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Design o a co ela ion e lec ome e adiome e
diagnos ic and measu emen s o he elec on
densi y– empe a u e c oss-phase angle in he
H-mode pedes al wi h small edge localized
modes a ASDEX Upg ade
Ci e as: Re . Sci. Ins um. 96, 033504 (2025); doi: 10.1063/5.0243894
Submi ed: 14 Oc obe 2024 •Accep ed: 14 Feb ua y 2025 •
Published Online: 4 Ma ch 2025
C. Yoo,1,a) G. D. Conway,2W. Bu ke,1P. A. Molina Cab e a,1,b) B. Vano ac,1R. Bielajew,1
D. J. C uz-Zabala,3A. Sil a,4A. E. Whi e,1and ASDEX Upg ade Teamc)
AFFILIATIONS
1Plasma Science and Fusion Cen e , Massachuse s Ins i u e o Technology, Camb idge, Massachuse s 02139, USA
2Max Planck Ins i u e o Plasma Physics, Bol zmanns . 2, 85748 Ga ching, Ge many
3Uni e si y o Se ille, Se ille, Spain
4Associação EURATOM/IST, Ins i u o de Plasmas e Fusão Nuclea , Ins i u o Supe io Técnico, Uni e sidade Técnica de Lisboa,
1049-001 Lisboa, Po ugal
a)Au ho o whom co espondence should be add essed: [email p o ec ed]
b)P esen add ess: École Poly echnique Fédé ale de-Lausanne (EPFL), Swiss Plasma Cen e (SPC),
CH-1015 Lausanne, Swi ze land.
c)See au ho s lis o H. Zohm e al., Nucl. Fusion 64, 112001 (2024), h ps://doi.o g/10.1088/1741-4326/ad249d
ABSTRACT
This wo k p esen s he ha dwa e design and i s esul s om a newly commissioned co ela ion e lec ome e adiome e diagnos ic
ha measu es he c oss-phase angle be ween elec on densi y and empe a u e luc ua ions in ASDEX Upg ade plasmas. This diagnos ic
employsc ossco ela ionsbe weensignalsmeasu edbya unable,con inuouswa e,pe pendicula incidence, luc ua ion e lec ome e ,anda
24-channel adiome e sha ing he same line o sigh . No el measu emen s in he pedes al o a helium H-mode plasma wi h small edge local-
ized modes show changes in he c oss-phase angle be ween he elec on densi y and empe a u e luc ua ions om ∼90○ o 120○, sugges ing
changes in he p ope ies o he u bulence d i ing anspo in he plasma edge.
©2025 Au ho (s). All a icle con en , excep whe e o he wise no ed, is licensed unde a C ea i e Commons A ibu ion (CC BY) license
(h ps://c ea i ecommons.o g/licenses/by/4.0/). h ps://doi.o g/10.1063/5.0243894
I. INTRODUCTION
Fluc ua ions due o d i -wa e plasma u bulence gene ally
domina e he anspo o ene gy,pa icles, and momen um inmag-
ne ically con ined plasmas, limi ing hei pe o mance.1The expe -
imen al cha ac e iza ion o hese luc ua ions o e a b oad ange o
plasma condi ions deepens ou unde s anding o u bulence-d i en
anspo and is impo an o imp o ing ou con idence in u bu-
len anspo models used o p edic he ene gy gain om u u e
usion de ices. As shown in Eq. (1), he ene gy anspo d i en by
elec os a ic luc ua ions, ˜
Q, depends on he sa u a ed ampli udes,
cohe encies, and c oss-phase angles be ween mul iple luc ua ing
quan i ies,
˜
Q=3kθ
2Bϕ[n0˜
T˜
ϕγ˜
T˜
ϕsin(α˜
T˜
ϕ)+T0˜
n˜
ϕγ˜
n˜
ϕsin(α˜
n˜
ϕ)] (1)
wi h he luc ua ions in empe a u e, densi y, and elec ic po en ial
gi en by ˜
T,˜
n, and ˜
ϕ, espec i ely; he cohe encies be ween he luc-
ua ing ields gi en by γ˜
T˜
ϕand γ˜
n˜
ϕ; he c oss-phase angles be ween
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he luc ua ing ields gi en by α˜
T˜
ϕand α˜
n˜
ϕ; he wa enumbe o he
luc ua ions gi en by kθ; he backg ound o oidal magne ic ield
gi en by Bϕ; and he mean densi y and empe a u e gi en by n0
and T0, espec i ely.2While he luc ua ing pa ame e s d i ing u -
bulence can be measu ed oge he simul aneously on he edge o
okamak plasmas using Langmui p obes, simila measu emen s in
he co e a e mo e challenging and pe o med less equen ly.2,3
In his wo k, we p esen he design and i s measu e-
men s om a newly commissioned co ela ion e lec ome e
adiome e (CRR) diagnos ic, also commonly e e ed o as a
densi y– empe a u e (nT)-phase diagnos ic, ha is used o mea-
su e he c oss-phase angle (α˜
ne˜
Te)be ween u bulen luc ua ions
in elec on densi y and empe a u e in ASDEX Upg ade (AUG)
plasmas. The CRR diagnos ic ha dwa e, composed o a e lec ome-
e and mul i-channel adiome e measu ing along he same line
o sigh , was designed o enable measu emen s in bo h he plasma
co e (ρpol =0.4–0.9)and edge (ρpol =0.9–1.0), u he ing ou abil-
i y o measu e mul iple u bulence pa ame e s simul aneously and
p o iding new capaci y o cha ac e ize u bulence h oughou he
plasma olume.
II. BACKGROUND
The measu emen o α˜
ne˜
Te, which was i s ca ied ou in he
co e o he W7-AS s ella a o ,4is impo an o in o ming ou
unde s anding o he u bulen luc ua ions ha d i e plasma ans-
po . A signi ican change in his c oss-phase angle indica es ha an
impo an change has occu ed in he physics unde lying he elec-
on densi y and empe a u e luc ua ions. P e ious wo k has ound
an associa ion be ween changes in he alue o α˜
ne˜
Teand changes o
whe he he u bulence is d i en p edominan ly by long-wa eleng h
iono elec onins abili ies,i.e., heIonTempe a u eG adien (ITG)
mode o he T apped Elec on Mode (TEM) (see, e.g., Re s. 2and
5–7). In addi ion, α˜
ne˜
Tecan be calcula ed om heo y and simula-
ion, including gy okine ic and quasilinea codes, and he e o e one
canapplyexpe imen al measu emen s o α˜
ne˜
Te owa d he alida ion
o compu a ional models.2Fu he mo e, measu emen s o α˜
ne˜
Tecan
beused oassess heimpac o densi y luc ua ionson adia ion em-
pe a u e luc ua ion measu emen s in egimes o low op ical dep h,
he eby aiding in he in e p e a ion o measu emen s om diag-
nos ics such as he co ela ion elec on cyclo on emission (CECE)
diagnos ic.8
P e ious measu emen s o α˜
ne˜
Tea AUG8–11 equi ed pai ing
oge he componen s o an exis ing e lec ome e and adiome e
ha we e no mally ope a ed as en i ely sepa a e diagnos ics. In his
wo k, we epo on he i s dedica ed CRR diagnos ic a AUG ha
enables con inuous α˜
ne˜
Temeasu emen capabili y. This diagnos ic
was designed o maximize compa ibili y be ween he cons i uen
e lec ome e and adiome e in o de o enable he measu emen
o long-wa eleng h luc ua ions in elec on empe a u e and den-
si y expec ed in he majo i y o AUG plasmas. The ope a ion o he
CRR diagnos ic has enabled he i s measu emen s o α˜
ne˜
Teassoci-
a edwi h luc ua ionsin hepedes alo anH-modeplasma ea u ing
small Edge Localized Modes (ELMs).
The emainde o hispape iso ganizedas ollows:Sec.IIIp o-
ides backg ound on he heo y o α˜
ne˜
Temeasu emen s. Sec ion IV
de ails he CRR diagnos ic ha dwa e. Sec ion Vp esen s he da a
analysis me hods o his diagnos ic. Sec ion VI gi es an o e iew
o he expe imen . Sec ion VII p esen s he CRR diagnos ic expe i-
men al measu emen s. Sec ion VIII gi es a discussion o he esul s.
Sec ion IX concludes his pape .
III. OVERVIEW OF α˜
ne˜
TeMEASUREMENT THEORY
TheCRR diagnos icα˜
ne˜
Temeasu emen sp esen ed in hiswo k
employ co ela ions o e lec ome e and adiome e signals mea-
su ed along a common line o sigh . He e, we desc ibe he basic
p inciples o his diagnos ic.
The luc ua ion e lec ome e componen o he CRR diagnos-
ic ope a es by ansmi ing X-mode-pola ized mic owa es in he
W-band ange o equencies (75–103 GHz) in o he plasma. The
ansmi ed signal is e lec ed and modula ed in phase and ampli-
ude by luc ua ions in he plasma densi y in he egion whe e he
ansmi ed signal’s equency is equal o he igh -hand cu o e-
quency.12 The e o e, an analysis o hese modula ions can p o ide
in o ma ion on he beha io o he u bulence a he cu o laye .
Howe e , depending on he s eng h o he densi y luc ua ions, he
esponse o he e lec ome e signal o he densi y luc ua ions can
be linea o non-linea .12 Fo su icien ly small densi y luc ua ions,
co esponding o he linea egime, phase luc ua ions ha e been
ound o be p opo ional o he densi y luc ua ions a he cu o
egion, al hough his p opo ionali y b eaks down o highe den-
si y luc ua ion le els, co esponding o he non-linea egime.13
Howe e , ampli ude luc ua ions ha e been ound o e ain hei
p opo ionali y o densi y luc ua ions be e a high luc ua ion le -
els.13 As epo ed in Re . 14 and no ed in Re . 11, a ini e phase
anglemayexis be ween he e lec ome e signal luc ua ions and he
densi y luc ua ions, dependen on ac o s ha include no only lin-
ea i y bu also he wa enumbe ange o he densi y pe u ba ion
and he e ec i e cu a u e be ween he adiome e beam and he
cu o laye . This ini e phase angle would yield a bias in he cal-
cula ed e lec ome e –ECE c oss-phase angle compa ed o α˜
ne˜
Te.11,14
E alua ing he condi ions unde which each possible e lec ome e
signalmay be used as anapp op ia e measu e o densi y luc ua ions
o α˜
ne˜
Temeasu emen s is an ongoing a ea o esea ch and equi es
ull-wa e modeling. Fo u he discussion, see p. 9 o Re . 11, p. 5 o
Re . 2, and he e e ences he ein.
The mul i-channel adiome e componen o he CRR diag-
nos ic measu es luc ua ions in he in ensi y o X-mode-pola ized
second ha monic elec on cyclo on emission (ECE) in he F-band
ange o equencies (109–124 GHz). Unde condi ions in which
he measu ed olume o he plasma is op ically hick (τ≳2), he
luc ua ions in he ECE in ensi y can be in e p e ed as luc ua ions
in he elec on empe a u e.15 The localiza ion o he adiome-
e measu emen s is de e mined by he equilib ium magne ic ield
wi h ini e- olume e ec s enhanced by Dopple b oadening and he
ela i is ic downshi .15,16
C oss co ela ion analysis o he signals measu ed by he e lec-
ome e and adiome e componen s o he CRR diagnos ic is pe -
o med o ob ain α˜
ne˜
Te. Measu emen s o cohe en α˜
ne˜
Tesignals
equi e ha he e lec ome e and adiome e measu e wi hin he
same u bulence co ela ion leng h in he adial di ec ion along he
line o sigh o he diagnos ic. The use o p og ammed e lec ome-
e ansmission equency s eps and a la ge a ay o adiome e
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FIG. 1. Lines o sigh o he CRR diagnos ic’s ansmi e (pu ple) and ecei e
(blue) an ennas o a 110 GHz beam calcula ed using a acuum-based Gaussian
beam model o discha ge 41455 du ing he in e al 3.25–3.75 s o e con ou s o
ρpol, whe e ρpol is de ined as he squa e oo o he no malized poloidal magne ic
lux.
channels employed by he CRR diagnos ic inc eases he likeli-
hood o adially co-loca ed e lec ome e and adiome e measu e-
men s, he eby inc easing oppo uni ies o ob aining cohe en α˜
ne˜
Te
measu emen s.
The CRR diagnos ic has a poloidal spa ial esolu ion se by he
wid h o he mic owa e beam a he measu emen loca ion. Bo h
he e lec ome e and adiome e channels a e sensi i e o u bu-
len luc ua ions wi h poloidal wa eleng hs longe han he poloidal
beam wid h, de ined he e as he 1/e2beam powe diame e o equi -
alen ly as he 1/eE- ield beam diame e , bu apidly lose sensi i i y
when he wa eleng hs a e sho e han he beam wid h.15,17 The
applica ion o a Gaussian beam model pe Re . 18 yields poloidal
beam wid hs be ween ∼11 cm a he sc ape-o laye (SOL) and
13.5 cm a ρpol =0.80, as shown in Fig. 1.
The ime esolu ion o he CRR diagnos ic is a ec ed by he
need o ensemble a e aging o ob ain a le el o cohe ence be ween
he e lec ome e and adiome e signals ha is abo e he sensi i i y
limi . The equa ions o hese pa ame e s a e shown in Sec. V. As
will be shown in Sec. VII, hal a second o ensemble a e aging was
equi ed o ob ain cohe ence le els abo e he sensi i i y limi o he
measu emen s p esen ed in his wo k.
IV. DESIGN OF THE CRR DIAGNOSTIC
A schema ic o he CRR diagnos ic is shown in Fig. 2. De ails
o he an ennas and componen s o he W-band he e odyne e lec-
ome e and he F-band he e odyne 24-channel adiome e ha
oge he make up he CRR diagnos ic a e gi en in Secs. IV A–IV C.
FIG. 2. Schema ic o he CRR diagnos ic ha dwa e. Bo h he e lec ome e and adiome e componen s o he o e all diagnos ic ha e hei own adio equency (RF) and
in e media e equency (IF) sec ions and sha e he same da a acquisi ion sys em. The ansmission pa h be ween he an ennas and he DC b eaks is simpli ied o cla i y.
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A. An ennas and diagnos ic lines o sigh
The ansmission and ecep ion o he e lec ome e and
adiome e signals u ilize a pai o bi-s a ic, W/V-band py amidal
ho n an ennas. The an ennas, ins alled on he low- ield side o he
okamak,a esepa a ed e ically by ∼56 mmasmeasu ed om hei
op icalaxes. The uppe an enna isused o ansmi he e lec ome e
signal and ea u es a downwa d e ical il o 3.6○, while he lowe
an enna is used o ecei e he e lec ome e signal e lec ed by he
plasma as well as he adiome e signals and ea u es an upwa d e -
ical il o 3.6○. These small il angles lead o app oxima ely no mal
incidence o he ansmi ed and measu ed beams wi h he con ou s
o cons an magne ic luxwi hin heplasma.Figu e1 shows helines
o sigh o he mic owa e beams ansmi ed and ecei ed by he
uppe and lowe an ennas a 110 GHz, espec i ely.
B. Re lec ome e ha dwa e
1. T ansmi ing ha dwa e
A unable syn hesize in he ansmission pa h ou pu s a
p e-p og ammed, con inuous-wa e, ixed- equency signal o a
sequence o signals a selec ed equencies wi hin he ange o
12.5–17.16 GHz. The oscilla o ha gene a es hese ou pu signals
uses a ixed 10 MHz e e ence signal p o ided by a clock in e nal o
he syn hesize . 6-m long low-loss Sub-Minia u e e sion A (SMA)
cables connec he e lec ome e in e media e equency (IF) and
adio equency (RF) sec ions.
A equency mul iplie in he RF sec ion inc eases he syn he-
size signal equency bya ac o o 6, esul inginW-band equency
co e age in he ange o 75–103 GHz. Fo s anda d AUG ope a-
ion wi h an on-axis magne ic ield o 2.5 T, his equency ange
enables he e lec ome e o measu e densi y cu o s be ween ∼2–6
×1019 m−3. An ampli ie in he mul iplie module inc eases he
e lec ome e signal powe up o 20 dBm. An a ached isola o p o-
ec s he ansmi e componen s om e lec ed powe . A W-band
low-pass il e wi h a passband up o 103 GHz ejec s equencies
105 GHz and abo e in o de o p o ec agains s ay adia ion om
elec on cyclo on esonance hea ing (ECRH) gy o on ope a ion a
105 and 140 GHz.
Be ween he W-band undamen al wa eguide a ached o he
low-pass il e and he ansmi ing an enna a e a pneuma ic swi ch
o op ional diagnos ic isola ion, a DC b eak, wo wa eguide ape s,
se en90○bends,a acuum eed- h oughGaussianpe iscope, and an
o e sized wa eguide. The 39 mm diame e ci cula o e sized wa e-
guide is used o minimize ohmic losses. The quasi-op ical Gaussian
pe iscope minimizes mic owa e mode con e sion h ough he ac-
uumb eak.Mode con e sion is also educed h ough heuseo long
wa eguide ape s om he o e sized o he undamen al ci cula
wa eguide. The desi ed X-mode mic owa e pola iza ion is selec ed
a he undamen al ci cula o ec angula wa eguide ansi ion. Sig-
nal losses a e educed by keeping he undamen al wa eguide as
sho as possible.
2. Recei ing ha dwa e
The ecei ing op ical ansmission pa h, s a ing wi h he
ecei ing an enna, is iden ical o he ansmi ing pa h up un il
a h ee-way wa eguide couple . One o he po s o he couple
connec s o he e lec ome e ’s RF sec ion. The signal hen passes
h ough a W-band low-pass il e iden ical o he one al eady
desc ibed in he ansmi ing pa h.
The incoming RF signal passes h ough a mixe , whe e i is
mixed wi h a local oscilla o signal gene a ed by a second unable
syn hesize in he e lec ome e ’s IF sec ion. The syn hesize in he
ecei ingpa h is iden ical o hesyn hesize in he ansmi ingpa h.
I uses he same 10 MHz e e ence signal o a oid in oducing sys-
ema ic phase shi s in o he ecei ed e lec ome e signal du ing he
demodula ion p ocess in he RF sec ion mixe . Howe e , he ecei -
ing pa h syn hesize is p og ammed such ha he ou pu equency
o he co esponding ×6 equency mul iplie is 500 MHz less han
he equency o he wa e emi ed by he ansmi ing an enna o
acili a e p ope demodula ion in he I/Q mixe .
The IF signal ou pu by he RF sec ion mixe is ampli ied,
bandpass il e ed (500 MHz cen e equency wi h 2 MHz band-
wid h), and ed in o he RF po o an I/Q mixe . The I/Q mixe ’s
LO po ecei es a signal om a 500 MHz phase-locked oscilla o ,
which i sel uses he same 10 MHz e e ence signal o ensu e i is
phase-locked o he wo syn hesize s. The in-phase (I) and quad a-
u e (Q) signals ou pu by he I/Q mixe a e hen ampli ied and
low-pass il e ed a 1 MHz o p e en aliasing be o e digi iza ion a
4 MHz. Special a en ion was gi en o he sc eening o e lec ome e
componen s and he a oidance o g ound loops.
C. Radiome e ha dwa e
The adiome e componen o he CRR diagnos ic measu es
elec on cyclo on emission om he plasma using he same ecei -
ing an enna as he e lec ome e . The design o he adiome e is
based on he CECE diagnos ic a AUG as desc ibed in Re . 19.
The hi d po o he h ee-way wa eguide couple connec s o
he adiome e signal’s W-band ansmission pa h. A e passing
h ough a W- o-F-band wa eguide couple and he subsequen
sec ion o he F-band wa eguide, he signal en e s he adiome-
e RF sec ion. The signal is i s il e ed using a side-band il e
(109–124 GHz) be o e downcon e sion o in e media e equencies
in a mixe (107 GHz), al hough he selec ion o side-band il e and
mixe can be econ igu ed o enable access o di e en equency
anges. Du ing s anda d AUG ope a ion wi h an on-axis magne ic
ieldo 2.5T, he109–124GHz equency angeco esponds oposi-
ions wi hin he ange o ρpol =0.35–1.03. The adiome e measu es
o e a subse o his adial ange, depending on he con igu a ion o
he IF sec ion, pa icula ly he IF il e cen e equencies. The se o
IF il e s ins alled a he ime o his wo k co esponds o he na -
owe adial ange ρpol =0.77–1.03. The IF ou pu o he mixe is
ampli ied be o e en e ing in o he diagnos ic’s IF sec ion.
TheIFsec ion ea u es24 ixed equencychannelso 200 MHz
il e bandwid hs spli among h ee chassis, wi h 50 MHz spacing
be ween adjacen il e bandwid hs. A e de ec ion, ampli ica ion,
and an i-aliasing a 1 MHz, he signals a e sampled a 4 MHz using
he same digi ize as he e lec ome e signals.
V. DATA ANALYSIS METHODS
Wi hin he ecei e sec ion o he e lec ome e , he ecei ed
signal is decomposed in a quad a u e demodula o (I/Q mixe )
in o an in-phase (I) and quad a u e (Q) signal. This demodula ion
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p ocess enables es ima es o he phase and ampli ude modula-
ions o he e lec ed signal ela i e o he ansmi ed signal as
a esul o he plasma luc ua ions. The unw apped phase, ϕ( )
=a c an(Q( )/I( )), ampli ude, A( )=√I( )2+Q( )2, homo-
dyne I-phase, A( )cos(ϕ( )), homodyne Q-phase, A( )sin(ϕ( )),
and he complex ampli ude, A( )eiϕ( ), can each be co ela ed wi h
he adiome e signals.2,9,20
Ensemble-a e aged es ima es o he one-sided au o-powe s
(G˜
ne˜
ne,G˜
Te˜
Te) and c oss-powe (G˜
ne˜
Te)spec al densi ies a e calcu-
la ed pe Re . 21 using he chosen densi y signal (i.e., he phase,
ampli ude, homodyne, o complex ampli ude e lec ome e signal)
and he empe a u e signal measu ed by an indi idual adiome e
channel. The c oss-powe spec al densi y (PSD) calcula ion uses
he con en ion o mul iplying he complex conjuga e o he Fou ie
ans o m o he densi y signal wi h he Fou ie ans o m o he
empe a u e signal.
The densi y– empe a u e c oss-phase angle, α˜
ne˜
Te, is calcula ed
(pe Re . 21) as
α˜
ne˜
Te( )=a c an(Im(G˜
ne˜
Te( ))
Re(G˜
ne˜
Te( ))). (2)
Thecohe ence unc ion,de inedhe e obe eal- alued, canalso
be calcula ed (pe Re . 21) as
γ˜
ne˜
Te( )=∣G˜
ne˜
Te( )∣
√G˜
ne˜
ne( )G˜
Te˜
Te( ). (3)
The s a is ical unce ain y on he c oss-phase angle is gi en by
i s s anda d de ia ion (pe Re s. 21 and 22) as
σα˜
ne˜
Te=¿
Á
Á
Á
À1
2nd⎛
⎝1−γ2
˜
ne˜
Te( )
γ2
˜
ne˜
Te( )⎞
⎠, (4)
whe e ndis he numbe o da a segmen s in he ensemble a e age.
The one s anda d de ia ion unce ain y on he cohe ence is gi en
(pe Re s. 19 and 22) as
σγ˜
ne˜
Te=√1
2nd(1−γ2
˜
ne˜
Te( )). (5)
The sensi i i y limi o he cohe ence unc ion is de ined as wo
s anda d de ia ions abo e ze o, in line wi h Re . 19.
VI. EXPERIMENT OVERVIEW
In his sec ion, we gi e an o e iew o AUG discha ge 41455,
du ing which CRR diagnos ic measu emen esul s we e ob ained a
he end o he 2022 expe imen al campaign. This was an auxilia y-
hea ed [neu al beam injec ion (NBI) and ECRH], 0.8 MA, H-mode
FIG. 3. (a) Co e and edge line-a e aged elec on densi ies om in e e ome y. (b) Co e (ρpol =0.20)and edge (ρpol =0.90)elec on empe a u es om he p o ile ECE
diagnos ic. (c) Inpu powe le els. (d) ELM moni o . The shaded egions indica e he wo ime in e als o in e es : 3.0–3.5 and 3.5–4.0 s.
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discha ge exhibi ing ma ked changes in ELM cha ac e is ics o e
he cou se o he discha ge. The plasma was majo i y helium wi h a
mino i y o deu e ium and ni ogen. Two ime in e als a e o in e -
es o he α˜
ne˜
Temeasu emen s p esen ed in his wo k: 3.0–3.5 and
3.5–4.0 s. As shown in Fig. 3, he co e o he plasma ea u ed a sligh
inc ease in he line-a e aged elec on densi y and a sligh dec ease
in he elec on empe a u e while he powe was s eady be ween he
woin e als.The i s imein e al ea u eda ewsmallELMs,while
he second ime in e al was ELM- ee. The esul s in Sec. VII a e
a e aged o e he ELMs.
Figu e 4 shows he elec on densi y and empe a u e edge
p o iles o bo h ime in e als as calcula ed using in eg a ed da a
analysis (IDA).23 Figu e 5 shows he co esponding no malized log-
a i hmicg adien scaleleng hs,de inedasR/Lne=R×d/d (ln(ne))
and R/LTe=R×d/d (ln(Te)), espec i ely. The pedes al op can
be iden i ied jus inside o ρpol =0.95. The neand Tep o iles and
hei g adien s a e no signi ican ly changed be ween he wo ime
in e als. The adiome e localiza ion and IDA p o ile mappings
we e de e mined ia magne ic equilib ium econs uc ion using
he in eg a ed da a analysis equilib ium (IDE).24 The e lec ome e
localiza ion was de e mined om a igh -hand cu o equency
p o ile gene a ed om he IDA nep o ile and IDE magne ic equi-
lib ium econs uc ion. The e lec ome e ansmission equency
was inc eased om 75 o 99 GHz in s eps o 6 GHz a each 1 s
ma k du ing his discha ge. Du ing bo h ime in e als o in e -
es , he ansmission equency was ixed a 93 GHz, yielding an
app oxima ely cons an e lec ome e localiza ion du ing he wo
in e als.The e lec ome e and adiome e localiza ionswe e ound
o o e lap a ρpol ≈0.98 du ing bo h ime in e als.
VII. RESULTS
In his sec ion, we i s p esen measu emen s om he
adiome e and e lec ome e componen s o he CRR diagnos ic,
ollowed by α˜
ne˜
Temeasu emen s. The spec a shown in his sec ion
we e calcula ed using as Fou ie ans o ms (FFTs) wi h 50% o e -
lapping Hamming windows and 0.25 ms da a segmen s, yielding
∼4 kHz equency esolu ion.
Figu e 6 shows he cohe ence spec a be ween wo neighbo -
ing adiome e (ECE) channels measu ing in he plasma edge a
FIG. 4. Edge (a) nep o iles and (b) Tep o iles om IDA o bo h ime in e als.
FIG. 5. Edge (a) R/Lnep o iles and (b) R/LTep o iles om IDA o bo h ime in e als.
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FIG. 6. Cohe ence spec a o wo adially adjacen adiome e channels o he
wo ime in e als a he same adial loca ion. A b oadband ea u e exis s a e-
quencies below 100 kHz in bo h spec a. The cohe ence is abou 50%highe in
he equency ange o 30–60 kHz du ing he second ime in e al.
ρpol ≈0.98. The spec a we e calcula ed by applying Eq. (3) o he
wo adiome e signals. The cohe ence le el is abou 50%–75%
la ge in he equency ange o 30–60 kHz du ing he second
ime in e al. Tu bulen elec on empe a u e luc ua ion ampli-
udes (δTe/Te)we e calcula ed om he cohe ence spec a using
Eq. (1) in Re . 11 by in eg a ing be ween 20 and 110 kHz and sub-
ac ing a backg ound alue aken as he mean cohe ence o e he
ange o 150–200 kHz. Fo 3.0–3.5 s, δTe/Te=1.27% ±0.06%, while
o 3.5–4.0 s, δTe/Te=1.66% ±0.05%. The op ical dep h (τ)a he
measu emen loca ion was on he h eshold o ma ginali y, wi h
τ≈2. Based on he poloidal beam wid h and empe a u e p o ile a
he measu emen loca ion, he adiome e measu emen s we e sen-
si i e o kθρs≲0.1, whe e kθis he no malized poloidal wa enumbe
o hemeasu ed u bulenceandρsis heionLa mo adiuse alua ed
a he sound speed.
Figu e 7 shows he au o-powe spec al densi ies (PSDs)
o h ee e lec ome e signals (ampli ude, phase, and quad a u e
homodyne signals) o bo h ime in e als. A h eshold-based mo -
ing a e age il e was implemen ed pe Re . 25 o emo e na ow-
band elec onics noise peaks om he spec a. As wi h he adiome-
e , he e lec ome e measu emen s we e sensi i e o kθρs≲0.1.
Simila o he adiome e cohe ence spec a, he e lec ome e au o-
PSD spec a all show a dis inc b oadband ea u e a equencies
less han ∼100 kHz. Howe e , in con as o he adiome e cohe -
ence spec a, he b oadband ea u es in he e lec ome e spec a all
exhibi a dec ease in signal le el om he i s o he second ime
in e al. A g ea e pe cen age dec ease in he e lec ome e phase
and homodyne signals is obse ed be ween he wo in e als com-
pa ed o he ampli ude signal. Gi en possible ambigui ies ega ding
whe he each o he e lec ome e phase, ampli ude, and homodyne
signals a e accu a e p oxies o he ac ual densi y luc ua ions, igo -
ouscalcula ionso heco espondingdensi y luc ua ionampli udes
equi e ull-wa e modeling and a e beyond he scope o his pape .
Figu e 8 shows how he CRR diagnos ic cohe ence and α˜
ne˜
Te
spec a change be ween he wo ime in e als. An inc ease in he
cohe enceandα˜
ne˜
Teoccu s om he i s o he second imein e al.
Themaximumcohe ence le elo heb oadband luc ua ions,wi hin
FIG. 7. Au o-powe spec al densi ies (PSDs) o he e lec ome e (a) ampli ude,
(b)phase,and(c)quad a u ehomodynesignals o bo h imein e als.Eachspec-
um shows a b oadband ea u e a equencies below 100 kHz. No e: y-axes a e
unca ed.
he equency ange o 20–80 kHz, inc eases ∼100% be ween he
wo ime in e als.Theinc easein he e lec ome e –ECEcohe ence
spec a is co ela ed wi h an inc ease in he ECE–ECE cohe ence
spec a bu is in e sely co ela ed wi h he change in he e lec-
ome e signal spec a be ween he wo ime in e als. The signal
bandwid hs o he e lec ome e –ECE cohe ence and α˜
ne˜
Tespec-
a a e simila be ween he wo ime in e als, al hough he α˜
ne˜
Te
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FIG. 8. Panels (a), (c), and (e) show he cohe ence spec a be ween he e lec ome e ampli ude, phase, and quad a u e homodyne signal, espec i ely, and a adially
co-loca ed adiome e channel o he wo ime in e als. Panels (b), (d), and ( ) show he c oss-phase angle spec a using he same signals. The cohe ence spec a a e
la ge , and he c oss-phase angles a e mo e ou o phase du ing he second ime in e al.
spec a display a mo e cons an end du ing he second ime in e -
al. The mean alue o he c oss-phase angle o 3.0–3.5 s is ∼90○
o e he equency ange o 30–60 kHz, while he mean alue o
he c oss-phase angle o 3.5–4.0 s is mo e ou o phase, ∼120○, o e
he same ange o equencies. I is in e es ing o no e he ela i ely
la ge change in he cohe ence le els (≈100%)be ween he wo ime
in e als compa ed o he ela i ely smalle change in he alues o
α˜
ne˜
Te(≈30%)wi hin 30–60 kHz. In addi ion, he cohe ence spec a
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be ween he e lec ome e andECEsignalsd opbelow hesensi i i y
limi by∼70kHz,while hecohe encespec abe ween heECE–ECE
signals emain abo e he sensi i i y limi beyond 100 kHz. Fu -
he mo e, he e lec ome e –ECE cohe ence spec a exhibi a mo e
p onounced dip a equencies below 30 kHz, while he cohe ence
spec a be ween he ECE–ECE signals do no . Ano he obse a-
ion o no e is ha nei he he magni ude o he e lec ome e –ECE
cohe ence no he equency bandwid h o he luc ua ing signal no
he alue o α˜
ne˜
Teappea o depend signi ican ly on he choice o
selec ed e lec ome e signal du ing ei he ime in e al.
I is impo an o add ess he ques ion o whe he densi y luc-
ua ions in he plasma edge could in luence he in e p e a ion o he
esul s o his wo k gi en he ma ginal op ical dep h in his plasma.
We no ed in Sec. II ha α˜
ne˜
Tecan aid in assessing he impac o den-
si y luc ua ions on adia ion empe a u e luc ua ions a low op ical
dep h. He e, we conduc his assessmen o he plasma condi ions
associa ed wi h discha ge 41455. We ollow he analysis conduc ed
in Sec. 3B o Re . 8. This analysis uses Eqs. (4) and (5) in Re . 26,
which model he adia ion in ensi y luc ua ion ampli ude as a
unc ion o op ical dep h, δTe/Te,δne/ne,α˜
ne˜
Te, and wall e lec i i y.
Fo his model, we assume ha δTe/Te=1.45%, as his is
app oxima ely ep esen a i e o he epo ed alues o δTe/Te o
he wo ime in e als in his discha ge. We assume a conse a-
i e alue o δne/ne=40%, as his is an uppe limi o he δne/ne
associa ed wi h he quasi-cohe en mode (QCM) as measu ed using
p obes in he edge o he ELM- ee discha ge epo ed in Re . 27.
A wall e lec i i y o 0.85 is used, in line wi h Re . 8. Th ough his
analysis, we ind ha he a io o he adia ion in ensi y luc ua ion
ampli udes o δTe/Tebecomes close o 1, i.e., ha ma ginal op i-
cal dep h has less o an e ec , as α˜
ne˜
Tebecomes mo e ou -o -phase.
We no e ha his quali a i e end holds ega dless o he assumed
alues o δne/neand δTe/Tebu ha i is mo e sensi i e o he al-
ues o α˜
ne˜
Te. The esul s o his model p edic ha he measu ed
adia ion in ensi y luc ua ion ampli ude should dec ease by ∼25%.
Ins ead, he measu ed luc ua ion ampli ude was ound o inc ease
om 1.27% o 1.66%. In addi ion, he e is a dec ease in densi y luc-
ua ionle elsas indica ed by he d op in hepowe spec al densi ies
o he e lec ome e signals om he i s o he second ime in e -
al, as shown in Fig. 7. This sugges s ha any densi y luc ua ion
d i en-pollu ion o he adiome e signals should dec ease om he
i s o he second ime in e al, yielding a dec ease in he measu ed
empe a u e luc ua ion ampli udes. This is coun e o he obse ed
inc ease in δTe/Te. The e o e, he epo ed inc ease in δTe/Te om
he i s o he second ime in e al does no appea o be explained
by he impac o densi y luc ua ions on he ECE measu emen s a
ma ginal op ical dep h.
I is also possible o ma ginal op ical dep h condi ions o
impac α˜
ne˜
Tei sel . One possibili y is ha in low op ical dep h
plasmas, an inc ease in densi y luc ua ions would lead o a mo e in-
phase alue o α˜
ne˜
Tesince he same unde lying densi y luc ua ions
would be measu ed by bo h he e lec ome e and he adiome e .
A simila e ec could play some ole in he obse ed esul s, whe e
a dec ease in densi y luc ua ion le els occu s concu en ly wi h a
mo e ou -o -phase alue o α˜
ne˜
Te. In o de o e alua e his ques ion
mo e igo ously, u u e wo k will employ syn he ic CRR measu e-
men s o non-linea gy okine ic simula ions, coupled wi h ull-wa e
modeling, which is beyond he scope o he cu en pape .
VIII. DISCUSSION
Theno elCRR diagnos ic esul s p esen ed in hiswo k a e he
i s such measu emen s in he pedes al egion o a high densi y H-
mode plasma ac oss small ELM and ELM- ee phases. Impo an ly,
he b oadband cohe ence spec a and c oss-phase angles shown
in his wo k exhibi cohe ence le els and signal bandwid hs ha
a e consis en wi h mul iple p e ious measu emen s on AUG o
d i -wa e u bulence as pe Re s. 9–11 as well as u bulen luc u-
a ions associa ed wi h he edge weakly cohe en mode pe Re . 8.
The consis ency o hese new esul s wi h p e ious measu emen s
indica es ha his new diagnos ic is unc ioning p ope ly and
demons a es he compa ibili y be ween he cons i uen e lec ome-
e and adiome e componen s o α˜
ne˜
Temeasu emen s. The esul s
p esen ed he e a e also consis en wi h p e ious wo k showing
ag eemen inshapebe ween he e lec ome e ampli ude,phase,and
homodyne signals in H-mode plasmas wi h low densi y luc ua ion
le els in he CCT okamak.13 The ag eemen be ween each o he
au o-powe spec a shown in Fig. 7 and, sepa a ely, each o he α˜
ne˜
Te
spec a shown in Fig. 8 as calcula ed using he e lec ome e ampli-
ude, phase, and homodyne signals sugges s ha he e lec ome e
esponse is in he linea egime and ha each o hese signals is
p opo ional o he unde lying densi y luc ua ions. This esul is
also consis en wi h p io wo k epo ing ag eemen be ween α˜
ne˜
Te
as calcula ed using he e lec ome e phase and ampli ude signals.7
Fu u e wo k employing non-linea gy okine ic simula ions, coupled
wi h ull-wa e modeling, can con i m he linea i y o hese mea-
su emen s. Such modeling can also be used o in es iga e he in lu-
ence o ac o s ha may lead o ini e c oss-phase angles be ween
he e lec ome e signals and he densi y luc ua ions, as no ed in
Sec. III.
I isno ewo hy ha hedischa ge ea u edin hiswo kwasno
speci ically designed o commissioning measu emen s o he CRR
diagnos ic, in con as o p e ious α˜
ne˜
Tes udies a AUG in which he
localiza ions o he e lec ome e and adiome e we e delibe a ely
ac o ed in o he planning o he discha ges o ensu e adially co-
loca edmeasu emen s.Theabili y oob aincohe en measu emen s
in his wo k none heless highligh s he impo ance o s epping he
e lec ome e ansmission equency in o de o inc ease he possi-
bili y o o e lapping measu emen s. Fu he mo e, gi en he use o
a sha ed ecei e an enna and he use o adjacen mic owa e e-
quency bands, he W-band e lec ome e and F-band adiome e
a e sensi i e o e y simila wa eleng hs o u bulen luc ua ions.
In addi ion, he chosen diagnos ic equency bands enable he co-
loca ion o he e lec ome e and adiome e measu emen s ac oss a
wide ange o plasma densi ies.
An in e es ing poin is ha he measu ed CRR signals showed
signi ican changes be ween he i s and second ime in e als while
he p o iles and hei g adien s exhibi ed only sligh changes. The
obse ed inc eases in he e lec ome e –ECE cohe ence and α˜
ne˜
Te,
he inc ease in δTe/Te, and he dec ease in e lec ome e au o-PSDs
migh be explained in pa by he sligh changes in he local g a-
dien s, which could a ec he s eng h o he u bulence d i e. On
he o he hand, he e could be some addi ional physical mecha-
nism leading o he measu ed changes in he cha ac e is ics o he
u bulence. Fu u e wo k will in es iga e addi ional possible sou ces
o d i e leading o hese obse ed changes in he beha io o he
u bulence. Ano he open ques ion is o wha physics eason he
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