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