PAPER
Beam ion losses due o ene ge ic pa icle
geodesic acous ic modes
To ci e his a icle: R.K. Fishe e al 2012 Nucl. Fusion 52 123015
View he a icle online o upda es and enhancemen s.
Rela ed con en
Con ec i e beam ion losses due o Al én
eigenmodes in DIII-D e e sed-shea
plasmas
-
P omp non- esonan neu al beam-ion
loss induced by Al én eigenmodes in he
DIII-D okamak
-
Measu emen s o as -ion losses induced
by MHD ins abili ies using a scin illa o -
based p obe in he HL-2A okamak*
-
Recen ci a ions
Anomalous losses o ene ge ic pa icles in
he p esence o an oscilla ing adial
elec ic ield in usion plasmas
Da id Za zoso and Diego del-Cas illo-
Neg e e
-
Simula ion o ene ge ic pa icle d i en
geodesic acous ic modes and he ene gy
channeling in he La ge Helical De ice
plasmas
Hao Wang e al
-
Chi ping and Sudden Exci a ion o
Ene ge ic-Pa icle-D i en Geodesic
Acous ic Modes in a La ge Helical De ice
Expe imen
Hao Wang e al
-
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IOP PUBLISHING and INTERNATIONAL ATOMIC ENERGY AGENCY NUCLEAR FUSION
Nucl. Fusion 52 (2012) 123015 (5pp) doi:10.1088/0029-5515/52/12/123015
Beam ion losses due o ene ge ic pa icle
geodesic acous ic modes
R.K. Fishe 1, D.C. Pace1, G.J. K ame 2, M.A. Van Zeeland1,
R. Nazikian2, W.W. Heidb ink3and M. Ga c´
ıa-Mu˜
noz4
1Gene al A omics, PO Box 85608, San Diego, CA 92186-9784, USA
2P ince on Plasma Physics Labo a o y, PO Box 451, P ince on, NJ 08543-0451, USA
3Uni e si y o Cali o nia-I ine, I ine, CA 92697, USA
4Max Planck-Ins i u ¨
u Plasmaphysik, Ga ching, Ge many
Recei ed 24 May 2012, accep ed o publica ion 31 Oc obe 2012
Published 20 No embe 2012
Online a s acks.iop.o g/NF/52/123015
Abs ac
We epo he i s expe imen al obse a ions o as -ion loss in a okamak due o ene ge ic pa icle d i en geodesic
acous ic modes (EGAMs). A as -ion loss de ec o ins alled on he DIII-D okamak obse es bu s s o beam ion
losses cohe en wi h he EGAM equency. The EGAM ac i i y esul s in a signi ican loss o beam ions, compa able
o he i s o bi losses. The pi ch angles and ene gies o he measu ed as -ion losses ag ee wi h p edic ions om a
ull o bi simula ion code SPIRAL, which includes sca e ing and slowing-down.
(Some igu es may appea in colou only in he online jou nal)
1. In oduc ion
Fas ions om neu al beam injec ion, ion cyclo on hea ing,
and usion eac ions play a undamen al ole in he hea ing
and s abili y o okamak plasmas. La ge as -ion densi ies
can d i e collec i e ins abili ies, which in u n deg ade as -
ion con inemen and plasma pe o mance. Losses o ene ge ic
alpha pa icles om DT usion in ITER will educe he alpha
hea ing a ailable o each igni ion, and ha e he po en ial o
cause majo damage o he i s wall. Hence he beha iou
o as ions and hei in e ac ion wi h plasma ins abili ies in
usion plasmas has been ex ensi ely s udied [1,2], mo i a ed
by he undamen al impo ance o alpha pa icle hea ing in DT
plasmas [3–5].
Ene ge ic pa icle d i en geodesic acous ic modes
(EGAMs) occu ea ly in he amp-up o he plasma cu en
in he DIII-D okamak du ing coun e neu al beam injec ion
[6]. EGAMs a e ene ge ic pa icle modes wi h a mode
equency ∼50% below he ideal geodesic acous ic mode
(GAM) equency. A luid-kine ic model [7] quali a i ely
eplica es he obse ed mode cha ac e is ics, including apid
mode bu s ing and equency chi ping, and la ge elec on
densi y luc ua ions wi hou de ec able elec on empe a u e
luc ua ions. The nonpe u ba i e elec os a ic model shows
he ene ge ic pa icle p essu e d i es an n=0 adial elec ic
ield and a GAM-like m=1 densi y pe u ba ion. The
modes occu in plasmas wi h an ele a ed cen al sa e y ac o
(qmin ⩾2)and wi h compa able elec on and ion empe a u es,
ele an o p oposed s eady-s a e plasma egimes [2]. Sha p
d ops (∼10–15%) in he neu on p oduc ion a e indica i e o
s ong beam ion edis ibu ion and/o loss [6]. This pape
concen a es on he obse a ion o beam ion losses due o he
EGAM mode ac i i y.
A scin illa o -based as -ion loss de ec o (FILD) [8]
has ecen ly been ins alled on DIII-D ( o oidal magne ic
ield =2.1 T, majo adius =1.66 m, and mino adius =
0.67 m) o s udy ene ge ic ion losses induced by Al ´
en
eigenmodes (AEs) and o he MHD ins abili ies. Based on
he design used on ASDEX Upg ade [9,10], he ligh pa e n
esul ing om ions s iking a as ime esponse (decay ime
∼500 ns) scin illa o is imaged by a CCD came a, allowing
measu emen s o he pi ch angle and gy o adius o he beam
ions eaching he de ec o . Ligh om he scin illa o is
also measu ed by a ib e-coupled pho omul iplie o allow
iden i ica ion o AE and o he high equency ins abili ies.
This pape epo s he i s expe imen al obse a ions o beam
ion losses in a okamak due o EGAMs. The measu ed losses
a e compa ed o he esul s o a ull o bi simula ion code
SPIRAL o be e unde s and he beam ion anspo esul ing
om in e ac ions be ween he modes and con ined ions. The
EGAM-ion in e ac ion occu s only in ene gy space, compa ed
o he AE-ion in e ac ion ha in ol es he ene gy, canonical
momen um, and magne ic momen o he ions. The EGAM-
ion in e ac ion is p ima ily elec os a ic, wi h he n=0
na u e o he EGAM leading o changes only in he ion ene gy
(compa ed o AE-ion in e ac ions ha a ec bo h ion ene gy
and canonical momen um), hus p o iding a undamen al es
o ou abili y o model he impac o MHD ins abili ies on
ene ge ic ions [11].
0029-5515/12/123015+05$33.00 1© 2012 IAEA, Vienna P in ed in he UK & he USA
Nucl. Fusion 52 (2012) 123015 R.K. Fishe e al
Time (ms)
log( au opowe ) (au)
Ip
(MA)
FILD PMT (V)
210L 210R
(a) Sho 142111
(b)
(c)
800600400200
F equency (kHz)
0.001
0.200
FILD Au opowe
EGAM
Al én
Eigenmodes
1.2
1.0
0.8
0.6
0.4
0.2
0.0
4
3
2
1
0
120
100
80
60
40
20
0
Figu e 1. Time dependence o (a) neu al beam injec ion om
210R (shown in ed and pulsed) and 210L (shown in blue and on
con inuously om 300 ms o 1000 ms) ion sou ces, (b) beam ion
loss measu ed by FILD PMT and (c) ime- esol ed powe spec um
o he beam ion loss signal showing s ong EGAM ac i i y a
∼15–45 kHz occu ing e y ea ly a e he s a o he beam
injec ion.
2. Measu ed EGAM-induced beam ion losses
Neu al beam injec ion coun e o he di ec ion o he plasma
cu en ea ly in he amp-up o he plasma cu en in DIII-D
s ongly exci es EGAMs. Figu e 1is an example o a DIII-D
discha ge wi h signi ican AE and EGAM ac i i y. Deu e ium
beams (labelled 210L and 210R) injec 75–81 keV neu als
in he o oidal di ec ion opposi e he plasma cu en and a e
he p ima y beams esponsible o exci ing he EGAMs. The
210L beam is injec ed mo e pe pendicula o he o oidal
magne ic ield han he 210R beam [12]. Figu e 1(a) shows
ha he 210L beam sou ce is on con inuously om 300 o
1000 ms, while he 210R sou ce is pulsed o 10 ms on and
20 ms o , s a ing a 320 ms. Figu e 1(b) shows he beam ion
loss signal measu ed by he FILD scin illa o de ec o , while
igu e 1(c) shows he powe spec um o he as -ion losses
wi h o oidal Al ´
en eigenmode (TAE), e e se shea Al ´
en
eigenmode (RSAE) and EGAM ac i i y. The pulsed losses
in phase wi h he 210R beam injec ion include bo h p omp
losses and ins abili y-induced losses. O bi modelling shows
ha he p omp -loss con ibu ion om he 210R beam eaches
he FILD de ec o (loca ed app oxima ely 45◦below he ou e
midplane) a lowe alues o he plasma cu en . As he plasma
cu en inc eases, he ene ge ic ion banana wid hs dec ease,
esul ing in wall s ike posi ions ha a e o he midplane and
no longe de ec able by he FILD (a e ∼600 ms). The losses
cohe en wi h AE ac i i y in he 50–100 kHz egion [13,14] all
as he plasma cu en inc eases since he AE ac i i y becomes
mo e co e localized while he as -ion loss bounda ies a e
mo ing ou wa d, educing he abili y o he AEs o place
beam ions di ec ly on o loss o bi s. This pape concen a es
on he EGAM ac i i y be ween 15 and 45 kHz ha domina es
he losses e y ea ly ( om 300 o 350 ms) in he discha ge,
when he ene ge ic pa icle p essu e is a signi ican ac ion
o he o al plasma p essu e. The low plasma cu en a his
ime esul s in an ele a ed qmin, allowing he modes o a ise
wi hou subs an ial he mal ion Landau damping and leading
o a low as -ion be a βh h eshold o he EGAM mode
onse [6].
Figu e 2shows an expanded iew o he 300–450 ms ime
pe iod when he EGAM ac i i y is la ges . The ime- esol ed
equencyanalysiso an ex e nalmagne ic pickup coilisshown
in igu e 2(a). Figu e 2(b) shows ha he EGAM ampli ude
measu ed by an ex e nal magne ic ield pickup coil (blue ace),
and he cohe en componen o he FILD measu ed beam ion
loss signal ( ed ace). Bo h signals a e calcula ed based on an
∼2 kHz band cen ed on he ime- a ying EGAM equency.
The cohe en beam ion loss peaks sho ly a e beam injec ion
s a s a 300 ms, and hen decays apidly, while he mode
ampli ude indica ed by he magne ic pickup coil decays mo e
slowly. The cohe en componen o he FILD loss signal also
clea ly co ela es wi h he pulsed ime beha iou o he 210R
beam sou ce. The measu ed cohe en loss shows bo h a ‘ apid’
signal ha occu s in phase wi h he 210R beam injec ion, and
a ‘delayed’ componen ha decays o e se e al milliseconds
a e he 210R beam u ns o . This decay ime is a longe han
he calcula ed <100 µs ansi ime o ions kicked on o a di ec
loss o bi , indica ing ha he measu ed EGAM-induced losses
a e he esul o esonances ins ead o a simple modula ion o
he neu al beam p omp loss. Once he 210R sou ce u ns
o , he ene gy o he emaining con ined beam ions decays
on he classical slowing-down ime scale. This educes he
numbe o beam ions capable o in e ac ing wi h he EGAMs,
and is hough o lead o he obse ed decay in he cohe en
loss signal a e each 210R beam pulse. On a slowe ime
scale, he inc ease in plasma cu en wi h ime mo es he
loss bounda y o highe ene gies whe e he e a e ewe beam
ions o in e ac wi h he EGAMs. This e ec , combined
wi h he mode ampli ude educ ion, is quali a i ely consis en
wi h he d op in he obse ed cohe en losses be ween
325 and 425 ms.
The bu s ing beha iou cha ac e is ic o EGAMS is
clea ly isible when he measu ed as -ion loss signal is iewed
on an expanded ime scale, as shown in igu e 3(a). The
2
Nucl. Fusion 52 (2012) 123015 R.K. Fishe e al
300 350 400
Time (ms)
0.0
0.2
0.4
0.6
0.8
1.0
Ampli ude (au)
FILD Loss a EGAM
dB/d a EGAM
210R Beam
Sho 142111
300 350 400
Time (ms)
10
15
20
25
30
35
40
(kHz)
-1.4
-1.2
-1.0
-0.8
Log (c oss-powe )1/2 (au)
-0.6
-0.4
-0.2
0.0
Magne ics
(a)
(b)
Figu e 2. (a) Time- esol ed powe spec um om an ex e nal
magne ic pickup coil showing EGAM mode ac i i y, and (b) ime
beha iou o he EGAM ac i i y om he ex e nal magne ic pickup
coil (blue ace) and he FILD measu ed beam ion loss ( ed ace).
Bo h signals a e he bandwid h il e ed esponse in an ∼2 kHz band
cen ed on he ime- a ying EGAM mode equency. Also shown is
he pulsed neu al beam injec ion om he 210R ion sou ce (black
ace).
cohe en oscilla ions a he EGAM mode equency ∼15 kHz
a e a signi ican ac ion o he o al loss signal. A 320 ms, he
addi ional coun e injec ion due o he 210R beam inc eases he
measu ed losses. Figu e 3(b) shows consecu i e ames om
he CCD came a imaging he ligh pa e n c ea ed by beam ion
losses s iking he FILD scin illa o pla e. A g id indica ing he
gy o adius and pi ch angle o he impac ing ions is o e plo ed
in whi e. The alse colou images show signi ican losses
occu ing in wo egions. The came a was ope a ing a a ame
a e o ∼160 ames s−1and an exposu e ime o ∼500 µs
pe ame. The ame aken a 325 ms shows a signi ican
inc ease in he EGAM-induced losses ( egion ci cled in yellow
in igu es 3(b) and (c)) a pi ch angles nea 45◦–50◦. Analysis
o he came a da a shows ha he EGAM losses build up
du ing a 210R beam pulse and decay a e wa ds, consis en
wi h he ime beha iou o he PMT-measu ed cohe en loss
signal shown in igu e 2.
The o he egion o losses, a pi ch angles nea ∼70◦
( egion ci cled in ed in igu e 3(b)), does no change
signi ican ly be ween ames. Re e se o bi modelling shows
ha he losses nea 70◦a e p ima ily due o p omp losses
om he 210L beam, which is on con inuously du ing his
ime pe iod [14]. P omp losses, o i s o bi losses, esul
om ions bo n wi h o bi s ha in e sec he ou e wall. The
Figu e 3. (a) Beam loss signal measu ed by FILD shows bu s s o
cohe en ( ∼15 kHz) losses cha ac e is ic o EGAMs. The
addi ional coun e beam injec ion by he 210R sou ce s a ing a
320 ms inc eases he measu ed loss a e. Consecu i e ames a
319 ms (b) and 326 ms (c) om a CCD came a measu ing he pi ch
angle and gy o adius o he losses show ha he cohe en losses
appea a pi ch angles nea 45◦–50◦. The losses a pi ch angles nea
70◦ou lined in ed do no change signi ican ly and a e
p edomina ely due o p omp losses om he 210L sou ce ha is on
con inuously du ing his ime pe iod. The losses nea 45◦–50◦in
pi ch angle a e due o EGAM in e ac ions (ci cled in yellow) and
210R p omp losses (ci cled in g een).
losses nea 50◦in pi ch angle a e due o bo h i s o bi ( egion
ci cled in g een in igu e 3(b)) and EGAM-induced losses, and
a e p ima ily due o he 210R neu al beam sou ce. These
losses occu o e a ange in gy o adii om ∼2 o 4 cm. The
magne ic ield a he de ec o is 1.5 T, so his ange o gy o adii
co esponds o deu e ium ion ene gies om ∼25keVup o he
maximum injec ed beam ene gy o Eb=81 keV. The 210L
and 210R sou ces a e he only neu al beams injec ing coun e
o he di ec ion o he plasma cu en in DIII-D (co-cu en
beams p o ide ano he ∼2 MW o inpu hea ing in his sho ),
so he esul ing beam ions a e bo n on he inne leg o hei
banana o bi s and i is no su p ising ha hey domina e he
obse ed loss signals.
3
Nucl. Fusion 52 (2012) 123015 R.K. Fishe e al
1.0 28.3
E adial (kV/m)
0.0
E adial
1.0 1.5 R
(
m
)
Z (m)
2.0 2.5
0.0
–1.0
80 70 60
Pi ch Angle (deg)
50 40 30
4.5
3.5
2.5
1.5
Gy o Radius (cm)
100
0
Coun s
210L hi d
210L hal
210L ull
210R hi d
210R hal
EGAM losses
Figu e 4. (a) Resul s o a ull pa icle-o bi ollowing code SPIRAL
used o simula e he losses due o EGAMs a e consis en wi h
measu ed FILD esul s. (b) Calcula ed loss o bi (gold) o a beam
ion de ec ed in he EGAM-induced loss egion o he FILD came a
da a (E=75 keV, pi ch angle =45◦–50◦). Also shown is he
calcula ed adial elec ic ield om he m=0, n=0 elec os a ic
po en ial pe u ba ion esul ing om EGAM ac i i y.
3. Modelling and in e ed EGAM loss mechanism
SPIRAL is a ull pa icle-o bi ollowing code ha was
de eloped o model ene ge ic ion beha iou in okamaks
[16,17]. Figu e 4shows he esul s o SPIRAL used o
simula e he losses due o EGAMs. In hese SPIRAL code
simula ions1, ions wi h he bi h ene gy deposi ion p o ile
om NUBEAM [18] a e ollowed as hey slow down and
pi ch angle sca e while in e ac ing wi h he m=0, n=0
adial elec ic ield esul ing om he EGAM ac i i y. The
adial elec ic ield used in SPIRAL is calcula ed based on a
o oidally symme ic elec ic po en ial which is a lux unc ion,
and whose magni ude is chosen o ma ch he esul ing densi y
1SPIRAL code was un on 512 AMD op e on p ocesso s using UNIX and
ollowed 250000 pa icles (50000 pe beam).
pe u ba ion measu ed by a beam emission spec oscopy
diagnos ic. The EGAM-induced losses occu be ween 45◦
and 50◦in pi ch angle and o e a b oad ange o gy o adii
( egions ci cled in yellow in igu es 4(a) and 3(b)) as he
EGAMs in e ac wi h he slowing-down dis ibu ion o he
210R injec ed ions. Po ions o he egion nea 45◦–50◦
can also include p omp losses om he 210R sou ce. An
example is he egion ci cled in g een ha is only p esen
du ing 210R injec ion and is consis en wi h p omp losses
o he one- hi d and one-hal ene gy componen s o 210R.
The SPIRAL esul s in igu e 4a e in good ag eemen wi h he
measu ed esul s in igu e 3and he same colou -coding is used
o iden i y he di e en loss egions in bo h igu es. Bo h he
FILD measu emen s and he SPIRAL code p edic ions show
signi ican EGAM-induced losses, compa able in magni ude o
he p omp losses o he coun e -injec ed beams. The SPIRAL
esul s a e also consis en wi h he measu ed ime beha iou o
he losses shown in igu e 2, including he ‘delayed’ cohe en
componen a e he 210R beam is u ned o .
Re e se o bi ollowing echniques a e used o calcula e
he o bi s o he beam ions eaching he FILD de ec o based on
hei measu ed pi ch angles and gy o adii. The magne ic ield
con igu a ion inside he plasma is de e mined using he plasma
equilib ium code EFIT [19], cons ained by cu en p o iles
(based on mo ional S a k e ec measu emen s o he magne ic
ield pi ch) and he measu ed plasma p essu e. Figu e 4(b)
shows he SPIRAL esul o he poloidal p ojec ion o he
calcula ed ajec o y (shown in gold) o a 75 keV beam ion
a a pi ch angle o 45◦–50◦ eaching he FILD de ec o . The
inne po ion o his uncon ined apped pa icle o bi is close
o he o bi s o con ined coun e -injec ed beam ions. As he
coun e -injec ed beam ions lose ene gy o he wa e, he change
in hei pi ch angle pu s hem on an uncon ined apped pa icle
o bi , leading o he measu ed FILD loss signal cohe en wi h
he EGAM ac i i y. Loss o he beam ions educes he d i e
mechanism o he mode, which in u n educes he beam loss
a e un il he cycle s a s again. This p eda o –p ey beha iou
o he ins abili y leads o he obse ed bu s s in he mode
ampli ude and measu ed beam ion loss.
4. Conclusions
A new scin illa o -based as -ion loss de ec o on DIII-D has
allowed he i s expe imen al obse a ions o as -ion losses
due o EGAM ac i i y in a okamak. Neu al beam injec ion
coun e o he di ec ion o he plasma cu en s ongly exci es
he EGAMs. F om he measu ed pi ch angle and gy o adii
o he cohe en beam ion loss signal, e e se o bi ollowing
echniques yield a apped ion loss o bi wi h a la ge banana
wid h ha eaches well inside he plasma. Th ough he
in e ac ion wi h he EGAM, con ined beam ions on coun e -
passing o bi s expe ience a change in hei pi ch angle ha
places hem on apped pa icle loss o bi s. The measu ed
as -ion loss exhibi s he bu s ing beha iou cha ac e is ic o
EGAMs, wi h a measu ed g ow h a e consis en wi h he as -
ion p essu e d i ing he modes. The measu ed pi ch angles and
gy o adii o he measu ed as -ion losses a e consis en wi h
he p edic ions o he ull o bi ollowing code SPIRAL used
o model he EGAM-induced losses.
4

Nucl. Fusion 52 (2012) 123015 R.K. Fishe e al
Acknowledgmen s
This wo k was suppo ed in pa by he U.S. Depa men o
Ene gy unde DE-FC02-04ER 54698, SC-G903402 and DE-
AC02-09CH11466. The assis ance o he DIII-D eam is
g a e ully acknowledged.
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5