Uni e si y o Se ille
Mas e in Nuclea Physics
Cha ac e iza ion o he ion pedes al in low and high
collisionali y plasmas
Diego Jos´e C uz Zabala
Supe iso :
Eleono a Viezze
Depa amen o de F´ısica A ´omica, Molecula y Nuclea
Facul ad de F´ısica
Resumen
El modo de al o con inamien o (H-mode) es un ´egimen muy impo an e pa a u u os dis-
posi i os de usi´on. En es e ´egimen, el con inamien o global se inc emen a y se desa olla
una es uc u a de pedes al en los pe iles. Sin emba go, oda ´ıa al a una comp ensi´on
comple a de c´omo es o mado. En es e ´egimen, el pe il de la elocidad o oidal de las
impu ezas p esen a un m´ınimo local ce ca de la ´ul ima supe icie de lujo magn´e ico ce -
ada y, bajo cie as condiciones, las impu ezas en el bo de del plasma pueden o a en
di ecci´on opues a compa ada con el cen o del plasma.
Una base de da os sob e el pedes al ha sido compilada con da os de ASDEX Upg ade pa a
in en a p og esa en la comp ensi´on de la ´ısica del pedes al. Es a esis es ´a en ocada
en el es udio del pe il de la empe a u a i´onica y del pe il de la elocidad o oidal de
las impu ezas, ob enidos con el sis ema ”cha ge exchange ecombina ion spec oscopy”, a
baja y al a colisionalidad. La co elaci´on en e las ca ac e ´ıs icas del pedes al y el m´ınimo
en la elocidad o oidal de las impu ezas ha sido es udiada. Se ha obse ado que el m´ınimo
en la elocidad o oidal de las impu ezas alcanza alo es nega i os en desca gas de baja
colisionalidad, mien as que es posi i o en desca gas de al a colisionalidad. Adem´as, la
posici´on del m´ınimo de la elocidad o oidal de las impu ezas es ´a co elacionada con la
posici´on de la pa e supe io de los pedes ales de la empe a u a i´onica y densidad en
desca gas de al a colisionalidad, mien as que, pa a desca gas de baja colisionalidad, solo
es ´a co elacionada con la posici´on de la pa e supe io del pedes al de la empe a u a
i´onica.
3
Abs ac
The high con inemen mode (H-mode) is a e y impo an egime o u u e usion de ices.
In his egime, he global con inemen is inc eased and a pedes al s uc u e is de eloped
in he p o iles. Howe e , a comple e unde s anding o how i is o med is s ill missing. In
his egime, he o oidal impu i y eloci y p o ile exhibi s a local minimum close o he
sepa a ix and, unde ce ain condi ions, he impu i ies a he plasma edge can o a e in
he opposi e di ec ion compa ed o he plasma co e.
A pedes al da abase was compiled wi h da a om ASDEX Upg ade o y o p og ess
in unde s anding he pedes al physics. This hesis is ocussed on he s udy o he ion
empe a u e and o oidal impu i y eloci y p o iles, ob ained wi h he cha ge exchange
ecombina ion spec oscopy sys em, a low and high collisionali y. A co ela ion be ween
he cha ac e is ics o he pedes al wi h he minimum in he o oidal impu i y eloci y was
s udied. I has been obse ed ha he minimum in he o oidal impu i y eloci y eaches
nega i e alues in low collisionali y discha ges, while i is posi i e in high collisionali y
discha ges. Mo eo e , he posi ion o he minimum in he o oidal impu i y eloci y
is co ela ed wi h he posi ion o he ion empe a u e and densi y pedes al ops in high
collisionali y discha ges, while i is only co ela ed wi h he posi ion o he ion empe a u e
pedes al op in low collisionali y discha ges.
5
Con en s
1 In oduc ion 9
1.1 Nuclea usion.................................. 9
1.2 Magne ic con inemen and okamak . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Goals....................................... 13
2 Theo y o e iew 14
2.1 Pa icled i s .................................. 15
2.1.1 E×B-d i ............................... 15
2.1.2 ∇B-d i ................................. 15
2.1.3 Cu a u ed i ............................. 16
2.2 Pa icleo bi s.................................. 16
2.3 H-mode and Edge T anspo Ba ie . . . . . . . . . . . . . . . . . . . . . 17
2.4 Edge Localized Modes (ELMs) . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Diagnos ics 21
3.1 Elec on empe a u e and densi y measu emen s . . . . . . . . . . . . . . . 21
3.2 Ion empe a u e and impu i y o a ion measu emen s . . . . . . . . . . . . 23
3.3 P o ilealignmen ................................ 25
3.4 ELMsynch oniza ion.............................. 27
4 Da abase 28
4.1 Pedes al cha ac e iza ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1.1 Modi ied hype bolic angen unc ion (m anh me hod) . . . . . . . 29
4.1.2 Splineme hod.............................. 30
4.2 Da abasepa ame e s.............................. 30
7
5 Resul s 34
5.1 Compa ison be ween p o iles a low and high ν∗............... 34
5.2 Dependency o ωmin
on ν∗........................... 35
5.3 Co ela ions be ween posi ions o pedes al op and ωmin
........... 39
6 Summa y and conclusions 42
8
Chap e 1
In oduc ion
1.1 Nuclea usion
I is well known ha he wo ld’s inc easing ene gy consump ion demands o new clean
and abundan sou ce o ene gy o he u u e. Fusion ene gy is one o he mos p ominen
candida es o mee hese demands. This kind o ene gy is p oduced in he Sun and in all
he s a s. The ene gy is ob ained when wo ligh nuclei use o a hea ie one. In o de o
p oduce his eac ion, he kine ic ene gy o he nuclei has o be high enough o o e come
he Coulomb epulsion. Inc easing he kine ic ene gy means inc easing he empe a u e,
which has o be o he o de o hund eds o million o deg ees in o de ha usion can
ake place. A high empe a u es a gas is ully ionized. This s a e o he ma e is called
plasma. The main cha ac e is ic o a plasma is ha i s kine ic ene gy is much highe han
i s po en ial ene gy. On Ea h, he mos p ominen usion eac ion is be ween deu e ium
(D) and i ium (T), wo iso opes o hyd ogen (H):
2D+3T→4He +n+ 17.6MeV (1.1)
The high c oss-sec ion (see igu e 1) and high ene gy yield makes he D-T eac ion he
mos a ou able one [1]. The p oduc s o he eac ion a e 4He and neu ons. Dis p esen
in wa e . App oxima ely 0.015% o he hyd ogen in ocean wa e is deu e ium. Howe e ,
Tis no p esen in na u e since i has hal li e o abou 12 yea s. In o de o p oduce T,
he neu ons p oduced in he main usion eac ion a e used o p oduce ano he eac ion
wi h li hium
6Li +n→4He +3T+ 4.8MeV (1.2)
9
16 CHAPTER 2. THEORY OVERVIEW
whe e ⊥is he eloci y pe pendicula o he magne ic ield. In his case, he di ec ion
and alue o he d i is di e en o ions and elec ons as he ∇Bd i depends on cha ge
and mass o he pa icle.
2.1.3 Cu a u e d i
As he pa icles gy a e along he magne ic ield lines, hey ollow cu ed ield lines and
he e o e eel a cen i ugal o ce. The exp ession o he cu a u e d i is
cu =−m 2
k
qB3∇B×B(2.8)
whe e kis he pa allel eloci y o he magne ic ield. Simila o he ∇B-d i , he
cu a u e d i depends on he sign o he cha ge and on he mass so ha he di ec ion
and alue o he d i a e di e en o ions and elec ons.
2.2 Pa icle o bi s
As men ioned abo e, a cha ged pa icle mo ing in a magne ic ield gy a es a ound a
magne ic ield line while he guiding cen e mo es wi h cons an eloci y. The d i s
in oduced in he p e ious sec ion esul in wo ypes o guiding cen e o bi s i collisions
a e no aken in o accoun [1]. Pa icles wi h a su icien la ge eloci y pa allel o he
magne ic ield gy a e con inuously a ound he o us. These a e called he passing pa icles.
Figu e 2.2(a) shows an example o a passing pa icle o bi .
In a o us, he magne ic ield is s onge in he inne egion (high ield side) han in he
ou e egion (low ield side) due o he 1/R dependence o he o oidal magne ic ield.
When a pa icle is mo ing o a highe magne ic ield egion, ⊥inc eases as a consequence
o he conse a ion o he magne ic momen µ. Then, kdec eases due o he conse a ion
o he ene gy. A a ce ain poin k= 0 and he pa icle will be e lec ed o he ou e
egion and ge s apped in a magne ic mi o , which is p oduced due o he o ce on he
magne ic momen , F=µ∇kB. This ype o o bi is called banana because o i s shape
in a poloidal plane p ojec ion. An example o a apped pa icle o bi is shown in igu e
2.2(b). Figu e 2.2 also shows he las closed lux su ace, also called sepa a ix.
E=1
2m 2=1
2m( 2
⊥+ 2
k) ; µ=
1
2m 2
⊥
B.(2.9)
2.3 H-MODE AND EDGE TRANSPORT BARRIER 17
Figu e 2.2: Poloidal plane p ojec ion o a passing o bi (a) and a banana o bi (b).
2.3 H-mode and Edge T anspo Ba ie
In di e o okamaks, a high ene gy con inemen egime is ob ained when enough powe
is injec ed [3]. The high ene gy con inemen egime, called H-mode, is cha ac e ised by
an inc ease o densi y and empe a u e compa ed o he low ene gy con inemen egime
(L-mode). The ansi ion om L-mode o H-mode esul s in an inc ease in plasma con-
inemen by app oxima ely a ac o o 2. Du ing he ansi ion in o H-mode, an edge
anspo ba ie (ETB) e ol es causing a educed le el o pa icle and hea anspo
pe pendicula o he magne ic ield. The ETB causes a s eepening o he densi y and
empe a u e g adien s, and consequen ly p essu e g adien a he plasma edge (see igu e
2.3). The o oidal impu i y eloci y p o ile in H-mode discha ges exhibi s a e y deep well
close o he sepa a ix which can ha e nega i e alues unde ce ain condi ions [4]. The
p o iles de elop a pedes al s uc u e wi hin he ETB, which causes he imp o emen o
he con inemen in he H-mode as e lec ed in he inc ease o he s o ed ene gy shown in
blue in igu e 2.4(a). When he NBI is u ned on, he s o ed ene gy, elec on empe a u e
and densi y inc ease and he plasma en e s in he H-mode.
18 CHAPTER 2. THEORY OVERVIEW
Figu e 2.3: Typical p o iles in H-mode discha ges. The pedes al ops a e he op o he pedes al
s uc u e. The sc ape o laye (SOL), whe e he magne ic ield lines a e no closed, is ep esen ed
in g ey.
2.4 EDGE LOCALIZED MODES (ELMS) 19
Figu e 2.4: a) Time aces o ECRH powe , NBI and plasma s o ed ene gy (WMHD). b) Elec on
empe a u e and densi y. c) The mo-cu en s in he di e o which is used as an ELM moni o .
2.4 Edge Localized Modes (ELMs)
The H-mode egime is accompanied by Edge Localized Modes, which a e cyclic ins a-
bili ies ha expel pa icles and ene gy [5,6]. ELMs ha e been obse ed in all okamak
de ices when hey a e ope a ing in H-mode. ELMs ejec pa icles om he pedes al e-
gion, causing a deg ada ion o he pedes al s uc u e in densi y, empe a u e and p essu e
p o iles. A e an ELM, he p o iles eco e hei s eep g adien s un il he nex ELM oc-
cu s. The physics igge ing o an ELM is no well known ye , bu i is belie ed ha
hey a e linked o he la ge g adien s o he edge p o iles. The mos p ominen candida e
o explain he ELMs is he peeling-ballooning s abili y limi . The peeling s abili y limi
implies a limi on he edge plasma cu en , while he ballooning s abili y limi esul s
in a limi on he edge p essu e g adien . Figu e 2.5 shows a compa ison be ween he
empe a u e p o iles be o e and a e an ELM. The p o iles expe ience a deg ada ion as
a consequence o he ELM.
The ELMs ac also as a egula o o he impu i ies since hese a e also ejec ed du ing
an ELM. The common way o de ec an ELM is an inc ease o a he mo-cu en in he
di e o due o he pa icles which a e ejec ed. Figu e 2.4 c) shows he he he mo-
20 CHAPTER 2. THEORY OVERVIEW
Figu e 2.5: Compa ison be ween empe a u e p o iles be o e and a e an ELM.
cu en s in he di e o . A spike in he signal indica es an ELM. The e a e wo big ELMs
a ound 1.54 s and 1.59 s. Du ing hese wo ELMs, he s o ed ene gy dec eases a li le
bi , due o he deg ada ion o he pedes al.
Fo u u e usion de ices like ITER, i is e y impo an o mi iga e o supp ess he
ELMs o a oid damage o he machine, while main aining he imp o ed con inemen o
he H-mode.
Chap e 3
Diagnos ics
High- esolu ion diagnos ics a e key o usion esea ch. The pedes al egion is a e y hin
egion ( hinne han 2 cm on AUG) wi h la ge g adien s ha needs e y high spa ial
and empo al esolu ion. In o de o cha ac e ize p ope ly he pedes al egion, he ime
esolu ion has o be good enough o measu e in-be ween wo ELMs. In his sec ion, he
diagnos ics ha ha e been used du ing his hesis will be in oduced (see igu e 3.1).
3.1 Elec on empe a u e and densi y
measu emen s
In his wo k, he elec on empe a u e (Te) has been measu ed wi h he elec on cy-
clo on emission (ECE) and Thomson sca e ing (TS) diagnos ics. Fo he densi y (ne),
lase in e e ome y (DCN), impac exci a ion spec oscopy on a li hium beam (LIB) and
Thomson sca e ing (TS) we e used. The TS diagnos ic gi es in o ma ion on elec on
empe a u e and densi y and hus, allows us o align bo h wi h espec o he sepa a ix
posi ion, as shown in sec ion 3.3. A b ie o e iew is in oduced in he nex sec ions.
Elec on cyclo on emission (ECE)
The ECE diagnos ic gi es in o ma ion on Te. I measu es he emission o elec on adia ion
a i s angula cyclo on equency ωc,e =eB/meand i s ha monics ωk,e =kωc,e. Assuming
ha he elec on empe a u e is he adia ion empe a u e and ha elec ons ollow a
Maxwellian dis ibu ion, he in ensi y a he cyclo on equency ollows Planck‘s law o
21
22 CHAPTER 3. DIAGNOSTICS
Figu e 3.1: To oidal (le ) and poloidal ( igh ) iew o he diagnos ics used du ing his hesis a
AUG.
black-body adia ion. A high empe a u es, his esul s in he Rayleigh-Jeans exp ession
Iω=ω2
2π2c2kBTe.(3.1)
In a okamak, he o oidal magne ic ield, which is he dominan pa o he o al magne ic
ield, a ies like 1/R. This dependency allows us o associa e he emission o a adial
posi ion. The assump ion o black-body is only alid i he plasma is op ically hick. I
he plasma is no op ically hick, as a he plasma edge due o he dec ease in he densi y,
he black-body law is no applicable. Due o his e ec , he ECE measu emen s exhibi a
peak close o he sepa a ix. Hence, in his egion, he ECE da a ha e no been used o
i ing he elec on empe a u e p o ile. A AUG, he ECE sys em has a spa ial esolu ion
o 1 cm and a empo al esolu ion o 1 µs [7,8].
Thomson sca e ing (TS)
The Thomson sca e ing sys em measu es he elec on empe a u e (Te) and densi y (ne).
The TS diagnos ic is based on he elas ic sca e ing o an elec omagne ic wa e by a
cha ged pa icle. When an elec omagne ic wa e eaches he plasma, i accele a es he
pa icles and he wa e is sca e ed. The pa icles ha e eloci ies wi h espec o he ini ial
3.2 ION TEMPERATURE AND IMPURITY ROTATION MEASUREMENTS 23
and sca e ed wa es and, due o he Dopple e ec , he equency o he sca e ed wa e
is shi ed. Due o he di e ence be ween elec on and ion mass, mainly he elec ons
a e accele a ed. I is common o measu e he sca e ed wa e a 90◦. The wid h o he
sca e ed wa e signal gi es a measu e o Te. The in ensi y o he signal gi es in o ma ion
abou ne. A AUG, he e a e wo TS diagnos ics, one iewing he plasma co e and one
he edge. The edge sys em has a spa ial esolu ion o 3 mm and he co e sys em has a
esolu ion o 25 mm [9]. The TS diagnos ic can measu e e e y 8 ms. Due o i s high
esolu ion, he edge sys em is p ope o cha ac e ize he pedes al egion.
Impac exci a ion on a li hium beam
The li hium beam diagnos ic injec s high ene gy Li a oms in o de o measu e he densi y.
When he Li a oms in e ac wi h he plasma, hey a e exci ed and emi adia ion [10].
The p o ile o his adia ion is co ela ed wi h he densi y. Due o se e al e ec s, he Li
beam is a enua ed when i pene a es he plasma. Hence, he Li beam diagnos ic only
gi es in o ma ion on he ou e mos egion o he densi y p o ile. A AUG, he Li beam
diagnos ic has a spa ial esolu ion o 5 mm and a empo al esolu ion o 50 µs [11].
DCN lase in e e ome y
The DCN diagnos ic akes ad an age o he in e ac ion o he elec ons wi h elec omag-
ne ic wa es adding he dependence on he a ia ion o he plasma e ac i e index N.
A phase shi is ob ained when compa ing he p opaga ion o an elec omagne ic wa e
h ough he plasma wi h he p opaga ion h ough he acuum. This phase is di ec ly co -
ela ed wi h he line-in eg a e densi y h ough he beam pa h. A AUG, his diagnos ic
has a empo al esolu ion o 300 µs [12].
3.2 Ion empe a u e and impu i y o a ion
measu emen s
The mos common echnique o measu e ion empe a u e and impu i y o a ion is cha ge
exchange ecombina ion spec oscopy (CXRS) [13]. The CXRS diagnos ic measu es he
spec al lines emi ed due o cha ge ans e om neu al o impu i y ion species:
AZ++D→A(Z−1)+∗+D+→A(Z−1)+ +hν +D+.(3.2)
24 CHAPTER 3. DIAGNOSTICS
Figu e 3.2: Typical spec um measu ed wi h a CXRS diagnos ic a AUG. The FWHM (Full
Wid h a Hal Maximum) is co ela ed o he empe a u e and he shi ∆λis co ela ed o he
o oidal impu i y eloci y. Figu e aken om [14].
The neu als a e usually deu e ium (D) o hyd ogen (H) and a e injec ed ia neu al
beam injec ion. The ligh emi ed is analyzed wi h a spec ome e . Each species emi s a
a di e en wa eleng h and he measu ed spec um gi es in o ma ion on i s empe a u e
and o a ion. In pa icula , he empe a u e is de i ed om he wid h o he signal and
eloci y is de i ed om he Dopple shi (see igu e 3.2).
The lines o sigh (LOS) o he CXRS sys em a e he iewing lines o he plasma whe e
he diagnos ic is poin ing a . The ac i e line comes om he poin s whe e he LOS
in e cep he neu al beam. The passi e lines a e emi ed a he plasma edge, due o
cha ge exchange wi h he mal neu al deu e ium and elec on impac exci a ion [15].
The impu i ies ha a e usually measu ed a AUG a e bo on (B) and ni ogen (N) bu in
helium (He) plasmas he main ion can be measu ed. Usually low Z impu i ies a e measu ed
because hey a e ully ionized, while high Z impu i ies ha e a smalle concen a ion in
he plasma and hey a e no ully ionized h oughou he whole plasma.
Figu e 3.2 shows he spec al adiance ob ained wi h one o he edge CXRS sys ems a
AUG [16, 17]. The ull wid h a hal maximum (FWHM) o he spec al adiance is
di ec ly co ela ed wi h he empe a u e o he measu ed species:
T=mc2
8ln(2)λ2
0e2FWHM2(3.3)
whe e mis he mass o he measu ed species, cis he speed o ligh , λ0is he heo e ical
wa eleng h o emission and eis he elec on cha ge. The shi due o Dopple e ec
3.3 PROFILE ALIGNMENT 25
p o ides he o a ion eloci y o he conside ed species
∆λ
λ= ·eLOS
c(3.4)
whe e eLOS is he uni ec o along he LOS. No e ha =ω ×R.
In his hesis, wo CXRS sys ems a AUG ha e been used o cha ac e ise he edge p o iles
[16,17]: he o oidal edge CXRS sys em, which has a spa ial esolu ion o 1-3 mm, and
he poloidal edge CXRS sys em, which has a spa ial esolu ion o 3-5 mm in he s eep
g adien egion. Bo h CXRS sys ems ha e a s anda d empo al esolu ion o 2.3 ms bu
i can be u ned down o 50 µs [17].
3.3 P o ile alignmen
The di e en p o iles a e ob ained by combining he da a o a ious diagnos ics. The
magne ic equilib ium is assumed o be o oidally symme ic. As he diagnos ics measu e
a di e en o oidal and poloidal posi ions, small unce ain ies in he adial posi ion can
a ise when mapping he p o iles on o he magne ic equilib ium. Thus, he measu ed
p o iles o he di e en diagnos ics ha e o be aligned in o de o educe unce ain ies in
he adial posi ion. This adjus men is e y impo an in he ETB egion which has a
spa ial ex en o only 1.5-2 cm a AUG. The s eep g adien s in he ETB allow o educe
he unce ain ies down o 2-3 mm [18].
Powe balance and pa allel hea anspo s udies based on a 1D hea conduc ion model
[19, 20] de e mine ha elec on empe a u e a he sepa a ix has o be app oxima ely
100 eV in H-mode discha ges o AUG. The p ocedu e o align he p o iles is he ollowing:
i s , he Tep o ile om TS is shi ed o ob ain 100 eV a he sepa a ix. Then, he Te
p o ile measu ed wi h ECE is shi ed o ma ch he p o ile measu ed wi h TS. As men ioned
abo e, TS gi es in o ma ion on Teand ne. The shi used o he TS Tep o ile is applied
o he TS nep o ile. A e ha , he li hium beam nep o ile is shi ed o ma ch he
TS nep o ile. Thus, he Tep o ile and nep o ile a e aligned. The Tip o ile, measu ed
wi h he CXRS sys ems, is aligned by shi ing Tisuch ha he posi ion o he s eepes
g adien s ma ches he one o Te. This assump ion is alid o high collisionali y discha ges
as a high collisionali y he ions and elec ons a e well coupled [21]. The unce ain y in
he alignmen be ween Teand Tiis less han 5 mm. The o oidal impu i y eloci y (ω )
p o ile is in insically aligned o he Tip o ile because hey a e measu ed wi h he same
diagnos ic. Figu e 3.3 shows an example o he expe imen al da a be o e and a e he
alignmen .
32 CHAPTER 4. DATABASE
Figu e 4.5: Typical sa e y ac o (le ) and collisionali y ( igh ) p o iles.
whe e j=i, e, s ands o elec ons o ions, νjis he collision equency and ωbj is he
bounce equency. The exp essions used o calcula e he elec on and ion collisionali y
[23] a e he ollowing
ν∗
e= 0.0012 ·qR3/2
0Ze ne[1019m−3]
1/2(Te[keV ])2(4.4)
ν∗
i= 4.9·10−5·qR3/2
0Z4
e (17.3−1
2ln(ni[1020m−3]) + 3
2ln(Ti[keV ]))ni[1019m−3]
1/2(Ti[keV ])2(4.5)
whe e qis he sa e y ac o , R0is he majo adius, Ze is he e ec i e cha ge s a e , is
he adial coo dina e and is he a io be ween he mino and he majo adius =a/R0.
Figu e 4.5 shows a ypical qp o ile and collisionali y p o ile. No e ha he sa e y ac o
and collisionali y go o in ini e a he sepa a ix.
The cha ac e is ics o a plasma depends on he elemen s o which i is composed. The
da abase includes deu e ium, hyd ogen and helium discha ges. In some discha ges, im-
pu i y seeding, usually ni ogen, is applied. When applying impu i y seeding i has been
obse ed di e ences in he loca ion o he densi y pedes al op [24]. The amoun o gas
in oduced in he plasma pe uni o ime is he uelling. The iangula i y δand he
elonga ion κa e pa ame e s ha desc ibe he shape o he plasma. Bo h pa ame e s e e
o he sepa a ix poloidal c oss sec ion shape. The elonga ion is bigge when he shape
looks mo e hinne (see black shape in igu e 4.6a) and he iangula i y is bigge when
he shape looks mo e like a iangle (see black shape in igu e 4.6b).
Table 4.1 shows he ange he pa ame e s included in he da abase. Phea is he hea ing
powe , ELM is he ELM equency, Ipis he plasma cu en and B is he o oidal magne ic
ield.
4.2 DATABASE PARAMETERS 33
Figu e 4.6: a) Sepa a ix o a high (low) elonga ion discha ge in black ( ed). b) Sepa a ix o a
high (low) iangula i y discha ge in black ( ed).
Pa ame e Range
Phea 3.5 - 15.4 [MW]
ELM 32.4 - 201.7 [Hz]
Ip0.62 - 1.14 [MA]
B 1.97 - 2.5 [T]
δ0.18 - 0.40
κ1.59 - 1.74
ν∗
e(ρ= 0.97) 0.62 - 4.20
ν∗
i(ρ= 0.97) 0.24 - 3.15
D uelling 0 - 2.81 [1022 pa /s]
H uelling 0 - 2.56 [1022 pa /s]
N uelling 0 - 2.47 [1022 pa /s]
Table 4.1: Range o he pa ame e s included in he da abase.
Chap e 5
Resul s
The pedes al is a e y impo an egion o unde s and he beha iou o he plasma. The
impac o he collisionali y on he p o iles as well as unde s anding he ela ion o he
posi ion ( alue) o he di e en pedes als wi h he posi ion ( alue) o he minimum in he
o oidal impu i y eloci y could help o p og ess in pedes al physics. This sec ion shows
he esul s ob ained du ing his hesis.
5.1 Compa ison be ween p o iles a low and high ν∗
This sec ion will show he main di e ences be ween p o iles a high and low collisionali y.
Figu e 5.1 shows ime aces o discha ge #33207. In his discha ge, ou imes windows
we e analyzed. F om he i s ime window (black) o he second one ( ed) he NBI
powe is inc eased. The o oidal impu i y eloci y inc eases in he co e bu dec eases in
he edge. Fu he mo e, he densi y dec eases and ion and elec on empe a u e inc ease.
Compa ing he second ( ed), hi d (blue) and ou h (g een) ime windows, he NBI powe
is cons an bu he deu e ium uelling dec eases. The o oidal impu i y eloci y in he co e
keeps cons an bu i dec eases a he edge. Again, densi y dec eases and ion and elec on
empe a u e inc ease. Exp essions 4.4 and 4.5 show ha he collisionali y dec eases when
he densi y dec eases and when he empe a u e inc eases, while keeping he sa e y ac o
cons an . This beha iou is obse ed in he empo al e olu ion o he selec ed ime
windows in his discha ge. Thus, he collisionali y in his discha ge is dec easing in all
analyzed ime windows. Speci ically, he ion collisionali y a ρpol = 0.97 goes om 1.31
o 0.24. Figu e 5.2 compa es he p o iles in he i s ime window (highes collisionali y)
wi h he p o iles in he ou h ime window (lowes collisionali y). As men ioned abo e,
34
5.2 DEPENDENCY OF ωMIN
TON ν∗35
Figu e 5.1: Time aces: a) plasma cu en , o oidal magne ic ield and sa e y ac o a he lux
su ace con aining 95% o he o al poloidal lux inside he sepa a ix, b) plasma s o ed ene gy, c)
NBI, ECRH and adia ion powe , d) densi y, e) uelling, ) ELM equency, g) o oidal eloci y,
h) elec on and ion empe a u e o discha ge #33207. Analyzed imes windows a e highligh ed
in colou s.
he empe a u e is highe in he low collisionali y case and he densi y is highe in he
high collisionali y case. Fu he mo e, he ion empe a u e is la ge han he elec on
empe a u e a low collisionali y. A high collisionali y, he ion and elec on empe a u e
a e coupled and a low collisionali y hey a e decoupled. The minimum in he o oidal
eloci y is nega i e in he low collisionali y case and posi i e in he high collisionali y case
[25].
5.2 Dependency o ωmin
on ν∗
This sec ion desc ibes he co ela ions be ween he minimum in he o oidal impu i y
eloci y p o ile wi h he collisionali y. The ela ion be ween he alues o Ti,Teand nea
he pedes al op wi h he alue o he minimum in he o oidal impu i y o a ion p o ile
36 CHAPTER 5. RESULTS
Figu e 5.2: Compa ison be ween p o iles o discha ge #33207 a low collisionali y ( ed) and high
collisionali y (black).
5.2 DEPENDENCY OF ωMIN
TON ν∗37
Figu e 5.3: Co ela ions be ween he alues o Tped. op
i,Tped. op
e,nped. op
eand ωmin
in he ou
ime windows selec ed o he discha ge #33207.
o he ou ime windows conside ed in discha ge #33207 is ep esen ed in igu e 5.3.
When he densi y dec eases and he empe a u e inc eases, i.e collisionali y dec eases,
he alue o he minimum in ω dec eases eaching nega i e alues. As men ioned in
he p e ious sec ion, he minimum in he o oidal impu i y eloci y changes sign when
collisionali y is low enough. Nega i e alues o he o oidal impu i y eloci y means ha
he pa icles a e mo ing in he coun e -cu en di ec ion and in opposi e di ec ion o he
plasma co e.
Figu e 5.3 will be ep oduced in igu e 5.4 including all he ime windows o he da abase.
The end is he same in bo h igu es. When he empe a u e inc eases enough (o he
densi y is low enough), he minimum in he o oidal impu i y eloci y becomes nega i e
as he collisionali y is dec easing. In igu e 5.4, a linea i is included o deu e ium
discha ges (black) and o deu e ium wi h ni ogen seeding discha ges (blue). The i s o
he empe a u e da a wi hou ni ogen seeding a e sligh ly s eepe han he i s o he
38 CHAPTER 5. RESULTS
Figu e 5.4: Co ela ions be ween he alues o Tped. op
i,Tped. op
e,nped. op
eand ωmin
o all he
da abase.
da a wi h seeding. The i o he densi y da a wi hou ni ogen seeding has an o se o
a ound 5 k ad/s wi h espec o he i o he da a wi h ni ogen seeding.
To con i m he dependency o he minimum in ω on he collisionali y, bo h quan i ies
a e ep esen ed in igu e 5.5. The collisionali y is aken a ρ= 0.97. When he collision-
ali y is low enough, he minimum in ω eaches nega i e alues, while o high alues o
he collisionali y, he minimum in ω is posi i e. The unce ain ies in he collisionali y
shown in igu e 5.5 a e calcula ed ia Gaussian e o p opaga ion using unce ain ies o
empe a u e and densi y. Unce ain ies in he majo adius, sa e y ac o and Ze ha e
no been aken in o accoun . E o ba s a e only included o one da a poin on each
g aph o cla i y. This da abase shows a obus dependence o ω on ν∗including changes
in shape, plasma cu en , uelling, ELM equency and o oidal magne ic ield.
5.3 CORRELATIONS BETWEEN POSITIONS OF PEDESTAL TOP AND ωMIN
T39
Figu e 5.5: Co ela ions be ween collisionali y and ωmin
.
5.3 Co ela ions be ween posi ions o pedes al op
and ωmin
The objec i e o his sec ion is o iden i y co ela ions be ween he posi ion o he pedes als
and he minimum in he o oidal impu i y eloci y. Figu e 5.6 shows he posi ion o ωmin
e sus he posi ion o nped. op
eand Tped. op
i o he whole da abase.
Including all poin s o he da abase, no co ela ion be ween posi ion o he ωmin
and he
posi ion o nped. op
eis obse ed. Howe e , when limi ing he pa ame e space o ν∗
i>0.9
(high collisionali y), 0.20 < δ > 0.26, Ip>1MA and 5 MW < Phea <16 MW, shows
a clea end be ween he adial posi ion o ωmin
and nped. op
eand Tped. op
i. Figu e 5.7
shows ha he adial posi ion o ωmin
is loca ed a nped. op
eand ωmin
mo es ou wa ds
when Tped. op
iand nped. op
emo e ou wa ds.
This dependence is also s udied a low collisionali y. The esul s o low collisionali y a e
shown in igu e 5.8. In his case, he e is no co ela ion be ween he posi ion o ωmin
and
he posi ion o nped. op
e, bu he e is a co ela ion be ween he posi ion o ωmin
and he
posi ion o Tped. op
i. This sugges ha he physics mechanism se ing he pedes al may
be di e en a low and high collisionali y. No e, howe e , ha he unce ain ies o he
adial p o ile alignmen a e la ge a low collisionali y as he elec ons and ions a e mo e
decoupled and, hence, he assump ion o ρ(∇Ti) = ρ(∇Te) may no be alid.
The ends obse ed in igu es 5.7 and 5.8 a e clea , bu i is impo an o men ion ha
he da a included in he igu es ha e unce ain ies. The posi ions de i ed om Teand ne
p o iles ha e a unce ain y o 5 mm due o he spa ial esolu ion o he diagnos ics, ha
co esponds o 0.01 in ρa AUG. On he o he hand, he posi ions de i ed om Tiand
40 CHAPTER 5. RESULTS
Figu e 5.6: Co ela ions be ween posi ion o he minimum in he o oidal impu i y eloci y and
posi ion o nepedes al op (le ) and posi ion o Tipedes al op ( igh ).
Figu e 5.7: Repe i ion o igu e 5.6 o only high collisionali y discha ges. The dash line is he
iden ical line y=x.
Figu e 5.8: Repe i ion o igu e 5.6 o only low collisionali y discha ges.
5.3 CORRELATIONS BETWEEN POSITIONS OF PEDESTAL TOP AND ωMIN
T41
ω p o iles ha e wo sou ces o unce ain ies: he spa ial esolu ion o he diagnos ics and
he unce ain ies due o he adial p o ile alignmen .
