Alfvén range instabilities in H-1:
Interpretation, mode structure, andrelation to rational surfaces.

B. D. Blackwell , D.G. Pretty, J. Howard , D.R. Oliver , G.
Potter, F. Detering , D. Byrne, M. Hegland , C.A.
Nuhrenberg*, R.L. Dewar , S.T.A.Kumar , M. McGann,M.J. Hole and **J.H. Harris
Australian National University, *Max Planck IPP Greifswald, and**Oak Ridge National Laboratory
Blackwell, ISHW/Toki Conference 10/2007

Outline
H-1 Heliac
MHD Data
Data mining
SVD, fluctuation structures
Clustering

Interpretation
Alfvén Scaling
Iota an additional fit parameter
Radial location
Accurate iota confirmation
Scaling discrepancies
Beta–Induced modes, sound and drift modes
Helical Alfvén eigenmode
Radial Structure

SummaryBlackwell, ISHW/Toki Conference 10/2007

H-1NF: National Plasma Fusion
Research Facility
A Major National Research Facility established in 1997 by theCommonwealth of Australia and the Australian National University
Mission:• Detailed understanding of the behaviour of magnetically confined hot plasma inthe HELIAC configuration• Development of advanced plasma measurement systems• Fundamental studies including turbulence and transport in plasma• Contribute to global research effort, maintain Australian presence in the field ofplasma fusion power

Contract extended until 2010: includes some operational funding
and limited collaborative funding
The facility is available to Australian researchers through the AINSE1 andinternationally through collaboration with Plasma Research Laboratory, ANU.
1) Australian Institute of Nuclear Science and Engineering

International collaboration played an important role in thesuccess of H-1 in obtaining facility funding
Blackwell, ISHW/Toki Conference 10/2007

H-1 CAD

Blackwell, ISHW/Toki Conference 10/2007

H-1 Heliac: Parameters
3 period heliac: 1992
Major radius1mMinor radius
0.1-0.2m
Vacuum chamber 33m2 excellent access
Aspect ratio5+toroidal
Magnetic Field≤1 Tesla (0.2 DC)
Heating Power
0.2MW 28 GHz ECH
0.3MW 6-25MHz ICH
Parameters:nTβBlackwell, ISHW/Toki Conference 10/2007

achieved to date::expected
3e18 :: 1e19
<200eV(Te)::500eV(Te)
0.1 :: 0.5%

H-1NF Photo

Blackwell, ISHW/Toki Conference 10/2007

H-1 plasma configuration is very flexible• Original heliac:
limited configuration range.

• “flexible heliac” :helical winding, withhelicity matching the plasma,⇒ 2:1 range of iota
• H-1NF can control 2 out of 3 oftransform (ι)
magnetic well andshear ∆ι• Reversed Shear, Normal Shear

Blackwell, ISHW/Toki Conference 10/2007

Santhosh Kumar

Experimental confirmation of configurations
Rotating wire array••

64 Mo wires (200um)
90 - 1440 angles

High accuracy (0.5mm)
Moderate image quality
Always available
Excellent agreement with computation

T.A. Santhosh Kumar
B.D.Blackwell, J.Howard

Blackwell, ISHW/Toki Conference 10/2007

Large Device Physics on H-1
Confinement Transitions,Turbulence (Shats, 1996--)

D3D tokamak32H-180

P inj (MW)– High Confinement mode (’96)
10Edge n e (10 19 m –3 )– Zonal Flows 2001
– Spectral condensation of0.3
Edge T e (keV )0.2
turbulence 2005

06

Magnetic Island Studies

2000t (ms)030
20102400– H-1 has flexible, controlled and verified geometry– Create islands in desired locations (shear, transform)– Langmuir probes can map in detail

Alfvén Eigenmodes– May be excited in reactors by fusion alphas, and destroy
their confinement– (more)Blackwell, ISHW/Toki Conference 10/2007

n e (r/a = 0.3) (1017 m –3 )

30.1

1600

P rf (kW )

40

12800

Edge T e (eV)

2040t (ms)60Plasma Production by ICRF
ICRF Heating:•B=0.5Tesla, ω = ωCH(f~7Mhz)•Large variation in newith iota

Backward Wave
Oscillator
Scanning Interferometer(Howard,Oliver)Blackwell, ISHW/Toki Conference 10/2007

Axis

D. Pretty, J. Harris

Configuration scan: Magnetic Fluctuations
ICRF plasma configuration
scan

5/4

7/54/
3

Mode spectrum changes asresonances enter plasma
No simple explanation for“gap”
left side corresponds tozero shear at resonanceA clear connection withrational twists per turn –but what is it?
Resonant layer in plasma
seems to aid formation orconfinement.
Variation with iota notpronounced in ECH.
Blackwell, ISHW/Toki Conference 10/2007

gap
5/
4

4/
3

7/
5

Magnetic fluctuations
approach “high temperature” conditions:

••
•
•
•

H, He, D; B ~ 0.5T;
ne ~ 1e18; Te<50eV
ρi,e << a,λmfp >> lconn

spectrum in excess of 100kHz
Low mode numbers: m ~ 0 - 7, n ~ 0 - 9
δb/B ~ 2e-4
both broad-band and coherent/harmonicnature
abrupt changes in spectrum randomly
or correlated with plasma events

Blackwell, ISHW/Toki Conference 10/2007

Poloidal mode number measurements
phase
Expected form =2magnitude
Two “bean-shaped” 20 coil Mirnov arrays• Phase vs poloidal angle is not simple––

Magnetic coordinates
External to plasma• Propagation effects• Large amplitude variation
Significant interpretation problem inadvanced confinement configurations

Blackwell, ISHW/Toki Conference 10/2007

coil number (poloidal angle )Identification with Alfvén Eigenmodes: ne••••Coherent mode near iota = 1.4, 26-60kHz,
Alfvénic scaling with nem number resolved by bean array of Mirnov
coils to be 2 or 3.

phase1/√neVAlfvén = B/√(µoρ)∝ B/√neScaling in √ne in time (right) andover various discharges (below)
nef ∝ 1/√neBlackwell, ISHW/Toki Conference 10/2007

H-1NF Data: MDSPlus + MySQL
gas properties
id12818

namehydrogenheliumoxygenargon

gauge fact
2.2
5.5
0.99
0.78

flow
2.90.72
8.0
8.0

Machineand human
generateddata tables

Summary Database: one entry per shot - machine generated ~100 columns
Id
9001
9002
9003
9004
9005
…..

Shot
45001
45002
45003
45004
45005
….

iring
6500
6500
6600
6700
6800

Gas
He
He
H/He
H/He
H/He

flow_2
0.0
2.0
0.5
0.5
0.5

rf_power
59.1
57.4
59.4
55.1
61.7

p_iong1.1e-62.5e-6
1.1e-6
1.1e-6
1.2e-6

ne_18
1.18
1.51
1.61
1.63
1.69

p_iong1.1e-6
1.2e-6
1.1e-6
1.1e-6
1.2e-6

lenth.09.091.09.09.091

Comment
Test new MOSS camera
Test new MOSS camera
Test new MOSS camera
Test new MOSS camera
Test new MOSS camera

L og E ntry D atabase: m any entries per shot, 21 colum nstopics
idtopic
descripti
1 operations
currents, tim
2 RF
RF heating
3 ECH
ECH system
4 MHD
equilibrium
5 MOSScameras, wh
6 probes
LP, TMT,
create table topics (id int unique auto_increment,
topic enum('shotnote','unknown','operations','config','datasys','RF','ECH'

mySQL
database server
php web
interface

Graphic andtextual queries
Blackwell, ISHW/Toki Conference 10/2007

Id50015002

Shot45001
45001

50035004

45001
45001

5005
… ..

45002
….

topic
datasysim puriti
esshotnote
M O SSshotnote

precisN i im purity
increase flow to 1.5
m odulation voltage
too low
H e flow 2.0

O w ner
cam acbdb112
cam 112cam 112cam 112

C om m ent
D isk fu ll error
Possib le line at
4047

scriptneed to m odify
analysisfact=2.5 &anal_m oss,foo,fact

C om

plot_ccd_spectrum , sel28
neeana

D. Pretty

Mode Decomposition by SVD and Clustering•

Initial decomposition by SVD Æ~10-20 eigenvalues• Remove low coherence and low
amplitude• Then group eigenvalues byspectral similarity into fluctuation
structures• Reconstruct structures
to obtain phase difference atspectral maximum• Cluster structures according tophase differences (m numbers)
Æ reduces to 7-9 clusters for an iota
scanGrouping by clustering potentiallymore powerful than by mode
number––Recognises mixturesof mode numbers
caused by toroidal
effects etc
Does not depend
critically onknowledge of thecorrect magnetic
theta coordinate

Blackwell, ISHW/Toki Conference 10/2007•4 Gigasamples of data–

128 times–

128 frequencies–

2C
20 coil combinations–

100 shots

Data mining

Data Mining Classification by Clustering

Fulldataset

See Poster and thesis by David Pretty P2: 83 Wed.
Blackwell, ISHW/Toki Conference 10/2007

Mode numbers consistent with iota
• Mode analysis of the clusters found is complex, but isconsistent with the rotational transform
dominant n=4

Iota=4/3
Blackwell, ISHW/Toki Conference 10/2007

dominant m=3

Identification with Alfvén eigenmodes: k||, iota
= k|| B/√(µoρ)•ωres = k|| VAlfvén•k|| varies as the angle between magnetic••

field lines and the wave vector
for a periodic geometry the wave vector isdetermined by mode numbers n,mComponent parallel to B is ∝ ι - n/m

k|| = (m/R0)(ι - n/m)

ωres = (m/R0)(ι - n/m) B/√(µ ρ)o•Low shear means relatively simple
dispersion relations

Alfvén dispersion (0-5MHz)

Alfvén dispersion (0-50kHz)
Nearrationals,resonant
freq. islowBlackwell, ISHW/Toki Conference 10/2007

David Pretty

Identification with Alfvén eigenmodes: k||, iota
ωres = k|| VA = (m/R0)(ι - n/m) B/√(µ ρ)o•k|| varies as the angle between magnetic fieldlines and the wave vectork|| ∝ ι - n/m•

iota resonant means k||, ω Æ 0

Expect Fres to scale with δ iota

Resonant ιι = 4/3

Blackwell, ISHW/Toki Conference 10/2007

ιota Æ

Alfvén eigenmode frequency: radial variation
ωres = k|| VA = (m/R0)(ι - n/m) B/√(µ ρ)oGlobal modepossible

Iota ~ 7/6

just below iota ~ 5/4

iota ~ 4/3

Gap mode possible

Blackwell, ISHW/Toki Conference 10/2007HAE gap likely
asn1-n23=m1-m22

Carolin Nuhrenberg

CAS3D: 3D and finite beta effects
Continuum frequency
usually decreases

Beta induced gap ~5-10kHz
Blackwell, ISHW/Toki Conference 10/2007

David Pretty

Closer inspection Æ radial location
Better fit of frequency to iota, ne obtained if the location ofresonance is assumed be either at the zero shear radius, orat an outer radius if the associated resonance is not present.

Assumed mode
location

Blackwell, ISHW/Toki Conference 10/2007

ι ~ 5/4

Two modes coexisting at different radii

Cross-power between ne
and Mirnov coils shows
two modes coexisting
Probably at different radii as
frequency is different,mode numbers the same
Blackwell, ISHW/Toki Conference 10/2007

Santhosh Kumar

Accurate cross-check of iota
Potential to be iota diagnostic (if shear low)
Original iota calibration at reduced field

Transform decreases by
0.5% at high field

Corrected iota agrees better with dispersion
1.400

iota

δ iota ∝ I2

Æ discrepancy halved
Blackwell, ISHW/Toki Conference 10/2007

1.408

Scaling discrepancies= k|| B/√(µoρ)

phase•ωres = k|| VAlfvén•

Numerical factor of ~ 1/3 required for quantitative agreement:– Impurities (increased effective mass) may account for 15-20%– 3D MHD effects ~ 20-40%– Still a factor of 1.5-2x required•

Magnetic field scaling is unclear– Ion cyclotron resonant heating with fixed frequency couples plasma
preparation with magnetic field variation– Possible that expected scaling (f ~ B) applies, but indications of f ~ 1/B•

Unknown drive physics– VA ~5e6 m/s – in principle, H+ ions are accelerated by ICRH, but poorconfinement of perpendicular H+ at VA and VA/3 in the heliac
configuration makes this unlikely.
– Electron energies are a better match, but the coupling is weaker.
– The bounce frequency of the higher energy thermal H+ is in the rangeof observed frequencies

Blackwell, ISHW/Toki Conference 10/2007

David Pretty

Helical Alfvén eigenmode
Helical gap mode likely at coalescence of 7/5 and 10/7
n=10, m=7n=7, m=5

as
n1-n2
m1-m2

Good scaling with ne,Correction is ~ 0.7 –typical of 3D effectBlackwell, ISHW/Toki Conference 10/2007=32

Beta-induced Alfvén eigenmodes?
••
•
•

•

•

At low beta in H-1 (10-4), the betainduced gap is in the range 5-10kHz.
This is within the range of the modes
near resonance, when iota-n/m issmall
Beta induced gap scales withtemperature rather than magnetic
10kHz
field
Æ interactions between the beta
induced gap and Alfvén continuum
could help explain the ambiguous B
dependence.
Scaling of f ~n/m (not ι- n/m) does
not explain frequency dependenceon ι.
Evidence of electrostatic modes, but
not at resonance where GAM-likebehaviour may be expected.

Blackwell, ISHW/Toki Conference 10/2007

Howard, Byrne, Oliver

Radial Structure: interferometry and optical emission
Mode simulated by rotating m=4 Fourier
Bessel object in magnetic coordinates
m=4 simulation

Measured projections near iota=5/4

Average minor radius

Height above magnetic axis

Mode is strong in outer region, indication thatthe central amplitude is reduced.
Blackwell, ISHW/Toki Conference 10/2007

Summary
H-1 National• SeveralFacility
Configurational effects demonstrated:

See also
Michael Shats: Wed 14:10
David Pretty: P2: 83 Wed.
R. Numata: P2: 59 Wed.

– Confinement,
magnetic fluctuations spectra– Configurational
flexibility• Alfvénicmodesobserved– Largedevicephysics
accessible• Datamining – Transitions,unsupervised
reduction
into significant
clusters
Confinement
AlfvénEigenmodes,
MagneticIslands• NewDiagnostics(J. HowardThurs PM)– TestBed
for Advanced
Diagnostic
Development– H1 plasma can be used to develop reactor edge plasma diagnostics

Alfvénic modes observed– Iota scan is a valuable additional test parameter, especially at low shear– Increased dimensionality of data space (iota, ne, B, frequency, m, n) is
handled by datamining– Strong evidence for Alfvénic scaling in ne, k||, f– Unclear B scaling (resonant plasma production)– Around resonance, frequency is low by a factor of ~ 3.
– Sensitive interferometer and PMT array Æ valuable mode profile information– In low shear configurations, near resonant AEs can provide sensitive iota
diagnostics under full plasma conditions.
– Will apply technique to Heliotron J and TJ-II data.
Blackwell, ISHW/Toki Conference 10/2007