ?Ûž·(5è²ßZ(Ï…}ÒbË%¶ïõ¶{HeL°ýC‡zv·½6ÜÇŽ5¹=ó \ ÅFÃþ�¾Þrb¿Ö®sc#±ý@é3Òf_²Þh_×µ§Å¾¦í>aßj ûÅášæ×œ¹Hl(̹v_ç˜>c×!äoˆí–35àZëiJzõ„½ÙSôø‰×"JÏe ¾¾ðÈZ�—Ô ¬q>ÎíŸgû��é£÷ú-í·bÏ�-ùÿ@¸´µù[ õ±cæ@kû%gÝtùäô„k¯�+™—¬�ˆ_][ŒéÑÇ¿ÔÀ5Ûliý›�9KýÚ8þ-Í5ÿµ3^-¹‡í¡_:×ÓBxØü®µý{#¦…°l~+�—¬OZ�ÓB˜?/•ž_Û~IIL áále ß6¶û¤Z�Ï}­ñ/„i¶YRK1Em#ñ/„é´ç#—ä‰Ûl¶$÷Eü az=³=ëtLÍã˜\3ñ/„åv›£ó°�nl=G|�©@L ·`·C{tc_Tüc;O–ø¶ñ|Λ+!1-Üb|;t¶yðCÆ)ãß©öCA¸¤Zåœ: CŽé7UL÷b'¦…k­Á(Ý`{aŒõC§ŠiãÄ´p� }Eï9~iˆÇøÅ�¶ærLLk{NÓµûÇ9vbçç¡:«Ü}IÄ´¦ÙLÎù"a>›ê\dëg�¹o[½ó*kžP+ó÷!‡ÎÓ þó˜ó†dþ:çKîo_ÓVßß'^cjÛÓ€o ×d·b�ËmmDž9Ĩ2'�Éuíï“ûw�ÍÙ–3ºOÛX0&a­±pœ÷±k6¥}^!„‡Ù‹ 6ÊÙ–B!„B!„ðXüÕû¾Và÷OÚk¤N@@­„B!„ð§.6øøm¼ðÑÛïßu|tò£æ=÷õƒwäùîÉ;_6ß7ß¼jšß|ð´¹n¾j~Ø]¾>sün÷³D ?ß=öŸ?Ÿ´í¼`é@Ç€Ž@Ç c€Ž@Ç cÐ1˜¶9ƒû>ê[è~DÇ`¸¾¾~½ƒíœàä뼺ºBÇ`aÐM.//ñ+ÀR¡‡\ÎçN c0;lÃat  �ónnnÐ1X*´g» òÐ1X*´�ùÙÙ:ÓãîîÎ�‘N^ÚF×}qqá”W,ÙóósŸ?v·ò)¶ƒ¹Èèx‹p ö‚sÂu‚»ÙÁ=èÝY§ì\5û›Ó±3÷£»›·�ÛÛ[m?«‹ŒŽ7¯9§c'²ýg�ÚTân4M´ ¯þèõÎBÜ­tAdVon$Öéº^ãäèf÷ï ”õ”ÛÖÅM!Ïí"£ã A½ÕÁ… §N?*¾rÐ0ì1èL9§,ëQgÎÁèyYŠû«¡ä|.2:ÞTs‰®ªº¶=Nˆ¸õhT -æs‘Ññ†`�~My½ú¾N¬]޲=–¶ë>šEv†�ŽÁd:N¹‡ÒÛ°ö€ŽÁXØ"÷ÄKt(í’í2JÏ}ôe­É>t Jüã¬�KÕß:$Ûzù1ã::ÙùЬÚv•`«W`ïÙcšHžÉEFÇ‚ú©~ù­@ýû‰ 952!Ô›ÛEFÇÛu-]UM$w�¦ZdÜ¿h2«‹ŒŽ·+ÊþŽÖQ¼Õ ¶‹Ï¾N¨³Z ãÍAkÛ{²Â=:nu‚uHîѨú'‰öƒŽA´ (w�ºG©ê%÷¸ÝzŸt׃T)–ûÖƒk(úš®!YSÑýî:%Rî*D¶ñ™“�ˆ= ÍеÞPŸu˜¼! 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The Ohmic heating power then scales as A reactor can not be heated to the temperatures needed for fusion reactions to occur using only the Ohmic heating since it s efficiency decreases with increasing temperature ¡óóªPUjS…Fó?Ÿ¨Additional forms of heating Ÿ úSeveral types of waves can be absorbed by the plasma (will not be discussed further) One can inject neutral particles with high energies into the plasma This is known as  Neutral beam heating This is the most efficient form of heating applied today ¡þþóCŸ¨A real discharge again óE Ÿ¨Current profile Ÿ¨ÍTemperature / conductivity / current profile is peaked Safety factor is smaller at smaller radius A critical value of 3 at the edge does lead to the stability of the plasma as a whole but not locally óAŸ¨&Saw-tooth instability / Internal kink Ÿª óG!óI"Ÿ¨*Transport in a homogeneous magnetic field ¡++ Ÿ¨ˆParticles undergo scattering. 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