j. k. anderson
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Bulk Ion Heating with Neutral Beam Injection and Confinement of Fast Ions
in the Reversed Field Pinch
J. K. Anderson with A. F. Almagri, B. E. Chapman, V. I. Davydenko, P. Deichuli,
D. J. Den Hartog, C. B. Forest, G. Fiksel,
A. A. Ivanov, D. Liu, M. D. Nornberg, J. S. Sarff,
N. Stupishin, and J. Waksman
Siberian Branch of Russian Academy of ScienceSiberian Branch of Russian Academy of Science
Budker Institute of Nuclear Physics Budker Institute of Nuclear Physics
Outline
• The Reversed Field Pinch (RFP) magnetic geometry– Not an Open System, – Unique parameter space to consider fast ion physics-- weak, strongly sheared B field
• Neutral beam injection in the Madison Symmetric Torus (MST)
• Fast ions confined much better than bulk plasma
• Majority ion (deuterium) heating observed during NBI – First measurements: data presented without complete explanation. – Upcoming experiments with more diagnostics planned
• Summary
RFP magnetic geometry
Magnetic field maximum at geometric center
Tangential NBI sources fast ions in region of peak magnetic field
RFP magnetic geometry: magnetized particles quickly lost
Considering magnetic perturbations, field lines at core stochastically wander to boundary
e ~ 1msec
NBI is significant factor in MST discharge
NBI pulse: 20 msec, MST pulse: ~70 msec
NBI power: 1 MW (25 kV, 40A)MST ohmic input: ~4-10 MW
NBI electron source negligible
NBI fuel doped with 3% D2; fusion neutrons some measure of fast ion density
Approximate calibration: peak neutron flux ~ 1.5x1010 s-1
Flux decays after beam turn off
Classical fast ion slowing down time
1Efi
dEfi
dt=−
Zfi2e4nemfi
1/ 2 lnΛ
4 2πε02meEfi
3/ 2
43π 1/ 2
me
mfi
Efi
Te
⎛
⎝⎜
⎞
⎠⎟
3/ 2
+me
mD
nD
ne
+me
mi
niZi2
nei∑
⎛
⎝⎜⎜
⎞
⎠⎟⎟
electrons 82% ions 15% impurities 3%
slowing down =30 ms ne =1013 cm-3
Te = 400 eVEfi = 25 keV
For MST-like parameters
Used to estimate fast ion confinement time
Fast ion parameters comparable to bulk plasma
Bulk Plasma (typical MST parameters)
Neutral Beam Injected 1 MW, 25 keV, = 30ms
Thermal energy
Density
Toroidal momentum
Current density
(x 50% – 75%)
WNBI =3.5 ×104 J
nfi =
WNBI
eEbeam
Vpl
=1.2 ×1018 m ne =1019 m−3
mfinfivbeam =4.4 ×10−3 kg⋅m−2 / s
enfivbeam =0.17MA / m2 : 1MA/ m2
minevrot =10−3 kg⋅m−2 / s
32
nek(Te +Ti )Vpl =1.8 ×104 J
-3
Fast ion confinement estimated by neutron decay
Infinite fast ion confinement: neutron flux decays due to classical slowing of fast ions
Actual neutron decay rate is faster due to finite loss rate of fast ions
fi >> e
Good fast ion confinement is understood
Fast ion guiding center rotational transform deviates from magnetic transform
Overlapping magnetic islands (br ) rapid electron transport
Non-overlapping islands in fast ion transform (vr ) regions of good confinement
€
qM =rBφRBθ
€
q fi =rvφRvθ
Fast ion confinement increases with confining field
Counter-injection: poor fast ion confinement.
Co-injection: fi increases as B2
fi slight increase with ne
Magnetic field scanned by varying plasma current;Te increases ~ linearly with |B|
Classical transport modeling predicts fast ion density
Tokamak transport code shows strongly peaked profile.
Ramp-up and decay consistent with observed fast ion confinement
Fast ion density ~15% of local bulk ion density
Appreciable heating of e- and ions expected. Ion heating measured.
Bulk ion temperature measured by Rutherford Scattering
NBI No NBI
16.6 keV He beam injected vertically into plasma.
Scatters from D+; energy spectral width determines Ti
Not perfectly symmetric gaussian; instrument broadening signficant.
Tail effect of fast H+?
Ti ~ 180eV Ti ~ 220eV
Ion temperature heats rapidly, cools quickly.
He beam: 4ms pulse
40 eV Ti within 5 msec of turn-on
Ti flat vs t until beam turn-off
Ti decays quickly, 1.5 msec timescale.
Simulation of Ti does not reproduce measured features
Overall temperature change can be increased by assuming higher energy confinement or more localized heating.
Higher confinement leads to longer ramp-up and decay times.
Simulation of Ti does not reproduce measured features
Overall temperature change can be increased by assuming higher energy confinement or more localized heating.
Higher confinement leads to longer ramp-up and decay times.
X
X
X X
Recall approximate data
Summary
• Initial results of 1 MW NBI into RFP presented
• Fast ions confined much better than background plasma – Confinement time increases with confining field, ~ B2
• Thermal background ions heated during NBI beyond expectations – Core temperature change 2-4 times larger than simple calculation– Time scale on which heating occurs too fast
• Further exciting experiments planned for campaign July-September 2010– MST will make use of 3 neutral beams
• NBI and 2 diagnostic beams for bulk and impurity ion temperature – Evolution of electron temperature (critical for quantitative comparison) to be measured– Compact neutral particle analyzer with up to 30keV range to be installed
– Development of fast H diagnostic to measure fast ion dynamics
– NBI into RFP high confinement mode: e increased by factor of 10, Te > 1keV
Fast Ion D Diagnostic for NBI can utilize DNB
Doppler shift likely to be obscured by high shear on ~vertical views.
Net red shift expected on toroidal viewing chords
Some FIDA systems use fast-ion CX with neutrals from the same beam.
Signal (small) is on top of large background from beam emission.
CX with DNB neutrals will put a several nm red shift on signal carrying photons
Measurement of nfi profile very important
RutherfordScattering
Decay of rate of Ti slightly faster than decay rate of neutrons
Core mode amplitude suppressed; rotation increased
Optimal up-down alignment
Co-injected fast ions have very low prompt losses
• MST favors co-injection. Even near wall born ions are well confined.
outboardinboard
co
counter
lostlostconfined
Exit
Entry
Ip=400kA, E=25keV
Pit
ch
Global (0-d) modeling predicts measureable effects
notable increase in Te with time
0-D prediction for enhanced confinement dischargeTe(0) ~800 eV; ~ 10ms
Classical collisions
Fast ion pressure significant fraction of bulk plasma pressure. Profile peaking can lead to local fast ion > bulk
Injection into high discharges may expose limiting physics; pellet-fueled shots already exceed Mercier
Momentum, current and beta all follow lower time trace
0-D modeling of fast ions energy and momentum exchangewith plasma
dnfi
dt=Sfi −
nfi
filoss
dEfi
dt=−νε
fi/ eEfi −νεfi/ iEfi
dTe
dt=
23
νεfi/ eEfi / ne −νε
i/ e(Te −Ti ) −Te
eloss
dTi
dt=
23
νεfi/ iEfi / ne −νε
i/ e(Ti −Te) −Ti
iloss
νεfi/ e(ne,Te,Efi )
νεi/ e(ne,Te,Ti )
νεfi/ i(ne,Ti ,Efi )
All collision rates are classical
(similar equation for momentum)
Fast ion energy losses
Fast ion particlesources and losses
Plasma electrons heating
Plasma ions heating
fi
loss =30ms Efi > 7keV
iloss Efi ≤7keV
⎧⎨⎪
⎩⎪
Fast ion confinement
Beam Geometry: Tangential injection
Launch at midplane not possible on MST; starting slightly above midplane with -6 degree angle– maximize beam deposition
shine-thru
detector
Beam composition: 86% in fundamental
86% E 10% E/2; 2% E/3 ~2% E/18
Beam divergence: at distance 2.1m, r = 67mm
Measured beam radius acceptable: total distance traversed in MST = 2.8 m
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